Nondegenerate Two-wave Mixing Research Articles

Nearly degenerate two-wave mixing in saturable absorbers

We present a theory to describe nondegenerate two-wave mixing in saturable absorbers. The theory takes into account the saturation of the travelling grating produced by the intersection of two light beams and the two-wave mixing process is regarded as the zero-order self-diffraction of the incident waves in this grating. The results are in agreement with experimental data obtained for ruby.

Non-linear optics in artificial Kerr materials

Non-resonant optical third-order non-linearity can be observed in liquid suspensions of dielectric microparticles as a result of diffusive rearrangements of the particle distribution function. Wave-combination experiments, such as non-degenerate two-wave mixing and degenerate four-wave mixing, show the presence of two different kinds of light-induced refractive-index gratings. These gratings originate from the modulation of the local particle number density and preferred orientation respectively. The resulting non-linearities differ considerably because of the tensorial nature and the time response and they can be controlled separately by varying the suspension and the particle parameters. Experimental results are always in good agreement with a simple single-particle diffusive model.

The effects of optical activity and absorption on two-wave mixing in Bi 12SiO 20

We consider non-degenerate two-wave mixing in photorefractive Bi 12SiO 20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

Measurement of the diffusion coefficient of strongly interacting colloidal suspensions by nondegenerate two-wave mixing.

Abstract : We have measured the diffusion coefficient of strongly interacting liquids near the phase transition using nondegenerate two-wave mixing. We self-consistently calculate the diffusion coefficient as the product of the elastic modulus and a relaxation time which is identified as the time taken for a particle to diffuse one-tenth of the average interparticle distance. This procedure also predicts an electrolyte concentration where the diffusion coefficient vanishes which is identified with the melting point of the colloidal crystal. This is shown to be essentially identical to the Lindemann criterion. In addition, we find that the colloidal liquid-solid transition as a function of ionic concentration gives a critical exponent gamma=0.08+/-0.003.

Nondegenerate two-wave mixing in GdAlO_3:Cr^3+

We have measured the nearly degenerate two-wave mixing in GdAlO(3):Cr(3+) crystals. In contrast to that in other chromium-doped materials, the signal in this sample arises from a mixed phase absorption grating where the absorption contribution is intensity dependent. The real (n(2)') and the imaginary (n(2)'') parts of the nonlinear index of refraction, the saturation intensity, and the excited-state lifetime are determined. The ratio r = n(2)''/n(2)' changes linearly with the intensity. Owing to saturation, the grating presents anharmonicities that give rise to self-diffracted beams (forward four-wave mixing). For comparison, results are also presented for ruby and alexandrite.

Polarization-resolved nondegenerate two-wave mixing in shaped microparticle suspensions

We observe polarization-resolved coherent beam combination through nondegenerate two-wave mixing in water-glycerol suspensions of shaped polytetrafluoroethylene microparticles. Coherent energy transfer that arises from translational and orientational moving index gratings was observed. A theory for beam combination through nondegenerate two-wave mixing is presented and found to be in excellent agreement with these measurements.

Temperature and spectral dependence of the nonlinear index of ruby via nondegenerate two-wave mixing

We have studied the nonlinear index of refraction of pink ruby between 565 nm and 610 nm using nondegenerate two-wave mixing at 77 K and 294 K. Our new results support the model originally proposed by Venkatesan and McCall based on the large cross section of the transition from the Kramers doublets to the charge transfer band. In addition, we show that two-wave mixing can be used for accurate determination of the 2E lifetime under conditions where radiation trapping makes fluorescence decay measurements difficult.

Viscosity of picoliter volumes measured by nondegenerate two-wave mixing

Using nondegenerate two-wave mixing in colloidal suspensions we measure the viscosity of liquids with as little as 20 picoliters of volume. In addition, changes in the frequency signature with intensity are observed which are interpreted in terms of self-focusing effects.

Dynamics of refractive-index changes and two-beam coupling in resonant media

The dynamics of light-induced change in the refractive index of a resonant medium are examined. For illumination with weak fields, the two relevant relaxation times are T1, the population lifetime and T2, the dipole-dephasing time. The response time of the index change is determined by the slower relaxation time of the medium which is usually the time T1 taken by the excited system to relax back to its thermal equilibrium value. Illumination with two beams of the same frequency that intersect within the medium leads to the formation of a volume grating in the medium that is spatially local. Hence there is no exchange of energy between the beams that write the grating, each beam merely reducing the absorption experienced by the other beam. Illumination with a moving, spatially periodic intensity pattern leads to gain for one beam and additional absorption for the other beam as they propagate through the medium. A complete set of coupled equations describing the intensities and phases of the beams undergoing non-degenerate two-wave mixing in the resonant media is derived using third-order perturbation theory, and the solutions are studied numerically. In particular, the two-beam coupling constant for intensity is shown to depend on the frequency difference between the two beams and on the pressure-induced collisional relaxations in the system.

Saturation effect in nondegenerate two-wave mixing

Saturation effects in nondegenerate two-wave mixing are analyzed theoretically for saturable absorbers. A gain saturation effect in the process of energy transfer has been observed. The fact that the frequency difference of two incident waves at which the gain reaches maximum varies with the pump intensity has been predicted and demonstrated. It has also been demonstrated that parameters such as T 1, I s and χ (3) can be determined sucessfully by nondegenerate two-wave mixing experiments.

Role of thermal fluctuations in nondegenerate two-wave mixing

The influence of thermal fluctuations on nondegenerate two-wave mixing in the nondepleted pump approximation is examined. For the specific case of an optical Kerr medium the spectrum of both amplitude and phase fluctuations as well as the signal-to-noise ratio are obtained. Detailed calculations suggest that a signal-to-noise ratio of order unity at argon-ion wavelengths and room temperatures requires a probe power of 15 μW in the strong signal regime.

Two-wave mixing in nonlinear media

The physics of the photorefractive effect is briefly discussed. A coupled-mode theory is then developed to analyze the coupling of two coherent electromagnetic waves inside a photorefractive medium. Both codirectional and contradirectional coupling are considered. The coupled-mode theory is then extended to consider the case of nondegenerate two-wave mixing. A discussion of the fundamental limit of the speed of photorefractive effect is then introduced. The coupling of two polarized beams inside photorefractive cubic crystals is considered. The formulation is focused on the cross-polarization two-beam coupling in semiconductors such as GaAs. The coupling of two electromagnetic waves inside a Kerr medium and the electrostrictive Kerr effect are discussed. A new concept of nonlinear Bragg scattering is introduced. The similarity among various kinds of two-wave mixing, including stimulated Brillouin scattering and stimulated Raman scattering are pointed out. Several applications of two-wave mixing are discussed. These include photorefractive resonators, optical nonreciprocity, resonator model of self-pumped phase conjugators, real-time holography, and nonlinear optical information processing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Photorefractive two-beam coupling in cubic crystals II General case (ϕ ≠ π/2)

Photorefractive two-beam coupling in cubic crystals in which the spatial phase shift between the index grating and the intensity pattern is not π/2 is considered. Exact solutions for codirectional cross-polarization two-wave mixing are obtained. The results are useful for the case of nondegenerate two-wave mixing when the spatial phase shift is not π/2.

Nondegenerate two-wave mixing in ruby

We demonstrate energy exchange by nondegenerate two-wave mixing in ruby. Our results are in agreement with the theory of nondegenerate two-wave mixing when the theory is generalized to take into account a complex nonlinear index. Two-wave mixing gain exceeding the absorption and reflection losses is demonstrated, and we show that these experiments provide a simple and accurate method for determining the complex nonlinear index, response time, and saturation intensity of the medium.

Frequency shift and cavity length in photorefractive resonators

Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.