Thermal effects in picosecond optical phase conjugation in soluble polydiacetylene

Volume 57, number 5

OPTICS COMMUNICATIONS

1 April 1986

THERMAL EFFECTS IN PICOSECOND OPTICAL PHASE CONJUGATION IN SOLUBLE POLYDIACETYLENE W.M. D E N N I S and W. B L A U Laser Group, Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland

Received 17 September 1985

Degenerate four-wave mixing of picosecond laser pulses in a polydiacetylene/toluene solution is reported. Phase conjugate reflectivities of 500% and larger are reported. The dominant mechanism is found to be a thermally induced refractive index grating in the solvent.

1. Introduction

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Recently [1] we have demonstrated nonlinear optical phase conjugation via degenerate four-wave mixing (DFWM) utilising two soluble polydiacetylenes as nonlinear media. The nonlinear mechanism for this process was shown to be a resonantly enhanced opti. cal Kerr-effect. This nonlinearity was capabl.e of generating a phase conjugate reflectivity o f 40% at pump pulse intensities o f ~'1 GW/cm 2 combined with picosecond response times. In this letter we wish to report a competing mechanism. In this case phase conjugate refleetivities of up to 1000% were generated. Optical coupling is provided by thermally induced refractive index changes in the solvent. The role o f the polymer in this mechanism is to convert the incident optical energy efficiently into spatial modulation o f the density o f the solvent.

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The nonlinear medium consisted of 3.5 X 10 - 3 Mol/1 solution o f the polydiacetylene depicted in the insert in fig. 1 dissolved in toluene in a 1 mm euvette. A solution o f this concentration has a transmission of 0.5 at ?, = 532 nm [2] (absorption coefficient ot = 690 m - l ) . Optical pulses eharacterised by wavelength ?~= 532 nm pulsewidth r 1, = 180 ps, single pulse energy o f 5

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Fig. 1. Intensity dependence of the phase conjugate peak refleetivity for a polydiacetylene/toluene solution (absorption coefficient of the sample ,~ = 690 m-l). The chemical structure of the polymer used is shown in the insert. mJ and a repetition rate o f 10 Hz, generated by a frequency doubled, amplified modelocked Nd3+:YAG laser were directed onto an experimental set-up sinai371

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lar to that of ref. [1]. Counterpropagating pump pulses were obtained by a retrorefleetion geometry and the probe beam was incident on the sample at an angle of 6 ° to the first pump beam. The ratio of the incident pulse peak intensities I 1 :/2:13 was given by 20:10:1, where I1, I2,I 3 are peak intensities of the first pump, second pump and probe pulses respectively. In order to investigate the dependence of the degenerate four-wave mixing signal (/4) on the incident intensity (I1), a ?,/2-plate/Glan-polarizer combination was used to vary the intensity o f I 1 from 0.5 to 2.0 GW/cm 2. First pump peak intensities are measured from the intensity dependent transmission of di-iodomethane [3]. In order to examine the temporal response of the aaonlinear mechanism, the behaviour of the DFWM signal under conditions of a delayed second pump pulse was observed. This was achieved by translating the retrorefiecting mirror (used for the generation of the second pump pulse) away from the sample cell. To evaluate the non-zero independent tensor elements of the third order effective susceptibility the dependence of the DFWM signal on the incident beam polarization was investigated. Four eases were examined: (a) all incident beams of the same polarization, (b) both pump beams with horizontal polarization and the probe beam with vertical polarization, (c) first pump and probe beam with horizontal polarization and second pump beam with vertical polarization, (d) second pump beam and probe beam vertical and the first pump horizontal. The polarization conditions were obtained by utilising wave plates according to Case (a) no wave plates, (b) half wave plate in E3, (c) quarter wave plate in E2, (d) half wave plate in E3, quarter wave plate in E2• The temporal behaviour of the DFWM signal under conditions o f a delayed second pump was examined for all the cases described above.

3. Results and discussion

A DFWM signal was easily detected, counterpropagating to the probe beam. This signal was found to vanish on being deprived of the probe and pump 372

1 April 1986

beams, demonstrating the optical AND gate property predicted by DFWM theory [4]. No signal can be detected using the neat solvent or the dissolved monomer. The phase conjugate reflectivity (Rpc = I4/I3) was found to vary quadratically with first pump pulse peak intensity (I1) (see fig. 1). This is again predicted theoretically [4]. Phase conjugate reflectivities of 500% were obtained stably at an incident pump intensity o f I 1 = 1.5 GW/cm 2. Values of the phase conjugate reflectivity as high as 1000% were observed at incident intensi. ties o f I 1 ~ 2 GW/cm 2, accompanied by severe degradation of the sample. The results shown in fig. 1 together with the theory of ref. [5] can be used to calculate an experimentally derived value for the effective third-order susceptibility (all incident polarizations parallel)

