J. Chem. SOC., Faraday Trans. 2, 1983, 79, 865-883

Raman Amplification Spectroscopy Using Mode-locked Lasers

J. BARAN,? D. ELLIOTT,$ A. GROFCSIK,~ W. JEREMY JONES,* M. KUBINYI,~ A. J. LANGLEY AND V. U. N A Y A R ~

Edward Davies Chemical Laboratories, The University College of Wales, Aberystwyth SY23 1NE

Received 22nd October, 1982

The theory necessary for an understanding of the Raman amplification process is reviewed in order to accentuate the factors which are of significance in designing an instrument to take advantage of the sensitivity potentially available with the techniques of inverse-Raman or Raman-gain spectroscopy. The dependence of the signal intensity on the product powers of the pump-and-probe lasers leads to a need for pulsed rather than continuous-wave lasers, while the requirements for a low noise level accompanying the signal dictate the need for a rapid-pulse system capable of being utilized with fast lock-in amplifiers. These requirements are most suitably met by synchronously pumped mode-locked and/or cavity-dumped dye lasers. The detailed design of systems combining either two synchronously pumped mode- locked dye lasers or one mode-locked cavity-dumped laser and one synchronously pumped mode-locked dye laser are described and compared. Following a discussion of the factors influencing the signal-to-noise ratio attainable, representative spectra are presented which reflect the quality of the spectra attainable with this newly developed technique.

In recent years, following the development of laser light sources many remark- able developments have taken place in the field of Raman spectroscopy. Apart from the advantages brought to the study of conventional spontaneous Raman scattering studies, many new effects have been observed which depend on the high brightness of laser light sources. Perhaps the most striking of these developments has been in the study of coherent anti-Stokes Raman spectroscopy (CARS) which, being largely 'background free', has been shown to have a remarkably high sensitiv- ity for the study of the Raman spectra of solids, liquids and gases. More recently, particularly following the researches of Owyoung at the Sandia Research Laboratories, the benefits of investigations into the Raman amplification process have been made apparent. Raman amplification occurs when two beams of monochromatic radiation are incident on a Raman-active medium, the frequency difference of the two beams coinciding with a Raman-active transition in the molecules under study. In this process, when there are more molecules in the lower of the two vibrational states coupled by the process, the lower-frequency radiation is amplified with energy being abstracted from the higher-frequency radiation. Essentially the system behaves as an amplifier of Raman radiatiyn (fig. 1). The effect was first observed in the studies of Jones and Stoicheff, who observed absorption from an anti-Stokes continuum synchronised in time and space with a

1- On leave from the Institute of Chemistry, Wroclaw University, Poland. $. Present address: Department of Inorganic Chemistry, University of Oxford. D Present address: Department of Physical Chemistry, Politechnical University, Budapest, Hungary. ll Present address: Physics Department, Kerala University, Trivandrum, India.

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866

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RAMAN AMPLIFICATION SPECTROSCOPY

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megawatt pulse of 694.3 nm ruby-laser radiation at a wavenumber shift correspond- ing to the vibrational interval of the strongest Raman transition in the molecular system under study. To this process they gave the name inverse Raman effect. Subsequent developments improved the methods for recording such spectra significantly but dramatic improvements arose only with the advent of high-power tunable lasers, notably the tunable dye laser in its various forms. The spectra that are generated by this process are conventional spectra in the sense that they are linearly dependent on the differential Raman scattering cross-sections, unlike CARS spectra which depend on the square of this parameter. To understand the benefits that accrue in this type of spectroscopy it is necessary to investigate the general theory of the process before considering the advantages arising from the use of picosecond pulsed lasers in the experimental system described in this paper.

GENERAL THEORY OF RAMAN AMPLIFICATION

The propagation of light waves in a medium is by the wave equation for the electric field of the radiation, E,

where PNL is the non-linear polarisation, n the refractive index and c the velocity of light. For consideration of Raman amplification spectroscopy

(2)

where k and o are the wavevector and frequency of the light field, respectively, the 0 and -1 subscripts refer to the higher and lower laser frequencies, and C.C. represents the corresponding complex conjugates.

~ ( z , t ) =+{EO exp [i(koz - - o o t ) l + ~ - ~ exp [i(k-lz -o-lt)l+c.c.)

The non-linear polarisation is written as2

pNL(z, t) = ${P,"" exp (-ioot> +~p.Jk exp (-io-lt) + c.c.1.

From eqn (1) - (3) one obtains (3 1

with an equivalent expression for the higher-frequency laser field Eo. In the absence of this non-linear polarisation, homogeneous plane waves in the

medium propagate independently of each other.4 The non-linearity of the medium provides a coupling between different homogeneous waves, the lowest-order non- vanishing term being a cubic function of the electric-field amplitudes. x ' ~ ) , the third-order non-linear susceptilility, is a complex fourth-rank tensor with elements ~ $ 2 , which depend on the frequencies present. The itB Cartesian component of

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the non-linear polarisation at the Stokes frequency is given by5

( 5 )

The subscripts i, j , k and 1 denote the polarisation directions of the generated and incident electric fields. The expression for the non-linear polarisation at the Stokes frequency given by eqn ( 5 ) can be shown to lead to an exponential change of the Stokes wave according to

NL (3) P-ii = C xijkl(-@-l, 00 , -00, W - l ) E O j E ; k E - 1 [ exp ( i L z ) .

jk l

for parallel polarisations of the two incident beams w o and o - ~ . Integration of this expression leads to a growth of the Stokes wave

where z is the distance traversed by the beams through the Raman sample and E t l is the amplitude of the incident wave.

