A Generalized Method for Calculating Phase Matching Conditions inBiaxial Crystals
- *Corresponding Author:
- Huo G
College of Control Engineering
Xijing University, Xi’an 710123, China
Tel: (8629) 85628198
E-mail: [email protected]
Received Date: November 11, 2016; Accepted Date: December 13, 2016; Published Date: December 30, 2016
Citation: Huo G, Chen H, Zhang M (2016) A Generalized Method for Calculating Phase Matching Conditions in Biaxial Crystals. J Laser Opt Photonics 3: 143. doi: 10.4172/2469-410X.1000143
Copyright: © 2016 Huo G, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
We present a generalized method for calculating phase matching conditions in biaxial crystals, especially in nonlinear monoclinic and triclinic crystals. Exploiting the angle definition introduced by Japanese mathematician Kodaira Kunihiko, we deduce the angular relations in geometry and obtain the expressions of refractive indices depending on angular orientation of wave vector k and optical axis angle. Then we calculate the phase matching parameters with bismuth borate BiB3O6 (BIBO) crystal in spontaneous parametric down conversion (SPDC) process for the type I and type II. On its basis, we discuss the angular gradients of the pump and emission wave refractive index near the exact phase matching direction, and compare the SPDC with double frequency process in geometrical relations of the refractive index ellipsoids. It indicates the anisotropic structures of nonlinear crystals making a capability of filtering effect, and the nonzero linear mismatch described by refractive index angular gradients can be used to estimate the beam width in crystal. This method is convenient to calculate the phase matching parameters in orthorhombic crystals without solving the quadratic Fresnel equations.