Survey on Laser Spectroscopic Techniques for Condensed Matter

Survey on Laser Spectroscopic Techniques for Condensed Matter

Coherent Radiation Sources for Small Laboratories CW: Tunability: IR Visible Linewidth: 1 Hz Power: μw 10W Pulsed: Tunabality: THz Soft X-ray Pulse width: ns, ps, fs Linewidth: Transform limited Power: up to TW for fs pulses Quasi-cw: ~100 MHz mode-locked pulses Tunability: IR Visible Frequency Comb: Periodic fs pulses Spectral components with~100 MHz spacing and <KHz linewidth Stable carrier/envelope phase relation

Light Scattering n > ω 1 ω 2 f > dσ dω ωω r r < f er e? n>< n er e g > 3 1 2 1 2 [ 4 c n ω1 ωng r r < f er e? 1 n>< n er e2 g > ] ω + ω 2 ng g > 2

Raman Scattering n > Rayleigh Scattering n > ω 1 ω 2 ω 1 ω 1 f > f > g > g > dσ S = N ΔΩ( I / hω) V photons/sec dω

dσ dω Estimates of Signal Strength Scattered #photons in d Ω per sec Incoming photon intensity N N dσ ( ) Raman ~ 10 cm d Ω dσ ( ) Rayleigh ~ 10 cm d Ω 8-1 6-1 For a 1-mW beam focused to a spot of 10x10x10 μm 3, 15 ( I / hω) V ~ 10 photons/sec S S Raman Rayleigh 7 ~ 10 ΔΩ photons/sec 9 ~ 10 ΔΩ photons/sec

Luminescence/Fluorescence Rate of lum. trans. σl = σabsηr = σabsηr RT L Total decay rate β = absorption coefficient = #Photons emitted #Photons absorbed R Nσ = η RT L 1 abs Luminescence >> Rayleigh Scattering (Single Molecule Detection) 1

Fluorescence Quenching Intermolecular Interaction = C/ R 6 Excitation energy transferred to neighbors through interactions: M Fluorescence quenching of molecules on metals Fluorescence resonance energy transfer (FRET) between molecules

ω 1 ω 2 g > Resonant Light Scattering & Hot Luminescence n > f > r r dσ ωω < f er e? n>< n er e g > ( ) Raman dω c + i T σ L 3 1 2 1 2 4 n ω1 ωng / 2 emission rate = σabs total decay rate r r < n er e? g > T < f er e n> T 2 2 1 2 2 1 2 Resonant enhancement of scattering: 1/ T η ω ω sc 2 2 3-1 4-1 ~ ~ 100 if 1/ T2 ~ 10 cm, ng ~ 10 cm ω ω ng

Excitation Spectrum σ = σ η σ L abs R Rayleigh σ abs emission rate Total decay rate r r < f er e? n>< n er e g > ω ω + i/ T 1 2 2 n 1 ng 2, ng Resonant enhancement in σ L or σ Rayleigh yields the excitation spectrum A sensitive method to obtain absorption spectrum

A Single Carbon Nanotube

Excitation Spectra of Rayleigh Scattering of Carbon Nanotubes SC Metal Bundle M.Y. Sfeir et al, Science 306, 1540 ( 2004 )

Resonance Raman Scattering from Single-Wall Carbon Nanotubes M.Y. Sfeir et al, Science 306, 1540 ( 2004 )

Multi-Phonon Raman Scattering from Single SW Carbon Nonotubes

Labeling Spectroscopy Elimination or reduction of inhomogeneous broadening Selective detection or probe of species in an ensemble Studies of interactions and energy transfer between neighbors Examples: Carbon nanotubes Semiconductor nanoparticles

Spectral Hole Burning hole width ~ homogeneous linewidth = 1/dephasing time hole recovery time ~ population relaxation time S hole broadening with time ~ excitation transfer to neighbors (spectral diffusion) ω

Absorption Spectra of Be 3 Al 2 Si 6 O 18 :Cr (Emrald) at 2.5K

Multi-Photon Excitation Multi-photon absorption r r < f er e? n>< n er e g > σ [ (2) 1 2 abs n ω1 ωng r r < f er e? n>< n er e g > ω ω 1 2 2 + ] Multi-photon-excited Luminescence (2) (2) Rate of lum. trans. (2) σ = σ η L abs R = σ η abs RRT L Total decay rate #Photons emitted #Photons absorbed 2 ng = η RT R L 1 1 ω 1 ω 2 f > n > g >

Two-Photon Excitation Spectra of Single-Wall Carbon Nanotubes F. Wang et al, Science 308. 838

F. Wang et al, Science 308. 838

Hyper-Light Scattering n > n > ω 1 ω 2 ω 1 ω2 ω 1 f > ω 1 f > g > g > r r r < f er e? n' >< n' er e n >< n er e g > Ω + dσ d ' 2 1 2 + ' nn, ' ( ω1 ω ng )( ω1 ω1 ω ng ) 1 [ ]

