Fundamental Dynamics in High Intensity Laser Ionization

Transcription

1 Fundamental Dynamics in High Intensity Laser Ionization DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Patrick J. Randerson, B.S., M.S. * * * * * The Ohio State University 5 Dissertation Committee: Approved by Professor Linn Van Woerkom, Adviser Professor Louis DiMauro Professor Eric Herbst Professor Dongping Zhong Adviser Graduate Program in Physics

2 ABSTRACT The study of ionization by intense laser fields is an important component of understanding light/matter interactions in highly nonlinear regimes. Typical intensities are between 1 and 1 W/cm, generated in this case from 1 fs pulses from an 8 nm Ti:Sapphire laser system. Study of this highly nonlinear, so-called above threshold ionization (ATI) of atoms has led to a single active electron model. In this model, the laser interacts only with a single valence electron, which can absorb upwards of 3 photons from the field during ionization. Ionization yield is highly enhanced via resonance with Stark shifted atomic states, leading to peaks in the photoelectron energy spectrum known as Freeman resonances. This work extends the study of ATI photoelectron spectroscopy from noble gases to diatomic molecules, and finds no clear deviation from the single active electron picture. Photoelectron spectra from N (IP = ev), O (IP = 1.6 ev), and CO (IP = 1.1 ev) were collected and analyzed. These spectra are remarkably similar to noble gas spectra and appear perfectly consistent with dynamics dominated by a single electron interaction. Clear Freeman resonances are observed for all species. In fact, two Rydberg series are observed for N and O, perhaps originating from ionization through states associated with excited states of the ion. ii

3 We propose that the single active electron picture is an accurate shorthand for these, and perhaps all non-fragmenting, ionization events. This suggests the universality of single electron behavior. Moreover, our work demonstrates the difficulty of examining atomic or molecular structure using ATI photoelectron spectroscopy the characteristic Freeman resonances are more indicative of valence electron behavior rather than atomic structure. iii

4 For Susan, with all my love. iv

5 ACKNOWLEDGMENTS There is not time nor space enough to properly thank all the people who contributed their efforts and advice to my graduate education. I am particularly indebted to my adviser, Linn Van Woerkom who has served alternately as a resource, reference, and role-model, both scientifically and otherwise. His enthusiasm and insight kept me from making good on my constant threats to quit school and become a goat farmer. I addition, I d like to thank the members of my defense committee, whose names begin this document, for their comments and advice. I am also grateful to have worked in the company of the fine students of the Van Woerkom Lab Mark Walker, Glen Gillen, Richard Patterson, Dustin Offerman, Matt Whitaker, James Campbell, Tom Weisgarber, Matt Maeder, Tomm Scaife, and Emily White. I am especially grateful for Richard s friendship, and Mark s constant support. I d also like the record to reflect that my fellow students Leslie Schradin, Meredith Howard, Wesley Pirkle, Brian Gibbons, and Reni Ayachitula are among the nicest and smartest people I know. Physics is lucky to have them. I owe my Mom and Dad for everything that s happened since my birth. Their love and support has been a foundation since before I was old enough to appreciate it. I d hoped to have saved all the best adjectives for my wife, Susan, but it turns out there aren t words enough to explain what she means to me. She has been endlessly loving and patient during the difficult times, and she s been there to celebrate the v

6 good times as well. I am grateful for every day I get to spend with her and our new son, Alex. vi

7 VITA June, Born - Corvallis, Oregon, USA B.S., Computational Physics, Carnegie Mellon University M.S., Physics, The Ohio State University Graduate Fellow, The Ohio State University Graduate Teaching Associate, The Ohio State University 3-present Graduate Research Associate, The Ohio State University FIELDS OF STUDY Major Field: Physics Studies in High-Intensity Photoionization Under: Prof. Linn Van Woerkom vii

8 TABLE OF CONTENTS Page Abstract Dedication Acknowledgments Vita List of Tables ii iv v vii xi List of Figures xii Chapters: 1. Introduction Motivation A Grand Tour of Light-Matter Interaction Linear Optics Nonlinear Optics Intense Field Relativistic Fields Methods and Goals Theory Electron Field Interaction Stark Shifts Nonresonant Multiphoton Ionization Above Threshold Ionization and Resonances Transient Freeman Resonances viii

9 .5.1 Long Pulse Experiments Short Pulse Experiments Tunnel Ionization The Keldysh Parameter Rescattering Model Diatomic Molecules Bound State Configurations Alignment Effects Dissociation and Explosion Experimental Arrangements Laser Source Femtosecond Oscillator Amplification Intensity Control Diagnostics Focusing Target Area Interaction Region Vacuum System Detection Methods Flight Tube Micro Channel Plate Assembly Timing Electronics Data Analysis Ion Analysis Electron Analysis Intensity Calibration Importance of Resonances: Krypton Photoelectron Spectra Introduction Intense Field Resonances Method Intensity Calibrations Partial Yields Spin-Orbit Splitting Resonances Long Range Structure Conclusion ix

10 5. Atoms and Molecules Background Ionization Suppression High Energy Plateaus Ar and N Xe and O Kr and CO Low Energy Electrons Ar and N Xe and O Kr and CO Angular Distributions Discussion Diatomic Freeman Resonances Introduction Intense Field Ionization Background Experiment Atomic Resonance Structure Diatomic Resonance Structure Nitrogen Resonance Structure Oxygen Resonance Structure Carbon Monoxide Resonance Structure Discussion Summary and Outlook Appendices: A. Ion Spectra for Diatomic Ionization x

11 LIST OF TABLES Table Page 3.1 Settings for the Ortec picosecond time analyzer (pta) for data collection 5.1 Properties of species xi

12 LIST OF FIGURES Figure Page 1.1 Fundamental intense field processes Schematic of multiphoton ionization processes Schematic of Stark-shifted resonances Schematic of high field ionization processes Block diagram of laser system Example of mode-locking Sample FROG trace A contour plot of a Gaussian laser focus intensities Diagram of interaction region Micro channel plate (MCP) Detail Detector assembly Ion spectra from a clean, baked chamber Raw and calibrated electron data Calibration of average power to intensity using reference argon spectra 51.1 Lowest intensity krypton spectra, for calibration xii

13 . Partial yield in argon Krypton partial yield the spin orbit splitting Krypton Photoelectron Spectra: Low Intensities Krypton Photoelectron Spectra: High Intensities Krypton long range structure High energy plateau of H, from Walker et al N and Ar envelope spectra, TW/cm N and Ar envelope spectra, 1-5 TW/cm N and Ar envelope spectra, 5-61 TW/cm N and Ar envelope spectra, TW/cm N and Ar envelope spectra, 7-91 TW/cm O and Xe envelope spectra, 7-35 TW/cm O and Xe envelope spectra, TW/cm O and Xe envelope spectra, 6-8 TW/cm CO and Kr envelope spectra, 1 and TW/cm CO and Kr envelope spectra, 7-35 TW/cm CO and Kr envelope spectra, 37-9 TW/cm CO and Kr envelope spectra, TW/cm CO and Kr envelope spectra, 69-9 TW/cm N and Ar ATI peaks, 9 and TW/cm N and Ar ATI peaks, 7-58 TW/cm xiii

14 5.17 N and Ar ATI peaks, 3-38 TW/cm O and Xe ATI peaks, 76 and 8 TW/cm O and Xe ATI peaks, 38-9 TW/cm O and Xe ATI peaks, 19 - TW/cm CO and Kr ATI peaks, 77-9 TW/cm CO and Kr ATI peaks, - 5 TW/cm CO and Kr ATI peaks, 1-3 TW/cm Theoretical angular distributions from aligned O and N Total electron angular distributions for O and N for a moderate intensity Angular distributions for different kinetic energy regions Xenon electron data for the ATI s=1 peak, collected from - TW/cm, corresponding to a that grows to nearly.6 ev Argon energy levels Example argon photoelectron spectrum Example of diatomic Rydberg states converging on molecular excited states N Energy Levels N Rydberg series for the lowest intensities N resonances for mid-range intensities N resonances for higher-range intensities O energy levels xiv

15 6. O spectra at low intensities O resonances for mid-range intensities O resonances for higher-range intensities CO energy levels CO Photoelectron spectra for all intensities O Photoelectron spectra and calculated f resonances A.1 N Ion spectra at 9 TW/cm A. O Ion spectra at 9 TW/cm A.3 CO Ion spectra at 9 TW/cm xv

16 CHAPTER 1 INTRODUCTION 1.1 Motivation Light brings us news of the universe. William Henry Bragg, The Universe of Light Light is central to the history of physics. The unification of the electric and magnetic phenomena into the electromagnetic force, which describes light, was the crowning achievement of 19th century physics. The remaining mysteries of the nature of light sparked investigations that led to relativity and quantum mechanics, the hallmarks of th century physics. Given that grand history, it is no surprise that the study of light-matter interactions continues to be fertile. Technological innovations have led to the development of lasers that produce peak powers in excess of petawatts as well as lasers whose pulses are only a few optical cycles in duration. With these light sources, researchers can probe matter from regimes where light is a nearly negligible perturbation to where the light-field is so intense it entirely dominates the dynamics and the atom can be treated as a perturbation. 1

17 In this work, we examine individual atoms and molecules in the somewhat murky region where neither the light nor the matter can be easily treated theoretically, as they are too strongly entwined. The results, we are fond of saying, are akin to dissecting an atom with both a jackhammer and a scalpel simultaneously. 1. A Grand Tour of Light-Matter Interaction An actual grand tour of light-matter interaction would involve vastly more space than is available here, as the electromagnetic spectrum runs from gamma ray to radio wave and matter densities vary over many orders of magnitude. To make this discussion more concrete, we will restrict ourselves to visible wavelengths of light interacting with a single atom or molecule. As the intensity of the light increases, we can divide light-matter interactions into roughly four groups: linear optics, nonlinear optics, intense field, and relativistic field. Because light acts as a particle and a wave, it is helpful to consider these groups from each perspective light as a wave and light as a particle Linear Optics Linear optics is the light-matter interaction of everyday experience. Thinking of photons, this is the scattering and/or absorption of a single photon at a time. This depends on how likely an atom is to interact with a photon and how many photons pass by the atom in a given unit of time (or photon flux Φ with units of number per second per unit area). In terms of waves, linear optics is the distortion of an atom by an electromagnetic wave. The electrons in the material are driven by the light field within their atomic potentials, creating a polarization that can capture or re-direct the incoming energy.

18 This results in the scattering and absorption of energy from the light wave, P = χ E. (1.1) The susceptibility (χ) of the atom to light can depend on wavelength, polarization, or propagation direction of the light, and contains the essential features of linear optics. We can show that the continuous wave view of optics is indeed equivalent to the photon picture. The photon flux is trivially proportional to intensity which describes the amount of energy in the light field: I = 1 cɛ E = hνφ. (1.) The intensity, commonly given in units of watts per square centimeter (W/cm ) is the key measure of the strength of a laser field. Linear optics holds well for intensities below 8 W/cm. This simple description is enough to describe all everyday optical effects, from rainbows and the blue sky to holograms and optical fibers. 1.. Nonlinear Optics Thinking still of electrons under the influence of an incident electric field, one can imagine the driving field becoming so strong that the electrons start to sample larger regions of atomic potential. Just like a driven harmonic oscillator that begins to over-stretch its spring, the electron begins to sample regions of the potential that cannot be characterized by a simple restoring force. The resulting polarization can then be written as a perturbation in increasing powers of the incident field. P = χ () E + χ (1) E + χ () E (1.3) As in the case of the driven oscillator, this gives rise to harmonics of the driving field. 3

19 From a photon perspective, nonlinear optics is merely the interaction of a small number of photons simultaneously, which leads naturally to the production of harmonics. An atom can absorb two lower energy photons and emit a single photon with twice the energy. The perturbation theory of multiphoton interaction was first suggested by Göppert- Meyer in 1931 [1], as a two-photon extension to Einstein s explanation of the photoelectric effect. It was not, however, observed until the introduction of the laser in 1961, when sufficient intensities were available []. The intensity for nonlinear optical effects depends on the material s nonlinear susceptibility, but is roughly 8 1 W/cm. Nonlinear optics is the basis for many of the peculiar and useful effects found in modern optical technologies: frequency doubling, frequency mixing, self-focusing, and electro-optical effects [3] Intense Field Larger intensities begin to push the boundaries of perturbation theory. The electric field strength begins to approach the field strength which binds valence electrons and nuclei; this leads to ionization. This regime is particularly difficult to model, as one must consider the details of the atom and the details of the field equally. It is somewhat easier to think of this intensity region in terms of photons. Electrons can simultaneously absorb dozens of photons and become highly excited. These excited electrons can either ionize or relax to the ground state, releasing a high energy photon in the process.

