Ultrafast Optical Physics II (SoSe 2017)

Transcription

1 Ultrafast Optical Physics II (SoSe 2017) Noah Chang & Franz X. Kärtner, Bldg. 99, Room O3.111 & O & phone: Office hour: Tuesday, 9-10 am Lectures: Fr SemRm IV, BLDG 99 Recitations: Fr SemRm IV, BLDG 99 Start: Teaching Assistant: Lu Wang, Office O3.125, phone , Nicolai Klemke, Office O3.118, phone , Office hour: Thursday 9:30-11am Course Secretary: Christine Berber O3.095, phone x-6351, Class website: 1

2 Prerequisites: Ultrafast Optical Physics I or basic course in Electrodynamics Required Text: Class notes will be distributed in class. Requirements: 8 Problem Sets, Term Paper, and Term paper presentation Collaboration on problem sets is encouraged. Grade breakdown: Problem set (30%), Participation (30%), Term paper and presentation (40%) Recommended Text: Ultrafast Optics, A. M. Weiner, Hoboken, NJ, Wiley Additional References: Waves and Fields in Optoelectronics, H. A. Haus, Prentice Hall, NJ, 1984 Ultrashort laser pulse phenomena: fundamentals, techniques, and applications on a femtosecond time scale, J.-C. Diels and W. Rudolph, Academic Press, Few-Cycle Laser Pulse Generation and Its Applications, Ed. F. X. Kärtner, Topics in Applied Physics Vo. 95, Springer Verlag, Principles of Lasers, O. Svelto, Plenum Press, NY, 1998 Optical Resonance and Two-Level Atoms, L. Allen & J. H. Eberly, J. Wiley, NY, Prof. Rick Trebino s course slides on ultrafast optics: 2

3 The metric system We will meet with both small and large numbers in this course. For example, the optical pulses discussed later are incredibly short and the powers and intensities can be incredibly high. Prefixes: Small Milli (m) 10-3 Micro (µ) 10-6 Nano (n) 10-9 Pico (p) Femto (f) Atto (a) Big Kilo (k) Mega (M) Giga (G) Tera (T) Peta (P) Exa (E) Adapted from Rick Trebino s course slides 3

4 The long and short of time A. E. Kaplan, No-when: the long and short of time, Optics and Photonics News (2006, February) 4

5 Time scale of physical events Ionization of K electrons 5x s Shortest event ever created: 67 attosecond (10-18 s) x-ray pulse (2012) Bohr orbit period in hydrogen atom: 150 attoseconds Single oscillation of 600nm light: 2 fs (10-15 s) Vibrational modes of a molecule: ps (10-12 s) timescale Electron transfer in photosynthesis: ps timescale Period of phonon vibrations in a solid: ps timescale Mean time between atomic collisions in ambient air: 0.1 ns (10-9 s) Period of mid-range sound vibrations: ms How to measure a fast event? 5

6 Characteristic timescales of atomic and molecular motions Controlling the quantum world: the science of atoms, molecules, and photons (2010) 6

7 Birth of ultrafast technology $25,000 bet: Do all four hooves of a running horse ever simultaneously leave the ground? (1872) Leland Stanford Eadweard Muybridge Muybridge's first picture sequence Adapted from Rick Trebino s course slides 7

8 What do we need to probe a fast event? The light signal received by the camera film is a train of optical pulse. Optical power Shutter open Shutter close Shutter open Shutter close Shutter open Shutter close Shutter open We need a FASTER event to freeze the motion. Here the FASTER event is shutter opening and closing. If we have an optical pulse source, we can record images of a running horse in a dark room. t 8

9 Early history of lasers 1917: on the quantum theory of radiation Einstein s paper 1954: MASER by Charles Townes ( ) et al. 1958: Charles If you re Townes a nobel prize (Nobel winner, Prize and 100 in years 1964) old, you and can Schawlow comment other winners using harsh words: (Nobel Prize in 1981) conceived basic ideas for a laser. 1960: LASER coined by Gordon Gould ( ). 1960: First laser (Ruby) by Maiman 1961: First HeNe laser, followed by invention of most lasers. 1977: Gordon Gould awarded the patent for the laser. Optics & Photonics News, 2014 MASER: Microwave Amplification by Stimulated Emission of Radiation (Means of Acquiring Support for Expensive Research) 9

10 Laser basics: three key elements Back mirror I p Output mirror gain medium Continuous wave (CW) laser Gain medium - Enable stimulated emission to produce identical copies of photons - Determine the light wavelength Pump - Inject power into the gain medium - Achieve population inversion Resonator cavity - make light wave oscillating to efficiently extract energy stored in the gain medium - Improve directionality and color purity of the light 10

