Ultrafast Laser Spectroscopy

Transcription

1 Ulrafas Laser Specroscopy How do we do ulrafas laser specroscopy? Generic ulrafas specroscopy experimen The excie-probe experimen Lock-in deecion Transien-graing specroscopy Ulrafas polarizaion specroscopy Specrally resolved excie-probe specroscopy Theory of ulrafas measuremens: he Liouville equaion Ieraive soluion example: phoon echo

2 Ulrafas laser specroscopy: How? Ulrafas laser specroscopy involves sudying ulrafas evens ha ake place in a medium using ulrashor pulses and delays for ime resoluion. I usually involves exciing he medium wih one (or more) ulrashor laser pulse(s) and probing i a variable delay laer wih anoher. Medium under sudy Exciaion pulses Signal pulse Variably delayed Probe pulse Signal pulse energy Delay The signal pulse energy (or change in energy) is ploed vs. delay. The experimenal emporal resoluion is he pulse lengh.

3 Wha s going on in specroscopy measuremens? The excie pulse(s) excie(s) molecules ino excied saes, which changes he medium s absorpion coefficien and refracive index. Unexcied medium Unexcied medium absorbs heavily a wavelenghs corresponding o ransiions from ground sae. Excied medium absorbs weakly a wavelenghs corresponding o ransiions from ground sae. Excied medium The excied saes only live for a finie ime (his lifeime is ofen he quaniy we d like o find!), so he absorpion and refracive index reurn o heir iniial (before exciaion) values evenually.

4 The simples ulrafas specroscopy mehod is he Excie-Probe echnique. Probe pulse E pr ( ) Excie he sample wih one pulse; probe i wih anoher a variable delay laer; and measure he change in he ransmied probe Sample medium pulse energy or average power vs. delay. Deecor Variable delay, Excie pulse E ex () E sig (,) The excie pulse changes he sample absorpion of he sample, emporarily. Change in probe pulse energy The excie and probe pulses can be differen colors. This echnique is also called he Pump-Probe echnique. Delay,

5 Modeling excie-probe measuremens Le he unexcied medium have an absorpion coefficien,. Immediaely afer exciaion, he absorpion decreases by. Excied saes usually decay exponenially: () = exp( / ex ) for > where is he delay afer exciaion, and ex is he excied-sae lifeime. So he ransmied probe-beam inensiy and hence pulse energy and average power will depend on he delay,, and he lifeime, ex : I I e ransmied inciden I e e inciden L ex e L L ex e L where L = sample lengh L ex I e e L assuming L << inciden ransmied ex I e L

6 Modeling excie-probe measuremens (con d) ransmied The relaive change in ransmied inensiy vs. delay,, is: ransmied ransmied I T I I T ex ransmied I I e L ransmied T T e ex L Change in probebeam inensiy Delay,

7 Modeling excie-probe measuremens (con d) Excie ransiion 3 Probe ransiion More complex decays occur if inermediae saes are populaed or if he moion is complex. Imagine probing an inermediae ransiion, whose saes emporarily fill wih molecules on heir way back down o he ground sae: Change in probebeam ransmied inensiy or power Excied molecules in sae : simulaed emission of probe Excied molecules in sae : absorpion of probe Delay,

8 Lock-in Deecion grealy increases he sensiiviy in excie-probe experimens. This involves chopping he excie pulse a a given frequency and deecing a ha frequency wih a lock-in deecor: Chopper Chopped excie pulse rain The excie pulse periodically changes he sample absorpion seen by he probe pulse. Probe pulse rain Lock-in deecor The lock-in deecs only one frequency componen of he deecor volage chosen o be ha of he chopper. Lock-in deecion auomaically subracs off he ransmied power in he absence of he excie pulse. Wih high-rep-rae lasers, i increases sensiiviy by several orders of magniude!