20 3 1 E nergy E hν HHG MP I hν AT I HHG Figure 1.1: Fundamental intense field processes. An energy level diagram for a level with ionization energy E from a free continuum (gray shaded region). The absorption of a number of photons can result in multiphoton ionization (MPI), resulting in a free electron with kinetic energy indicated by ɛ. Higher order processes result in above threshold ionization (ATI) which can result in electrons with kinetic energies larger than the MPI process by multiples of the photon energy. Conversely, highly excited electrons can relax to the ground state in a high harmonic generation (HHG) process resulting in a single high energy photon. Both processes are the subject of intense research. The relaxation process, called High Harmonic Generation (HHG), is used as a source of coherent UV or X-ray bursts of light. Recent experiments have used these harmonics to synthesize attosecond ( 18 s) pulses [, 5, 6, 7]. Electrons from a high field ionization process will quickly convert solid-density matter into a plasma. Intense pulses are currently being investigated as sources of 5

21 high energy charged particles, or as a way to ignite fusion sources [8]. Plasmas created by intense field interactions can be used to simulate astrophysical systems, and beams of charged particles produced in such plasmas may have medical applications. 1.. Relativistic Fields As intensity increases above 18 W/cm, the light field entirely dominates, and all atoms are rapidly stripped of electrons. In this regime, the details of the atom become less important as the field is overwhelmingly strong. The number of photons interacting simultaneously with an atom becomes enormous and enormously difficult to calculate. In these cases, the simplicity of the electric field picture makes theoretical predictions somewhat more manageable. However, at these large intensities, one must carefully consider previously ignored interactions with the laser field. The magnetic field of light, which can be ignored at lower intensities, is now strong enough to affect the dynamics significantly. The electric field can accelerate ionized electrons to relativistic velocities during a single optical cycle. The laser technology required to create such fields has only recently been developed, and practical applications are as yet unproven. It is hoped that the rapid acceleration of electrons can lead to improved particle accelerator technologies, and novel ways of creating beams of charged particles [9, ]. 1.3 Methods and Goals This work is a study of diatomic molecules in the intense field regime. Study of laser-matter interactions in this region provides: first, a test of the understanding 6

22 gained from lower intensity regions; and second, a way to develop fundamental theories that can be extended to even stronger fields. The focus on diatomic molecules is an extension as well, from earlier experiments on single atom interactions. A main goal is to determine the extent that molecules in intense fields behave like atoms and what effect molecular structure has on the ionization process. To study the ionization process, one basically has two options: collect the ionized electrons or the remaining ions. Our experiment (detailed in Chapter 3) has the capability to measure both via time-of-flight spectroscopy. Collecting ions is a more common experimental method which gives us a measure of the total ionization. Resolving the kinetic energies of the electrons gives a more detailed indication of the ionization process, and is a particular specialty of this lab. Our studies have focused on two particular diatomic molecules - oxygen and nitrogen. These molecules are readily compared with companion atoms that have similar ionization potentials. The companion atoms, xenon (comparable to oxygen) and argon (companion to nitrogen) have been studied in great detail in the intense field regime. What we find is that the photoelectron spectra for molecules are largely the same as those from noble gases. In fact, given a spectrum or even a series of spectra, one would be hard pressed to determine whether it is from an atom or molecule. This is something of a surprise, given that diatomic molecules are more complex than atoms. Atomic photoelectron spectra have been shown to be a product of a single electron interacting with the field, and we therefore believe that the similar spectra from molecules have the same origin. This means that, although atoms and diatomic molecules have very different structures, their interactions with intense laser fields 7

23 are largely determined by the light s effect on a single electron. These results, while somewhat surprising given the complexity of diatomic molecules, point towards the universality of single electron interactions in intense field dynamics. 8

24 CHAPTER THEORY There is a tremendous body of work on the theory of light-matter interaction, much of it extremely complex. Thankfully, we are able to use semi-quantitative, semi-classical models as a framework to guide our experimental investigations. This section presents the essential elements of high intensity laser ionization, beginning first with light interacting first with an electron, then an atom, and finally molecules..1 Electron Field Interaction In the beginning there was light, and light was the wave solution to Maxwell s equations in free space. The wave equation can be written in terms of fields as E 1 E =. (.1) c t The electric force acts on a charged particle with charge e, say an electron, according to F = ee. (.) Given that the magnetic field is smaller than the electric field by a factor of 1 c and that the magnetic force is given by F mag = ev B, (.3) 9

25 then the magnetic field s effect on the particle s motion will be negligible as long as v c, that is to say in the nonrelativistic limit. As shown below, in this work all fields are clearly in this regime. The simplest solution to equation.1 is the plane wave solution E(r, t) = E cos(k r ωt + φ), (.) where ω = ± k c where the wavevector k gives the direction of propagation, ω gives the frequency, and φ is a phase-factor. For all examples in this work, radiation with a wavelength of 8 nm is assumed. Starting with equation., we can determine the equations of motion of an electron in a plane wave of infinite extent. If the electron is initially at rest at the origin, the problem is in 1D along the polarization of the electric field (denoted x). Conceptually, the motion is an oscillatory or quivering with the electric field, and using Newton s equations, F = m e ẍ ẍ = e m e E cos(ωt) ẋ = e m e E ω sin(ωt) (.5) x = e E cos(ωt). (.6) m e ω Two results can be drawn from this simple picture. The first is to determine the maximum spatial excursion of an electron in a plane wave using equation.6. For an intensity of 1 W/cm we find the maximum excursion of the electron is.9å. This is almost Bohr radii (a ) for larger intensities, the maximum excursion

26 can be nanometers, which is much larger than an atom, but minuscule compared to typical focal dimensions. This guarantees that even an electron with a slow initial velocity will not sample a large spatial region of the field. The infinite plane wave approximation is therefore valid. The second result comes from using equation.5 to calculate the time averaged kinetic energy of an electron in a laser field. KE = 1 m e ẋ (.7) KE = e m e ω E (.8) For a relatively weak intensity of 1 W/cm, the average kinetic energy of a free electron is.6 ev. This is called the quiver, or ponderomotive, energy (denoted ), and is a useful figure of merit in high-field physics because it gives a scale for how much energy an electron must have to be considered free. Note that is directly proportional to the intensity.. Stark Shifts Now we consider the effect of a light field on an atom, specifically the response of the atomic energy levels when perturbed by an external light field [11]. To include the light-field in the quantum mechanical Hamiltonian, it is best to formulate the electromagnetic field in terms of potentials, rather than fields. A 1 c A t φ + 1 ( A) c t = (.9) ( A + 1 φ c t ) = (.) There are gauge freedoms associated with A and φ, and in this derivation, the so-called Coulomb gauge is used although the results are invariant [1]. The Coulomb 11

27 gauge sets A =. In free space (no charges or currents) φ = which results in φ =, causes the potential equations to reduce to A 1 A =. (.11) c t This gauge is also called the transverse gauge, because transverse electric fields are entirely represented by the vector potential. This can be seen by using the Helmholtz theorem to write an arbitrary electric field as the sum of transverse (no divergence) and longitudinal (no curl) components, E = E t + E l. E = φ A t E t + E l = φ A t (.1) (.13) E t + E l = φ A t (.1) but E l = and φ = so (.15) E t = A t (.16) The result: the vector potential describes transverse electric fields, including plane waves. This potential is included in a one electron Hamiltonian by replacing the classical momentum operator with a quantum momentum operator that includes the field; This changes the Hamiltonian to Π = p + e A. (.17) c H = 1 m Π + V (r) (.18) H = 1 m [p + e e (p A + A p) + c c A ] + V (r), (.19) 1

28 where V (r) is the atomic potential. This can be grouped into a field-free zeroth-order Hamiltonian H and an interaction term H 1. H = 1 m p + V (r) and H 1 = e (p A + A p) + e mc mc A (.) We can now approach the problem classically, using the potential for an infinite plane wave polarized along ẑ, A = E c ω cos(ωt)ẑ. (.1) This leads directly to a simplification of the interaction Hamiltonian in terms of the classical field, H 1 = 1 [ ] E m ω cos(ωt)p z + ee c cos (ωt). (.) ω We can evaluate the shift of energy levels using perturbation theory in second order, which results in a shift of energy level i by an amount E i which can be written as E i = e E ω 1 i f f fi ω fi ωfi. (.3) ω In this expression, the sum is over all final states of the electron, hω fi is the difference in energies of initial and final states, and f fi is the oscillator strength. There are two easily evaluated limits that are useful in guiding our thinking about atomic states in intense fields. For very weakly bound states, close to the continuum, ω fi ω and in fact approaches zero, leading to a simple expression for the energy shift that is the ponderomotive shift. This suits our intuition well, as weakly bound states are expected to behave much like free electrons. In the opposite extreme, very deeply bound states (for example the ground state) have energy spacings to other levels that are much larger than a photon, so ω fi 13

29 ω. In this case, the sum is dominated by the sum of oscillator strengths which is identically 1 according to the Thomas-Ritchie-Kuhn sum rule. This leads to an energy shift that is zero. This simple argument is used to justify the most common assumptions in understanding bound states in an AC field the ground state undergoes basically no shift. The weakly bound states and the free electron continuum shift by the ponderomotive potential. This has the net effect of increasing the ionization potential..3 Nonresonant Multiphoton Ionization Continuing the perturbative approach outlined above, one can imagine multiphoton ionization as an extension of single photon ionization, known as the photoelectric effect. For most atoms and molecules, having ionization potentials (IP) greater than a few electron volts, single photon ionization requires UV light, as shown in figure.1. The resulting electron kinetic energy is given by KE = hω IP. Now we extend the model to ionization by the absorption of multiple photons. In the absence of resonances, absorption of multiple photons would take place through virtual states, the lifetime of which is determined from the uncertainty principle and their detuning. This indicates that multiphoton absorption must be nearly instantaneous for bound states that require a large number of photons to ionize. This implies a requirement for large photon fluxes, or high intensity fields. The resulting electron kinetic energy after multiphoton ionization is then given by KE = M hω IP (I) (.) 1

30 ionization continuum } E E nergy E hν hν P hotoelectric MP I E ffect (nonres onant) R E MP I Figure.1: Schematic of multiphoton ionization processes, from a state with binding energy E. Each process results in a free electron with kinetic energy ɛ. The photoelectric effect which requires a single (typically UV) photon. A multiphoton ionization (MPI) process can occur with multiple lower energy photons the time scale of this process is given by the detuning E of the virtual state from the nearest real state. A resonant multiphoton ionization (REMPI) has a vastly higher probability, because the existence of a real resonance relaxes the uncertainty principle requirements. 15

31 where M is the minimum number of photons to ionize, and IP now depends on the intensity, because the AC Stark shift can not be neglected at high intensities. The Stark-shifted ionization potential is simply IP (I) = IP +. The MPI process results in KE hω, because we only consider the absorption of the minimum number of photons to ionize.. Above Threshold Ionization and Resonances The MPI assumption, however, is only realistic for relatively low intensities. In high intensity experiments, absorption of photons rarely stops at the minimum required. Laser ionization experiments routinely observe electrons from many orders of additional ionization photons (See figure.1). Therefore equation. should be modified to predict N kinetic energies, each spaced by the a photon. KE = (N + M) hω IP (.5) Moreover, one also needs to account for resonances during the MPI/ATI process. If some number S of photons is resonant with an excited state of the system, the rate of ionization will be much greater than for purely nonresonant ionization because of the larger cross section of the real intermediate state. This would predict a large photoelectron emission at some KE res when S hω = E res an exited state, as shown: KE res = (S + n) hω I p (.6) KE res = E res + n hω I p (.7) This resonant multiphoton process, or REMPI, has been exploited to perform spectroscopy on one-photon forbidden transitions. 16

