Degenerate four-wave mixing in organic azo dyes chrysoidin and benzopurpurin 4B

Sylvain Mailhot, Pierre Galarneau, Roger A. Lessard, and Marguerite-Marie Denariez-Roberge

Phase-conjugate reflectivity obtained by degenerate four-wave mixing are measured in different azo dye solutions. A reflectivity up to 80% was achieved. Values of the nonlinear susceptibility x(3) are calculated, and its origin is discussed.

I. Introduction Degenerate four-wave mixing (DFWM) is a simple

method to achieve phase conjugation by using the third order nonlinearity x(3) of the electric susceptibil­ity tensor.1 A lot of experiments have been performed on phase conjugation by DFWM over the years using several types of nonlinear medium. Semiconductors,2

photorefractive crystal,3 polymers,4 and organic dyes5

are the more currently used. Depending on applications, fast rising nonlinearities

and fast disappearing nonlinearities may be needed. The fastest nonlinearities reported to date are related to nonresonant electronic effects such as the optical Kerr effect6 and anharmonic motion of electrons,7

which result in relatively small magnitude nonlineari­ties.

Saturation of absorption is generally used when one is looking for a stronger effect and consequently reso­nant interaction. It can be promising to look for other types of nonlinearity involving population gratings in­duced by light. For example, cis-trans photoisomeri-zation of some azo dyes has been reported.8 By break­ing the double nitrogen bound, the two parts of the molecule can rotate around the remaining bound and thus produce the isomerization of the azo dye. This process should be fast enough in a nonviscous solvent.

We studied DFWM of two azo dyes in solution, chrysoidin and benzopurpurin 4B, for which the mo­lecular structure is shown in Fig. 1. For those mole­cules, one obtained reflectivities up to 80% with pump

The authors are with Universite Laval, Physics Department— LROL, Sainte-Foy, Quebec G1K 7P4, Canada.

Received 18 November 1987. 0003-6935/88/163418-04$02.00/0. © 1988 Optical Society of America.

intensity of the order of 6 MW/cm2. The influence of solvent, dye concentration, and pump intensity on the conjugate beam is reported and discussed.

II. Experiment The experimental setup is shown in Fig. 2. The

laser source was a Nd3+:YAG operating in a Q-switch mode, frequency doubled (λ = 532 nm) by a KDP crystal. A spatial filter (SP) was installed behind the crystal to smooth irregularities in the beam pattern. The laser pulse was polarized in the vertical plane with a duration of 20 ns FWHM, a typical energy of 10 mJ, and a repetition rate of 10 Hz. Four-wave mixing was produced using a retroreflection geometry.9 The laser pulses were divided by a beam splitter (BSl) to gener­ate a pumping beam I1 and a probe beam 12. The angle between the two beams was ~3°, and a proper ratio I2/ I1 - 1/10 was achieved by using neutral density (ND) filters. A mirror M2 was aligned to retroreflect the incident pumping beam 11 to provide the counterpro-pagating pump pulse I3 necessary for phase conjuga­tion. The dye solutions were contained in a 5-mm thick quartz cell. The pulses were focused into the dye cell with a lens L 1 (focal length = 1 m) to give a peak pump intensity of ~2.5 MW/cm2 in an area 2 mm in diameter. Another lens L2 (ƒ = 50 cm) was placed in front of M2 to focus the third beam I3. A glass plate BS2 was used to deflect both the phase conjugated and the input pump beams to precalibrated (5-4) photodi-odes.

A four-wave mixing signal counterpropagating to the probe beam was easily observed with both dyes, chrysoidin and benzopurpurin 4B. The signal van­ished when any of the three beams, I1, I2, or I3, were blocked, demonstrating the optical AND gate property predicted by a four-wave mixing theory. Solutions of chrysoidin and bensopurpurin 4B in ethanol, metha­nol acetone, and glycerol were used in the dye cell. The

3418 APPLIED OPTICS / Vol. 27, No. 16 / 15 August 1988

Fig. 1. Molecular structure of the azo dyes used: benzopurpurin 4B; chrysoidin.

Fig. 3. Dependence of the phase-conjugate reflectivity R on the first pump beam intensity I1 for chrysoidin/methanol solution (2.4 ×

10-4 M).

Fig. 2. Experimental setup for DFWM using retroreflection geom­etry.

dye concentration (10-4-10-5 -M range) was first ad­justed to optimize the signal. No signal could be de­tected with pure solvent.

The pulse intensity was varied by changing the laser amplifier voltage. It was verified that the polarization plane remained vertical. Figure 3 shows the depen­dence of reflectivity on pump intensities for a chrysoi­din/methanol solution. The optimum concentration for this solution was found to be 2.4 × 10-4 M. A phase conjugate reflectivity of 4.7% was obtained with a peak pump intensity I1 = 2.6 MW/cm2. Reflectivities were found to follow a quadratic dependence on intensities. The other dye solutions showed the same quadratic behavior. It was found that the reflectivity varied slightly with the solvent except for glycerol, which gave poor reflectivity.

Much higher reflectivities were obtained by substi­tuting a glass plate for the beam splitter (BSl). The

Fig. 4. Dependence of R vs I1 (given in MW/cm2) with I2/I1 = 1/100

for chrysoidin/ethanol (2.7 × 10-4 M).

ratio between I1 and I2 was in this case I2/I1 ~ 1/100, giving rise to reflectivity up to 80% in chrysoidin/ ethanol (2.7 × 10-4M) with pump intensities of 6 MW/ cm2 (see Fig. 4).