9 Excie-probe sudies of bacerio-rhodopsin Rhodopsin is he main molecule involved in vision. Afer absorbing a phoon, rhodopsin undergoes a manysep process, whose firs hree seps occur on fs or ps ime scales and are poorly undersood. Probe a 46nm (increased absorpion): Zhong, e al., Ulrafas Phenomena X, p. 355 (996). Probe a 86 nm (simulaed emission): Naive Arificial Exciaion populaes a new sae, which absorbs a 46nm and emis a 86nm. I is hough ha his sae involves moion of he carbon aoms (, 3, 4). An arificial version of rhodopsin, wih hose aoms held in place, reveals his change on a much slower ime scale, confirming his heory!

10 Excie-probe measuremens can reveal quanum beas Since ulrashor pulses have broad bandwidhs, hey can excie wo or more nearby saes simulaneously. Exciaionpulse specrum Excie pulse Probe pulse Probing he - superposiion of saes can yield quanum beas in he excie-probe daa.

11 Excie-probe measuremens can reveal quanum beas: Experimen Here, wo nearby vibraional saes in molecular iodine inerfere. These beas also indicae he moion of he molecular wave packe on is poenial surface. A small fracion of he I molecules dissociae every period. Zadoyan, e al., Ulrafas Phenomena X, p. 94 (996).

12 Time-frequency-domain absorpion specroscopy of Buckminser-fullerene Elecron ransfer from a polymer o a buckyball is very fas. I has applicaions o phoo-volaics, nonlinear opics, and arificial phoosynhesis. Brabec, e al., Ulrafas Phenomena XII, p. 589 ().

13 The coherence spike in ulrafas specroscopy When he delay is zero, oher nonlinear-opical processes occur, involving coheren 4WM beween he beams and generaing addiional signal no described by he simple model. As in auocorrelaion, i s called he coherence spike or coheren arifac. Someimes you see i; someimes you don. This spike could be a very very fas even ha couldn be resolved. Or i could be a coherence spike. Excie pulse Probe pulse Sample Inensiy fringes in sample when pulses arrive simulaneously Alernae picure: he pulses induce a graing in he absorpion and/or refracive index, which diffracs ligh from each beam ino he oher.

14 Taking advanage of he induced graing: he Transien-Graing Technique. Two simulaneous exciaion pulses induce a weak diffracion graing, followed, a variable delay laer, by a probe pulse. Measure he diffraced pulse energy vs. delay: Excie pulse # Excie pulse # Sample Inensiy fringes in sample due o exciaion pulses Delay Probe pulse Diffraced pulse This mehod is background-free, bu he diffraced pulse energy goes as he square of he diffraced field and hence is weaker han ha in excie-probe measuremens. Diffraced pulse energy Delay,

15 A ransien-graing measuremen may sill have a coherence spike! When all he pulses overlap in ime, who s o say which are he exciaion pulses and which is he probe pulse? Excie pulse # (acing as he probe) Excie pulse # Delay Probe pulse (acing as an excie pulse) A ransien-graing experimen wih a coherence spike: Diffraced beam energy Inensiy fringes in sample due o an exciaion pulse and he probe acing as an exciaion pulse Delay,

16 Wha he ransien-graing echnique measures I measures he Pyhagorean sum of he changes in he absorpion and refracive index. The diffracion efficiency,, is given by: Absorpion (ampliude) graing L n kl 4 Refracive index (phase) graing This is in conras o he excie-probe echnique, which is only sensiive o he change in absorpion and depends on i linearly. If he absorpion graing dominaes and he excie-probe decay is exp(- / ex ), hen he TG decay will be exp(- / ex ): H. Eichler, Laser-Induced Dynamic Graings, Springer-Verlag, 986. Diffraced beam inensiy Delay, Transmied inensiy

17 Time-resolved fluorescence is also useful. Exciing a sample wih an ulrashor pulse and hen observing he fluorescence vs. ime also yields sample dynamics. This can be done by direcly observing he fluorescence or, Excie pulse Fluorescence Sample if i s oo fas, by ime-gaing i wih a probe pulse in a SFG crysal. SFG crysal Probe pulse Lens Slow deecor Delay Fluorescen beam power Delay