32 .5 Transient Freeman Resonances.5.1 Long Pulse Experiments The first experiments to observe ATI processes were performed using picosecond pulses to reach the necessary intensities. These long pulse experiments showed a series of photoelectron peaks spaced by the photon energy, as expected. However, the electrons did not shift to lower energies with higher intensities, as equation.5 would suggest. The problem was the long laser pulses. After ionization, electrons leaving the focus were able to sample the spatial variation of the field. The gradient of the ponderomotive potential accelerated the electrons, effectively converting their wiggle energy into kinetic energy. The electrons could slide down the potential hill that the focus created. This negates the effect of the Stark shift on the measured electron kinetic energies..5. Short Pulse Experiments When experimental methods allowed ionization with sub-picosecond pulses, drastically different photoelectron spectra were observed. The electric field from the laser focus turned off much faster than the electrons could sample its spatial variation. Electrons were no longer able to slide down the potential hill the hill simply disappeared out from under them. The ponderomotive energy was returned to the field, and the kinetic energies of the electrons were unchanged. Instead of observing equally spaced series of peaks whose kinetic energies decreased with increasing intensities (as equation.5 would suggest), a complex series of peaks spaced by photon energies was observed (for an example, see chapter 6, figure 6.3). 17

33 As in the long pulse case, this complex structure did not shift as the laser intensity was increased. The complexity was explained by considering the laser pulse itself for a peak intensity I, a laser pulse must ramp through all intensities below I. As the pulse grows in time, the Stark shift will increase and bound excited states of the atom will become resonant for a short time. This explains the existence of multiple kinetic energies during a single pulse, but what about the persistent peak structure? As in the long pulse case, the answer was the Stark shift. In section. it was shown that weakly bound Rydberg states shift linearly with the field. These ponderomotively shifting bound-states have intensity dependent energies E res (I) = E res +, leading to KE res = E res (I) + n hω I p (.8) = E res + + n hω I p (.9) = n hω (Ip E res ) (.3) When the field is in multiphoton resonance with a Stark shifted state, the resulting kinetic energy does not depend on intensity and is related to the field-free binding energy of the state. These transient resonances, called Freeman resonances, are shown schematically in figure.. As the field increases, weakly-bound states in the atom are shifted into an S photon resonance, one after the other. As the ponderomotive potential increases with intensity, eventually the ionization potential is raised by an entire photon s worth of energy, meaning that any ionization process requires an 18

34 additional photon. This is referred to as a channel closing, as S photon processes no longer participate in ionization and S + 1 photon resonances can begin to occur..6 Tunnel Ionization The preceding discussions use a photon model of the interaction to predict electron kinetic energies. However, this approach is of little use when trying to determine the numbers of electrons produced. For a different perspective on intense field ionization, it is helpful to consider the effect of the instantaneous field on the Coulomb potential. In each quasi-static instance, the field distorts the potential, creating a finite barrier for bound electrons. One can then calculate the ionization rate the rate at which bound electrons can tunnel through the barrier. For this tunneling model the field is entirely classical and the only parameters are bound state energy (ionization potential) and strength of the laser field. The most common formulation of this approach is the Ammosov, Delone, and Krainov [13] or ADK model, which is regularly used for calibrating intensities given ionization yields [1]. To determine photoelectron energies from this model, one must consider a twostep process. First the tunneling ionization of the electron and then the acceleration of the electron in the laser field. Tunneling is the small electron probability that extends past the classical turning point all tunneling electrons are born with essentially zero kinetic energy. The rate of production, however, is highly dependent on the field strength. The stronger the field, the smaller the barrier the ionization rate is exponential in field strength. Therefore, most electrons are produced at the peak of the laser field, and no electrons are able to escape at the nodes of the field. 19

35 I = I max (N min +) hν (N min +1) hν Energy N min hν I ~ I ~ res onances Up Time Figure.: Schematic of Stark-shifted resonances, plotted as an energy level diagram during the temporal progress of a laser pulse. The shifting of the ionization limit (thick line) and Rydberg states (thin lines) by is a result of the cycle-averaged field and proportional to the intensity of the pulse, from I to I max. Dashed lines are multiple photon energies at I, N min photons are required to ionize the system. As the intensities are increased, the number of photons required to ionize increases. Some resonances of bound states with N photons are indicated.

36 (a) Multiphoton (b) Tunneling (c) Barrier Suppresion Figure.3: Schematics of high field ionization processes, in order of intensity. The Coulomb potential and ground state electron wavepacket are displayed. (a) Multiphoton ionization involves a quasi-static electric field which is not strong enough to distort the potential, (b) Tunnel ionization involves a quasi-static field that tips the potential allowing the wavepacked to tunnel through the potential barrier in the direction of the applied field. In barrier suppression (c), the applied field depresses the Coulomb potential resulting in an entirely free ground state. The tunneling step determines the number of electrons, while the second step, acceleration in the field, determines their final kinetic energies. Electrons born at the peak of the field are unable to gain kinetic energy from the field, as after each half-cycle of the field the electron has zero velocity. If an electron were born at the zero crossing of the field, at any half cycle later it would have a maximum velocity. This results in a characteristic photoelectron spectrum that has an exponential falloff of electron kinetic energy. An extreme case of tunnel ionization occurs for large amplitude laser fields. The field suppresses the Coulomb potential entirely, leaving a formerly bound electron in the continuum. This is known as barrier suppression ionization, or BSI, and occurs above a critical field value, F c, given by F C = πɛ E b Z 1 (.31)

37 in the case of a pure Coulomb potential (nuclear charge Z in Coulombs) and a bound state of energy E b..7 The Keldysh Parameter Now we have two simple, yet very different, models for ionization in high field experiments MPI/ATI, which relies on a photon picture, and tunneling, which assumes a classical field. How does one determine which model is most applicable? In his paper describing many effects of high field ionization, Keldysh described an adiabaticity parameter γ, now known as the Keldysh parameter [15]. It measures the applicability of the tunneling model as a ratio of the tunneling time of a bound electron to the period of the laser field, γ = ω laser = ω laser IP me = ω tunnel ee IP (.3) where IP is the ionization potential of a Coulomb field, E is the field amplitude, and m e and e are the mass and charge of the electron. The Keldysh parameter can also be handily written in terms of the IP and the ponderomotive potential of the field. When γ 1, tunnel ionization clearly dominates, while the multiphoton process is dominant for γ 1..8 Rescattering Model Early intense field experiments reported three somewhat surprising observations. The first was an extensive range of high harmonics known has high harmonic generation (HHG)[16]. The second was a significant enhancement in the production of double ionization events[17, 18, 19,, 1]. Theories had predicted that double ionization would occur (via mechanisms described above) in a sequential manner: first

38 one electron would be ionized, then the second. This second ionization step would be orders of magnitude less common (due to the energy required to doubly ionize an atom) than single ionization events. The observation of significant doubly-charged ions when few were expected was termed non-sequential double ionization (NSDI). The third surprise was the observation of photoelectrons with kinetic energies much greater than would be expected from a tunneling model []. A simple and very satisfying explanation for all three observations came from a model that asserts the release of an electron from the core is by no means the end of the ionization process. The electron dynamics are then dominated by the intense field which produced it, which causes ponderomotive wiggling. If this electron, now accelerated by the field, re-encounters the core, what can we expect to happen? The electron can be re-captured and return to the ground state with the release of a high energy photon. The electron may also scatter elastically, gain more energy from the field, and be detected as a high energy electron. Finally, the accelerated electron might scatter inelastically with the remaining core, possibly doubly ionizing the atom. [5] This rescattering [] or three-step model has been used to construct S-matrix formalisms that provide physically rigorous quantum mechanical calculations. These calculations give accurate recreations of HHG, NSDI, and the high energy plateau electrons observed in intense field ionization [3]..9 Diatomic Molecules The nuclear potential for diatomic molecules is simply the sum of the potential from each nucleus. Although it sounds simple in theory, in reality this is hardly a 3

39 simple extension of atoms (for detailed discussion see Haken and Wolf []). The existence of a symmetry axis changes the physics dramatically. Diatomic molecules exhibit vibrational motion along the internuclear axis and rotational degrees of freedom about the axis; these simply do not exist in atoms. Second, the molecular symmetry axis provides a clear reference for interactions with a linear electric field the axis can be oriented from parallel to perpendicular with regards to the applied field. Finally, molecules can dissociate during intense field processes, leading to a more complex final state..9.1 Bound State Configurations Electronic states of a diatomic molecule are affected by breaking of the spherical symmetry of the potential. No longer is the angular momentum l a good quantum number however, the component of the angular momentum along the internuclear axis remains so, and is denoted λ. The orbital wavefunctions associated with λ are named in analogy to s, p, d, f as σ, π, δ, φ. In homonuclear molecules, for which the nuclear centers are indistinguishable, there is a notation for wavefunctions that are symmetric (g) or antisymmetric (u) with respect to inversion. This leads to electronic orbitals written as nλ symm,for example π g or 1σ g. Special attention is paid to the highest occupied molecular orbital (HOMO), which can quickly determine whether a particular diatotmic is covalently bonded. Vibrational states, states that differ in units of vibrational energy of the nuclei, are labeled with ν. The separation of ν energy levels are typically on the order of s of mev. The rotational states, labeled with J are very closely spaced in energy (mev), and will not be observable in this work.

40 For multi-electron configurations, the total angular momentum along the internuclear axis is labeled Λ and the spatial wavefunctions are named Σ, Π,, etc. Inversion symmetry is labeled as u or g, and spatial symmetry with respect to a reflection through the internuclear axis are labeled as + and. Spin multiplets are designated as in the atomic case (S + 1), as a superscript before the term. For example, the ground state of O is labeled 3 Σ g. From a multiphoton point of view, these electronic states in the diatomic potential are possibilities for multiphoton resonances. The great number of states suggests that contributions of non-ponderomotively shifting states may be quite large. From the tunneling picture, where the electric field is quasi-static, one imagines a tipping of the double-welled nuclear potential. The rate of tunneling will then depend on the electric field as well as the internuclear distance. In fact, it is well known that there is a critical internuclear separation, R c, for which tunneling ionization is maximized for a given electric field [5, 6, 7]. In general, the non-columbic shape of the potential should alter the tunneling characteristics of a molecule including the Keldysh parameter [8], in which the tunneling rate is based on a hydrogen-like potential. The strong dependance of ionization rate on internuclear distance can significantly alter the Frank-Condon picture of excitation. The Frank-Condon principle states that the absorption of photon is instantaneous with respect to nuclear motion, so the probability of excitation depends on the overlap of the ground and excited state electronic wavefunctions only. With an external field affecting the nuclear potentials, it has been shown in H ionization that the resulting excited state populations deviate from Frank-Condon predictions [9]. 5

41 The effect of vibrational motion on the internuclear positions has an effect on ionization rates, but only a relatively small one [3]..9. Alignment Effects Alignment of diatomic molecules in electric fields has been studied extensively [31]. A purely classical model of the diatomic system utilizing the electric polarizability anisotropy (α α ) can be utilized to calculate an estimate of the time required to align a molecule with a linearly polarized laser field [3]. ( ) cj 1/ T r = π (.33) I α This time constant given for 15 W/cm intensities is 16 fs for H and fs for N, which for 13 W/cm pulses results in picosecond alignment times. This approach relies heavily on a quasi-static approximation (the use of static polarizibilities), and there have been more realistic calculation[33]. Experiments have been reported with extremely short pulses (< fs) which serve as rotational impulses and result in dynamic alignment [3]. Moreover Coulomb explosion experiments have shown evidence of alignment for O, even for pulses as short as 35 fs [35], while alignment for N has not been seen in 5 fs ionization experiments [36]. Thus, the details of alignment in laser fields are still very much an open question. Ionization is known to be strongly affected by alignment [37, 38]. From a simple quasi-static picture, it is clear that fields aligned along the internuclear axis distort the potential more than fields aligned perpendicularly. 6

42 .9.3 Dissociation and Explosion Excited states of diatomic molecules are not necessarily bound, and if given enough energy to allow the internuclear axis to increase towards infinity, neutral dissociation can occur. Even bound states of the molecule may be coupled to states that dissociate this process is known as predissociation, as a bound state has enough overlap with a dissociating state, which usually occurs at some longer time scale. This process is, of course, influenced by the presence of a laser field which leads to bond softening [39]. Both processes may also occur in excited molecular ions, leading to dissociation that results in one or more charged atomic ions. If the molecule is highly ionized enough, the repulsion of the nuclei will produce a rapid Coulomb explosion, resulting in multiply charged ions [, 1,, 3]. Studies of multiply-charged molecular dissociation of molecules by measuring the kinetic energies of the dissociation products have been undertaken for decades [, 5, 6, 7, 8, 9]. In this work, we have sidestepped the dissociation process entirely, by choosing lower intensities that do not not result in multiply charged molecules (see appendix A). We intend to concentrate fundamentally on single ionization processes. 7

