Elsevier

Optics Communications

Volume 197, Issues 4–6, 1 October 2001, Pages 507-514
Optics Communications

Phase matching analysis of noncollinear optical parametric process in nonlinear anisotropic crystals

https://doi.org/10.1016/S0030-4018(01)01475-4Get rights and content

Abstract

Phase matching for noncollinear optical parametric generation is investigated. All the possible phase matching configurations and existence conditions for general noncollinear three-wave mixing interactions are derived for propagation within the crystal principal planes. Numerical expressions for the critical phase matching angles are presented wherever possible. Finally, as an application of these expressions, several numerical calculations of the phase matching angles for general noncollinear phase matched optical parametric amplification in the nonlinear-optical crystals such as β-BaB2O4, LiB3O5 and KTiOPO4 are completed, and the results are graphically presented.

Introduction

Optical parametric generation in a nonlinear crystal is an effective means to generate widely tunable coherent radiation. Parametric generation of wavelength-tunable ultrahigh intensity and ultrashort pulses has recently attracted much interest [1], [2], [3]. This is due largely to the recent advances in the development of high-quality nonlinear optical crystals and efficient pump sources of picosecond and femtosecond mode-locked lasers. Parametric generation is a nonlinear optical effect in which two optical beams, the signal and the pump, are mixed in a nonlinear crystal to produce either a sum or a difference frequency. This mixing process is efficient only if the interacting waves propagate at the same phase velocity in the nonlinear medium, namely, the phase matching conditions must approximately be satisfied, phase matching can usually be realized by the use of the birefringence and the group-velocity dispersion properties of the nonlinear crystal [4]. Noncollinear parametric interaction in nonlinear optical crystals has been reported early in 1967 [5], but noncollinear phase matched optical parametric generation is only recently attracting a great deal of attention as a novel method of ultrashort pulse generation [6]. Theoretical and experimental results have demonstrated that noncollinear phase matching in optical parametric generation offers several advantages over more conventional collinear phase matching: it can be used to extend the tunability of the collinear process, to separate the interacting wavelengths more easily, and to effectively increase the interaction length by compensating the Poynting vector walk-off. The group-velocity mismatch can be reduced, the acceptance angle increases and parametric gain can be increased by noncollinear parametric interaction in the generation of ultrashort pulses. High efficiencies, low-operational thresholds and single resonant oscillation (SRO) can be readily obtained in optical parametric oscillation (OPO). It is well known that a wide gain bandwidth is desirable for the generation of ultrashort pulses, the noncollinear geometry can realize the group-velocity matching between the signal and idler, and the broadest gain bandwidth is attained [7], [8], [9], [10], [11]. For arbitrary noncollinear optical parametric generation process, because optimum phase matching is essential in order to obtain high-energy conversion efficiencies, a phase matching analysis should first be considered. Calculations of the phase matching angle for collinear three-wave interactions in the principal planes of crystals have been described [12]. The calculation of noncollinear phase matching angle is far from trivial, especially biaxial crystals have a more complex phase matching geometry than the uniaxial material, therefore comparatively little work, however, has been carried out on noncollinear phase matching in the optical parametric generation, which offers certain advantages over the collinear case.

In this paper, all the possible phase matching geometries for noncollinear optical parametric generation in both uniaxial and biaxial crystals were analyzed and discussed in great detail. Conditions and equations were derived, calculation expressions for the noncollinear critical phase matching angles were given wherever possible. These expressions would greatly benefit the performance of a number of experiments in selecting the proper crystal and a suitable orientation for noncollinear mixing scheme. The optimum phase matching angle can be obtained by these expressions, provided that an appropriate choice of noncollinear angle and the Sellmeier equations of the crystal are given.

Section snippets

The conditions of three-wave noncollinear optical parametric generation

Parametric interaction is a typical three-wave coupled nonlinear process, conservation of energy and conservation of momentum for this process are required, that is [4],ℏωc=ℏωb+ℏωakc=ℏkb+ℏkawhere ωi and ki are the ith radian frequency and wave vector, respectively. When these relations are satisfied exactly, the conditions is described as ideal phase matching. If this phase matching relation is not satisfied exactly, the interaction may still occur. However, the efficiency of the

Phase matching analysis of noncollinear parametric generation

There are, in general, three types of noncollinear three-wave interactions, denoted as type I, type II, and type III, where we adapt the classification scheme outlined in Ref. [13] to distinguish them. For type I interaction, the a wave and b wave electric-field eigenvectors are approximately parallel in the crystal and are orthogonally polarized with respect to c wave eigenvector. For type II interaction, the b wave and the c wave electric-field eigenvectors are approximately parallel in the

Summary

In this paper, all the possible noncollinear phase matching configurations and conditions for 3WM in both uniaxial and biaxial crystals were presented. We derive general noncollinear phase matching analytical expressions. With these expressions, we are able to define and compute the phase matching parameters for any type of 3WM process. It is worth noting that these expressions presented here are not limited in their application to noncollinear parametric generation, but also can be applied to

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