18 Time-resolved fluorescence decay When differen issues look alike (i.e., have similar absorpion specra), looking a he imeresolved fluorescence can help disinguish hem. Svanberg, Ulrafas Phenomena IX, p. 34 (994). Here, a malignan umor can be disinguished from normal issue due o is longer decay ime. Normal issue Malignan umor

19 Temporally and specrally resolving he fluorescence of an excied molecule Exciing a molecule and waching is fluorescence reveals much abou is poenial surfaces. Ideally, one would measure he imeresolved specrum, equivalen o is inensiy and phase vs. ime (or frequency). Here, exciaion occurs o a predissociaive sae, bu oher siuaions are jus as ineresing. Analogous sudies can be performed in absorpion.

20 Ulrafas Polarizaion Specroscopy A 45º-polarized excie pulse induces birefringence in an ordinarily isoropic sample via he Kerr effec. A variably delayed probe pulse beween crossed polarizers waches he birefringence decay, revealing he sample orienaional 45 relaxaion. polarized excie 9 polarizer pulse HWP Sample Probe pulse polarizer Delay I s also possible o change he absorpion coefficien differenly for he wo polarizaions. This is called induced dichroism. I also roaes he probe polarizaion and can also be used o sudy orienaional relaxaion.

21 Oher ulrafas specroscopic echniques Phoon Echo Transien Coheren Raman Specroscopy Transien Coheren Ani-Sokes Raman Specroscopy Transien Surface SHG Specroscopy Transien Phoo-elecron Specroscopy Almos any physical effec ha can be induced by ulrashor ligh pulses!

22 Semiclassical Nonlinear-Opical Perurbaion Theory Trea he medium quanum-mechanically and he ligh classically. Assume negligible ransfer of populaion due o he ligh. Assume ha collisions are very frequen, bu very weak: hey yield exponenial decay of any coherence Use he densiy marix o describe he sysem. The densiy marix is defined according o: mn For any operaor A, he mean value is given by: Effecs ha are no included in his approach: sauraion, populaion of oher saes by sponaneous emission, phoon saisics. m n A Trace A

23 The densiy marix If he sae of a single wo-level aom is: c c The densiy marix, ij (), is defined as: * * cc cc * * cc cc Since excied sae populaions always evenually decay o ground sae populaions, ii generally depends on ime, ii (). And coherence beween wo saes usually decays even faser, so he off-diagonal elemens also depends on ime. ρ or ρ are he populaion densiies of saes and. ρ and ρ are he degree of coherence beween saes and.

24 The densiy marix for a many-aom sysem For a many-aom sysem, he densiy marix, ij (), is defined as: * * ( ) ( ) c () c () c () c () * * () () c( ) c () c( ) c( ) where he sums are over all aoms or molecules in he sysem. Simplifying: c * () ( ) c () c c * () c () c( ) The diagonal elemens (graings) are always posiive, while he offdiagonal elemens (coherences) can be negaive or even complex. So cancellaions can occur in coherences.

25 Why do coherences decay? A macroscopic coherence is he sum over all he aoms in he medium. Aom # Aom # Aom #3 Sum: The collisions "dephase" he emission, causing cancellaion of he oal emied ligh, ypically exponenially.

26 Graing and coherence decay: T and T A graing or coherence decays as excied saes decay back o ground. A coherence can also cancel ou if collisions have randomized he phase of each oscillaing aomic dipole. The ime-scales for hese decays o occur are always wrien as: Graing [ () or ()]: T Coherence [ () or ()]: T relaxaion ime dephasing ime Collisions cause dephasing bu no necessarily de-exciaion; herefore, i is generally rue ha T << T. The measuremen of hese imes is ofen he goal of nonlinear specroscopy!

27 Nonlinear-Opical Perurbaion Theory The Liouville equaion for he densiy marix is: i d d which can be formally inegraed: V, () ( ) / i V('), (') d' This can be solved ieraively: ( n) n - (in he ineracion picure) ( n) () () Noe ha i.e., a ime ordering. n n-... n ( ) / i d d... dn V ( ), V ( ),... V ( n), ( )... n

28 Perurbaion Theory (coninued) Expand he commuaors in he inegrand: V ( ), V ( ),... V ( n), ( )... Consider, for example, n = : V ( ), V ( ), ( ) V ( ), V ( ) ( ) ( ) V ( ) V ( ) V ( ) ( ) V ( ) ( ) V ( ) V ( ) ( ) V ( ) ( ) V ( ) V ( ) ( n) Thus, conains n erms.

