Observation of the phase of a Raman oscillation

Volume 70, number 5

OPTICS COMMUNICATIONS

1 April 1989

OBSERVATION OF THE PHASE OF A RAMAN OSCILLATION M a r t i n van E X T E R a) a n d A d L A G E N D I J K a b) ~ Natuurkundtg Laboratorzum, Valckemerstraat 65, 1018 XE Amsterdam, The Netherlands b) FOM Institute for Atomtc and Molecular Physws, 1098 SJ Amsterdam, The Netherlands

Recewed 2 August 1988, rewsed manuscript recewed 7 December 1988

We report the observation of the time evolution of the phase of a coherent Raman exc~tatmn, driven on and offresonance Thts reformation ~s derived from a time-resolved stimulated Raman experiment through a soph~sucated form of "fringe counting" This phase reformation is not obtainable from t~me-resolved CARS or CSRS

1. Introduction

In time-resolved p u m p - a n d - p r o b e optical techniques, a m o d e is excited by a p u m p pulse and the decay is m o n i t o r e d with a probe pulse at a variable delay Usually one only probes the decay o f the amplitude o f the excitation In case o f simple exponential decay this can be described with a single characterlstic decay constant We will prove experimentally that with time-resolved s t i m u l a t e d R a m a n spectroscopy ( T S R S ) it is possible to measure the phase in a d d i t i o n to the a m p l i t u d e o f the R a m a n response o f a m o d e (in a single scan) We will d e m onstrate this for several v i b r a t i o n a l excitauons all o f which can be described satisfactorily as simple d a m p e d h a r m o n i c oscillators The knowledge o f the d y n a m i c b e h a v i o r o f the phase o f the R a m a n response has great potential In the first place the knowledge o f the phase is crucial if one wants to reconstruct the spectrum in the frequency d o m a i n from t i m e - d o m a i n d a t a This becomes particularly i m p o r t a n t if one wants to perform high-resolution spectroscopy using techniques in the time d o m a i n A m b I g u m e s in i n t e r p r e t a t i o n o f spectra caused by the lack o f knowledge o f the phase are well-known Very recently a notorious "rise-fall" a m b i g u i t y has been discussed [ 1 ] In a d d i t i o n to resolution p r o b l e m s it 1s quite realistic to assume that for t i m e response m o r e c o m p l i c a t e d than that o f a simple d a m p e d h a r m o n i c oscillator the phase will

contain valuable new i n f o r m a t i o n with respect to the d y n a m i c s o f this system In time-resolved coherent R a m a n spectroscopy one tries to probe the d y n a m i c s o f a R a m a n - a c t i v e m o d e directly in the d o m a i n Various optical techniques are suitable for this task These techniques can be divided m coherent Stokes R a m a n scattering (CSRS) a n d coherent anti-Stokes R a m a n scattenng ( C A R S ) [2] on the one h a n d and s t i m u l a t e d R a m a n scattering ( S R S ) [ 3 - 6 ] or R a m a n gain spectroscopy on the other h a n d Recently the technique o f time-resolved impulsive stimulated R a m a n scattering has been a d d e d to this list [7] In the time-resolved variants o f CSRS, CARS and SRS the excitation o f the R a m a n - a c t l v e m o d e is equivalent, but the observation o f the evolved Ram a n oscillation differs In all three techniques the R a m a n - a c t i v e m o d e is coherently excited by a comb i n a t i o n o f two short pulses having a frequency difference close to its eigenfrequency The probing o f the excitation differs for the three techniques, but is always based on the fact that the coherent R a m a n excitation scatters a fraction o f the probe pulse (s) to the Stokes-shifted and anti-Stokes-shifted frequency The a m o u n t o f ( d i r e c t i o n a l ) inelastic scattering is m e a s u r e d as a function o f the time delay between the p u m p pair and the probe p u l s e ( s ) In this way the t i m e evolution o f the R a m a n excitation is directly observed in the time d o m a i n Let us denote the high a n d low frequency component o f the p u m p pair by toe (typically yellow) and

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o)s (typically r e d ) respectively In CARS and CSRS a single probe pulse is used, o f frequency o)~ a n d ~os respectively, and the scattered intensity is observed at the frequency (2o)~-¢o~) and (2o9~-o9~) respectively As this frequency differs from the frequencies of the original b e a m s the i n f o r m a t i o n o f the phase o f the coherent R a m a n excitation is lost In time-resolved s t i m u l a t e d R a m a n scattering ( T S R S ) two pulses, instead o f one, are used to probe the R a m a n excitation This probe pair is usually derived from the lasers that also produce the p u m p pair and both pairs have the same characteristics On passage through the sample part o f the yellow probe pulse is scattered to the red frequency and part o f the red probe pulse is scattered to the yellow frequency W h e n the p u m p and probe pairs originate from the same source the Stokes-shifted scattered light from the yellow probe b e a m will interfere with the red probe beam and will result either in a gain or a loss o f this beam, d e p e n d i n g on the ( o p t i c a l ) phase relation between all beams involved When one o f these four path lengths is slowly changed over a few wavelengths the m e a s u r e d gain on the red probe b e a m changes periodically from gain into loss a n d vice versa according to cos(~0~pump--~0~probe--~0spump+ tp~prob~+ ~0), where rp is the phase shift o f the R a m a n oscillation with respect to the phase o f the p u m p pulses The TSRS setup acts like a c o m p l i c a t e d interferometer for four laser b e a m s The interference o f the scattered light with one o f the probe pulses makes TSRS sensitive to the phase o f the coherent R a m a n excitation, here specified by (0 This feature is absent in time-resolved CARS and CSRS In time-resolved s t i m u l a t e d R a m a n spectroscopy ( T S R S ) the intensity variation o f the red probe b e a m is observed as a function o f the delay between the p u m p pair and the probe pair W h e n this delay, which will be d e n o t e d by T, is scanned the "optical crosstalk" periodically varies from gain to loss The amplitude o f this gain-loss m o d u l a t i o n , which will be d e n o t e d as R a m a n fringes, decreases as a function o f the time delay between the p u m p and the probe pair This decrease in a m p l i t u d e reflects the (T2) relaxation o f the R a m a n - a c t i v e m o d e a n d is n o r m a l l y the only i n f o r m a t i o n one uses from a TSRS e x p e r i m e n t There is more i n f o r m a t i o n in TSRS, besides the evolution o f the amplitude of the R a m a n flanges The spacing between successive fringes evolves almost, 434

1 April 1989

but not perfectly, slnusoldal in time and is related to the elgenfrequency o f the R a m a n - a c t l v e m o d e The phase o f the fringes reflects the phase o f the driven coherent R a m a n excitation W h e n the frequency o f the driving force (co~-o)s) differs slightly from the elgenfrequency o f the R a m a n - a c t l v e m o d e (.Q~) one expects the R a m a n oscillation to start with the frequency (¢o~- oA) and to return to its eigenfrequency in the free-induction regime ( T large) In this article we will show how to subtract phase information from TSRS m e a s u r e m e n t s and how it can be interpreted in terms o f the evolution o f the phase o f the coherent R a m a n excitation A point o f caution is the existence o f an instantaneous contribution to the TSRS signal [ 2 ] A r o u n d T = 0 ps the TSRS signal does not solely originate from the R a m a n effect, but also contains an electronic contribution and a contribution due to the Kerr effect Both contributions d i s a p p e a r with large T ( d i s a p p e a r i n g pulse o v e r l a p ) Theory predicts a phase evolution o f these Kerr a n d electronic signals that exactly matches the frequency difference between both lasers

2. Experimental details In fig 1 a schematic drawing o f our experimental setup IS presented [6] A mode-locked Ar+-laser synchronously p u m p s two dye lasers, with laser frequencies d e n o t e d by red and yellow, which produce pulses o f typically 7 ps (fwhm autocorrelate) The frequency difference between both lasers is easily tunable After splitting a n d recomblnlng the various b e a m s we end up with a p u m p pair and a probe pair, each containing a red a n d a yellow b e a m of about 20 m W average intensity and 82 M H z mode-locking frequency The p u m p and probe pairs are parallel, but not colhnear They are focused with a 50 m m a c h r o m a t i c lens into the sample and cross each other at about 2 ° After passage through the sample the red probe b e a m IS directed onto a p h o t o d l o d e ( E G & G S G D 100A) and ItS intensity change is measured Due to the lnterferometrlc nature o f TSRS the time resolution is related to the correlation time o f the pulses and can be (far) better than the widths o f the ind i v i d u a l pulses The m i n i m a l T2 observable with our setup is 0 8-1 0 ps

Volume 70, number 5

OPTICS COMMUNICATIONS

JAr ÷ LASER , ~ , PIEZO - •/

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We use a special double-modulation technique to observe the small (less than 0 1%) intensity change of the red probe beam The 8 4 MHz amplitude modulation of the yellow pump beam IS applied with an EO modulator The 500 Hz modulation of the probe beam is a phase modulation, which is applied with a piezo-electrlc element (PI P-170), being driven by a sinusoidal AC voltage Besides giving a good signal to noise ratio this modulation technique, in combination with the directional separation of the pump and the probe pair, provides a unique label for the pump and probe pulses The delay between the pump and the probe pair is scanned continuously at typical scan rates of 2-20 ~tm/s The position of the scanning delay line is accurately (within 1 ~tm) determined with a magnetic ruler of Sony Magnescale inc (ruler SR-721SP, processor unit LY 101-12) Every l ~tm the processor unit attached to the magnetic ruler sends a pulse to an IBM PC and a sample is taken The data thus collected are afterwards sent to a host computer (VX-11/750) and run through a digital filter This procedures yields the amplitude of the Raman fringes as well as their phase as a function of the delay Typical results for the evolution of the amplitude of a TSRS signal can be found in refs [2-5] To our knowledge this article is the first to discuss the evolution of the TSRS signal

1Aprd 1989

The phase 9(T) of the TSRS signal can be defined with respect to the elgenfrequency (12.) of the Raman mode or with respect to the frequency of the driving force (to~-tos) We have chosen for the latter definition and the pattern of the fringes IS thus compared with the function cos [ (o9~- cos) T - @(T) ] As will be shown later this choice results in an almost constant phase around T = 0 ps The data, consisting of a number of points taken at different delays T, is digitally processed in the following way The data points are first multiplied by cos [ (o9~- cos) T] and then filtered, with a low-pass filter, to reduce the noise and get rid of the second harmonic frequency generated by the multiplication stage The same original set of data points is also multiplied by sin [ (to~- oA) T] and filtered Combination of the first-mentioned "in-phase" component and the "outof-phase" (or quadrature) component of the TSRS signal immediately yields the amplitude as well as the phase of the (complex) function describing the energy transfer in TSRS The technique to deduce the phase information can be considered as a sophisticated form of "fringe counting" The strong dependence of the signal on the exact time-delay between the pump and probe pair imposes a strong requirement on the stability of the optical equipment as noted by Heritage [ 5 ] The stability should be as good as in holographic experiments Our experament is performed on a large metal table resting on air-filled tires and thus being disconnected from most vibrations of the floor The height of the optical components is chosen as small as possible to minimize the influence of vibrations We have tried to suppress air currents by erecting a curtain around the setup Unfortunately hardly anything was gained when the curtains were closed, because only the fast fluctuations m the optical path lengths were affected and the slow fluctuations (drift) did not seem to improve

3. Results We have performed TSRS measurements on the optical phonon of diamond at ( 2 n ) - ~ 2 . = 1 3 3 2 c m - ~ and the symmetric stretch ( u~ ) of liquid CS2 at 656 cm-~ For the (1332 cm-~) mode of diamond about 4 samples are taken per oscillation pc435

