Last Lecture Overview and Introduction 1. Basic optics and spectroscopy. Lasers 3. Ultrafast lasers and nonlinear optics 4. Time-resolved spectroscopy techniques Jigang Wang, Feb, 009
Today 1. Spectroscopy using incoherent light: case studies Absorption, Reflection, PL, PLE, FTIR; SWCNs, Conventional and HTc superconductors. Laser fundamentals 3. Laser-based CW spectroscopy Laser Raman/Raleigh, multi-photon nonlinear Spectroscopy; manganites, SWCNs Jigang Wang, Feb, 009
Conventional Spectroscopy Methods E T A - Absorption, Reflection, Emission, Interference R - Scattering - Spectrally resolved before or after sample
What is measured? Transition between the states π Probability W = < f H I i > δ ( E f Ei h f, i h) e,g, absorption is proportional to DOS x the transition Matrix element Oscillator strength m f = < f η. r i > h πe h e,g, an isolated transition leads to α( E) de = f mnc Other directly related quantities include ε()
Frequency Domain Detection Penetration depth into water vs. wavelength Dispersion elements 1 km Penetration depth into water 1 m 1 mm 1 µm Radio Microwave IR UV X-ray 1 km 1 m 1 mm 1 µm 1 nm Wavelength Visible spectrum
UV-VIS VIS-IR IR Grating Monochromatic.0 Absorption (cm -1 ) 1.5 1.0 absorption PL 1.5 1.0 0.5 PL Intensity (a.u.) 0.5 E 1 H 1 E H Metallic 1.0 1.5 Energy (ev).0.5 0.0 3.0
PL Excitation Spectroscopy (PLE)
Time domain interference Detection Fourier Transform Infrared (FTIR) Spectrometer White light Interference
FTIR Data Acquisition
Three Key Components
Example: FTIR Data Analysis Example: FTIR Data Analysis Reflectance Complex conductivity or dielectric function π σ ε i 4 ) ( 1 ) ( + = 1 ) ( 1 ) ( ) ( + = ε r r where )] ( exp[ ) ( ) ( 1/ θ i r = R = 0 ' ' ' ) ( ln ) ( π θ d R P Kramers-Kronig Transformation
What physics can be probed? Basov Lab at UCSD
#1: Many-body Physics in SWCNs C h = na + mb n m = 3M + ν 1) M = ν = 0 Metal ) M 0, ν = 0 Narrow Gap Semicond. 3) M 0, ν = ±1 Large Gap Semicond. Metallic Semiconducting
Separating the SWCNs M. Ichida et al., J. Phys. Soc. Jpn. 68, 3131 (1999). Jigang Wang, Feb, 009
Exciton Effects 3D JDOS E 1/ α 1s D E g hν 1s E g hν JDOS const. α s 3s E g E g
Exciton Effects in 1D 1D 1s JDOS E 1/ α s 3s E g hν E g hν Huge binding energy extremely stable Lineshape: 1-D VHS (asymmetric) 1-D excitons (symmetric) Sommerfeld factor < 1 (collapse of 1-D VHS)
PL Excitation Spectroscopy n m = 7 (10,3) n m = 4 n m = 1 n m = (7,6) (7,5) TB (11,4) (10,6) (8,7) (9,5) (8,6) (9,4) n m = 5 (10,) n m = 8 3 H H 1 E1 E H DOS (9,8) (9,7) (10,5) (11,3) (1,1) E 3 E O'Connell et al., Science 97, 6 (00)
#: EM Reponses of Superconductors σ 1 () σ ( ) = 1 4 p πi + iγ p σ 1 () n e σ ( ) = s [ πδ ( ) i ] * + m δ - func (condensate) σ () p = ne m * h σ () 1/ Gap h h h
Infrared Probe of Conductivity Gap in MgB > quasi- particles Cooper pair Cooper pair boson (e.g. phonon) Ω> 0 = 5meV R. A. Kaindl, PRL, 88, 07003 (00)
Infrared probe of Pseudogap in HTc Cuprate SC: Generic Phase Diagram Rotter, L.D., PRL, 67, 741 (1990)
The amazing light Laser Light amplification of stimulated emission of radiation (Laser) A laser will lase if the beam increases in irradiance during a round trip: that is, if I 3 > I 0 (threshold).
How Does Laser Work? The model system: Titanium-doped Sapphire laser e Rate Equations Analysis g stimulated spontaneous dn dt e = γ N eg e KnpN + e Kn p N g = dn g dt dn dt e = γ eg N e + Kn p ( N N ) g e
Rate Equation Analysis Photon number varies: dn dt p If N e > N g = Kn p ( N N ) = Kn N g A laser! e p Wait, in thermal equilibrium: E kt N e = e / N g < N g
Four-level system 3 1 and : Pumping rate for level : R p Pump 1 Lasing transition 3: stimulated transitions n p spontaneous decay γ 1 0 4: spontaneous decay γ 10 dn dt dn dt dn dt 1 0 = = = R γ p 1 γ N γ 10N1 1 N R Knp ( N 1 N) p + Kn p( N 1 N) γ 10N1
Solving Four-level Model Steady State N N 1 N = R γ p 10 γ γ 1 1 γ + Kn 10 p Population inversion (i.e., N < 0) if γ 10 > γ 1
Ti:sapphire - the Femtosecond Workhorse Al O 3 lattice oxygen aluminum τ 10 = 3. µs
Ti:sapphire - the Femtosecond Workhorse O - Ti 3+ Example: a 5 mm Ti:sapphire crystal (0.5%), in a cavity with 5% output coupler N th 10 17 cm 3
Gain Saturation N = R γ More Issues (I) γ γ γ + Kn γ γ p 1 10 1 10 = Rp 10 1 p γ 1γ10 1+ Wsigτ1 1 N 0 Kn p 1/γ 1 Pump 3 1 Gain saturates when signal intensity > 1/t 1 0
Next lecture 1. Laser-based CW spectroscopy. Fundamentals of ultrafast optics 3. Femtosecond lasers case studies Jigang Wang, Feb, 009