For small signal gains which is certainly the case in studies of Raman amplification spectroscopy using continuous-wave laser sources, the amplitude of the signal wave generated at wP1 is obtained from eqn (7) as

The signal generated at the Stokes frequency, here regarded as the probe laser, is modulated at any frequency impressed on the pump laser, 0 0 . (Methods of recording gain at the Stokes frequency generally involve an amplitude or polarisation modula- tion of the pump beam oo at a frequency f, the appearance of gain at frequency o - ~ being recorded by means of lock-in detection methods tuned to frequency f.) In this situation, heterodyne detection is intrinsically a part of the mixing process.

Neglecting incoherent background radiation, the intensity of radiation incident on a 'square-law' detector in a Raman-gain experiment is6

where EL': and I?': are the amplitude and intensity of the background, local- oscillator radiation which adds coherently to the signal at the detector surface. The signal response generated by the detector is proportional, with proportionality constant K, to 1 - 1 integrated over the detector surface. The term I?1 is generally too low to be detected under normal circumstances and the Raman signal of interest is recorded as the heterodyne signal, I", which is separated from the noise generated primarily by the local oscillator through the modulation impressed on the pump laser o0. The signal response is given by the real part of IH1 as

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868 RAMAN AMPLIFICATION SPECTROSCOPY

The local oscillator and signal amplitudes in this expression are provided from the amplified signal at w - ~ emanating from the gain cell. EL': is very nearly equal to El of eqn (8) (if it is assamed that all of this radiation falls on the detector), giving the signal response of the detector as

Since the intensity and amplitude of a wave are related by the expression I = ncE2/87r, eqn (11) reduces to

The fractional intensity increase of the Stokes beam is given by

81-1 s-1 1 9 2 ~ ~ 0 - 1 1 - 1 KI-1 non-lc

( i , y~~ / I~ ) ( r ) z . -- - -- -

The third-order susceptibility of eqn (1 3) contains contributions from non-resonant processes in addition to the resonant two-level Raman process. These non-resonant processes are collectively labelled ,y NR, and

where xFkl is the Raman contribution to the third-order susceptibility. This Raman contribution is given by2,'

where N is the number of molecules per unit volume, A the fractional population difference (N, - N b ) / N between the two states a and b involved in the Raman transition of frequency wR, and I' the full width at half-maximum for the spontaneous Raman line. The Raman matrix elements, ajj, relate to the differential spontaneous Raman scattering cross-sections.

For liquids and gases the susceptibility is averaged over all orientations of the molecules. The Raman matrix elements, aij, relate to the integrated spontaneous Raman scattering cross-section, (da/dfl)ij, by5

the horizontal bar indicating an average over all molecular orientations. In the usual experimental conditions employed in Raman-gain spectroscopy the

pump (w0) and probe (0-1) lasers are polarised in the same direction, the relevant Raman susceptibility term being given by

and the susceptibility term of eqn (13) by

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The total third-order susceptibility of eqn (18) contains real and imaginary parts

The imaginary part is due entirely to the Raman contribution and leads to a Lorentzian profile as expressed by eqn (196). Introduction of xi;! of eqn (18) into eqn (13) leads to the following equation for the fractional change of the intensity of the Stokes laser

This fractional change of the probe laser intensity is represented by the gain coefficient, g, given by

I-l = IYI exp (gIoz) (21) where g is given in terms of the Raman cross-section at the peak of the Raman transition by

32~’c’YA (”) hnon- lo - l r dfl ii

gpeak =

and in terms of the appropriate susceptibility component by

The gain coefficient g of eqn (22a) and (22b) is positive, the third-order susceptibil- ity term having a negative imaginary part which leads to the gain coefficient of eqn (22a).

For parallel polarisations of the pump and probe beams the imaginary part of x(3i is accessed with gain coefficient at the peak of the transition being given by eqn (22a), the depolarised component in a normal Raman scattering experiment being recorded in this type of spectroscopy by the use of crossed polarisations of the two incident beams. Additionally, however, it is possible in Raman-gain spectroscopy to derive information on the real part of the susceptibility given by eqn (19a) by using a circularly olarised pump beam with the linear or elliptically polarised probe beam.6” Maier records the spectral line shapes corresponding to the real and imaginary parts of x ( ~ ) given by eqn (19a) and (19b) and Owyoung’ displays the corresponding features observed in an experimental study of the Qol (1) transition in the Raman spectrum of gaseous hydrogen at a pressure of 2.5 atm.?

The gain coefficient shows that the enhancement in the intensity of the Stokes beam is linearly dependent on the spontaneous Raman scattering cross-section and, unlike the Raman scattering process, dependent on the population difference between the states involved. Since the spontaneous Raman line width, r, appears in the denominator of this expression it is clear that the process is ideal for the investigation of species displaying very narrow spectral lines in gases or low- temperature solids.

?

+ 1 a t m s 101 325 Pa.