43 CHAPTER 3 EXPERIMENTAL ARRANGEMENTS These experiments were performed by focusing intense femtosecond laser pulses into a vacuum chamber backfilled with target gas. When atoms or molecules were ionized by the laser, the electrons or ions could be collected at a detector and their flight times measured. Ions are collected by a sweeping voltage, and their flight times are used for species selectivity. For electrons, which were collected after field-free flights, the time of flight was converted to kinetic energy. This chapter details each element of the experiment in order, from laser source to data analysis. 3.1 Laser Source It is a testament to the rapid development of laser technology [5, 51] that the fields used in these experiments were generated by an entirely commercial laser system. Generating these high intensity laser fields requires high pulse energies, short pulse durations, and focusing to small spatial dimensions. Moreover, the demands of data collection require high repetition rates. A stock Spectra-Physics laser system, described in Figure 3.1, was used to meet these requirements. This system generates 1 mj pulses with a FWHM pulse width of 1 fs and a 1 khz repetition rate. 8

44 Millennia - Nd:YVO CW, 5W, 53nm Tsunami - Ti:Saph fs-oscillator 8-1 fs, 5 nj, 8 nm, 8 MHz Merlin - ND:YLF ~5 ns, 8 mj, 53 nm, 1KHz Spitfire - Ti:Saph Regen Amplifier 1 fs, 1 mj, 8 nm, 1 KHz Figure 3.1: Block diagram of Spectra-Physics laser system, consisting of a Tsunami oscillator pumped by a Millenia and a Spitfire Regenerative Amplifier pumped by a Merlin Femtosecond Oscillator Our laser system begins with the Millennia a continuous wave (CW) laser with a neodynium-doped yttrium orthovandatate (ND:YVO ) gain material pumped by two 89 nm diode bars. The 6 nm lasing of the ND:YVO is doubled by an intra-cavity lithium triborate (LBO) crystal to produce.5 W of 53 nm output. The Millennia is used to pump the Tsunami, a titanium-doped sapphire (Ti:Sapphire) mode locked laser [5] that serves as the oscillator of our setup by generating an 8 MHz train of fs pulses, each containing a few nj. From Fourier theory, a short temporal pulse must be composed of a large number of frequencies. Moreover, these frequencies must be phased in such a way that they sum to produce a pulse that is, at some location and time, each frequency component s maxima must superimpose as in figure 3.. 9

45 a) c) - - T ime - - T ime b) d) - - T ime - - T ime Figure 3.: Example of mode-locking. (a) Shows the result of the superposition of a cavity modes with random phases (b). The pulse in (c) is created by the superposition of modes locked to a constant phase (d). 3

46 The use of Ti:Sapphire is nearly universal in femtosecond laser design primarily because of its extremely wide gain profile, which is peaked at 8 nm, but has a width of more than nm. This bandwidth is more than sufficient for the 9 nm required for a fs pulse at 8 nm. The laser cavity of the Tsunami can therefore support the number of modes required for femtosecond operation, but it must also lock the phases of the modes together (mode-locking) and maintain this phase relationship as the modes propagate through the cavity. Mode-locking is achieved by exploiting the exponential gain of the laser media. If one can arrange for a mode locked (i.e. short) pulse to travel through the cavity with fewer losses, then this mode will quickly dominate the nonpulsing modes. In the Tsunami this is achieved by exploiting a nonlinear optical effect known as the Kerr effect [53]. The Kerr effect is a consequence of the third order nonlinear susceptibility of a material. For a material with a zero second order nonlinear susceptibility, the polarization of the material under the influence of a single electric field can be written P = χ (1) E + χ (3) IE, (3.1) where E is the electric field, I is intensity and χ s are terms of the susceptibility. The term χ (1) is the linear term that yields the index of refraction. When re-arranged P = ( χ (1) + χ (3) I ) E, (3.) it is clear that the third order term can be seen as an intensity-dependent index of refraction. A beam s spatial intensity profile (e.g. Gaussian) has the highest intensity in the center. This causes an intense beam to see a lens while propagating through a material. 31

47 In the case of the tsunami, the nonlinear lensing material is the Ti:Sapphire crystal itself. The laser cavity is adjusted such that there are the fewest losses for modes that undergo this Kerr lens self-focusing. This effect causes preferential gains for laser modes that are locked together to form a short pulse. Locking CW modes together to create a pulse does very little good if the modes disperse while traversing the laser cavity. Each round trip would find the pulse successively longer and longer. Therefore, the laser cavity also contains prism pairs which are used to correct dispersion within the cavity. By ensuring that longer wavelengths travel longer distances through the cavity, these prism pairs can be adjusted to ensure that the net first and second order dispersion is zero Amplification The Spectra-Physics Spitfire is used to amplify pulses from the oscillator to an energy of roughly 1 mj per pulse. The first difficulty is one of power it is energetically difficult to amplify each pulse in an 8 MHz train to 1 mj. The resulting average power would be 8, watts. Therefore, the amplifier must pick pulses to amplify, effectively down-sampling the pulse train to a more manageable energetic load. In our case, we down-sample to 1 khz. The gain region of the Spitfire is also Ti:Sapphire, pumped by a Spectra-Physics Merlin. The Merlin is a Q-switched, intracavity-doubled ND:YLF laser that produces ns, 8 mj pulses at 1 KHz. Even at a kilohertz, where the average power of our amplified beam is only 1 watt, the peak intensity for individual pulses is quite high. When focused into the 3

48 gain region, the peak intensity can easily surpass the damage threshold. To avoid this problem, the technique of chirped pulse amplification (CPA) is used. CPA was initially developed for radio wavelengths, and was applied to high intensity lasers in the 198 s. The idea is simple: stretch the short pulse using dispersion; amplify the resulting long pulse so that the peak intensity is low; then re-compress the pulse to the original duration [5, 55, 56]. The Spitfire is designed as a regenerative amplifier [57, 58]; that is, the gain region is contained in a separate laser cavity. Pulses from the oscillator are first stretched, then injected into the cavity to be amplified. The injected pulses seed the cavity and are amplified by 16 passes through the gain medium. This allows a certain amount of de-coupling of the oscillator and the amplifier the spectral and temporal profiles are due to the seeding of the amplifier, while the amplifier s cavity allows control of the spatial mode. Moreover, operating as a cavity minimizes amplified spontaneous emission (ASE) from the amplifier s gain medium Intensity Control Our experiments focus on monitoring ionization as a function of intensity. However, it is difficult to reliably adjust the pulse energy by means of adjusting the amplifier. Changing the pump power or the number of passes through the gain medium can affect the temporal and spatial mode. Nonlinear dispersive effects become a problem when propagating the short pulses through absorptive attenuators or thick polarizers. Our scheme attenuates the beam after amplification but before compression, when the peak intensity is still low. A stepper-controlled half-wave plate and polarizer are placed before the compressor. The stepper motor controller (Compumotor SX Series) 33

49 is interfaced via serial connection to a PC running LabView software. Our software allows manual control of the half-wave plate s angle to better resolution than our power diagnostics can detect Diagnostics A system of laser diagnostics allows constant monitoring of the laser system, specifically to measure changes in intensity. These diagnostics focus primarily on pulsewidth and energy for a well running system, there are no large changes to the spatial mode during day-to-day operation. A pyroelectric power meter (Molectron PowerMax 5) is used for measuring average power, providing a coarse measure for pulse energy. The response time of the head unit is in the millisecond range, meaning that at best one can only get a sense of the average power. For a more exact measure of the pulse energies, a photodiode is used. The photodiode is mounted in a photovoltaic configuration, and the output is amplified by a custom-built, battery operated amplifier. The amplified signal is digitized in a National Instruments DAQ board and read using custom LabView software. The software samples the photodiode voltage once per millisecond (a clock signal that is derived from the laser) and provides a voltage proportional to pulse energy for each laser shot. Averaging hundreds of laser shots and calibrating the average photodiode voltage to average power as measured by the power meter results in a voltage-power calibration that is accurate to a few percent. Moreover, using the photodiode, the pulse-to-pulse variations of laser power can be measured. This indicates shot-to-shot fluctuations below 1% with long-time fluctuations at a few percent. 3

50 Measuring pulse width is a more complicated endeavor, as one needs to both ensure the oscillator is producing suitable pulses for amplification and evaluate the amplified pulses themselves. The most straightforward technique for a quick check of the oscillator pulse width is to measure the spectral bandwidth. Pulses from the oscillator are picked off with a glass slide before the amplifier and sent into a spectrometer. By assuming a modelocked, Gaussian pulse, one can use the time-bandwidth product to infer a pulsewidth. This allows us to determine whether the Tsunami is running well. For added security, a bandwidth detector is used in the stretcher section of the amplifier. Composed of two photodiodes placed along a spread-frequency retroreflector, the bandwidth detector interlocks the pulse-picking electronics to ensure that the amplifier only operates when seeded by a pulse of sufficient spectral width. For monitoring the amplified beam we use a single-shot Second Harmonic Generation Frequency Resolved Optical Gating (SHG-FROG) technique that can reconstruct the full electric field of the pulse [59, 6]. The SHG-FROG is essentially a single shot second-harmonic autocorrelation which is then spectrally resolved. For our uses, we need not reconstruct the complex electric field of the pulse, but merely ensure our FROG signal looks clean, and use the spectral and temporal components for pulse analysis (see figure 3.3) Focusing The laser focus presents a considerable complication for studying high-intensity phenomena. Ideally, we would like to observe the effect of a single intensity, but we can only reach intensities of interest by focusing. Our sample therefore experiences 35

51 (a) Autocorrelation F R OG T R AC E fs - fs - b) S pectrum nm nm Figure 3.3: An example capture from the SHG-FROG during a data run. Inset (a) displays the integrated columns, yielding an autocorrelation. (b) is the spectrum, from integrated rows. 36

52 a spatially-varying peak intensity, and our measured signal is then a sum of the ionization events occurring at all intensities present in the focus. The beam is focused by a plano-convex lens mounted externally to the chamber, with focal a length of 5 mm (f/# 5). The intensity of the focused beam, for a pure TEM mode, is Lorentzian along the direction of propagation and Gaussian in the transverse directions. [ ] ω I(r, z) = I e ( r ω(z) ), (3.3) ω(z) where ω is the radius of the beam at the focus, and ω(z) gives the spot size as a function of position, ( ) z. ω(z) = ω 1 + (3.) z The quantity z is the Rayleigh range, which can be written as z = πω λ (3.5) and gives a measure of the size of the focus along the propagation direction. For the 5 mm lens, the spot size is roughly 5 µm and the Rayleigh range is.6 mm. The intensities in the focus are distributed as in figure 3. at the center of the focus is the peak intensity, I. The volume of the focus that extends from some given intensity to I is given by V (I, I ) = πz ω [ 3 ξ ξ 3 3 tan 1 (ξ 1 )] (3.6) where ξ = [ I I ]. I The signal recorded is the sum over all intensities in the focus, weighted by the number of atoms that experience a given intensity. Given the uniform density of atoms 37

53 r/w z/z Figure 3.: A contour plot of Gaussian laser focus intensities. The graph is significantly compressed along the z axis, in steps of the Rayleigh range; while the radial dimension is labeled in units of beam waist. Each contour is a factor of two smaller intensity than the previous. in our backfilled chamber, the number of atoms that experience a given intensity is simply proportional to the volume of the region that experiences a peak intensity between I and I + I is given by V = πz ω [ 3 (ξ 1 1 ξ ) + 9 (ξ 3 3 ξ ) 3 (tan 1 ξ 1 tan 1 ξ 1 ) (3.7) [ ] I I ξ = I [ ] I (I + I) ξ = I + I This describes a shell of relatively constant intensity. As the maximum I increases, the volume of one of these constant intensity regions increases as well, an increase that is proportional to I 3/. This is clearly seen in ion signals from laser pulses that are large enough to saturate the ionization process. The signal of ions, instead of remaining constant (or even dropping as single ions become doubly ionized) is seen to increase with intensity as I 3/. This is because the focal volume continues to increase, resulting in an increase of ionization signal. 38