Stimulated Raman Spectroscopy dn dz dn = = γ n1( n2 + 1) dz γ nn 2 1 1 2 γ nz 1 n n e n n z = (1 + γ ) 2 20 20 1 Raman Gain dσ N d Ω γ dσ 1 = γ n N n dω Γ 1 1 8-1 For ~ 10 / cm and Γ ~ 1 cm, 3 ~ 10 cm/mw Gain ~ 1 cm for I = nhω c ω 1 ~ 1 GW/cm 1 2 1 1 1 ω 2 n > f > g >

Estimate of Detection Limit Consider a 100-fs input pulse at ω 1 with 0.1 μj/pulse, focused to a 10 μm spot: I ~ 10 12 W/cm 2 Δn n ΔI = ( Gain) z, Gain = γn [ N( dσ / dω) / Γ] n I 2 2 20 20 6 detectable [( Gain) z] min ~ 10. 12 2 With ~1 mm and ~10 W/cm, z -11 detectable γ min ~10 cm/mw I 16 or [ N( dσ / dω)/ Γ] ~10 /cm as compared to typical min 8 ( / dω) / Γ~ 10 / cm Ndσ 1 1

Experimentals fsec Laser Continuum Generation Spectral Filtering Broadband Probe Narrowband Pump Sample Detector pump probe McCamant et al, Rev. Sci. Inst. 75, 4971(2004)

Probing Vibrations in Excited Electronic Configurations

Merits: Background elimination Fluorescence rejection (making resonant Raman studies possible) Fast data collection (pump intensity, ~1 GW/cm 2 ; path length, ~3 mm; SNR ~ 2 with single shot) Ultrafast time resolution (~ 100 fs) Reasonable spectral resolution (< 10 cm -1 ) Capable of probing transient vibrational modes in the excited electronic configurations

Example: Light-Induced cistrans Isomerization of Retinal in Rhodopsin Kukura et al, Science 310, 1006 (2005)

Quantum Beats (resulting from pulse excitation) Fourier transform Spectrum

Impulsive Excitations 100-fs pulse ~ 300 cm -1 spectral width fs pulse sets up coherent excitations in a set of excited states. Signal appears as oscillation on the fs time scale. Fourier transform of the time-dependent signal yields the spectrum.

Time-Resolved Impulsive Raman Spectroscopy

Impulsive Stimulated Raman Spectroscopy: Perylene Crystal Weiner et al JOSA B8, 1264 (1991)

Time-Resolved Impulsive Spectroscopy Molecular vibrations Phonons Plasmons Phonon-plasmons Magnons (spin waves) Other elementary excitations

Impulsive Spin Excitations in DyFeO 3 Detection by Faraday Rotation θ = + ω F γt γ ' t M z Ae Be cos t Kimel et al, Nature 435, 655(2005)

Optical field induces magnetization?

Optical Rectification & Opical-Field-Induced Magnetization Time-averaged Free Energy: F = F H H E E (1) * 0( dc) χij ( dc) i ( ω) j ( ω) i, j i, j, k χ E E ( ω) E ( ω) + (2) * ijk dc, i j k Induced dc polarization: F P = = χ E ( ω) E ( ω) (2) * dc, i ijk j k Edc, i jk, Induced dc magnetization: F Δ M = = E E 2 2 dc, z ( γ + 0 γ 0)( + ( ω) ( ω) ) / 2 H dc, z 2 2 [ ( γ + 0 γ 0 ) Hdc, z ( E+ ( ω) E ( ω) )/2]

Optical-Field-Induced Magnetization Δ F = ( γ γ ) H ( E ( ω) E ( ω) )/2= ΔM H 2 2 + 0 0 dc, z + z dc, z Δ M = ( γ γ ) E ( ω) = χ H 2 + z + 0 0 + H eff H eff = [( γ γ ) / χ ] E ( ω) + 0 0 H + 2 E 2 8 10 2 For ( ω) ~ 10 esu (2.5 10 W/cm ), + 8 0 ( γ + 0 γ 0) ~ 10 /gauss (~0.1 / gauss-cm), χ 4 and H ~ 10 emu (at T = 30 K), x H eff ~ 10 4 gauss (fs pulse of magnetic field)

Physical Interpretation (AC Stark Effect) ω 0 ω m m +m > -m > r r 2 r r* 2 < n er E( ω) g, ± m> < n er E ( ω) g, ± m> ΔΕ g, ± m = [ ] h( ω ω ) h( ω+ ω ) M = Ng β < J > J n ng, ± m ng, ± m z = Ng β[ < m J m > ρ +< m J m > ρ ] J z m z m +m> -m>

Frequency Comb E() t = A()cos[2 t π ft+ ( Δφ / τ)] t At ( ) = At ( + τ ) 2 π δ = ω 0 = [( Δ φ / τ ) t ] t = ( Δ φ ) / τ Feedback Control can yield Δφ < 10-3 rad.

Characteristics of Frequency Comb Well defined optical field: E(t)=A(t)cosωt Femtosecond periodic pulses: A(t)=A(t+T) Thousands of equally spaced spectral lines with KHz linewidth