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870 RAMAN AMPLIFICATJON SPECTROSCOPY

At the same time as there is observed an exponential increase of the Stokes wave [eqn (21)] there is an exponential loss at the-higher-frequency laser governed by4

lo =I : exp (-U.-lz) (23) where the loss coefficient, I , is related to the gain coefficient, g, by

The signal contribution outlined above has been derived in terms of the incident intensities of the probe and pump beams. In this formulation the signal is linearly dependent on the interaction length z . In practice, however, it is found that for physically realizable path lengths that can be produced with collimated laser beams the intensity gain (or loss) is so low that it is preferable to generate gain in the vicinity of the focus of the laser beams. The interaction length is then very short but the intensity (power per unit cross-sectional area) is extremely high and since the signal strength depends on the product intensities of the two laser beams this increased intensity more than compensates for the decreased length of the interac- tion zone. In practice it is found that the greater part of the gain (or loss) is produced in the vicinity of the focus of the two beams (assumed to be focussed together through the sample). The fractional gain at this focal region is given from eqn (21) and (226) (taking the negative imaginary part of the third-order non-linear susceptibility) with the angular frequency o replaced by 27rcV, where C is the corresponding wavenumber (in cm-l units) as

I. = P0/rW', and z is the confocal beam parameter 2.rrWino/Ao, Wo being the spot radius of the focussed pump beam of wavelength Ao. Po, the power of the pump beam, is expressed in ergs-' in this formulation. Owyoung and Percyg evaluated the negative imaginary part (x !:!)(i) of the third-order Raman susceptibility of the v 2 mode of benzene as 15.9 x cm3 erg-'. Using this value of the Raman susceptibility it is instructive to evaluate the fractional change of the intensity of a helium-neon probe laser under the influence of a pump beam of average power 50 mW in a sample of benzene liquid at the resonance condition (oR = 00 -0-1).

One assumes 2 mm diameter laser beams focussed by a lens of 20 mm focal length, the corresponding spot radius being 4.0pm and the confocal beam parameter [z in eqn (25)] 0.24 mm. With VF1 = 15 800 cm-' and assumed values of n-1 and no of 1.46 the average signal gain is found to be 1.1 x lop5. The gain measured experimentally by Owyoung and Jones" at the peak of this Raman transition was 1.75x1Op5, implying that the most significant part of the signal (ca. 60%) is produced in the focal region of the laser beams.

A more precise evaluation of the overall gain has been carried out by Owyoung and Jones" and by Barrett and Heller' by integrating the intensity-dependent gain through the focal region of the beams (assuming Gaussian beams). A relationship is obtained which, to a good approximation, is independent of focussing and linearly dependent on pump power

(26 j

providing the sample region of the two beams is entirely enveloped by the sample.

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It will be appreciated that the fractional change of the intensity of the probe laser is extremely small (only 1.75 x lo-' for a strong transition such as the v2 'breathing' mode of liquid benzene). To record such a small change of intensity of the probe laser it is apparent that a low-noise probe laser is likely to be essential. It is apparent from eqn (12) that the signal response of the detector is linearly dependent on the pump intensity and on the probe intensity at the detector surface. Levenson and Eesley6 considered the various terms contributing to the noise from the detector and identified the principal components as arising as a result of fluctuations in the probe laser intensity with mean-square values

( H 2 1 ) = k- l I$ , (81E)kBI; (27)

where J k - l is the root-mean-square fractional deviation of the probe laser intensity from its average value and (Hi) represents the mean-square fluctuation of the intensity of the background which adds incoherently to the local oscillation wave. In the experimental methods generally employed for the study of Raman amplification spectra this latter component can be neglected, although it acquires relevance in techniques such as optical heterodyne Raman-induced Kerr-eff ect spectroscopy7 (OHD-RIKES). Additionally, as a result of the quantised nature of radiation, there is shot noise at the detector with a mean-square value

where i is the intensity associated with a single photon. Considering the signal response generated by these intensity fluctuations the signal-to-noise ratio for this type of experiment as a whole can be written

The last term in the denominator arises from external noise factors including thermal noise in the detector load that would arise in the absence of any optical signals, and Q is the detector quantum efficiency. Levenson6" has considered the methods available for optimizing the local-oscillator intensity to maximize the signal-to-noise ratios for various non-linear optical techniques.

For a fixed sample and fixed pump and probe laser wavelengths the gain or loss realizable is dependent only on the pump power, as is the signal-to-noise ratio when probe-laser fluctuations dominate the noise contributions [i.e. k-lI"_: > iI"_,/Q and q in eqn (29)]. The ultimate sensitivity limit, however, is attained when shot noise dominates all other noise contributions and the signal-to-noise ratio scales as POP!? (in Raman gain). Under such circumstances improved signal-to-noise ratios may be obtained not only by increasing the pump power but also by increasing the probe power incident on the detector. However, this latter method of improving the signal-to-noise ratio tends to be of limited value because of the increasing difficulty of attaining shot-noise-limited performance with increas- ing probe power and because of the inability of detectors to handle powers substantially in excess of 10mW. At this power level, with a detector of 10% quantum efficiency at 633 nm, the minimum signals detectable with a 1 : 1 signal-to- noise ratio correspond to a gain (or loss) of ca. 2 x This sensitivity limit would lead to a signal-to-noise ratio of ca. 900: 1 for the v 2 vibration of liquid benzene under the conditions stated.