29 populaion of sae j = jj polarizaion operaor p is: and so he macroscopic polarizaion P is: N Tr N p Tr N p N P Hamilonian H = H + H in : * in E E E p H For an ensemble of -level sysems in he presence of a laser field: Densiy marix & Hamilonian E E H (we have defined he zero of energy as he energy of sae )

30 Diagonal elemens of Liouville equaion for he diagonal elemen: i H, i T eq H H H H i T eq H H i and similarly for. T eq Derive from hese an equaion for he populaion difference = - i H H i T

31 Off-diagonal elemens of Liouville equaion for he off-diagonal elemen: i i H H, i Now use he known form for he perurbaion: H T i T * i * i H E()e E () e i * i i E e Ee T i T i * i Ee E e i

32 Roaing wave approximaion () () n m (n) e (m) in e im Inser ino he previous equaions, and mach erms of like frequency: (n) i (n) E * i (n) (n) A E which can be inegraed o yield: (n) *(n) i (n) * d' E (') (n) i (n d' E(') E (n) (n) A T T (n) ) ' E(') exp T exp Ad ' ) " i *(n

33 Ieraive mehod for solving perurbaively We have a sysem of equaions of he form: Sar wih () = and () = and ierae: (n) (n) G F () () () () F F () G G (3) erm looks like: (3) i E( )E * ( 3 d )E( 3 (n) (n) () () G F (3) G G d )exp 3 d 3 exp Ad' E( Mus be a (3) process! Ad' T * )E( )E (3)exp 3 * A d'

34 Muliple pulses (3) i E( )E * ( 3 d )E( 3 d )exp 3 d 3 exp Ad' E( Ad' T * )E( )E ( 3)exp 3 * A d' Suppose here are wo pulses, boh shor compared o all relevan ime scales: k E() = E () e ikr + E ( ) e ikr k A produc of hree of hese E() fields gives 8 erms, each wih one of hese four wave vecors: k +k -k k +k -k k +k -k k +k -k phase maching, of a sor: pick he direcion you care abou

35 Example: applicaion o he wo-pulse echo k k k k (3) Choose he k -k direcion. Then only wo erms (of 6 in (3) ) conribue: i E ( ) ( E 3 ) ( d d d 3 exp Ad' T )exp Ad' () ( ) ( 3 )exp * A d' Firs erm: mus have AND = mus have AND = } signal only for = "coheren spike" Second erm: mus have < and > (no oher consrains); i gives rise o signal a values of oher han merely =

36 Example: applicaion o he wo-pulse echo k exp 3 (3) * ie E Ad' A d' > < k k -k Homogeneous broadening Polarizaion = N ~ exp[( + )/T '] measured signal S(): S where P (3) T d = T e + ' T ' T for oherwise P Inhomogeneous broadening We mus inegrae over he inhomogeneous disribuion g(): (3) ~ e d g T i de g P (3) is non-zero only a = S 4 e ' T (3) (3) T T S( ) P d e d e for oherwise

37 Echo vs. FID: can we ell? Homogeneous case: phase-mached free-inducion decay pulse # pulse # free-inducion decay: k -k Inhomogeneous case: phoon echo pulse # pulse # echo I can be difficul o disinguish beween hese wo cases experimenally!

38 Echo vs. FID: how o ell One way o disinguish: k k k -k FWM upconversion using a hird opical pulse e.g., M. Mycek e al., Appl. Phys. Le., 99

39 Phoon echo: wha s going on? The pseudo-vecor: z componen denoe populaion sae xy componens denoe polarizaion sae z z z The phoon echo is physically equivalen o he spin echo in NMR specroscopy, excep for he exra complicaion of wave-vecor phase maching (k k )