﻿ 双轴晶体中基于角度计算的相位匹配研究 The Study of Phase Matching Based on Angle Calculation in Biaxial Crystals

Applied Physics
Vol.06 No.08(2016), Article ID:18430,9 pages
10.12677/APP.2016.68024

The Study of Phase Matching Based on Angle Calculation in Biaxial Crystals

Guangwen Huo*, Heng Chen, Xianfeng Li

College of Control Engineering, Xijing University, Xi’an Shaanxi

Received: Aug. 11th, 2016; accepted: Aug. 26th, 2016; published: Aug. 30th, 2016

ABSTRACT

We present an effective method to calculate the phase matching parameters based on angle projection in biaxial crystal. By 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 and optical axis angle. It can be directly applied in phase matching conditions. Taking biaxial crystal BIBO as an example, we calculate the relations of phase matching angles and effective nonlinear coefficient in Spontaneous Parametric Down-Conversion process (SPDC) for the type I and type II. We further compare the SPDC with double frequency process, and discuss the physical meaning of angular gradient of refractive index. This approach is convenient to calculate phase matching parameters without solving the quadratic Fresnel equations.

Keywords:Phase Matching, Biaxial Crystale, Gradient of Refractive Index

Email: *guangwenhuo@126.com

1. 引言

2. 角度计算

(1)

( 2a )

(2b)

(3)

Figure 1. The schematic showing the coordinate transformation of the dielectric axis (), the crystal principal axis (abc), and the lab frame ()

(4)

(5)

(6)

(7)

(8)

xz面内的角满足

(9)

(10)

( 11a )

(11b)

(12)

(13)

(14)

(15)

(16)

(17)

Figure 2. The angle relations in monolithic crystal for

Figure 3. The angle relations and axial projection in triclinic crystal

3. 角度表象下的相位匹配

( 18a )

(18b)

( 19a )

(19b)

( 20a )

(20b)

(a) (b)

Figure 4. The angles’ relations of phase matching during SPDC process in BIBO crystal, (a) the type I at fundamental wavelength; (b) the type II at fundamental wavelength

( 21a )

(21b)

4. 角度表象下折射率的优势

(22)

(23)

(a) (b)

Figure 5. The variation relation of along with azimuthal angle in BIBO crystal, (a) the type I at fundamental wavelength; (b) the type II at fundamental wavelength

Figure 6. The optimal phasing matching of collinear parameter process in orthorhombic crystal

5. 结论

The Study of Phase Matching Based on Angle Calculation in Biaxial Crystals[J]. 应用物理, 2016, 06(08): 184-192. http://dx.doi.org/10.12677/APP.2016.68024

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21. NOTES

*通讯作者。