Even allowing for the attainment of near shot-noise-limited performance, the signal-to-noise ratio attainable by the simple procedures implied in the above

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872 RAMAN AMPLIFICATION SPECTROSCOPY

discussion for a strong Raman transition is not great. There is no possibility of reducing the noise below the shot limit, so that methods of improving signal to noise in this branch of spectroscopy depend on means of enhancing the signal from the detector. Since the signal intensity depends on the product of the powers of the two lasers employed it is clear that it is advantageous to use in place of high-power continuous-wave lasers pulsed lasers exhibiting high peak powers but relatively low average powers (to avoid excessive sample-heating effects). Regrett- ably, high-power pulsed lasers rarely have the very narrow spectral line widths necessary for the investigation of rotational structures of vibrational bands at very high resolution. Owyoung" overcame this disadvantage by amplifying the output from a single-frequency C.W. dye to megawatt power levels by means of a laser amplifier pumped by the frequency-doubled pulses from a Nd/YAG laser, thereby attaining an improvement of ca. lo3 over the C.W. methods previously employed. An alternative approach to that adopted by Owyoung, but designed for the study of condensed phase species at lower resolution (ca. 1-2 cm-I), also takes advantage of the increase in signal strength from the use of pulsed, in place of continuous-wave, lasers.

RAMAN AMPLIFICATION SPECTROSCOPY USING PICOSECOND LASERS

Current generations of commercially available lasers include mode-locked ion lasers which provide a continuous train of pulses exhibiting high peak powers but relatively low average powers. Typical characteristics of the ion laser are a repetition rate of 82 MHz and a pulse duration of 100-200 ps. The peak power in the pulses is thus raised by a 'factor of ca. 100 over the average output power (which is typically in the region of ca. 1 W). When such a laser is used to pump tunable dye lasers a synchronously pumped mode-locked dye laser can be produced in which the output dye laser pulses are synchronized with the output pulses from the ion laser, but individual dye laser pulses are reduced in duration to ca. 20 ps (transform limited for a laser line width of ca. 1 cm-l). The peak power in the 82 MHz pulses is thus raised by a factor of ca. 1000 over the average dye-laser output. With an average output power of ca. 100 mW the peak power is thus increased some three orders of magnitude over the powers typically employed in a C.W. Raman-gain or inverse- Raman experiment. To appreciate the benefit of the use of such lasers it is necessary to compare the signal generated in a continuous-wave experiment

S'" = c""p"d"p"_"1 (30)

with the average signal, S"", generated using picosecond lasers. Since the average power of a train of laser pulses relates to the peak power by the expression

R T (31) p a " = ppulse

where R and T represent the pulse repetition rate and pulse duration, the pulsed signal generated (assuming both lasers to be pulsed) relates to the average power of the pump and probe lasers by

Cpulse is distinguished from C"", the steady-state gain or loss factor, since it does not necessarily follow that these two proportionality constants are identical. With

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such rapid-repetition-rate lasers it is possible to use phase-sensitive detection methods and use detection bandwidths which are extremely small <1 Hz) in

this does not lead to improved signal-to-noise ratios). Under such circumstances the average signal power is relevant rather than the peak signal power, SPulse, of eqn (32). This average signal power depends on the pulse repetition rate Rs and r, at which the signal pulses are generated.

comparison with those used in the quasi-c.w. experiments of Owyoung' i (although

Using two synchronously pumped dye lasers, pumped by the same mode-locked ion laser, so that Ro and RP1 are identical, a signal pulse is generated each time a pump and probe pulse coincide. Eqn (33) then reduces to

PyP"_"1/Rr (34) S"" = CPulse

where the pump and probe pulses are assumed to have the same time duration as well as, of course, the same repetition rate. The enhancement of the signal produced over the signal produced by the use of C.W. lasers is thus

For the same average powers employed using pulsed laser excitation as compared with C.W. excitation the enhancement in the signal is ca. lo3 providing the pulsed gain (or loss) does not differ markedly from that attained in the C.W. experiment. At the shot-noise limit the ultimate noise figure is determined by the number of photons incident on the detector in unit time, i.e. on the average power incident on the detector rather than on any function of the pulse power. As a result, the enhancement in signal leads to a corresponding increase in the signal-to-noise ratio providing shot-noise-limited detection is attained.

Levine et a1.l' have considered the relationship between the pulsed gain in comparison with the C.W. gain as a function of the Raman relaxation time and the duration of the pump and probe laser pulses. For a band such as v 2 of benzene with pump and probe pulses of ca. 20 ps duration Cpu'se/Ccw ~ 0 . 4 , so that the enhancement in signal-to-noise ratio expected is ca. 250. In consequence of this dramatic signal enhancement Levine and Bethea13 were able to obtain a signal-to- noise ratio of ca. 200000 for the 992cm-' Raman band in bulk benzene. By introducing a double modulation (amplitude and frequency modulation) of the pump laser these authors show how it is possible to reduce the large thermal background produced by absorbing substrates by a factor of lo3-lo4, thereby permitting the full use of the ultra-high sensitivity which, seemingly, is sufficient to observe vibrational spectra of adsorbed monolayers. l4

It is interesting to observe that the enhancement in signal produced by the use of these pulsed lasers produces a fractional change of the probe laser intensity of ca. 0.1% for a transition such as the 992 cm-' band of benzene, so that further dramatic increases of pump beam power would lead to the onset of saturation effects in the signals generated.

