August 15, 1998 / Vol. 23, No. 16 / OPTICS LETTERS 1319

Optical heterodyne detection of laser-induced gratings

A. A. Maznev and K. A. Nelson

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

J. A. Rogers

Lucent Technologies, Murray Hill, New Jersey 07974

Received May 8, 1998

A novel optical arrangement for heterodyne detection of laser-induced gratings based on the use of aphase mask for both excitation and probe beams provides phase stability and control without the need foran active stabilization scheme. The arrangement greatly simplifies the laser-induced grating experiment.The performance of the technique in both transmission and ref lection geometries is illustrated throughmeasurements of bulk and surface acoustic waves generated by picosecond laser pulses. 1998 OpticalSociety of America

OCIS codes: 300.6310, 300.2570, 300.6500, 050.0050.

Laser-induced dynamic grating spectroscopy1 is a pow-erful time-resolved optical technique that is widelyused to study a broad range of phenomena suchas molecular and lattice vibrations,2 bulk and sur-face acoustic waves,3 – 5 and relaxation and transportprocesses. In this technique, two interfering laserbeams are crossed in the medium to produce spa-tially periodic material excitations that are monitoredthrough diffraction of a third (probe) laser beam. Thediffracted signal has the attractive feature of beingbackground free in the sense that in the absence of exci-tation there is no diffraction of probe light. However,detection of small signals by this method is diff icultbecause the diffraction efficiency is normally propor-tional to the square of the material excitation ampli-tude. Therefore the potential benefits of heterodynedetection that can be used to amplify the signal havelong been recognized.1

In the heterodyne scheme, a fourth (local oscillatoror reference) beam that is collinear with the diffractedprobe beam is introduced. The coherent interferenceof reference and diffracted beams results in an outputsignal intensity given by

IS ­ IR 1 ID 1 2p

IR ID cos u , (1)

where ID and IR are diffracted signal and reference in-tensities, respectively, and u is the phase difference be-tween their respective optical fields. For IR .. ID thesignal of interest is given by the third term in Eq. (1)because the first term is constant and the second isnegligibly small. Thus the signal is proportional tothe square root of IR , and one can increase it in magni-tude simply by increasing the reference beam intensity.This procedure can help to overcome noise that is dueto the detection electronics and, more importantly, toparasitically scattered light. Other advantages of het-erodyne detection are signal linearity with respectto the material response amplitude and retention ofphase information that would otherwise be lost.6 – 8

There are diff iculties in practical implementationof the heterodyne detection technique. The phasedifference u must be stable, a condition that is normally

0146-9592/98/161319-03$15.00/0

ensured by an active stabilization scheme that uses amirror mounted upon a piezoelectric transducer witha separate optical arrangement to provide feedback,1,8,9

which may require a separate laser source.8 In experi-ments with femtosecond time resolution7,8 care must betaken to avoid a time delay between the probe and thereference pulses. Another practical problem is thatthe diffracted and reference beams should be strictlycollinear to ensure the coincidence of their phase fronts;with weak diffraction levels, this requirement createsadditional alignment challenges.

The difficulties mentioned above have severelylimited the use of heterodyne detection in transientgrating measurements. Although attempts have beenmade to f ind an alternative to the introduction of areference beam, e.g., through heterodyning of the dif-fracted signal that arises from the material responseof interest with additional diffraction from a thermalgrating induced by the excitation pulses6 or throughheterodyning with light scattered parasitically fromsample imperfections,10 the need for a more widelyapplicable solution is obvious.

In this Letter we present a simple optical arrange-ment that makes optically heterodyned transientgrating spectroscopy simple and attractive. The keyfeature of our optical arrangement, presented in Fig. 1,is the use of a diffraction grating (referred to belowas a mask, to distinguish it from the laser-inducedgrating in the sample) to produce the excitation, probe,and reference beams, as suggested in Ref. 11. Themask is designed to optimize the diffraction efficiency

Fig. 1. Optical arrangement for heterodyne detection oflaser-induced gratings in transmission geometry.

1998 Optical Society of America

1320 OPTICS LETTERS / Vol. 23, No. 16 / August 15, 1998

of incident light into the f irst s61d diffraction orders.Upon diffraction of both excitation and probe beams bythe mask pattern, first-order diffraction maxima arerecombined by a telescope that images the mask pat-tern onto the sample, while all other diffraction ordersare blocked by a spatial f ilter. As a result, there arethe usual two excitation beams and also two (ratherthan the usual one) probe beams, of which one servesas the actual probe while the other is attenuated by aneutral-density filter and used as a reference beam.