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rlod, while for CS2 about 7-8 samples are taken per oscillation period Both sampling rates are high enough to allow for the retrieval of the phase of the Raman fringes In fig 1 the time evolution of the phase of the TSRS signal of a typical run on diamond is shown In this run the frequency difference between both lasers was tuned to ( v ~ - v~) = 1325 5 cm-~, while the eigenfrequency of the optical phonon is 1332 cm-~ The smooth curve is the outcome of a simulation of this experiment All things considered the correspondence is extremely good Lack of stability of the optical components (mirrors, beam splitters) can thoroughly destroy any phase measurement The correspondence between theory and experiment leads us to an estimate of the drift in phase, due to moving optical components, as good as ~zradlans during the 5 minutes this run took to record Just before and around T = 0 ps the phase is almost constant in time, while for large delays the linear increase in time of the phase is in perfect agreement with the frequency mlstunlng (o9~- o9S- oJ~) For very large delay the phase seems to vary rather wildly and rapidly as a function of time This is caused by the small signal to noise ratio of the TSRS stgnal for very large delay time The fringes disappear in the noise, and the phase informatlorr is lost The instantaneous contribution to the TSRS signal in diamond is only about 10% (for our alignment and pulse shapes) We are therefore mainly looking at the phase of the coherently-excited Raman-active mode The phase informatmn from the TSRS measurement shown in fig 2 is being lost so quickly (at T= 20 ps) because the T2 of the optical phonon of diamond is only 4 9( 1 ) ps (ref [4] ) and the TSRS signal decreases strongly as a function of delay time The much longer transverse relaxation time of the 656 c m symmetrtc stretch mode of l i q u i d C52 [ T2 = 19 5 (4) ps] made us decide to perform TSRS experiments on CS2 The large 7"2 allowed us to trace the phase of the Raman oscillation to larger delays The phase could consequently build up to higher values A complication in the TSRS measurements on CS2 is the fact that the instantaneous contribution around T = 0 ps is roughly 3 × larger than the actual Raman signal For this reason the phase of the TSRS signal of CS2 around T = 0 ps will be mainly determined by this instantaneous contribution 436

1 April 1989

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Time (ps) Fig 3 Measurements of the time evolution of the phase of the TSRS signal on the (656 cm -~ ) symmetric stretch of liquid CS2 for five different frequency differences between the lasers From top to bottom the runs were taken for ( v ~ - v s ) = 6 6 4 , 662, 657, 653 and 650 c m - ~ The difference is evident

In fig 3 the evolution of the phase of the TSRS signal of CS2 is shown for five different values of (o9~- oJs) Around and before T = 0 ps the phase ~0(T) is practically independent on T We have arbitrarily set this phase to zero When (o)~-ogs) is larger than

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OPTICS C O M M U N I C A T I O N S

I2,~, the phase of the TSRS signal tp(T) increases as a funcUon of the delay T, as the Raman oscillation returns to its eigenfrequency When (og~-ogs) is smaller than 12., ~ ( T ) decreases as a function of the delay time T All five measurements are in perfect agreement with theory Similar results, though more noisy were obtained for the optical phonon of diamond When the frequency difference between the lasers was tuned to ( v~- vs) = 647 5 c m - ~the Raman phase evolved differently from what we expected as can be seen in fig 4 While we expected the phase to decrease strongly as a function of the u m e delay T it instead increased slowly in the free-reduction regime This seems to indicate the presence of another Raman-active mode with an eigenfrequency shghtly lower than 647 5 c m - ~ Indeed one of the lines of the spontaneous Raman spectrum is situated xn this regime and has been assigned to the ( v~ ) mode of CS2 molecules that have one 32S substituted by the 345 isotope [8 ] The presence of this second mode can also be concluded from the quantum beats observable in the amphtude of the TSRS run at ( v~- Us) = 647 5 c m - 1 Both the perslstance of these quantum beats and the observablhty of the phase at large delays show that the transverse relaxation time of the 647 c m - ~mode is long and comparable to the

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Fig 4 The time evoluUon of the phase of the TSRS s~gnal of hquld CS2 exoted and probed with ( vQ-- us) = 647 5 c m - ~ In this measurement the phase of the TSRS signal is d e t e r m m e d by a weak mode around 647 c m - t, which is apparently excited stronger than the mode at 656 c m -

1 Aprd 1989

7"2 of the 656 c m - t mode, as one expects The spontaneous Raman spectrum of CS2 shows the presence of three other modes around 656 cm - t , neither of which show up m the evolution of the phase of the TSRS signal The phase of the TSRS signal is apparently determined by the phase of that Ramanactive mode that is excited most strongly For this reason the 647 c m - t mode showed up only when (v~-Us) =647 5 cm-~ m which case it was excited to a higher degree than the usually dominant 656 c m - ~ mode