The dependence of reflectivity on dye concentration is shown in Fig. 5. Since the nonlinearity x(3) is pro­portional to the amount of dye in the solution, hence to the absorption coefficient of the solution, the reflectiv­ity should be proportional to exp(—2αL) [1 -exp (—αL)]2, where L is the dye cell length. At low dye concentration the signal is weak because of the small coupling between the waves. At high dye concentration the reflectivity drops because of the disappearance of I3. The experimental points show a good fit with the theoretical function.

For each solution used in the DFWM experiment, we measured the coefficient of absorption α in our experi­mental conditions at λ = 532 nm. Absorption spectra at a low level of excitation have been recorded using a UV-visible spectrophotometer (HP-8450A). No spe­cial solvent effects have been noticed except in benzo-

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mal effects were found to be responsible for the in­duced nonlinar susceptibility.

The importance of these effects in our case can be evaluated by making use of an expression derived by Caro and Gower9 for the change in refractive index induced by heat absorption:

where T is the temperature in the medium, Φ is the fraction of absorbed radiation converted to heat, τ is the pulse duration, ρ and Cp are, respectively, the density and specific heat at constant pressure. The thermal constant

Fig. 5. Dependence of the phase-conjugate reflectivity on benzo-purpurin 4B concentration in glycerol with I1 = 1.5 MW/cm2.

purpurin/acetone solution where we observed an im­portant scattering joined to a smaller absorption coefficient and in chrysoidin/acetone solution where the absorption maximum is significantly frequency shifted. In the case of chrysoidin in glycerol, we ob­served the bleaching of the solution. Results are sum­marized in Table I.

III. Discussion As predicted by DFWM theory in absorbing media

the reflectivity follows a quadratic dependence on pump intensities.

For low reflectivity (R < 20%), it can be shown10 that

for our solvent (given in cm2/J) are 27 (acetone), 16 (methanol), and 24 (ethanol),11 and Φ was arbitrarily taken to be 0.5. For the chrysoidin/methanol solution we obtained x(3)

Th = 2-6 × 10 -19 m2/V2, which is slightly lower than the experimental value. In both dyes, one may notice that X(3)

exp follows the same progression that X(3)

Th with solvent properties. The X(3) that would be associated with a photoin-

duced concentration grating can also be estimated. One may estimate the Δα due to the photoinduced species and relate it to the imaginary part of the polar­ization variation X(3)"E2 by using

This approximation would give us also a correct order of magnitude for x3 if Δα/α is of the order of 50%, which seems reasonable.

where n is the refractive index and ω is the laser fre­quency. For the chrysoidin/methanol solution n = 1.33 and α = 0.66 cm-1. The experimental data were fitted to a quadratic behavior. Using Eq. (1), values of X(3) were calculated. For this solution x(3) = 1.46 × 10-18 πi2/V2 was obtained, which is within the same order of magnitude measured by Caro and Gower9 with rhodamine 6G in ethanol. In their experiment, ther-

IV. Conclusion Phase conjugation by degenerate four-wave mixing

has been demonstrated in azo dyes. The quadratic behavior of the curves shows that DFWM is a third order nonlinear process. The order of magnitude found for the third order nonlinearity does not allow us to choose between the thermal effect or photoinduced population grating. Time resolved studies are in pro­gress to clarify that point.

Table I. Summary of Results References 1. Y. R. Shen, "Basic Considerations of Four-Wave Mixing and

Dynamic Grating," IEEE J. Quantum Electron. QE-22, 1196 (1986).

2. R. K. Jain, "Degenerate Four-Wave Mixing in Semiconductors: Application for Phase Conjugation and to Picosecond-Resolved Studies of Transient Carrier Dynamics," Opt. Eng. 21, 199 (1982).

3. P. Yeh and A. E. T. Chiou, "Optical Matrix-Vector Multiplica­tion Through Four-Wave Mixing in Photorefractive Media," Opt. Lett. 12, 138 (1987).

4. W. M. Dennis, W. Blau, and D. J. Bradley, "Optical Phase Conjugation in a Soluble Polymer," Opt. Eng. 25, 538 (1986).

5. J. 0. Tocho, W. Sibbett, and D. J. Bradley, "Picosecond Phase-Conjugate Reflection from Organic Dye Saturable Absorbers," Opt. Commun. 34, 122 (1980).

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6. D. M. Pepper, D. Fekete, and A. Yariv, "Observation of Ampli­fied Phase Conjugate Reflection and Optical Parametric Oscil­lation by Degenerate from Wave Mixing in a Transparent Me­dium," Appl. Phys. Lett. 33, 41 (1978).

7. R. K. Jain and M. B. Klein, "Degenerate 4 Wave Mixing in Semi­conductors," in Optical Phase Conjugation, R. A. Fisher, Ed. (Academic, New York, 1983).

8. T. Todorov, L. Nikolova, and N. Romova, "Photoinduced An-isotropy in Rigid Dye Solutions for Transient Polarization Holo­graphy," IEEE J. Quantum Electron. QE-22, 1262 (1986).

9. R. G. Caro and M. C. Gower, "Phase Conjugation by Degenerate Four-Wave Mixing in Absorbing Media," IEEE J. Quantum Electron. QE-18, 1376 (1982).

10. C. Maloney and W. Blau, "Resonant Third-Order Hyperpolari-zabilities of Large Organic Molecules," J. Opt. Soc. Am. B 4, 1035 (1987).

11. G. Martin and R. W. Hellwarth, "Infrared-to-Optical Image Conversion by Bragg Reflection from Thermally Induced Index Gratings," Appl. Phys. Lett. 34, 371 (1979.

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