Xyyyy(3) = (1.4 + 0.7) X 10 -11 esu. The values of all of the independent elements were evaluated by examining the DFWM signal for varied conditions of incident beam polarization (cases (a) to (d) described above). The relative magnitudes of the components are presented in table 1. It should be noted, that within experimental error

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OPTICS COMMUNICATIONS

This is in good agreement with the experimentally derived value of

suggesting that the observed D F W M signalis due to a thermal mechanism. In order to obtain further insight into the nonlinear coupling mechanism, it isuseful to consider the incident beam polarization dependent second pump pulse delay curves. The general shape of these curves can be explained in terms of laser induced transient gratings [7]. For case (b) where the firstpump and probe pulses have the same polarization,while the second pump pulse is polarized at 90 °, 11 and 13 cause an interference pattern in the nonlinear medium which causes a transientgrating to be set up between these two beams. This grating decays by thermal diffusion with a decay time given by

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where p, Cp, r are the density, specificheat and thermal conductivity of the solvent respectively.A is the spacing between the interference fringes.This is a function of the angle/9 between the beams creating the interference fringes (A = )~/(2n sin(0/2)) with refractive index n). For the experimental conditions of ease (b) (X(x3y)xy)the thermal grating decay time can be calculated to be 7.2/as. Examination of fig. 2 shows that in this case the DFWM signal does not decay measurably over the time of 500 ps. In fact, a signal was still observed after delays of several tens of nanoseconds. This provides further evidence that the effect is of thermal origin. For the experimental conditions of case (c) (X(x3x)yy) the signal should decay according to eq. (2), with a time constant of 8.8 ns. However, in performing a second pump~pulse delay experiment, one of the pulses which is creating the grating is being delayed, therefore the DFWM should fall off with the pulse width. This is also shown in fig. 2. In case (a) the XyOy)yycomponent is being examined. According to eq. (1) contributions from both X(x3)xyy and X(3x~)xyshould be present.~This is also observed. The phase conjugate reflectivity measured for case (c) above was Rpc = 120%, at I 1 = 1.5 GW/cm2. The decay time is 8.8 ns. This suggests the possibility of picosecond optical phase conjugation with gain of

1 April1986

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Fig. 3. Experimental demonstration of aberration compensation, (a) undistorted probe beam, Co)undistorted phase conjugate beam, (c)double distorted probe beam, (d)Wave-front corrected probe beam.

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repetition values exceeding 100 MHz. In order to investigate the practicality of using this nonlinear mechanism for wave front correction a distorter (a drop of glass bond on a microscope slide) was inserted into the probe beam, close to the sample cell. At distances greater than ~80 mm, the distorter was found to scatter the probe beam outside the numerical aperture of the phase conjugate reflector. In order to compare wavefronts, the far-field patterns (in the focus of an f = 500 mm lens) of the undistorted probe beam, the undistorted phase conjugate beam, the double distorted probe beam, and the wave-front corrected beam were photographed from behind a transluscent screen. All four far-field patterns are shown in fig. 3. Aberration correction can clearly be observed.

5. Conclusions Optical phase conjugation has been demonstrated in a soluble polydiacetylene. The nonlinear coupling mechanism appears to be a laser induced refractive index grating in the solvent. Phase.conjugate reflectivities of over 500% have been observed. By selecting the appropriate tensor component of the effective susceptibility the possibility of high repetition rate picosecond phase conjugation with gain has been suggested.

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Acknowledgements The authors would like to thank Professor D.J. Bradley for his interest and invaluable advice, Professor R.C. Schulz for providing the PDA samples and helpful discussions. Financial support from British Petroleum Venture Research Unit, The Investment Bank of Ireland, Guinness Ireland Limited, and the Directorate for Scientific Research, DG XII/B2, European Economic Communities are gratefully acknowledged.

References [1] W.M. Dennis, W. Blau and DJ. Bradley, Appl. Phys. Lett. 47 (1985) 200. [2] C. Plaehetta, N.O. Rau, A. Hauck and R.C. Sehulz, Makxotool. Chem.: Rapid Commun. 3 (1982) 249. [3] A. Penzkofer and W. Falkenstein, Optics Comm. 17 (1976) 1. [4] A. Yariv, IEEE J. Quant. Electr. QE-14 (1978) 650. [5] R.G. Caro and M.C. Cower, IEEE J. Quant. Electr. QE-18 (1982) 1375. [6] C. Flytzanis, in: Quantum electronics, eds. H. Rabiand C.L. Tang (Academic Press, New York, 1975) p. 1. [7] H.J. Eichler, G. Salje and H. Stahl, J. AppL Phys. 44 (1973) 5383.