4. Conversion to frequency domain Conventional "spontaneous" Raman scattering IS a powerful spectroscopic techmque To compare results obtained with this technique with the new nonlinear techniques, like CARS and SRS, It can be very useful to transform the time-domain data to the frequency domain To derive the shape of Raman resonance (in the frequency domain) the phase information of the TSRS signal is of vital importance Knowledge of the time evolution of the amplitude is not sufficient, as this mainly reflects the decay times of the Raman-active modes and hardly contains Information on their exact elgenfrequencles The data points around T - - 0 ps have to be removed before the Fourier transformation IS performed The spectral contents of these points just matches the spectrum of the laser pulses Our results show that a Fourier transformation on the data points in the freeinduction regime gives a good spectral resolution The spectral resolution collapses when the phase information of the TSRS signal is lost and a Fourier transformation of the envelope of the TSRS signal IS made In time-resolved CARS and CSRS the detection frequency differs from the frequencies of pump and probe pulses In these experiments the phase of the Raman-active oscillation cannot be directly observed A more complicated method has to be applied In ref [9 ] it has been shown that the change in oscillation frequency of the Raman-active mode from (o9~-o9,) around T - - 0 ps to its elgenfrequency -Qc~ In the free-induction regime can also be observed in time-resolved CARS When a frequency run is made at a fixed delay between the pump pair and the probe pulse the spectrum consists of one line at 437

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OPTICS COMMUNICATIONS

(2o9~-0A) a n d one line at (09~-ogs+t2.) A r o u n d T = 0 ps the former xs the strongest, showing that the R a m a n oscillation has the frequency (o9~-cos), while for large delays the latter ~s the strongest, showing that the R a m a n - a c t l v e m o d e has returned to ~ts elgenfrequency The time-resolved C A R S experiments we have performed clearly support this point o f view In ttme-resolved CARS a n d CSRS the observation o f the change in spectral contents o f the scattered hght as a function o f the t i m e delay between p u m p a n d probe p u l s e ( s ) in p n n c l p l e yields the " i n s t a n t a neous frequency" ( d ~ / d T ) o f the R a m a n osclllatton H o w e v e r to o b t a i n the full phase i n f o r m a t i o n a full " t w o - d i m e n s i o n a l ( f r e q u e n c y - t i m e ) " experim e n t has to be p e r f o r m e d We have shown that timeresolved SRS yields the evolutton o f the phase ~ ( T ) o f the R a m a n oscillation directly

5. Conclusions We have accurately traced the almost smusoidal gam-loss modulation o f the red probe pulse in a timeresolved s t i m u l a t e d R a m a n e x p e r i m e n t The experimental accuracy a n d stablhty was good enough to observe the phase o f the coherently driven R a m a n active mode O f special interest is the s~tuatlon where the m o d e is driven o f f r e s o n a n c e In this situation we observed that the m o d e followed the frequency difference o f the laser pulses when it was driven a n d returned to its elgenfrequency after the laser pulses

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were gone The results are in perfect agreement with theory Through the evolution o f the phase o f the TSRS signal we could p i n p o i n t the elgenfrequency o f a second R a m a n - a c t l v e m o d e close to the usually d o m i n a n t 656 cm-~ m o d e o f ltqmd CS2

Acknowledgement This work is part o f the research p r o g r a m o f the "SUchting v o o r F u n d a m e n t e e l O n d e r z o e k der MaterIe ( F O M ) " , which is financially s u p p o r t e d by the " N e d e r l a n d s e Organlsatle voor Wetenschappelijk Onderzoek (NWO)"

References [ 1] C E Barker and A G Kostenbauder, Opttcs Lett 13 ( 1988 ) 865 [2]A Laubereau and W Kaiser, Rev Mod Phys 50 (1978) 607 [ 3 ] R Leonhardt, W Holzapfel, W Zlnth and W Kaiser, Chem Phys Lett 133 (1987) 373 [4] M van Exter, A Lagendxjkand E Spaans, Optics Comm 59 (1986) 411 [5]J P Hentage, Appl Phys Lett 34 (1979)470 [6] M van Exter and A Lagend0k, Optics Comm 56 (1985) 191 [7] S Ruhman, A G Joly and KA Nelson, J Chem Phys 85 (1987) 6563 [8] G Herzberg, Infrared and Raman spectra of polyatomlc molecules (Van Nostrand Reinhold, New York, 1945) [9] A Laubereau, H R Telle and G M Gale, Appl Phys B 34 (1984) 23