Criterion for Bragg and Raman-Nath diffraction regimes

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Abstract
The idea is well entrenched in the literature that thin phase gratings (whether holographic or acoustically induced) should exhibit Raman-Nath behavior (and thus give several diffracted waves), and that thick phase gratings should show Bragg behavior (one diffracted beam and that only for Bragg angle incidence). The parameter Q of Klein and Cook, which is a normalized measure of grating thickness, has been extensively used as a criterion for deciding which regime will apply. It is perhaps not generally realized that Q is not a reliable parameter for this purpose but requires, as indeed Klein and Cook noted, a limitation on grating strength. This limitation is a matter of practical concern. For example, we have observed Raman-Nath behavior with Fe-doped LiNbO3 even for very large values of Q. The purpose of the present paper is to note that a parameter ρ (first defined by Nath) is an effective replacement for Q, since ρ is reliable and Q is not. ρ is defined as λ02/Λ2n0n1, where λ0 is the vacuum wavelength of the light, Λ is the grating spacing, n0 is the mean refractive index, and n1 is the amplitude of the sinusoidal modulation of the refractive index. The grating thickness does not enter ρ, so the terms thin and thick are, strictly speaking, irrelevant to the question of which regime is operative. However, thin enough gratings will tend to operate in the Raman-Nath regime because the index modulation must be large for a thin grating to produce appreciable diffraction.

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