54 It is possible to use a small aperture between the focus and the detector to reduce the effects of spatial averaging on the signal. This can significantly simplify the averaging over components of the focus in the z direction. 3. Target Area These experiments were performed using one of two vacuum chambers Ema or Peggy. Ema was built for gas-phase experiments and features a computer controlled servo leak valve for admitting target gas into the chamber. Peggy was built primarily for atomic beam experiments (not covered in this work) but allows for gas backfilling via a manually controlled leak-valve. Both chambers feature nearly identical interaction regions and detection systems and differ mainly in the particulars of construction Interaction Region The beam focuses into the interaction region displayed in figure 3.5, which is constructed of oxygen-free copper plates mounted on threaded rod and alumina spacers. There are two distinct experimental configurations which can be selected by translating the focus pinhole or full-volume. The pinhole configuration uses two plates: the pinhole plate features a 1 mm pinhole that restricts the detector s view of the spatial focus variation. The voltage on the repeller plate can be adjusted using an external supply. When both the pinhole and repeller plates are grounded, the system is configured for electron collection. For ion collection, a large (typically V) voltage is placed on the repeller plate (hence the name) while the pinhole plate remains grounded. 39

55 ceramic spacer FV focus position Flight Tube pinhole plate RV focus position repeller plate Figure 3.5: Diagram of interaction region, showing the laser focus for full (FV) and restricted volume (RV) configurations. In the full volume (FV) configuration, there is no obstruction to simplify the z- direction spatial variation. For electron collection, all plates are grounded as before. For ion sweeping, a voltage is instead placed on the pinhole plate which then functions as the repeller. Configurations can be changed by simple re-alignment of the focusing optics and movement of the voltage supply. 3.. Vacuum System The vacuum requirements for these experiments are set mostly by chamber contaminants. Ion detection, because it is species sensitive, has a lower vacuum requirement, typically tenths of microtorr. Detecting electrons is much more stringent, requiring UHV pressures for background gasses. The vacuum chambers are pumped by turbomolecular pumps backed by Welch-style roughing pumps. Each turbo pump

56 is attached to the chamber through a pneumatic gate valve connected to a safetyinterlock system. Upon power or roughing-pump failure, the interlock system closes the gate valve to the chamber, ensuring system safety. Each chamber is also fitted with a liquid nitrogen trap for additional pumping when necessary. When cleaned, pumped, and baked at 15 C for a few days, these chambers can maintain base pressures of a few hundred picotorr for months. 3.3 Detection Methods Charged particles travel down a field-free flight tube, are detected by a pair of micro-channel plates, and processed by timing electronics. The end result is an accurate measurement of particle time of flight Flight Tube The flight tube, also maintained at UHV pressures, is an aluminum tube which connects on one end to the interaction assembly and on the other to the detection assembly. The inner surface of the tube is coated with Aerodag-G, a spray-on colloidal graphite coating that serves to minimize surface imperfections and oxides which may be a source of electric patch fields. To shield electrons from magnetic fields, the flight tube is wrapped in mu-metal. The shielding requirements for electrons are much greater than for heavy ions, particularly for low kinetic energy electrons during the initial flight. For this reason, the interaction region is shielded more heavily. In Ema, this is accomplished with two layers of mu-metal foil separated by glass spacers. For Peggy, a single-piece, custom mu-metal shield was built. It surrounds both the interaction and flight tube with a 1/8 layer of mu-metal, again separated by glass spacers. The mu-metal shielding, 1

57 particularly in Peggy, has allowed for a dramatically higher collection efficiency for low energy electrons than our earlier shielding methods Micro Channel Plate Assembly Electron detection is accomplished by micro-channel plates (MCP s). An MCP is an electron-multiplier that works by accelerating charged particles through small channels lined with a low work function coating. These channels are biased at a shallow angle with respect to the potential, so that collisions with the channel walls cause electron cascade. The plates can be stacked in a chevroned, or back-to-back configuration, for additional amplification. In this manner, gains from 6 8 are typical. The one-inch-diameter MCP s used in these experiments were of two types, both produced by Burle. The lower-gain plates have µm diameter channels with an aspect ratio of 1:, while the higher-gain plates have an aspect ratio of 1:6 and smaller diameter 6 µm channels (therefore many more channels). The high-gain plates provide excellent sensitivity for electron data, while the low-gain plates are more suited to the strong signals of ion collection. The amplified current signal is accelerated by a small voltage to the anode, which is formed as a conical waveguide to match impedance to the 5Ω BNC connector feedthrough [61] Timing Electronics The time of flight information is recorded by an Ortec 937 picosecond timing analyser (pta), a multiple-stop time spectrometer that can record time delays between start and stop events with remarkable (up to ps) accuracy. The high

58 P R IMAR Y E LE C T R ON CHANNE L WALL OUT P UT E LE C T R ONS VS upply CHANNE L PLATE C HANNE L DE T AIL Figure 3.6: Micro channel plate (MCP) showing construction and operation detail. Figure from Hamamatsu Photonics sales literature. Screen MCP Front MCP Back BNC Feedthrough -HV Supply Current Limit Coupling Capacitor Flight Tube Conical Anode To Timing Electronics Voltage Divider Signal/Supply Box Figure 3.7: Complete detector assembly. Note the grounded flight tube, chevroned MCP stack, and the conical anode waveguide. The signal/supply box supplies the high acceleration voltages, ensuring the highest voltage at the anode. A pf coupling capacitor is used as a high-pass filter for the timing electronics. 3

59 Data Type Time Span Bin Size Ions.8 µs 31 ps Electrons.56 µs 39.6 ps Table 3.1: Settings for the Ortec picosecond time analyzer (pta) for data collection timing accuracy comes from the interpolation of multiple slow clock signals, each with a slightly different frequency [6]. The start pulse is generated by a fast photodiode located at the compressor of the Spitfire. This signal is discriminated by a Lecroy fast discriminator and the resulting NIM pulse serves as the start. The stop pulse is the detected signal from the flight tube. This 5 mv signal from the detector assembly is fed directly into an Ortec 937 combination amplifier/discriminator with a 1 GHz bandwidth. The pta is configured in a histogramming mode the desired time span is divided into 65,536 bins and the on-board memory stores the count per bin for a data run. A longer time span is used to record ion data than for electrons, which have a much faster time of flight (see table 3.1. The precision of the pta s timing comes at the cost of dead-time; for 5 ns after recording a stop pulse, the pta is unable to record additional inputs. This is particularly important when recording ion data, because the sweeping voltage ensures that nearly % of created ions are measured. Moreover, all ions from a single species have nearly identical times-of-flight (within roughly 5 ns). For the best data, one must ensure that dead-time counts do not result in significant under-counting of a bin. This can be done by limiting the number of counts in any 5 ns span to a few percent of the total number of shots.

60 While counting ions, the sweeping voltage ensures a large signal, and sample pressures are usually held to < nanotorr. Under these conditions, collecting thousand laser shots generally provides adequate signal. The field-free electron collection proceeders at a much slower pace, because the MCP s only collect a small solid angle of the interaction volume. In these cases, sample pressures are 1- microtorr, and counting times are extend from 1- million laser shots. These longer data runs are collected in increments of 5 thousand laser shots and summed during the analysis procedure. A rudimentary consistency check allows an additional method of monitoring the laser during data collection. 3. Data Analysis The conversion of time-of-flight data into physical quantities (mass and kinetic energy), is performed by an analysis package written for Igor Pro software. Ion data is simple to process, as mass peaks are readily identifiable. A combination of experience and consistency allows accurate calibration of electron data Ion Analysis An ion of mass m and charge q in a region of electric field will accelerate and gain kinetic energy. KE = qe (3.8) KE = 1/mv (3.9) Our measurement is of the flight time through the flight tube, a distance L. The actual flight time recorded t includes some delay t. This accounts for the delay 5

61 C ounts per K shots B ackground pressure 5E - torr Laser intensity ~ 1 T W/cm Mass S pec (amu/e) 3 35 Figure 3.8: Ion spectra from a clean, baked chamber with a pressure below a nanotorr. H +, H +, and H O + are clearly visible, with small amounts of N and O between the start pulse (pulse leaving the laser) and ionization event (pulse focuses into chamber), as well as any delay added by pulse processing electronics. Solving for the mass/charge ratio gives m q = E L (t t ), (3.) a quadratic equation in time, with three unknowns E, L, and t. The most straightforward approach to converting the time axis to mass/charge is to use the readily identifiable mass peaks. As figure 3.8 shows, even a clean chamber contains measurable quantities of H +,H +, and H O +, with m s of 1,, and 18, respectively. q With these three peaks, it is trivial to determine the parameters to convert time to absolute mass/charge. Due to the quadratic scaling, the equal-spaced time bins from the pta are converted to quadratically-spaced mass bins. Under typical conditions, E 5 V,L =.5 6

62 m, and t 5 ns, these natural mass bins scale from 1E-3 amu/e to.5 amu/e. These bins are then resampled into equal-sized mass bins, typically.1 amu. Figure 3.8 shows the results of the conversion process. 3.. Electron Analysis Electron analysis follows a very similar procedure, although the calibration points are not as easily identifiable. We again begin with the kinetic energy equation, KE = m L (t t ) E (3.11) with L the flight distance, t an experimental delay, and the addition of a kinetic energy term, E, to take into account any energy accumulated from static fields during the flight. Note that the relationship between between kinetic energy is inverse and quadratic: short flight times are from high energies, and long flight times are from low energy electrons. This is clearly seen in figure 3.9, which shows raw and calibrated data from argon. The conversion process converts each equally spaced time bin ( ps) into variablyspaced energy bins. The natural energy resolution of these bins runs from 3 mev at 6 ev to 5 µev at.5 ev. However, a laser bandwidth of nm yields an energy uncertainty of roughly mev. This energy uncertainty is associated with each photon, so we cannot expect an energy resolution better than mev. Therefore the electron spectra are resampled to equal-spaced mev bins. The determination of the calibration constants is not as simple as in the case of ion data. Without clear calibration points, we must turn to our physical understanding to determine the unknowns. We use the data to calibrate the parameters, which 7

63 e C ounts 3 s=1 s= Argon R aw Data µs s= s=1 Argon C alibrated Data C ounts (arb) 1 8 ev 6 8 Figure 3.9: Raw and calibrated electron data. The inverse-quadratic relationship between KE and flight time makes interpreting the raw data difficult without calibration. 8

64 we then apply to the data in a process we call the self consistent iterative method. The hallmark feature of ATI is the series of electron kinetic energy peaks spaced by the photon energy. The first task is to adjust the parameters to ensure this 1.55 ev spacing, by adjusting t. The t time delay has the largest effect on high energy electrons with short flight times, so we observe those peaks while making adjustments to the delay. The next step is to adjust L, which has the greatest effect on lower energy electrons, to ensure that the Freeman resonance features are spaced by 1.55 ev Finally, one adjusts the constant offset E to fine-tune the absolute alignment. This fine tuning requires some features that have known kinetic energies. After the exceptional agreement of Nandor s [63, 6] argon data with Müller s calculation [65], our lab has adopted argon as a calibration reference. We adjust the offset to align the argon f series with their expected positions. Generally, we use a calibrating run of argon to determine parameters, and then collect data with another species. 3.5 Intensity Calibration With a good understanding of the peak power and focus geometry of a laser pulse, it is trivial to calculate the peak intensity. However, the difficulty in characterizing the spatial focus forces us to rely heavily on spectrum-based calibration methods. Many groups use ionization yields total ion production as a function of intensity as a method of determining absolute intensities. The intensity at which the probability of ionization reaches unity, called saturation, is easily measured as a change of slope on an ion yield curve. ADK theories are sufficient to predict saturation intensities, as well as the complete ion yield, so many groups use these curves to calibrate their absolute intensity. 9

65 Our method of calibration uses photoelectron spectra, rather than the ion yields. If one knows the states responsible for the Freeman resonances, one can calculate the intensity at which they should begin to appear. Using this technique, we have been able to calibrate intensities and check for consistency. After the excellent comparison of argon photoelectron spectra with calculation, these spectra can be used as an intensity calibration standard. By collecting argon photoelectron spectra as a function of power, comparing them with the reference argon data, one can convert average power measurements to absolute intensity (See figure 3.). These calibrations are then used while collecting photoelectrons from other species. 5

