Holography, coherent light amplification and optical phase conjugation with photorefractive materials

The development of a theory of four-wave mixing in photo-refractive crystals is described. This theory is solved in the undepleted pumps approximation with linear absorption and without using the undepleted pumps approximation for negligible absorption. Both the transmission and reflection gratings are treated individually. The results are used to analyze several photorefractive phase conjugate mirrors, yielding reflectivities and thresholds. The use of photorefractive crystals as optical distortion correction elements and experimental demonstrations of several of the passive phase conjugate mirrors are described.

/pdf/theory-and-applications-of-four-wave-mixing-in-1oxcbuhwqs.pdf

Theory and applications of four-wave mixing in photorefractive media

Large values of the exponential gain coefficient Γ are obtained (Γ≂8–12 cm−1) when recording with a moving grating in photorefractive BSO crystals (nearly degenerate two‐wave mixing; drift recording mode). The resolution of the Kukhtarev’s equations with a moving grating shows a resonance effect which at the optimum velocity makes the modulation of the photoinduced space charge field Esc higher. An optimum of the grating spacing also exists: Λopt:2π(E0/NA)(μe/eγR)1/2. In such conditions, the space charge field is phase shifted by π/2 with respect to the incident fringe pattern; this allows an efficient beam coupling between the two recording beams. The dependence of the gain Γ versus the incident beam ratio β of the two interfering waves is interpreted by including the second‐order term in the Fourier development of Esc. The conditions allowing one to obtain a reasonable agreement between the theory and experiments are presented and discussed, as well as the adopted values of the crystals’ parameters.

Two‐beam coupling in photorefractive Bi12SiO20 crystals with moving grating: Theory and experiments

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. >

Two-wave mixing in nonlinear media

We have grown and optically characterized strontium‐barium niobate crystals, including both undoped and cerium‐doped crystals having two different Sr/Ba ratios (61/39 and 75/25). By measuring the coupling of two optical beams in the crystals, we have determined the following photorefractive properties: the effective density, sign, and spectral response of the dominant charge carrier, the grating formation rate, dark conductivity, and carrier diffusion length. We find that electrons are the dominant photorefractive charge carriers in all of our samples; the typical density of photorefractive charges is ∼1×1016 cm−3 in the undoped samples. The grating formation rate increases with intensity, with a slope of ∼0.3 cm2/(W s) over an intensity range of ∼1–15 W/cm2 in undoped samples. Cerium doping improves both the charge density (increased by a factor of ∼3) and the response rate per unit intensity (∼5 times faster).

A. Marrakchi

Papers

Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals