中国物理B ›› 2022, Vol. 31 ›› Issue (5): 54201-054201.doi: 10.1088/1674-1056/ac4747

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A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Jianbo Pan(潘剑波)1,†, Jianfeng Chen(陈剑锋)1,†, Lihong Hong(洪丽红)1, Li Long(龙利)1, and Zhi-Yuan Li(李志远)1,2,‡   

  1. 1 School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China;
    2 State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2021-09-14 修回日期:2021-12-07 发布日期:2022-04-18
  • 通讯作者: Zhi-Yuan Li,E-mail:phzyli@scut.edu.cn E-mail:phzyli@scut.edu.cn
  • 基金资助:
    Project supported by the National Key Research and Development Program of China (Grant No.2018YFA 0306200),the National Natural Science Foundation of China (Grant No.11974119),the Science and Technology Project of Guangdong Province,China (Grant No.2020B010190001),and the Guangdong Innovative and Entrepreneurial Research Team Program (Grant No.2016ZT06C594).

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Jianbo Pan(潘剑波)1,†, Jianfeng Chen(陈剑锋)1,†, Lihong Hong(洪丽红)1, Li Long(龙利)1, and Zhi-Yuan Li(李志远)1,2,‡   

  1. 1 School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China;
    2 State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China
  • Received:2021-09-14 Revised:2021-12-07 Published:2022-04-18
  • Contact: Zhi-Yuan Li,E-mail:phzyli@scut.edu.cn E-mail:phzyli@scut.edu.cn
  • About author:2021-12-31
  • Supported by:
    Project supported by the National Key Research and Development Program of China (Grant No.2018YFA 0306200),the National Natural Science Foundation of China (Grant No.11974119),the Science and Technology Project of Guangdong Province,China (Grant No.2020B010190001),and the Guangdong Innovative and Entrepreneurial Research Team Program (Grant No.2016ZT06C594).

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摘要： Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell's law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light-matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

关键词: birefringence crystal, comprehensive solution, complete physical picture

Abstract: Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell's law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light-matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

Key words: birefringence crystal, comprehensive solution, complete physical picture

中图分类号:  (Wave propagation, transmission and absorption)

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42.25.Ja (Polarization)