Interference between the excitation pulses resultsin a periodic intensity pattern and associated materialexcitation grating characterized by the wavelengthL ­ ML0y2, where L0 is the period of the phase maskand M ­ f2yf1 is the magnification ratio of the imag-ing system. Provided that the magnification M is thesame at the excitation and the probe wavelengths, theprobe and reference beams of wavelength lp alwaysenter the sample at an angle wp that satisfies theBragg diffraction condition, sin wp ­ lpy2L. Thischaracteristic by itself offers substantial advantagesfor alignment of transient grating experiments inthick samples where probe beam diffraction occurs inthe Bragg regime. More important is the fact thatthe diffracted probe beam is automatically collinearwith the reference beam; i.e., no additional alignmentis needed for heterodyne detection. The excitationand probe beams are merely made collinear andoverlap at the mask pattern. In fact, a finite anglecan be introduced between the two beams incidentupon the mask in the vertical plane perpendicular tothe drawing, which yields a vertical separation of thesignal from the transmitted excitation light. Thusthe signal is spatially isolated, even if all the beamshave the same wavelength and polarization. Thebeams then pass through the imaging system onto thesample, and the signal appears. Even quite a weaksignal can be located by eye because it is collinearwith the reference beam.

The relative phase stability of the diffracted and ref-erence beams results from the fact that the excitationbeams are produced by the same mask pattern as thereference and the probe. The optical phase of the dif-fracted probe beam depends on the spatial phase ofthe material excitation grating in the sample. Thelatter is determined by the phase difference betweenthe excitation beams, which is equal to the phase dif-ference between the probe and the reference beams.Consequently, the phase difference between the ref-erence and diffracted probe beams is stable, and onecan control it by varying the optical path length of thereference beam. The optical path can be varied by tilt-ing the filter that attenuates the reference beam orthrough the use of a phase plate.

Thus we have a compact setup that greatly sim-plifies phase-stabilized heterodyne detection oflaser-induced gratings. Additional benef its includesimplicity in finding the signal, the absence of adelay between the excitation pulses, and automaticBragg angle adjustment and the possibility to varythe grating period L easily by switching among maskpatterns with different spacings. Note that, whereasFig. 1 shows the laser-induced grating experiment in

transmission geometry, the setup has also been usedto detect laser-induced ref lection gratings upon thesurfaces of opaque materials.

In both transmission and ref lection geometries,the frequency-doubled output of a mode-locked,Q-switched, and cavity-dumped Nd:YAG laser (pulseduration 100 ps, wavelength le ­ 532 nm, energy100 mJ) was used for excitation and an electro-opticallygated beam from a cw argon-ion laser (pulse duration10 ms, wavelength lp ­ 514 nm, cw power 0.5 W) wasused as a probe. The excitation and probe beams, bothvertically polarized, were focused onto the mask withspherical lenses (not shown in Fig. 1) of focal lengths60 and 40 cm, respectively. To image the maskpattern onto the sample, we used spherical lenseswith focal distances f1 ­ 25 cm and f2 ­ 15 cm. Onthe sample, the laser spot diameter was .150 mm forthe excitation pulses and .100 mm for the probe andreference beams. The heterodyne signal was detectedby a preamplified avalanche photodiode whose outputwas fed into an oscilloscope, with a 1-GHz overallbandwidth of the detection system.

The phase mask had a rectangular profile, introduc-ing a periodic variation of the optical path length equalto ley2. The mask diffracted .75% of the energy intothe two first s61d diffraction maxima at both 532 and514 nm. The mask spacing was 20.5 mm, resulting inthe grating period on the sample of L ­ 6.15 mm.

Figure 2(a) shows the signal obtained in the ref lec-tion geometry with or without heterodyning (i.e., withthe reference beam open or blocked) from a 0.7-mm-thick nickel film on silicon. Optical absorption of theexcitation pulses gives rise to sudden thermal expan-sion at the grating peaks, which launches counter-propagating surface acoustic waves (SAW’s) ofwavelength L that form a standing wave within the ex-citation region. The acoustic and thermal responsesproduce a spatially periodic modulation (ripple) on thesample surface, which acts as a grating and diffractsthe probe light. The signal includes fast (570-MHz)SAW oscillations, slow oscillations that are due toacoustic waves in the air, and a slowly decaying ther-mal grating contribution.5 As expected, the polarityof the heterodyne signal depends on the phase differ-ence between the diffracted signal and the referencebeam. The data shown represent averages over 1000repetitive measurements. The phase stability wasgood, with no visible f luctuations observed during thecourse of the experiment.