In the experiments described in this paper the two lasers employed are a synchronously pumped mode-locked Rhodamine 6G dye laser as probe laser (R = 82 MHz, r == 20 ps) and a cavity-dumped and/or synchronously pumped mode- locked DCM laser as pump laser (R = 4 MHz, r = 20 ps). Since only one in twenty

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874 RAMAN AMPLIFICATION SPECTROSCOPY

A

ME LASER 1

Fig. 2. The picosecond Raman amplification spectrometer. A, mode-locked synchronously pumped dye laser; B, mode-locked synchronously pumped and cavity-dumped dye laser; L, lenses; M, mirrors; BS, beam splitter; P, polarizer; CC, corner cube retroreflector;

PD, photodiode.

of the synchronously pumped laser pulses coincide with each of the cavity-dumped pulses, signal is generated only at a rate of 4 MHz so that the average enhancement over the C.W. system is precisely the same as for the system employing two synchronously pumped dye lasers for the same average laser powers.

EXPERIMENTAL ARRANGEMENT

The experimental apparatus employed in the study of Raman amplification spectra using picosecond lasers is displayed in fig. 2. The drive laser in these experiments is a mode-locked Spectra Physics model 17 1 argon-ion laser producing >1 W average power at 514.5 nm in a mode-locked continuous train of pulses, each pulse being of duration ca. 200 ps with a repetition rate of 81.8 MHz. The output of this laser is split into two beams of nearly equal intensity by beam splitter BS1, these two beams being employed to pump synchronously two dye lasers, A and B. Dye laser A is operated with Rhodamine 6G dye to scan the wavelength range 570-630nm, dye laser B using DCM dye to scan from 600 to 700nm. Bx this combination of dyes it is possible to scan the Raman interval 0-3300cm- with relatively little inconvenience. Dye laser A is employed simply as a mode- locked synchronously pumped laser with a 15% output coupler, giving a 81.8 MHz pulse train at an average power of 30-100mW and pulse durations of 5-2Ops depending on the particular conditions employed. Laser B on the other hand can be employed similarly by using mirror MI as the end mirror of the dye-laser cavity, or as a mode-locked cavity-dumped laser giving pulses of 3 2 0 p s duration at a preselected repetition rate ~4 MHz. (Conversion from cavity -dumped operation to synchronously pumped operation is readily achieved by removing the folding mirror of the cavity dumper.)

The output beams from the two dye lasers are collimated and matched by telescopes formed by lenses L1 - L4, and the beams, after the introduction of suitable time delays by means of mirrors M2 and M3 and the corner cube retroreflector CC, are combined at the beam splitter BS2. Lenses Ls and L6 focus the combined

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1

I

.d

cd M

c cd

5 d

m - 0"

2 C cd

E

I 1 I 1 t 1 I 1 I I I

4 00 200 0 200 400 Raman shift/cm-'

Fig. 3. The inverse-Raman/Raman-gain spectrum of carbon tetrachloride liquid. For this spectrum beam splitter BS, of fig. 2 was a plane glass plate. The intense feature near zero shift arises from pump laser radiation transmitted by the monochromator; with an appropriate

experimental arrangement this feature may be removed totally.

beams through the Raman sample in an appropriate cell and subsequently onto the entrance aperture of the double monochromator, which serves to separate the pump and probe beams. The probe beam is incident on a UDT PIN 5D or 6D silicon photodiode, PD, connected to a fast (70MHz) preamplifier and the low- impedance output fed into a EG and G model 5202 lock-in amplifier with a frequency response of $50 MHz. The output from the lock-in amplifier is fed to a two-pen recorder, the second channel of which is driven by the in-quadrature output of the lock-in amplifier or, alternatively, by the output of an optogalvanic detector used for calibration purposes. In all experiments the synchronously pum- ped dye laser A serves as probe laser and operates at a fixed wavelength, the scannable DCM dye laser B serving as pump laser. Suitable amplitude modulation of the pump laser up to 10 MHz is achieved by the use of an electro-optic modulator driven by an r.f. oscillator and amplifier (Electro-optic Developments Ltd, VLA30) when the system is employed with two synchronously pumped lasers of the same repetition rate, or without further modulation when used with dye laser B in the cavity-dumped mode. In the latter case, since only one pulse in 20 of the cavity- dumped laser (at a repetition rate of 4 MHz) coincides with a synchronously pumped laser pulse from dye laser A, it is enough to feed the trigger pulses from the cavity dumper driver to the model 5202 to achieve satisfactory performance of the lock-in amplifier. The average output power of dye laser B is significantly greater when synchronously pumped as compared with the cavity-dumped output (ca. 100 mW as compared with ca. 30mW), but since in the former case it is also necessary to modulate the beams the average modulated power incident on the sample is not too dissimilar in the two cases.

