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
DOI: 10.12677/APP.2016.68024, PDF,    科研立项经费支持
作者: 霍广文*, 陈 恒*, 李险峰*：西京学院控制工程学院，陕西 西安
关键词: 相位匹配；双轴晶体；计算；折射率梯度；Phase Matching； Biaxial Crystale； Gradient of Refractive Index
摘要: 本文介绍了一种通过角度投影方法计算双轴晶体中相位匹配参数的有效方法。该方法利用日本数学家小平邦彦对角度概念的推广，借助两个光轴与光波矢量之间的角度关系，通过角度投影方法确定了折射率计算所需角度参量的解析表达式，可直接用于相位匹配条件。文章以双轴晶体BIBO为例，数值模拟自发参量下转换过程中I类、II类相位匹配的角度关系和有效非线性系数。通过进一步对比自发参量下转换和倍频过程，讨论了角度表象下折射率梯度的物理意义。该方法在求解参量过程中的相位匹配参数时，避免了求解二阶菲涅尔方程过程，理论计算更便捷。
Abstract: We present an effective method to calculate the phase matching parameters based on angle pro-jection 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.
文章引用：霍广文, 陈恒, 李险峰. 双轴晶体中基于角度计算的相位匹配研究[J]. 应用物理, 2016, 6(8): 184-192. https://dx.doi.org/10.12677/APP.2016.68024

参考文献

[1] Franken, P.A., Hill, A.E., Peters, C.W. and Weinreich, G. (1961) Generation of Second Harmonic. Physical Review Letters, 7, 118. http://dx.doi.org/10.1103/PhysRevLett.7.118 [Google Scholar] [CrossRef] 
[2] Kwiat, P.G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A.V. and Shih, Y. (1995) New High-Intensity Source of Polarization-Entangled Photons. Physical Review Letters, 75, 4337. http://dx.doi.org/10.1103/PhysRevLett.75.4337 [Google Scholar] [CrossRef] 
[3] Scarcelli, G., Valencia, A., Gompers, S. and Shih, Y. (2003) Remote Spectral Measurement Using Entangled Photons. Applied Physics Letters, 83, 5560. http://dx.doi.org/10.1063/1.1637131 [Google Scholar] [CrossRef] 
[4] Jin, R.B., Zhang, J., Shimizu, R., Matsuda, N., Mitsumori, Y., Kosaka, H. and Edamatsu, K. (2011) High-Visibility Nonclassical Interference between Intrinsically Pure Heralded Single Photons and Photons from a Weak Coherent Field. Physical Review A, 83, 031805. http://dx.doi.org/10.1103/PhysRevA.83.031805 [Google Scholar] [CrossRef] 
[5] Kwiat, P.G., Waks, E., White, A.G., Appelbaum, I. and Eberhard, P.H. (1999) Ultrabright Source of Polarization-En- tangled Photons. Physical Review A, 60, R773. http://dx.doi.org/10.1103/PhysRevA.60.R773 [Google Scholar] [CrossRef] 
[6] Kuklewicz, C.E., Fiorentino, M., Messin, G., Wong, F.N.C. and Shapiro, J.H. (2004) High-Flux Source of Polarization-Entangled Photons from a Periodically Poled KTiOPO4 Parametric Down-Converter. Physical Review A, 69, 013807. http://dx.doi.org/10.1103/PhysRevA.69.013807 [Google Scholar] [CrossRef] 
[7] Hayat, A., Ginzburg, P. and Orenstein, M. (2008) Observation of Two-Photon Emission from Semiconductors. Nature Photonics, 2, 238-241. http://dx.doi.org/10.1038/nphoton.2008.28 [Google Scholar] [CrossRef] 
[8] Yoshino, K., Aoki, T. and Furusawa, A. (2007) Generation of Continuous-Wave Broadband Entangled Beams Using Periodically Poled Lithium Niobate Waveguides. Applied Physics Letters, 90, 041111. http://dx.doi.org/10.1063/1.2437057 [Google Scholar] [CrossRef] 
[9] Rangarajan, R., Goggin, M. and Kwiat, P. (2009) Optimizing Type-I Polariza-tion-Entangled Photons. Optics Express, 17, 18920-18933. http://dx.doi.org/10.1364/OE.17.018920 [Google Scholar] [CrossRef] 
[10] Halevy, A., Megidish, E., Dovrat, L., Eisenberg, H.S., Becker, P. and Bohatý, L. (2011) The Biaxial Nonlinear Crystal BiB3O6 as a Polarization Entangled Photon Source Using Non-Collinear Type-II Parametric Down-Conversion. Optics Express, 19, 20420-20434. http://dx.doi.org/10.1364/OE.19.020420 [Google Scholar] [CrossRef] 
[11] Armstrong, J.A., Bloembergen, N., Ducuing, J. and Pershan, P.S. (1962) Interactions between Light Waves in a Nonlinear Dielectric. Physical Review, 127, 1918. http://dx.doi.org/10.1103/PhysRev.127.1918 [Google Scholar] [CrossRef] 
[12] Berger, V. (1998) Nonlinear Photonic Crystals. Physical Review Letters, 81, 4136. http://dx.doi.org/10.1103/PhysRevLett.81.4136 [Google Scholar] [CrossRef] 
[13] Fedorov, M.V., Efremov, M.A., Volkov, P.A., Moreva, E.V., Straupe, S.S. and Kulik, S.P. (2007) Anisotropically and High Entanglement of Biphoton States Generated in Spontaneous Parametric Down-Conversion. Physical Review Letters, 99, 063901. http://dx.doi.org/10.1103/PhysRevLett.99.063901 [Google Scholar] [CrossRef] 
[14] Yao, J. and Fahlen, T.S. (1984) Calculations of Optimum Phase Match Parameters for the Biaxial Crystal KTiOPO4. Journal of Applied Physics, 55, 65. http://dx.doi.org/10.1063/1.332850 [Google Scholar] [CrossRef] 
[15] Huo, G.W., Zhang, T.Y., Cheng, G.H. and Zhao, W. (2013) Calculation of Effective Nonlinear Coefficient in BIBO for Spontaneous Parametric down Conversion. Journal of Nonlinear Optical Physics & Materials, 22, 1350010. http://dx.doi.org/10.1142/s0218863513500100 [Google Scholar] [CrossRef] 
[16] Born, M. and Wolf, E. (1970) Principles of Optics. Pergamon, Ox-ford.
[17] Ito, H., Naito, H. and Inaba, H. (1975) Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals. Journal of Applied Physics, 46, 3992-3998. http://dx.doi.org/10.1063/1.322151 [Google Scholar] [CrossRef] 
[18] Kodaira, K. (2003) An Introduction to Calculus. Iwanami Shoten, Publishers, Tokyo.
[19] Tzankov, P. and Petrov, V. (2005) Effective Second-Order Nonlinearity in Acentric Optical Crystals with Low Symmetry. Applied Optics, 44, 6971-6985. http://dx.doi.org/10.1364/AO.44.006971 [Google Scholar] [CrossRef] 
[20] Huo, G. and Zhang, M. (2015) Monolithic Symmetry Effect on Optimizing the Phase Matching Parameters of a Biaxial Crystal for Spontaneous Parametric down Conversion. Journal of Optoelectronics and Advanced Materials, 17, 116-121.

为你推荐