11 Laser basics: three key elements Back mirror I p Output mirror gain medium Continuous wave (CW) laser power Continuous wave output power Spectrum time frequency/wavelength 11

12 Ultrafast laser: the 4 th element mode locker Back mirror I p Output mirror Ultrashort pulse output gain medium Mode locker Ultrafast laser t 12

13 Ultrafast laser: the 4 th element mode locker Back mirror I p Output mirror Ultrashort pulse output gain medium Mode locker Ultrafast laser t τ World shortest pulse: 67 attoseconds. The center wavelength is 20 nm. It is generated by high harmonic generation. K. Zhao et al., Tailoring a 67 attosecond pulse through advantageous phase-mismatch, Opt. Lett. 37, 3891 (2012) t SHORTEST PULSE DURATION 10ps 1ps 100fs 10fs Nd:glass Dye CW Dye S-P Dye CP M Dye w/compression Nd:YAG Diode Color Center Nd:YLF Ti:sapphire Cr:LiS(C)AF Er:fiber Nd:fiber Cr:YAG Cr:forsterite YEAR

14 Long vs. short pulses of light Longer pulse corresponds to narrower spectrum. power vs. time time Spectrum frequency Shorter pulse corresponds to broader spectrum. time frequency But a light bulb is also broadband. What exactly is required to make an ultrashort pulse? Answer: A Mode-locked Laser Adapted from Rick Trebino s course slides 14

15 Ultrafast laser: the 4 th element mode locker Back mirror I p Output mirror Ultrashort pulse output gain medium Mode locker Ultrafast laser t τ t 15

16 Ultrafast laser: the 4 th element mode locker Back mirror I p Output mirror Ultrashort pulse output gain medium Mode locker Ultrafast laser t τ t 16

17 Examples of ultrafast solid-state laser media Solid-state laser media have broad bandwidths and are convenient. 17

18 Two-photon absorption properties of fluorescent proteins M. Drobizhev et al., Two-photon absorption properties of fluorescent proteins Nat. Methods 8, 393 (2011). 18

19 Main workhorse: Ti:sapphire oscillator Typical parameters of a commercial product - Pulse duration: ~100 fs - Pulse energy: 1-10 nj - Pulse rep-rate: MHz - Average power: mw - Center wavelength: tunable in nm. 19

20 Ultrafast: pump-probe spectroscopy 20

21 Applications of ultrafast lasers: femtosecond chemistry Prof. Ahmed Zewail from Cal Tech used ultrafast-laser techniques to study how atoms in a molecule move during chemical reactions (1999 Nobel Prize in Chemistry). 21

22 Ultra- accurate: timing distribution Jungwon Kim et al., Nature photonics 2, 733 (2008) 22

23 Ultra- accurate: fs laser frequency comb Time domain f CEO = f R φce mod 2π f R = 1 T R Frequency domain 0 Frequency comb has two degrees of freedom: f = nf R + f CEO f 23

24 Ultra- accurate: fs laser frequency comb C.-H. Li et al., Nature 452, 610 (2008). 24

25 Ultra- intense: femtosecond laser machining Sub-micron material processing: Material milling, hole drilling, grid cutting Surface structuring: Photolithographic mask repair, surface removal or smoothing without imparting any thermal influence into the underneath sub-layers or the substrate Photonics devices: Machining of optical waveguides in bulk glasses or silica, and inscription of grating structure in fibers Biomedical devices: Use of femtosecond lasers for stent manufacture or eye surgery Microfluidics: Microfluidic channels and devices Displays and solar: Thin-film ablation, solar cell edge isolation Laser processing examples on glass with a 266 nm (UV) ns-laser (left side) and with a 780 nm 100- fs laser (right side). L. Lucas and J. Zhang, Femtosecond laser micromachining: A back-to-basics primer, Industrial Laser Solutions (2012) 25

26 Ultra-intense: extreme light infrastructure (ELI) ELI s goal is to explore new frontiers in physics, including trying to trigger the breakdown of the vacuum the fabric of space-time itself. Designs of the three pillars are shown. Top: Hungarian attosecond pillar. Middle: Czech beam-line pillar. Bottom: Romanian photonuclear pillar. J. Hecht, Photonic frontiers: the extreme light infrastructure: the ELI aims to break down the vacuum, Laser Focus World (2011) 26

27 Nonlinear optical microscopy Intrinsic sectioning ability, making 3D imaging possible. Longer excitation wavelength, which reduces tissue scattering and allows larger penetration depth. New contrast mechanisms: N-photon excitation fluorescence, Harmonic generation, Coherent Raman scattering, etc. Ultrashort pulses as the excitation source many ultrafast optics technologies can be employed. W. R. Zipfel et al., Nat. Biotechnol. 21,1369(2003). N. G. Norton et al, Nat. Photonics 7, 205 (2013). 27