66 1x 3 E lectron C ounts (Arb) 8 6 ev 6 Ar (35 mw) Ar (S tandard 96 T W/cm ) 3 1 ev 3 5 E lectron C ounts (arb) 6 ev 3 Ar ( mw) Ar (S tandard 35 T W/cm ) ev 3 5 Figure 3.: Calibration of average power to intensity using reference argon spectra. Reference spectra (darker blue) and recently collected (lighter red). Inset graphs compare the entire spectra. Note that recent spectra have a higher transmission for lower KE ( < 1.5 ev) electrons. 51

67 CHAPTER IMPORTANCE OF RESONANCES: KRYPTON PHOTOELECTRON SPECTRA In this chapter we present high resolution photoelectron kinetic energy spectra for the ionization of krypton with 1-fs, 8-nm, laser pulses focused to intensities of - TW/cm. Plateau shape and structure are discussed as well as the spectrum of transient resonances. In addition, we report what we believe to be the first observation of the spin-orbit splitting of krypton by careful measurement of resonance intensities. Moreover, a discussion of resonances in noble gas spectra provides a useful introduction for our observations in diatomic molecules..1 Introduction.1.1 Intense Field For nearly two decades, high intensity laser ionization has been studied with noble gases. Early experiments resulted in the observation of above threshold ionization (ATI) the absorption of more photons than necessary to ionize [66]. Further investigations uncovered high harmonic generation (HHG) the surprisingly efficient conversion of energy from the light field into energetic harmonics of the laser frequency [16]. This was quickly related to the increased production of energetic photoelectrons 5

68 that formed a high energy plateau of the electron distribution. These observations were explained by appealing to a rescattering model where electrons are ionized then accelerated by the oscillating electric field [5, ]. The re-collision of the electron with the remaining ion core can account for HHG and plateau electron productions, and can also cause double ionization to occur at a much higher rate than expected (known as non-sequential double ionization) []. Experiments measuring the ionization yields as a function of intensity have been made for all noble gases, and compare tolerably well with theory..1. Resonances These effects are generic and do not require any knowledge of the excited state structure of the particular sample. An intensity of 35 TW/cm is.1% of the atomic unit of intensity; at these intensities one might expect that valence electron dynamics are becoming overwhelmed by the laser field. However, careful examination of the photoelectron spectra taken with subpicosecond pulses revealed a series of peaks in each ATI order [67]. In these short pulse conditions, the wiggle energy ( ) of the electrons in the field is returned to the field before the electron can be accelerated by the spatial gradient of the field. The ATI structure corresponds to multiphoton resonances of high-lying excited states of the neutral atom. The Stark shifting of these excited states by the laser pulse serves as a continuous tuning of the atomic potential. This shifting of the atomic potential as a function of intensity serves to bring many atomic states into resonance during the duration of the pulse. The net result is that details of atomic structure can be observed, even for intensities that dramatically alter the atom. 53

69 Photoelectron kinetic energy spectra have been published for many systems, particularly noble gases: He [68], Ne [69], Xe [7, 71, 7, 73], and Ar [63, 7, 75]. Freeman resonances [76] have been studied in great detail in these systems and others [77, 78]. Moreover, angular distributions [79, 8, 81, 8, 83, 8] have been collected under many different experimental conditions. Moreover, close examination of the high energy plateau ATI orders electrons reveals structure suggestive of resonances [71, 7]. The mechanism for creating these resonance-like peaks of high energy electrons is still the subject of debate. Recent work has shown that infinite-range, Coulomb-type potentials that support bound states and short range, delta-function-type potentials can both give rise to high KE resonant structure [85, 86]. Experimental and theoretical work on intense field ionization of krypton has been largely limited to measurements of total ionization yields [87, 88, 89, 9, 91]. Somewhat surprisingly, a detailed spectrum of photoelectrons from multiphoton ionization of krypton has not been reported, although ATI has been studied in krypton using longer picosecond pulses [87, 9].. Method The experimental apparatus consists of a commercial Spectra-Physics Ti:Sapphire oscillator and regenerative amplifier and a time of flight photoelectron spectrometer (described in Chapter 3). Electrons were detected by chevroned MCP s after a fieldfree time of flight down a mu-metal flight tube. Flight times were recorded by an EG&G Ortec 936 picosecond timing analyzer set-up with a system-wide timing jitter of ps. 5

70 The data were collected by Mark Walker in 1997 but have remained un-analyzed for several years. Using the self-consistent iterative method we have developed for converting electron flight times into kinetic energies, it was possible to confirm the initial energy calibration..3 Intensity Calibrations The calibration of intensity without a suitable reference is also one of self-consistency. One can use the master equation of ATI spectra, KE = N hω IP (I), (.1) which relates a one-to-one correspondence of kinetic energy (modulo the photon energy) to intensity, given knowledge of the ionization potential. For low intensities with small ponderomotive shifts, one can infer the photon order directly from the kinetic energy. For krypton with an IP of ev, a low-field process will take photons, with energy 1.55 ev, to ionize resulting in a kinetic energy of 1.51 ev. As the intensity increases, the Stark shift will increase the IP, resulting in lower kinetic energies until the intensity reaches 11 photon processes, where the process will repeat. This change of photon order is referred to as a channel closing. If one can estimate the intensity using other means, one can use these low intensity spectra before the first channel closing to confirm the intensity calibration. For an actual laser focus, the measured signal is the spatio-temporal average of intensities up to and including the maximum intensity I. Therefore, during a pulse with maximum intensity I, one can expect to measure kinetic energies that shift to lower energy from the field-free value, up to a maximum shift of (I ). Comparing two such low 55

71 3..5 K rypton T W/cm, = 1.3 ev 7 T W/cm, = 1.61 ev 1.61 ev 1.3 ev E lectronc ounts (arb) ev = 3.3 T W/cm ev Figure.1: Lowest intensity krypton spectra, for calibration. Note the increasing ponderomotive potential, which shifts photoelectrons to lower kinetic energy. intensity spectra, the difference in ponderomotive shifts should appear as the amount of growth in the spectra versus KE from the lower intensity to the higher intensity. Figure.1 demonstrates just such a measurement, as a double-check of our intensity. For further calibration, one can check the growth of the spectrum for each successive channel closing. For 8 nm light, a change in ponderomotive energy of 1.55 ev is roughly 6 TW/cm. Therefore, spectra separated by 6 TW/cm should show roughly the same maximum shift from the field-free region. 56

72 . Partial Yields This suggests an approach of following a single kinetic energy over a range of intensities. Akin to an ion yield, which is the total number of ions as a function of intensity, we use a Partial Yield (PY) to denote the sum of electrons of a particular kinetic energy versus peak intensity. For the case we have been discussing above one with no resonances one expects a somewhat simple partial yield. For a kinetic energy range smaller than the field-free kinetic energy, one expects to measure no electrons until the peak intensity becomes large enough to shift the IP enough, (I ) = N hω KE IP. (.) At this threshold intensity, one expects the electron yield to rise dramatically. As the intensity is increased beyond this threshold, there is an increase in electron yield associated with the spatial growth of the focus; a growth proportional to approximately I 3/ (for an unrestricted, full volume experiment). This volumetric growth will increase until the (N + 1) photon process becomes allowed in addition to the N photon process. This will result in another drastic increase in yield. We can then include the effects of resonances intensities which greatly enhance ionization by multiphoton absorption to real excited states. Resonant ionization will increase the yield when the peak intensity allows the multiphoton process to take place. For pondermotively shifted resonance states, the resonant intensity also determines the resulting kinetic energy (see equation.8). This means the increase in ionziation from nonresonant processes and the increases in ionization from resonant processes occurs at the same intensity. 57

73 An example can be found in the spectrum of argon. The 5f/g states have the same binding energies (the difference in quantum defects for high l states is very small), and result in kinetic energies of 1 ev,.55 ev, etc. Figure. shows the partial yields around the 5f/g peak of the first ATI order, at.55 ev. As intensity increases, the sharp turn-on of the resonances are clearly visible. For kinetic energies that do not directly correspond to resonances, partial yields appear very similar each channel closing brings an increase in ionization. For an ideal resonance, the increase in yield as a new channel is opened would be nearly a step function. As a resonance intensity is just barely reached, it has a volume of nearly zero which then grows as the peak intensity increases. Moreover, the energy uncertainty of each photon due to the bandwidth of the pulse leads to uncertainty in the resonance condition. Our laser has a bandwidth of roughly nm leading to an energy uncertainty of E = mev, which corresponds to.33 TW/cm. For an N photon process, the total uncertainty is N E. This means that the resonance condition for an 11 photon resonance will have a turn-on uncertainty of nearly 1 TW/cm. This serves to broaden the shape of the turn-on significantly..5 Spin-Orbit Splitting Equation. immediately suggests a complication, one that arises if there is more than a single ionization potential involved. This is exactly the case in krypton and the other noble gases. There are two spin-orbit cores, P 3/ and P 1/, each of which leads to different excited states and ionization potentials. In a kinetic energy spectrum, the measured value is merely the difference between the photon energy and the IP 58

74 Part ial Yield ( A. U.) phot on J =1/ 5 f r es ona nc e I = TW/ c m 1 phot on J =3/ 5 f r es ona nc e I = TW/ c m 13 phot on J =1/ 5 g r es ona nc e I = TW/ c m 1 Partial Yield 5 f/ g peak, s =1 PY from Modeled S pect ra PY from Dat a.1 13 phot on J =3/ 5 g r es ona nc e I = 8. 6 TW/ c m. 1 6 I ( TW/ c m ) 8 1 Figure.: Partial yield in argon. Large dots are data; diamonds are modeled data. Resonance intensities for 5f/g states for each spin-orbit core are indicated. and both IP s scale identically with. However, the PY will show the presence of two channel closings per 6 TW/cm, rather than one. In the case of argon, the spin-orbit splitting of the IP is only 177 mev, corresponding to an intensity difference of 3 TW/cm. This is not clearly visible in our data. In calculations, this splitting is clearly visible, as shown in figure.. For xenon, the splitting is 1.3 ev, or TW/cm. This is nearly an entire photon energy, and will therefore occur within TW/cm of the next photon order. We are not able to resolve this easily in our data. If argon is too small and xenon is too large, then krypton is just right.666 mev or 11 TW/cm. The P 1/ level produces a field free kinetic energy of 83 mev and will cross a photon boundary at a smaller intensity, while the P 3/ IP will cross the photon boundary at an intensity 11 TW/cm higher. Figure.3 shows a partial yield taken for kinetic energies around 1.55 ev. The measured values for the photon boundaries are 7 TW/cm and the spin orbit splitting is measured to be TW/cm, good agreement, considering our coarse intensity step 59

75 K rypton E lectron P artial Y ield P 1/ 11 photon E lectron Y ield (arb) P 1/ photon 7 T W/cm 7 T W/cm P 3/ 11 photon T W/cm P 3/ photon T W/cm 8 9 Figure.3: Krypton partial yield the spin orbit splitting. sizes. The absolute positions also agree fairly well with values predicted by linear Stark shifting of the IP..6 Resonances The nonresonant production of electron kinetic energy spectra by Stark shifted IP s is only slightly modified by multiphoton resonances to bound excited states. These resonances greatly increase the rate of ionization, and for states that shift ponderomotively, do not change the observed kinetic energies. For these states, which shift identically with the ionization potential, the binding energy does not depend on intensity, 6

76 KE res = n hω (Ip E res ). (.3) In this case, the measured kinetic energy reflects the field-free binding energy of the resonant state. In argon and xenon, prominent resonances are observed which correspond fairly well with f-series states. As expected, those with high principal quantum numbers n align well with the field-free binding energies. These states are more Rydberg-like, and are most likely to have directly ponderomotive shifts. For lower n s, argon and xenon show some differences, including broadening and shifts. This may be because of the closer coupling of these states with the core. In argon, single electron calculations with an accurate model potential have reproduced these effects, including a puzzling split of the peak near 5f. Krypton at lower intensities also shows a splitting of the 5f peak. At higher intensities, the f peaks of xenon and argon were found to have small shifts towards lower intensities. Again, calculations in argon have reproduced these shifts, which are only 5 mev. A small shift to lower kinetic energies appears to develop between 6 and 7 TW/cm in krypton. The mechanism behind these shifts is unclear. Another recognizable spectral feature is the photon order dependance of the f peak. The electric dipole selection rule l = ±1 requires that a transition from the p ground state to an f state occur via absorption of an odd number of photons for even numbers of photons, this transition is forbidden. This would suggest that f resonance peaks would appear every other photon order. However, for n > levels, the series of g states are available and have nearly the same energies. Therefore the series of f peaks in the spectrum that grow into resonance for even numbers of 61

77 E lectronc ounts (arb) K rypton 7 T W/cm T W/cm T W/cm 37 T W/cm 3 T W/cm 1 ev 3 Figure.: Krypton Photoelectron Spectra: Low Intensities photons are actually g states. The n = peak, for which there are only f states accessible, does indeed show the every-other-order growth. This behavior can help to answer a commonly posed question: given that the measured spectra come from the sum of all parts of the laser focus, can we be assured that the resonant features are correlated with the peak intensity of the pulse, and not a lower intensity elsewhere in the focus? In other words, for the highest intensities measured, near TW/cm, do the transient resonance peaks reflect resonances Stark shifted by nearly 6 ev, or are they merely effects from lower Stark shifts? In figure., one can easily see the f peak shift into resonance between 37- TW/cm. However, at higher intensities it becomes harder to discern the f peak, as the large blob structure that grows in below it somewhat muddies the waters. In xenon and argon, this blob feature is more clearly separated from the f peak. 6

78 E lectronc ounts (arb) 3 K rypton 77 T W/cm 73 T W/cm 7 T W/cm 67 T W/cm 63 T W/cm 6 T W/cm 57 T W/cm 1 ev 3 Figure.5: Krypton Photoelectron Spectra: High Intensities.7 Long Range Structure The overall structure of the photoelectron spectrum is largely due to the rescattering of electrons. These re-scattered electrons form the high energy plateau structure clearly visible in the noble gases krypton is no exception. Figure.6 shows the large scale structure at various intensities. The cuttoff for electron energies is observed, as well as the familiar enhanced plateau seen in argon and xenon. Recent experiments by Grasbon et al. [93] have recorded plateau spectra from intense, few cycle laser pulses. They see a reduction of the plateau for -fs pulses, which is expected for a pulse that is too short for much re-scattering to occur. However, it is remarked that krypton does not exhibit a plateau for intensities above 5 TW/cm even for longer pulses this is attributed to lower a scattering cross section 63

79 for Kr. From this data, one can clearly see electrons out to the, but the enhanced plateau seen in argon is not visible in mid-range krypton spectra. However, our data at TW/cm shows a clear plateau enhancement. In addition, the low intensity plateaus are significant as well..8 Conclusion This is the first high resolution characterization of krypton photoelectron spectra for 8-nm, 15-fs pulses. The essential features of these spectra are identical to the more studied noble gases, xenon and argon. As we will see in the following chapters, these features are also present in the photoelectron spectra of diatomic molecules. 6

80 ev /Up I = 6 T W/cm = 6.3 ev 3 ev 5 6 ev /Up I = 67 T W/cm = 3.99 ev 3 ev 5 6 ev /Up I = T W/cm =.6 ev.1 3 ev 5 6 ev /Up I = 3 T W/cm = 1.79 ev 3 ev 5 6 Figure.6: Krypton long range structure 65

81 CHAPTER 5 ATOMS AND MOLECULES Tunneling theories that include rescattering dynamics have provided a solid framework for understanding atomic ionization experiments. Diatomic molecules are believed to undergo very similar processes, but experiments and theories have been unable to accurately agree, particularly in the case of O. We have collected photoelectron spectra for ionization of O, N, and CO with - TW/cm laser pulses. These spectra have the familiar features associated with the recattering model. 5.1 Background The study of single electron ionization by intense lasers began with noble gases [66], and there it largely remained. Experimental and theoretical efforts focused on determining ionization rates; then photoelectron kinetic energy spectra; and then angular distributions [79, 9]. Models for understanding these interactions were developed for tunneling (ADK) and multiphoton regimes. However, puzzling observations were made: the existence of large numbers of high energy photoelectrons [], high harmonic generation (HHG), and an enhancement of double ionization events called non-sequential double ionization (NSDI). These results were explained by including effects from electrons that are 66

82 accelerated by the laser field and re-scatter from the atomic core. This lead to a threestep model of ionization, acceleration, and rescattering which formed a compelling physical picture for the more realistic quantum calculations. An important feature of these theories is their reliance on single-electron effects. This was underlined especially in the work by Nandor, comparing photoelectron spectra from argon with the results from an integration of an explicitly single electron Schrödinger equation [63, 6]. The remarkable qualitative agreement between the numerical calculation and the actual data is a persuasive argument that a single electron interaction following the rescattering picture produce the effects of high field ionization. The extension of these models, successful for noble gases, to other atomic species and to molecules is important to verify strong-field theories and to pave the way for understanding strong field dynamics in more complicated systems. Work began, as it often does, in the simplest possible molecules, homonuclear diatomics. In the purely multiphoton regime (at 38 nm and 616 nm), N was observed to exhibit ATI and Freeman resonances [95]. Similar results were reported in H [96]. In the far infrared, well described by tunneling, the ADK model has been successful [97, 98]. However, these models were quickly found to be insufficient to describe ionization of several diatomic molecules. 5. Ionization Suppression According to quasi-static tunneling theories, ionization rates are dictated by the field and the ionization potential. Therefore it was unsurprising when N, with an IP of ev, was found to match the ionization of Ar, which has an IP of

83 ev. However, when compared with Xe (IP = 1.13 ev), ion yields taken at 8 nm of O (IP=1.6 ev) were suppressed by at least an order of magnitude[99]. Further studies extended the observations, and the data were unambiguous : O and D were found to be suppressed compared to companion atoms Xe and Ar. N and F were found to compare favorably with their companion, Ar [, 1]. There have been a number of proposals to explain these results. Initial investigations suggested the suppression of O was a result of multi-electron screening effects on the single electron ionization []. For the open valence orbital of O, the lack of charge screening results in a higher effective ionization potential, reducing ionization. This model, however, does not seem to apply to D ionization. Other proposals note the differing symmetries of O and N. The nitrogen molecule has a HOMO of bonding (σ g ) symmetry, while oxygen has an antibonding (π g ) symmetry [3]. Faisal and co workers propose that interference of electronic wavepackets from each nuclear center is destructive in the antibonding case, thereby supressing ionization [, 5, 6]. This interference model fails to explain the suppression of D (bonding σ g HOMO) and predicts suppression in F which does not exhibit any. Tong et al. have proposed a modified ADK theory that begins with non-hydrogenic wavefunctions as a source for tunneling [7]. Molecular systems with σ character orbitals compare favorably to their atomic counterparts and show no suppression, while π orbitals have electron density that is not well aligned with the field. This predicts suppression for O and D, but fails to account for the lack of suppression in F. It is extremely difficult to make a direct, quantitative comparison between ion yields of two different species without simultaneous measurement []. Careful 68

84 pressure determinations between different gas species are difficult without specialized instrumentation (such as a residual gas analyzer, or RGA). Moreover, the atomic data presented here was largely collected in a different experimental system (Ema) than the diatomic data. Differences in detector efficiencies and data collection standards between the two systems make it nearly impossible to quantitatively determine absolute ion or electron yields between species. Despite the difficulties in comparing overall ionization yields between molecules and companion atoms, all is not lost. We will compare the energy resolved photoelectron spectra of companion species, paying careful attention to any differences we might ascribe to molecular effects. 5.3 High Energy Plateaus An electron that has escaped the nuclear core via tunneling is born into the field with zero kinetic energy. The maximum energy such an electron can subsequently acquire from the field is The observation of a high energy plateau of electrons from high energy ionization of noble gases [79] was eventually identified as a signature of re-scattering. Theories that include a re-scattering event produce electrons with kinetic energies out to Ar and N The excellent agreement of ionization yields for Ar and N is interpreted as a validation of ADK-like approaches for molecules. There has been comparatively little work comparing the photoelectron spectra from these two species, presumably because of this agreement. This work is the first to report a comprehensive, high resolution comparison of photoelectron spectra of the N, for intensities from -1 TW/cm 69

85 Figure 5.1: High energy plateau of H, from Walker et al. [3]. Photoelectron spectrum taken with 78 nm, TW/cm, resulting in a Keldysh parameter of.7. Dotted line is a calculation including rescattering effects. Species IP (ev) γ TW/cm γ TW/cm HOMO Ar Kr Xe N σ g CO σ g O π g D σ g H σ g Table 5.1: Properties of some atomic and diatomic species. Ionization potential (IP), Keldysh parameter (at and TW/cm ), and highest occupied molecular orbital (HOMO) are listed. 7

86 at 8 nm. Figures 5. through 5.6 below provide a direct comparison between N and argon across this entire intensity range. In these figures one can note the similarity between the spectra particularly in the cutoff energies, which are as expected, roughly. One also notices the extremely large plateaus of argon, which between 6-8 TW/cm are only an order of magnitude smaller than the main (so called direct electron) peaks. This plateau enhancement is a feature of argon, the source of which is believed to be a fortuitous constructive interference of tunnel-ionized electron wavepackets [8, 9]. That N does not demonstrate these enhancements at similar intensities is not terribly surprising; because of different rescattering pathways. However, it does appear that N exhibits some plateau enhancements near -53 TW/cm, the enhancement for argon and N is very similar. These are the largest plateau enhancements for N, smaller than the direct peak by a factor of, while argon exhibits very large enhancements at higher intensities (7 TW/cm ) that are only a factor of smaller than the direct peak Xe and O It is unclear whether observed suppression of total ionization of O should manifest itself in the structure of the photoelectron spectrum. Grasbon et al., observe a significant reduction of high energy electrons in O as compared with Xe. This is attributed, via their interference model, to the suppression of low kinetic energy electrons [1]. A smaller flux of low energy electrons results in a drastically smaller number of recollisions, eliminating the plateau of O. It is unclear how this model 71

87 N 38 T W/cm Ar 38 T W/cm N 36 T W/cm Ar 36 T W/cm N 33 T W/cm Ar 33 T W/cm Figure 5.: N and Ar envelope spectra, TW/cm. 7

88 N 9 T W/cm -1 Ar 5 T W/cm N 7 T W/cm - Ar 6 T W/cm N T W/cm Ar 5 T W/cm N 1 T W/cm Ar 1 T W/cm Figure 5.3: N and Ar envelope spectra, 1-5 TW/cm. 73

89 N 61 T W/cm Ar 61 T W/cm N 58 T W/cm Ar 57 T W/cm N 55 T W/cm Ar 55 T W/cm N 5 T W/cm - Ar 5 T W/cm Figure 5.: N and Ar envelope spectra, 5-61 TW/cm. 7

90 N 7 T W/cm -1 Ar 71 T W/cm N 69 T W/cm Ar 69 T W/cm N 66 T W/cm Ar 67 T W/cm N 63 T W/cm Ar 63 T W/cm Figure 5.5: N and Ar envelope spectra, TW/cm. 75

91 N 91 T W/cm Ar 91 T W/cm N 8 T W/cm 1.1 Ar 85 T W/cm N 77 T W/cm Ar 78 T W/cm N 7 T W/cm Ar 73 T W/cm Figure 5.6: N and Ar envelope spectra, 7-91 TW/cm. 76

92 accommodates the observed extension of HHG in O, as the relaxation of re-scattered electrons is cited as the source of these high frequency emissions [111]. The following figures ( ) detail the comparison of spectral envelopes of xenon and O from 18-8 TW/cm. It is arguable xenon exhibits a larger plateau structure than O across the entire intensity range. In particular, xenon has more striking peaks, reminiscent of those in Ar. However, it is equally clear that there is significant production of electrons out to, a sign of re-scattering. This is the first report of a clear plateau for O. Moreover, the cutoff kinetic energies for Xe and O are remarkably similar. This is directly at odds with the previous observation of O spectra where the plateau is entirely suppressed [1]. One might argue that the high energy electrons in these spectra are not those from O O +, but are those from dissociated atomic oxygen, or events from background gases. Ion measurements at the highest intensities, above 1 TW/cm show a ratio of O + O + of.6% (see appendix A), an observation corroborated by other measurements [99, 11] Kr and CO In the same manner, one can compare the photoelectron envelope spectra of krypton (IP = 1 ev) and carbon monoxide (1.1 ev). Ion yield measurements show that CO has a slightly suppressed yield when compared with Kr, but not the drastic order-of-magnitude suppression seen in O [1]. Figures show Kr and CO for intensities -9 TW/cm. 77

93 O 35 T W/cm Xe 3 T W/cm eV O 3 T W/cm Xe 3 T W/cm eV O 3 T W/cm Xe 3 T W/cm eV O 7 T W/cm Xe 7 T W/cm eV 78 Figure 5.7: O and Xe envelope spectra, 7-35 TW/cm.

