Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

Analysis and applications of optical diffraction by gratings

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

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

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

Polarization of light and topological phases

We report two-beam coupling experiments at 1.06-μm wavelength using photorefractive semi-insulating GaAs:Cr in the moving-grating recording mode. The steady-state gain coefficient Γ is measured as a function of fringe spacing Λ, fringe velocity υ, applied voltage V0, and incident beam ratio β. A maximum Γ as high as 6–7 cm−1 is observed for Λ ≃ 18 μm, υ ≃ 1 mm/sec, β > 103, and V0 ≃ 5 kV (interelectrode distance 5.8 mm). The agreement with the theory of two-beam coupling with moving fringes is discussed. In particular, a set of numerical values is obtained for some crystal parameters. Image amplification is demonstrated.

High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals.

Application of phase conjugation in Bi12Si O20 crystals to mode pattern visualisation of diffuse vibrating structures

In a device for switching a light beam, the conditions of propagation of the beam are modified locally under electric control by interposing on the beam path a fluid which modifies the conditions of refraction of the medium traversed by the beam.

Device for optical switching by fluid displacement and a device for the composition of a line of points

We demonstrate that holographic speckle-free imaging is possible when a dynamic recording medium, such as a Bi12SiO20 crystal, and a four-wave mixing configuration are used. The method is based on time integration in the conjugate-image plane of N coherent images having an independent speckle pattern. We apply this concept to a real-time optical processing operation. A speckle-free time-averaged interferogram of a vibrating structure is obtained.

Speckle-free imaging in four-wave mixing experiments with Bi(12)SiO(20) crystals.

New configurations for spatial beam steering of a near-infrared laser beam are presented. They are based on the interaction of the beam from a semiconductor laser with a dynamic grating photoinduced in a photorefractive crystal such as Bi12SiO20 (BSO). The demonstrated large values of the deflection angles (12°) result from a change in both the grating period and the orientation achieved by optical means. The Bragg condition over this large scan angle is maintained by either recording the grating with a variable wavelength (dye laser) or taking advantage of the spatial nonlinearities of the photorefractive effect. The respective advantages of these two techniques are discussed. Possible application to interconnection between optical fibers for broadband communication is considered.

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Jean-Pierre Herriau

Papers

High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals.

Application of phase conjugation in Bi12Si O20 crystals to mode pattern visualisation of diffuse vibrating structures

Device for optical switching by fluid displacement and a device for the composition of a line of points

Speckle-free imaging in four-wave mixing experiments with Bi(12)SiO(20) crystals.

Dynamic beam deflection using photorefractive gratings in Bi 12 SiO 20 crystals