28 Three channel OPA (optical parametric amplification) system: what optics lab looks like 28

29 20W green light in our lab

30 Topics to cover Linear and nonlinear pulse propagation: Optical solitons and pulse compression. Laser dynamics: CW operation, Q-switching, mode locking. Pulse characterization: Autocorrelation, FROG, SPIDER and 2DSI. Noise in mode-locked lasers and frequency combs. Laser amplifiers and optical parametric amplifiers/oscillators. Mid-infrared sources and terahertz sources Soft and hard X-ray sources including attosecond pulse generation. 30

31 Ultrafast lasers emit pulse train 5fs t f R =1/T R : pulse repetition rate 2.7fs W : pulse energy P ave = W/T R : average power τ FWHM : Full Width Half Maximum pulse width P p : peak power 31

32 Some physical quantities Average power: Repetition rate: Pulse energy: (Average power = Rep-rate X Pulse energy) Pulse width (duration): Peak power: (Peak power = Pulse energy / duration) (peak) Intensity: If an optical beam with 1 PW peak power is focused to 1um 2 area, the peak intensity is W/cm 2. 32

33 An ultrashort laser pulse has an intensity and phase vs. time. Neglecting the spatial dependence for now, the pulse electric field is given by: Electric field E (t) It () Time [fs] 1 E ( t) I( t) exp{ j[ ω t φ( t)]} + c. c. 0 2 Intensity Carrier frequency Phase A sharply peaked function for the intensity yields an ultrashort pulse. The phase tells us the color evolution of the pulse in time. Adapted from Prof. Rick Trebino s course slides 33

34 The real and complex pulse amplitudes Removing the 1/2, the c.c., and the exponential factor with the carrier frequency yields the complex amplitude, E(t), of the pulse: Electric field E (t) It () E( t) I( t) exp[ jφ( t)] Time [fs] This removes the rapidly varying part of the pulse electric field and yields a complex quantity, which is actually easier to calculate with. It () is often called the real amplitude, A(t), of the pulse. Adapted from Prof. Rick Trebino s course slides 34

35 The Gaussian pulse For almost all calculations, a good first approximation for any ultrashort pulse is the Gaussian pulse (with zero phase). 2 Et ( ) = E0 exp ( t/ τ 1/ ) HW e = E0 exp 2ln2( t/ τ FWHM ) = E0 exp 1.38( t/ τ FWHM ) τ HW1/e is the field half width at 1/e maximum, and τ FWHM is the intensity full width at half maximum. 2 2 The intensity is: τ FWHM It ( ) E0 exp 4ln2( t/ ) E 2 2 exp 2.76( t/ τ FWHM ) Adapted from Prof. Rick Trebino s course slides 35

36 The Fourier transform To think about ultrashort laser pulses, the Fourier Transform is essential. ~ E( ω) = E( t) e jωt dt E( t) 1 ~ = E( ω) e 2π j ω t d ω We always perform Fourier transforms on the real or complex pulse electric field, and not the intensity, unless otherwise specified. Adapted from Prof. Rick Trebino s course slides 36

37 Frequency-domain electric field The frequency-domain equivalents of the intensity and phase are the spectrum and spectral phase. Fourier-transforming the pulse electric field: 1 E ( t) I( t) exp{ j[ ω0t φ( t)]} + c. c. 2 yields: Note that φ and ϕ are different! ~ 1 E( ω) = S( ω ω0) exp{ j[ ϕ( ω ω 0 )]} S( ω ω0) exp{ + j[ ϕ( ω ω 0 )]} 2 The frequency-domain electric field has positive- and negative-frequency components. Note that these two terms are not complex conjugates of each other because the FT integral is the same for each! Adapted from Prof. Rick Trebino s course slides 37

38 Complex frequency-domain pulse field Since the negative-frequency component contains the same information as the positivefrequency component, we usually neglect it. We also center the pulse on its actual frequency. S(ω) Carrier Frequency So the most commonly used complex frequency-domain pulse field is: ~ E( ω) S( ω) exp{ j[ ϕ( ω)]} Thus, the frequency-domain electric field also has an intensity and phase. S is the spectrum, and ϕ is the spectral phase. Adapted from Prof. Rick Trebino s course slides 38