94 O 55 T W/cm.1.1 Xe 56 T W/cm eV O 9 T W/cm Xe 9 T W/cm eV O T W/cm 1 Xe 1 T W/cm eV O 38 T W/cm 1 Xe 39 T W/cm eV Figure 5.8: O and Xe envelope spectra, TW/cm. 79

95 O 8 T W/cm Xe 81 T W/cm eV O 76 T W/cm 1.1 Xe 77 T W/cm eV O 7 T W/cm Xe 73 T W/cm eV O 6 T W/cm Xe 6 T W/cm eV Figure 5.9: O and Xe envelope spectra, 6-8 TW/cm. 8

96 C O T W/cm K r T W/cm C O 1 T W/cm K r T W/cm Figure 5.: CO and Kr envelope spectra, 1 and TW/cm. The existence of a plateau in CO is confirmed, although the size is not as large as the Kr peaks. Mass spectra from CO ionization show there is very little dissociation at these intensities. For the 9 TW/cm measurement, the ratio of dissociation products to CO + was 3% (see appendix A for details). This is also comparable to dissociation seen in other experiments [113]. 5. Low Energy Electrons The resonance structure of noble gases has been widely explored [68, 75, 11, 115], and experiments in this lab have observed the resonance structure of some diatomic molecules [116]. Since these resonances are reflections of particular excited states 81

97 C O 35 T W/cm K r 35 T W/cm C O 3 T W/cm K r 3 T W/cm C O 3 T W/cm 1 K r 3 T W/cm C O 7 T W/cm 1 K r 8 T W/cm Figure 5.11: CO and Kr envelope spectra, 7-35 TW/cm. 8

98 C O 9 T W/cm 1 K r 9 T W/cm C O 6 T W/cm 1 K r 6 T W/cm C O T W/cm 1 K r T W/cm C O 38 T W/cm K r 37 T W/cm Figure 5.1: CO and Kr envelope spectra, 37-9 TW/cm. 83

99 C O 65 T W/cm.1.1 K r 65 T W/cm C O 59 T W/cm.1.1 K r 6 T W/cm C O 57 T W/cm K r 56 T W/cm C O 51 T W/cm 1-1 K r 5 T W/cm Figure 5.13: CO and Kr envelope spectra, TW/cm. 8

100 C O 89 T W/cm K r 9 T W/cm C O 8 T W/cm K r 8 T W/cm C O 76 T W/cm K r 78 T W/cm C O 69 T W/cm.1.1 K r 7 T W/cm Figure 5.1: CO and Kr envelope spectra, 69-9 TW/cm. 85

101 of the system, it is clearly unreasonable to expect the exact structure of resonances in each companion species to match. Moreover, tunneling theories face particular difficulties for low kinetic energy electrons these electrons are essentially multiphoton in nature [117]. However, a general comparative survey of ATI structure for companion species underlines the similarity of ionization processes in atoms and molecules. The general features of noble gas ATI resonant structure have been described in detail by Walker [75, 116] and include: 1. Rydberg series corresponding to high orbital momentum electronic states (discussed in detail in chapter 6).. A blob broad peak located below the clear Rydberg series. This blob peak has a similar shape for all noble gases and is thought to be the result of ionization through excited states coupled by a photon. It should be noted that the noble gas spectra presented in this section were collected in a different vacuum chamber, Ema, than the diatomic data which were taken in Peggy (see Chapter 3). At the time of data collection, Ema was not as well shielded as Peggy, leading to a small transmission function for low KE electrons in the noble gas data. With improved shielding in Peggy, low KE electron signal is accumulated even at zero kinetic energy. These electrons are believed to be accelerated to small kinetic energies by patch fields in the experiment. 86

102 5..1 Ar and N At low intensities (figure 5.17), the Ar spectra is clearly dominated by resonances, visible for all ATI orders shown. The N spectra also clearly shows resonances, although their sizes are on the same order of the broad, blob feature. One also notices that the resonance series appear more complicated than the Ar ATI spectra, and become indistinct at larger ATI orders. This is partially due to the larger transmission of lower KE electrons for the diatomic molecules improvements in magnetic shielding greatly improved collection efficiencies for low energy electrons. For mid-range intensities (figure 5.16), the two spectra appear qualitatively very similar. Resonances and the broader features are of similar heights the two spectra look even more similar at higher intensities, although the ATI-order contrast is larger for the argon spectra (figure 5.15). 5.. Xe and O We were able to collect data for Xe and O at lower intensities, because the smaller ionization potential means that lower photon-order processes are visible. At these intensities (figure 5.), where is less than a photon energy, the spectra look remarkably similar. At the slightly higher intensities in figure 5.19, the two spectra exhibit resonances and broad features, although the broad features in O are much more prominent. At the highest intensities (figure 5.), the xenon spectrum is becoming indistinct, although resonances at low KE are still visible. This may be an experimental artifact, although the features are consistent with our observations of photoelectron spectra at high intensity. As we reach a more purely tunneling regime, resonances are expected 87

103 E lectroncounts (arb) 3 Argon T W/cm 91 T W/cm ev 6 8 E lectroncounts (arb) 5x Nitrogen 5 T W/cm 91 T W/cm ev 6 8 Figure 5.15: N and Ar ATI peaks, 9 and TW/cm. The MPI and ATI orders are shown. to disappear xenon has a low IP, and should reach the tunneling regime at a lower intensity. Although Oxygen has a similar IP, the ionization suppression may be characterized as an increased IP, which may make comparisons between xenon somewhat invalid Kr and CO Figures show comparisons of kinetic energy spectra for a range of intensities. As in the case of homonuclear diatomics, the CO spectrum appears largely similar to krypton, its atomic companion. At the highest intensities, the modulation depth of the ATI orders is smaller in carbon monoxide, but the resonances are still clearly visible. 88

104 E lectroncounts (arb) Argon 55 T W/cm 53 T W/cm 5 T W/cm 8 T W/cm. ev 6 8 E lectroncounts (arb) Nitrogen 55 T W/cm 5 T W/cm 9 T W/cm 7 T W/cm ev 6 8 Figure 5.16: N and Ar ATI peaks from 7 to 55 TW/cm. The MPI and ATI orders are shown. 5.5 Angular Distributions A major difference of atomic and diatomic systems is the existence of an internuclear symmetry axis. Tunneling theories describe electron probability leaking through a potential barrier the shape of that barrier is a significant factor. When considering ionization from diatomic molecules, one must not forget that these molecules can be either parallel or perpendicular to a linearly polarized laser field. The effect of molecular orientation on ionization rates for the multiphoton regime is less intuitive, as the multiphoton process is a cycle averaged effect arguments about field polarization are replaced with photon angular momenta. 89

105 E lectroncounts (arb) Argon 38 T W/cm 36 T W/cm 35 T W/cm 33 T W/cm. ev 6 8 E lectroncounts (arb) Nitrogen 38 T W/cm 36 T W/cm 33 T W/cm 3 T W/cm ev 6 8 Figure 5.17: N and Ar ATI peaks, 3 to 38 TW/cm. The MPI and ATI orders are shown. ElectronCounts (arb) Xenon 81 T W/cm 77 T W/cm ev 6 8 ev ElectronCounts (arb) 5x 3 3 Oxygen 8 T W/cm 76 T W/cm ev 6 8 Figure 5.18: O and Xe ATI peaks, 76 and 8 TW/cm ; the MPI and ATI orders are shown. 9

106 ElectronCounts (arb) Xenon 9 T W/cm 3 T W/cm 39 T W/cm ev 6 8eV ElectronCounts (arb) 8 6 Oxygen 9 T W/cm T W/cm 38 T W/cm ev 6 8 Figure 5.19: O and Xe ATI peaks, 38 to 9 TW/cm ; the MPI and ATI orders are shown. ElectronCounts (arb) 3 Xenon T W/cm 1 T W/cm 19 T W/cm ev 6 8eV ElectronCounts (arb) Oxygen T W/cm 1 T W/cm 19 T W/cm ev 6 8 Figure 5.: O and Xe ATI peaks, 19 to TW/cm ; the MPI and ATI orders are shown. 91

107 E lectron C ounts (arb) K rypton 9 T W/cm 83 T W/cm 77 T W/cm ev 6 8 E lectron C ounts (arb) 1x C arbon Monoxide 89 T W/cm 8 T W/cm 76 T W/cm ev 6 8 Figure 5.1: CO and Kr ATI peaks, 77 to 9 TW/cm ; the MPI and ATI orders are shown. E lectron C ounts (arb) K rypton 5 T W/cm 9 T W/cm 6 T W/cm T W/cm ev 6 8 E lectron C ounts (arb) C arbon Monoxide 51 T W/cm 9 T W/cm 6 T W/cm 3 T W/cm ev 6 8 Figure 5.: CO and Kr ATI peaks, to 5 TW/cm ; the MPI and ATI orders are shown. 9

108 E lectron C ounts (arb) K rypton 3 T W/cm 8 T W/cm T W/cm T W/cm ev 6 8 E lectron C ounts (arb) C arbon Monoxide 3 T W/cm 7 T W/cm T W/cm 1 T W/cm ev 6 8 Figure 5.3: CO and Kr ATI peaks, 1 to 3 TW/cm ; the MPI and ATI orders are shown. Issues of diatomic alignment have played an important role in Coulomb explosion experiments. In these experiments, very intense pulses are used to rapidly ionize molecules resulting in rapid dissociation. The measurement of the resulting fragment ion velocities can provide insight into the ionization process. Experiments in H ionization, which does show suppression, were explained by arguing a greatly reduced ionization rate from molecules which are not aligned along the laser polarization [118]. However, a calculation of H + ionization rates shows very little dependence on alignment and N does not show any suppression (due to alignment or otherwise). This work did not include an exhaustive collection of photoelectron angular distributions at many intensities. However, electron data were collected at various polarization angles to serve as a consistency check. Figure 5.5 shows the total electron 93

109 yield as a function of angle from 18, taken at a moderate intensity for N and O. Molecular ADK calculations [7] of angular distributions of outer molecular orbitals are displayed in figure 5.. Coulomb explosion experiments have reported angular distributions that nearly match these predictions [35]. In the total ionization data, one notices the distributions strongly peaked towards the direction of laser polarization. The overall shapes of the N and O look similar, which is consistent with significant alignment during the laser pulse or selective ionization of aligned molecules. Adiabatic alignment for O molecules would surely distort the molecular orbitals from their field-free values, shifting them towards the polarization axis. It is worth noting that O does have a more significant number of electrons detected at 9 to the polarization. This may reflect the symmetry of the π molecular orbital. Considering that electrons in the plateau are produced by a re-scattering event, one would expect a qualitatively different angular distribution than for the direct electrons. Indeed, distributions in atomic systems are strongly peaked along the laser polarization, while plateau electrons have a much wider angular range. The distributions for plateau electrons and direct electrons are displayed in figure 5.6. Indeed, the distributions from the plateau electrons are more broad, agreeing with the re-scattering model. The highest kinetic energy electrons, those approaching energies near the cutoff, would be electrons that directly backscatter. For the highest kinetic energies, the angular distribution appears sharply narrowed for N, while in O, the distribution is only somewhat narrower. It is also interesting to note the similarities between N and O for 9 polarization for the higher energies, both species show hardly any electrons. This indicates that the electrons that appear at 9

110 Figure 5.: Theoretical angular distributions from aligned O and N (left). Schematic molecular orbitals at right. Figure from Alnaser et al. [35]. 9 are largely direct electrons. The rescattered electrons, since their evolution is field-driven are more centered along the laser polarization. The data collected were of insufficient angular resolution to determine if rescattering rings, observed in noble gas angular distributions, were present in diatomic ionization[9, 119]. 5.6 Discussion This analysis was undertaken to provide more detailed information on diatomic ionization in light of the well-known weaknesses of current theories to account for 95