Heterodyne detection not only results in an increasein the signal intensity but also provides additionalinformation because of its phase sensitivity. Thisfact is illustrated well through observation of acousticoscillations in a traveling SAW detected with the probeand reference beams moved away from the excitationspot. Heterodyne data that correspond to variousdistances between the excitation and probe beamsare shown in Fig. 2(b). A diffraction signal withoutthe reference beam reveals only the envelope of thetraveling wave, with no time-dependent oscillationsobserved. Note that outside the excitation region weobserved only a SAW signal without contributions fromthe thermal grating (which does not propagate) or

August 15, 1998 / Vol. 23, No. 16 / OPTICS LETTERS 1321

Fig. 2. Ref lection mode measurements on a 0.7-mm-thicknickel f ilm on silicon. (a) Diffraction signal (with thereference beam blocked) and heterodyne signals with phasedifferences between the probe and the reference beams of0± and 180±. (b) Heterodyne signals obtained with variousdistances L between the excitation and the probe beams onthe sample.

Fig. 3. Diffraction signal without heterodyning and het-erodyne signal obtained in transmission mode from a1 mm-thick liquid CS2 sample.

acoustic waves in the air (which do not propagate farbecause of strong damping).

Another example of heterodyne detection is givenby Fig. 3, which shows signals observed from liquidcarbon disulfide in the transmission geometry. Thismeasurement was performed in the Bragg diffractionregime and took advantage of the setting of the probebeam to the Bragg angle by the phase mask. Here, be-sides acoustic oscillations (in this case they are due tobulk longitudinal acoustic waves) and a thermal grat-ing, we observe a peak at t . 0 that is due to thenonlinear polarizability x

s3d1111 that originates from both

nonresonant electronic and molecular orientational mo-tion responses.12 In the heterodyne data the sign ofthe x s3d contribution is opposite that of the thermalgrating. This is so because at the grating peaks (i.e.,the excitation interference maxima) the thermal grat-ing that is due to thermal expansion of heated mate-rial yields minima of the density and refractive index,whereas the x s3d grating yields maxima of the refrac-tive index, in accordance with the positive sign of x

s3d1111.8

In conclusion, the optical arrangement consideredhere offers an effective solution for phase-controlledheterodyne detection of laser-induced gratings. Con-sidering the great simplification in the experimentalsetup and alignment as well as in the signal enhance-ment, this arrangement will be beneficial not onlyfor acoustic measurements but for virtually any laser-induced dynamic grating experiment. In addition, theenhancements in information content that follow fromthe phase sensitivity of the technique offer new impor-tant capabilities such as independent determinationof real and imaginary contributions to the materialresponse.

The authors appreciate stimulating discussions withT. F. Crimmins. This research was supported byNational Science Foundation grant DMR-9710140.

References

1. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-InducedDynamic Gratings (Springer-Verlag, Berlin, 1986).

2. L. Dhar, J. A. Rogers, and K. A. Nelson, Chem. Rev. 94,157 (1994).

3. M. D. Fayer, IEEE J. Quantum Electron. QE-22, 1437(1986).

4. T. Sawada and A. Harata, Appl. Phys. A 61, 263 (1995).5. A. R. Duggal, J. A. Rogers, and K. A. Nelson, J. Appl.

Phys. 72, 2823 (1992); J. A. Rogers and K. A. Nelson,J. Appl. Phys. 75, 1534 (1994).

6. P. Vohringer and N. F. Scherer, J. Phys. Chem. 99,2684 (1995).

7. Y. J. Chang, P. Cong, and J. D. Simon, J. Phys. Chem.99, 7858 (1995).

8. S. Matsuo and T. Tahara, Chem. Phys. Lett. 264, 636(1997).

9. D. W. Pohl, IBM J. Res. Dev. 23, 604 (1979).10. H. J. Bakker, S. Hunshe, and H. Kurz, Phys. Rev. Lett.

69, 2823 (1992).11. J. A. Rogers, M. Fuchs, M. J. Banet, J. B. Hanselman,

R. Logan, and K. A. Nelson, Appl. Phys. Lett. 71, 225(1997).

12. S. Ruhman, L. R. Williams, A. G. Joly, B. Kohler, andK. A. Nelson, J. Phys. Chem. 91, 2237 (1987).