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876 RAMAN AMPLIFICATION SPECTROSCOPY

Whether one records a Raman-gain spectrum or an inverse-Raman spectrum depends entirely on the relative wavelength values selected for the two lasers. This situation is demonstrated in fig. 3, which displays on one side the Raman-gain spectrum of liquid carbon tetrachloride and on the other side the inverse-Raman spectrum recorded on one continuous scan of the DCM dye laser with the Rhodamine 6G synchronously pumped dye laser A set at 614nm. (For this experiment beam splitter BS2 is simply a thick optical flat, the only disadvantage of this arrangement being the relatively low reflectivity of the probe beam, ca. lo%, with a consequent reduction of ca. 3 in the attainable signal-to-noise ratio.) With this particular set of dyes it is possible to record Raman-gain or inverse-Raman spectra for low-wavenumber Raman shifts ( 4 0 0 cm-'), but only inverse-Raman spectra for the larger-wavenumber shifts. This particular combination was selected deliberately since it is for the larger-wavenumber shifts that one expects the greater rejection of the inverse-Raman method against fluorescence effects to be of the greatest value. (It should be remembered in assessing these spectra that the loss or gain measured depends, since this is an overall absorption process, on the population difference of the two states involved in the transition.)

PERFORMANCE OF THE RAMAN SPECTROMETER

Probably the most difficult aspect of the study of Raman amplification spectra arises from the problems of attaining near shot-noise-limited performance from notoriously noisy lasers. Problems arising from the synchronisation of the laser pulses can generally be resolved given suitably stable laser systems, as can the problems associated with matching the temporal profiles of the laser pulses. The problems associated with laser noise, however, are often outside the experimenters' control, and although noise sources such as bubbles in the dye laser jet stream or mode competition effects can, with care, be reduced significantly they can rarely be totally eliminated. Recently Levine and BefhiaI3'l4 have measured the probe laser noise of a synchronously pumped mode-locked dye laser on a spectrum analyser and found a broad minimum from ca. 3-20 MHz, with the noise at 10 MHz being ca. 3 orders of magnitude less than at 2 kHz. Use of modulation at 10 MHz allowed these authors to attain near shot-limited performance in their studies with synchronously pumped mode-locked dye lasers, although to approach the theoreti- cal limit they still found it necessary to introduce an intracavity etalon to eliminate laser mode fluctuations. Our experience confirms the observations of these authors, although we did not find it necessary to introduce the intracavity etalon to reduce the laser noise. The use of an intracavity etalon is of value, however, in decreasing the spectral line width of the probe laser and increasing the pulse duration, thereby enabling the user to match the time duration of the shorter probe laser pulse to the longer pulse of the cavity-dumped laser and at the same time to improve the spectral resolution. With 1 mW of probe laser power incident on a detector of ca. 50% quantum efficiency the fractional noise present at the shot noise limit is ca. 3.5 x decreasing to ca. 1.1 x lop8 for an incident power of 10 mW, these factors setting the limit to the signal-to-noise ratios attainable. In practice we found these noise levels difficult to attain using the two synchronously pumped lasers, in part because of the appearance of an 82MHz modulation on the output of the probe detector. Introduction of an electronic filter with a low-frequency cut-off at ca. 3.5 MHz and a high-frequency cut-off below 80 MHz served to solve this problem satisfactorily and allowed near shot-noise-limited performance to be obtained routinely. The only remaining problems we have observed in using the

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two synchronously pumped lasers have arisen from pick up of r.f. energy from the oscillator-amplifier-modulator combination, although this can be eliminated with appropriate screening.

In our experience attainment of shot-noise-limited performance with the syn- chronously pumped-cavity-dumped arrangement has not been so easy to achieve. In part this is because the appropriate modulation frequency with this arrangement is 4MHz rather than the 7MHz generally employed when using the two syn- chronously pumped lasers. Rather more significant, however, is the difficulty of obtaining a satisfactory trigger pulse for the lock-in detector. Use of a trigger pulse from a fast photomultiplier activated by the 4 MHz pulses from the cavity-dumped dye laser was found to be unsatisfactory, presumably because of amplitude fluctu- ations in the output from the laser. The synchronous output from the cavity-dumper driver gave far more satisfactory performance although certain difficulties remained. The trigger pulse from the cavity-dumper driver effectively opens a shutter in the cavity-dump laser which dumps out the next available pulse in the circulating mode-locked train of pulses. The trigger pulse is thus not locked rigidly to the mode-locked train of pulses of the probe laser. Use of a photomultiplier as probe detector which is suitably fast to resolve the individual pulses of the mode-locked train leads to a marked periodic ‘noise’ with genuine noise superimposed. This periodic ‘noise’ arises from the temporal uncertainty between the probe laser pulses and the trigger pulses and is largely eliminated when using the silicon photodiodes in place of very much faster photomultiplier. Remnants of this periodic ‘noise’ are eliminated by means of the filter referred to above allowing performance reasonably close to the shot-noise limit. To date the best noise figure achieved (with two synchronously pumped lasers) is ca. 2.5 x lo-* with ca. 2 mW average power on the probe detector.

