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Significance Statement
Nonlinear frequency conversion has great deal of applications in laser technology and quantum optics, especially now that spontaneous parametric down conversion (SPDC) in nonlinear crystals has been the mainstay for entanglement production. In the nonlinear frequency conversion process, phase mismatch severely limits the conversion efficiency. Biaxial crystal has excellent optical characters, with complex optical structure of two optical axes, and then it is complicated to calculate the phase matching parameters. Here we present an effective method for calculating phase matching conditions in biaxial 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. Using the results, the phase matching conditions in SPDC process can be directly calculate and gain the optimum phase matching schemes for the type I and type II. This method based on angle-dependent refractive index can be applied to three-wave interactions. It is convenient to calculate the phase matching parameters without solving the quadratic Fresnel equations.
Journal Reference
Applied Physics B, 2015, Volume 120, Issue 2, pp 239-246.
Guangwen Huo1 , Yongcang Wang1, Meizhi Zhang2
[expand title=”Show Affiliations”]- Department of Applied Science, Xijing University, Xi’an, 710123, China
- School of Electronics Engineering, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China
Abstract
We present an effective method for calculating phase-matching conditions in biaxial crystals, especially for nonlinear orthorhombic 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 directly calculate the phase-matching conditions with BIBO crystal in spontaneous parametric down-conversion (SPDC) process and gain the optimum phase matching schemes 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. This method based on angle-dependent refractive index can be applied to three-wave interactions. It is convenient to calculate the phase matching parameters without solving the quadratic Fresnel equations.
Go To Applied Physics BFigure Legend
The schematic of coordinate transformation for dielectric axis (),crystal principal axis ( abc ), and lab frame ().