39 Often used pulses Pulse width and spectral width: FWHM (full width at half maximum) 39

40 Operators used in Maxwell s Equations 40

41 Operators used in Maxwell s Equations 41

42 Operators used in Maxwell s Equations 42

43 Maxwell s equations of isotropic and homogeneous media Maxwell s Equations: Differential Form Ampere s Law Current due to free charges Faraday s Law Gauss s Law No magnetic charge Free charge density Material Equations: Bring Life into Maxwell s Equations Polarization Magnetization 43

44 Vector Identity: Derivation of wave equation Vacuum speed of light: 44

45 Derivation of wave equation No free charges, No currents from free charges, Non magnetization In the linear optics of isotropic media without free charges, Simplified wave equation: Wave in vacuum Source term Laplace operator: = 2 = x y z

46 Interaction between EM waves and materials 0.5 nm Wavelength of green light is about 500 nm. So the optical wave experiences an effective homogeneous medium, which is characterized by Electric permittivity ε and Magnetic permeability The velocity of light is different from the vacuum speed by a factor called the refractive index

47 Dielectric susceptibility and Helmholtz Equation In a linear medium, dielectric susceptibility is independent of optical field Can be complex Refractive Index light speed (dependent on frequency) in a medium: 47

48 Lorentz model of light-atom interaction Important assumptions The atomic core is -- positively charged -- static (heavy, fixed within the crystal lattice) -- with the center of charge at x = 0. The electrons are -- light weight -- elastically bound by a massless spring with spring constant with equilibrium position at x = 0 -- carrying out a damped movement; that is, after removing the force, the movement decreases and finally ends. -- the electron and atomic core form an oscillator with a resonant frequency w 0. H. A. Lorentz ( ) Juergen Popp et al., Handbook of biophotonics (2012). 48

49 Lorentz model: forced electron harmonic oscillator Dipole moment is defined as the product of magnitude of charges and the distance of separation between the charges. Without an applied field, the centers of the negative and the positive charges coincide. The dipole moment is zero. If a field constant in time is applied, the electrons are displaced relative to their position in the absence of an external field. The centers of the positive and negative charges no longer coincide and a static dipole moment is induced. If a time-dependent electric field interacts with the atom, then the electron starts to oscillate around its equilibrium position with the same frequency of the electric field. Such an oscillating dipole moment will emit a new electromagnetic wave at the same frequency as well. Juergen Popp et al., Handbook of biophotonics (2012). 49

50 Oscillating dipole moment emits new EM wave at the oscillating frequency It does not emit in the oscillating direction! From wiki 50

51 Forced oscillator and resonance When we apply a periodic force to a natural oscillator (such as a pendulum, spring, swing, or atom), the result is a forced oscillator. Examples: Child on a swing being pushed Periodically pushed pendulum Bridge in wind or an earthquake Electron in a light wave Nucleus in a light wave Tacoma Narrows Bridge oscillating and collapsing because oscillatory winds blew at its resonance frequency. (collapsed under 64 km/h wind conditions the morning of November 7, 1940) The forced oscillator is one of the most important problems in physics. It is the concept of resonance. Adapted from Rick Trebino s course slides 51

52 One more example: child on a swing If you give the swing a push it will swing back and forward. If you just give it one push it will swing back and forth a few times and then come to rest. (That s because of friction and damping.) To keep the swing moving you have to push again each time the swing reaches the closest point to you. You have to match the frequency of the swing to make it swing high. Course note, MIT & 52

53 Lorentz model of light-atom interaction When light of frequency ω excites an atom with resonant frequency ω 0 : Electric field at atom Electron On resonance (ω = ω 0 ) Emitted field x () E () t e t E () t The crucial issue is the relative phase of the incident light and this emitted light. For example, if these two waves are ~180 out of phase, the beam will be attenuated. We call this absorption. + = Incident light Emitted light Transmitted light Incident Light excites electron oscillation electron oscillation emits new light at the same frequency incident light interferes with the new light leading to the transmitted light. Adapted from Rick Trebino s course slides 53

54 Interference depends on relative phase When two waves add together with the same complex exponentials, we add the complex amplitudes, E 0 + E 0 '. ~ ~ Constructive interference: Destructive interference: Quadrature phase: ±90 interference: = = -0.2i + = i time time time Laser Absorption Adapted from Rick Trebino s course slides Slower phase velocity (when accumulated over distance) 54

55 Dielectric Permittivity: Lorentz model Density (# of atoms per unit volume) Elementary Dipole Lorentz Model: x(t) p( t) = ex( t) x (t) is much smaller than the wavelength of electric field. Therefore we can neglect the spatial variation of the E field during the motion of the charge. 55

56 Response to a monochromatic field force mass quality factor frequency of undamped oscillator 56

57 Real and Imaginary Part of the Susceptibility Plasma frequency ω = p Ne ( ε m ) 1/ 2 57