The signal loss generated in these experiments depends on many factors, the pump beam power, the temporal profiles of the pump and probe lasers, the relative temporal stabilities of the two lasers and the optical matching of the beams. Of these factors the temporal profiles of the beams and the relative stabilities of the laser pulses are undoubtedly the most important. The pulse durations are measured by a Michelson-type autocorrelator constructed as part of this project. The output of the Michelson is frequency doubled and the U.V. output recorded as a function of the optical path difference in the Michelson interferometer. With proper align- ment of the synchronously pumped lasers, transform-limited pulses are obtained of ca. 10 ps duration, the spectral line width being determined by the three-plate birefringent filter employed for wavelength selection. The relative temporal stability is readily determined since the Raman process under investigation is a natural probe of the degree of coincidence of the pulses of the two lasers. By displacing the corner cube retroreflector (CC in fig. 2) along its axis while monitoring the Raman loss or gain one is able to generate a cross-correlation profile. A typical example of such a cross-correlation is displayed in fig. 4, obtained by monitoring the peak intensity of the 992 cm-’ Raman line of liquid benzene as a function of the displacement of the retroreflector. The shape of the peak suggests that the pulses are approximately gaussian with a cross correlation time of ca. 30 ps, fairly typical of the type of profile observed with two synchronously pumped lasers. In general, short pulses are more difficult to obtain with a cavity dumped laser than with a synchronously pumped laser. For such a laser a pulse duration of ca. 20-30 ps is typical with a cross correlation of ca. 50ps when probed with a synchronously pumped laser of ca. 10 ps duration. The spectrum of liquid benzene under condi- tions similar to those employed for obtaining the cross-correlation of fig. 4 is shown

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878 RAMAN AMPLIFICATION SPECTROSCOPY

-40 -20 0 20 40 t/PS

Fig. 4 The Raman cross-correlation profile of two synchronously pumped dye lasers. With the two lasers held at the resonance condition this profile was obtained by delaying one of

the beams with respect to the other.

in fig. 5. The average pump power employed in this spectrum was ca. 10 mW, the probe power on the detector being 1.3 mW and detection time constant 0.: s. The fractional probe power loss recorded in this spectrum is ca. 4.6 x 10- with a fractional root-mean-square noise figure of lo-'. For a 1 s integration time constant this would correspond to a signal-to-noise ratio of ca. lo4. For maximum probe laser loss, careful matching of the beams, both temporally and spatially, is required and to the present the best signal obtained on this transition corresponds to a fractional loss of 1.1 x with 25 mW average pump power, within ca. 20% of the loss calculated from the C.W. data of Owyoung" using the known spectral line widths and pulse durations of our lasers. (The corresponding figure using a syn- chronously pumped probe laser and ca. 15 mW cavity-dumped pump laser power is ca. 6 x Improvements in signal-to-noise ratio over the figure of ca. 40 000 possible with the existing system will follow by increasing the probe and pump laser powers. Improvements currently in train will provide the capability of record- ing spectra with a signal-to-noise ratio > lo5 for this particular transition in benzene. It might be thought that further dramatic improvements in signal-to-noise ratio would be possible by increasing the pump laser power significantly. In practice, however, such improvements, although significant, will not be dramatic for strong transitions because of saturation effects in this absorption process.

The equipment as at present constituted is capable of recording excellent quality spectra of liquid, solution and crystal, spectra with extremely high signal-to-noise ratios at a resolution limit of ca. 3-4 cm-'. Interestingly these spectra are recorded with low average laser powers incident on the sample, typically 20-30mW total

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879

1020 990 970 Raman shift/cm-'

Fig. 5. The inverse-Raman spectrum of v2 of liquid benzene under two different conditions of sensitivity. For both spectra. the average pump and probe powers were 10 and 1.3 mW,

respectively, with a detection time constant of 0.1 s.

power, so that sample heating effects are not likely to be apparent. Even with as little as 1 mW total average power it is possible to obtain very good quality spectra from many liquid and solid samples with relatively short recording times. Further, since the spectra are almost wholly generated in the focal volume of the laser beams, typically a cylinder of dimension ca. 200 p m in length x 10 p m in diameter, it is apparent that very small samples may be investigated. Because of the well defined polarisation characteristics of the laser beams, crystal spectra may be investigated readily. Fig. 6 displays a series of 3 spectra of triglycine sulphate in the range 100-1400 cm-' taken with 3 different orientations of the crystal axes in relation to the polarisation direction of the laser beams. In this series of spectra the two laser beams are polarised parallel to each other. For each of these orientations, by inserting a half-wave plate in the pump beam prior to beam splitter

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880 RAMAN AMPLIFICATION SPECTROSCOPY

ll I

I I

I I l I I I I I 1 I I 1 I

200 500 1000 Raman shift/cm

Fig. 6. The inverse-Raman spectrum of a single crystal of triglycine sulphate for three different polarisations of the laser beams relative to the crystal axes. For all spectra the

pump and probe lasers were polarised parallel to each other.

BS2 it would be possible to determine the depolarisation ratios for each of the transitions recorded in fig. 6. Since these spectra are recorded with a time constant of 0.1 s it is apparent that the technique affords an extremely powerful method of recording complete Raman spectra of oriented single crystals. Additionally, as the sample temperature is lowered towards zero Kelvin and spectral lines decrease in width, the signal-to-noise ratio will improve proportionately so that the technique promises to be of particular value for the investigation of matrix-isolation spectra. That spectra are recorded with lasers at the red end of the visible spectrum is also an advantage since the effects of sample fluorescence are then likely to be sub- stantially less marked.

Typical of the spectra that may be investigated in detail using these techniques are the resonance Raman spectra of the various laser dyes operating in the yellow-

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1 I I I 1 I I I 1 600 1000 1400

Raman shiftjcm-'

Fig. 7. The inverse-Raman spectrum of lop3 mol dmP3 Rhodamine 6G dye in methanol solution. For this spectrum the probe laser was set at 614 nm. The trace above the spectrum

displays the optoacoustic calibration spectrum of an iron-neon hollow-cathode lamp.

red region of the spectrum. The Raman spectra of the various molecular species present in these dye solutions are particularly important because of the use of these dyes in the variety of lasers operating in this region of the spectrum. It is well known that the operating range of many of these dyes is concentration dependent because of the existence of dimeric and higher polymeric species present in the dye solution. Fig. 7 displays a portion of the resonance Raman spectrum of Rhodamine 6G in methanol solution obtained with the probe laser set at 614 nm and the pump laser scanning in the region 633 to ca. 675 nm to span the Raman interval 500 to 1450cm-l. Interestingly the lasers here are set far from the resonance condition and the fractional absorption in the focal distance in which the Raman signal is generated is only 0.003. Investigation of the temporal behaviour of the spectrum establishes that the narrow spectral features occur only during the coincidence of the laser pulses, as would be expected of resonance Raman spectra, but the broad feature at low-wavenumber shifts exhibiting gain rather than loss can occur outside the temporal coincidence of the laser pulses and is clearly associated with absorption-emission processes in the dye under the influence of the probe and pump lasers. This gain signal is absent when the probe laser precedes the pump laser, rising rapidly at coincidence and subsequently decaying with an exponential decay of half-life ca. 1OOps as the probe laser is delayed from the pump. Moving the two lasers to shorter wavelengths by ca. 20nm enhances the intensity of the peaks even though the concentration is reduced to mol dm-3, presumably because the lasers are moved closer to the resonant absorption of the

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882 RAMAN AMPLIFICATION SPECTROSCOPY

species and the enhancement is increased significantly. A similar spectrum to that displayed in fig. 7 was recorded by Lau et U L . ' ~ using a pulsed nanosecond ruby laser as pump laser, the spectrum being recorded against a background continuum synchronised with the pump laser. The inverse-Raman signal is enhanced in this experiment by several orders of magnitude into the observational range for this photographic process since the pump laser is introduced into the cavity of the probe laser and the pump laser peak power is substantially greater than in our experiments. In a recent publication comparing the Raman detection limit for continuous-wave inverse-Raman and CARS techniques at excitation near molecular one-photon resonance, Pfeiff er et a1.I6 suggest that the background contribution arising from the scattering molecules themselves will determine the maximum attainable signal- to-noise ratio and such effects may mask inverse-Raman signals near exact resonance while not contributing to CARS. These authors suggest, however, that the station- ary excitation conditions on which their theory is based may not be applicable with picosecond lasers with pulse durations shorter than the longitudinal relaxation times in the dye solution. Our observations would certainly tend to support the latter suggestion since it is apparent that with shorter wavelength excitations species concentrations many times lower than the mol dmP3 concentration limit used in the present study will give extremely good signal-to-noise ratios in these reson- ance Raman spectra.

There are many areas other than those described above in which the high sensitivity of these picosecond Raman techniques will prove to be of particular value, but none of greater potential than for the study of surface-adsorbed species at gas/solid and even liquid/solid interfaces. There are few techniques currently available for investigating the nature of the surface-adsorbed species in the environ- ment of the working catalyst, or for probing the species present at the electrode surface in an electrochemical cell. To investigate such spectra will prove a formi- dable task even with the potential sensitivity of these picosecond laser techniques, but the characteristics of the methods of inverse-Raman spectroscopy lend them- selves to studies of this sort. Current studies with this equipment are concerned with investigations of single-crystal and resonance Raman spectra of laser dye materials, but as the modifications to the equipment allow, the investigations will be extended to the study of surface-adsorbed species when the full benefits of this new spectroscopic technique are likely to become apparent.

We are indebted to the S.E.R.C. for the award of research grants with the aid of which the equipment described in this paper was developed.

W. J. Jones and B. P. Stoicheff, Phys. Reu. Lett., 1964,13, 657.

L. A. Rahn and P. L. Mattern, Laser Spectroscopy, 1978. 158, 76. N. Bloembergen, A m . J. Phys., 1967, 35, 989. J. J. Barrett and D. F. Heller, J. Opt. SOC. Am., 1981, 71, 1299. M. D. Levenson and G. L. Eesley, A p p l . Phys., 1979, 19, 1 . M. D. Levenson, J. Raman Spectrosc., 1981, 10, 9. A. Owyoung, Opt. Lett., 1978, 2, 91. A. Owyoung and P. S. Percy, J. A p p l . Phys., 1976,48, 674. A. Owyoung and E. D. Jones, Opt. Lett., 1977, 1, 152. A. Owyoung, in Laser Spectroscopy IV, ed. H. Walther and K. W. Rothe (Springer-Verlag, Berlin, 1979), p. 175. B. F. Levine, C . V. Shank and J. P. Heritage, IEEE J. Quantum Electron., 1979, QE-15, 1418. B. F. Levine and C. G. Bethea, IEEE J. Quantum Electron., 1980, QE-16, 8 5 .

* M. Maier, A p p l . Phys., 1976, 11, 209.

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B. F. Levine and C. G. Bethea, A p p l . Phys. Lett., 1980,36, 245. A. Lau, W. Wernelle, M. Pfeiffer, K. Lenz and H-J. Weizmann, Kwantowa Elektronika, 1976, 3, 739. M. Pfeiffer, A. Lau, W. Werneke and L. Holz, Opt. Commun., 1982, 41, 363.

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