Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface

doi:10.1088/1674-1056/ac9fc5

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50301-050301.doi: 10.1088/1674-1056/ac9fc5

Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface

Ya-Ting Qiu(邱雅婷)^†, Li-Hong Hong(洪丽红)^†, and Zhi-Yuan Li(李志远)^‡

School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China

收稿日期:2022-08-15 修回日期:2022-10-31 接受日期:2022-11-03 出版日期:2023-04-21 发布日期:2023-04-26
通讯作者: Zhi-Yuan Li E-mail:phzyli@scut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11974119), the Science and Technology Project of Guangdong Province, China (Grant No. 2020B010190001), the Guangdong Innovative and Entrepreneurial Research Team Program, China (Grant No. 2016ZT06C594), and the National Key Research and Development Program of China (Grant No. 2018YFA 0306200).

Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface

Ya-Ting Qiu(邱雅婷)^†, Li-Hong Hong(洪丽红)^†, and Zhi-Yuan Li(李志远)^‡

School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China

Received:2022-08-15 Revised:2022-10-31 Accepted:2022-11-03 Online:2023-04-21 Published:2023-04-26
Contact: Zhi-Yuan Li E-mail:phzyli@scut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11974119), the Science and Technology Project of Guangdong Province, China (Grant No. 2020B010190001), the Guangdong Innovative and Entrepreneurial Research Team Program, China (Grant No. 2016ZT06C594), and the National Key Research and Development Program of China (Grant No. 2018YFA 0306200).

摘要/Abstract

摘要： Considering the transmission and reflection of TE-polarized pump light at the air-crystal interface, the second harmonic generation (SHG) in a lithium niobate (LN) crystal is investigated theoretically and systematically in this work. In previous studies, the theoretical analyses of reflection and transmission of incident wave in the process of nonlinear frequency conversion were not considered in LN crystal on account of the complicated calculations. First, we establish a physical picture describing that a beam of light in TE mode transports in the LN crystal considering transmission and reflection at the crystal surface and generates nonlinear second-order optical polarization in crystal. Then we analytically derive the reflection coefficient and transmission coefficient of pump light by using the dispersion relationships and electromagnetic boundary conditions. We construct the nonlinear coupled wave equations, derive and present the small signal approximation solution and the general large signal solution exactly. Under the transmission model and reflection model, we find that the conversion efficiency of the second-harmonic wave is obviously dependent on transmission coefficient and other general physical quantities such as the length of LN crystal and the amplitude of pump light. Our analytical theory and formulation can act as an accurate tool for the quantitative evaluation of the SHG energy conversion efficiency in an LN crystal under practical situations, and it can practically be used to treat other more complicated and general nonlinear optics problems.

关键词: nonlinear frequency conversion, transmission, reflection

Abstract: Considering the transmission and reflection of TE-polarized pump light at the air-crystal interface, the second harmonic generation (SHG) in a lithium niobate (LN) crystal is investigated theoretically and systematically in this work. In previous studies, the theoretical analyses of reflection and transmission of incident wave in the process of nonlinear frequency conversion were not considered in LN crystal on account of the complicated calculations. First, we establish a physical picture describing that a beam of light in TE mode transports in the LN crystal considering transmission and reflection at the crystal surface and generates nonlinear second-order optical polarization in crystal. Then we analytically derive the reflection coefficient and transmission coefficient of pump light by using the dispersion relationships and electromagnetic boundary conditions. We construct the nonlinear coupled wave equations, derive and present the small signal approximation solution and the general large signal solution exactly. Under the transmission model and reflection model, we find that the conversion efficiency of the second-harmonic wave is obviously dependent on transmission coefficient and other general physical quantities such as the length of LN crystal and the amplitude of pump light. Our analytical theory and formulation can act as an accurate tool for the quantitative evaluation of the SHG energy conversion efficiency in an LN crystal under practical situations, and it can practically be used to treat other more complicated and general nonlinear optics problems.

Key words: nonlinear frequency conversion, transmission, reflection

中图分类号: (Classical electromagnetism, Maxwell equations)

03.50.De

42.70.Mp (Nonlinear optical crystals) 78.20.Ci (Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity))

Ya-Ting Qiu(邱雅婷), Li-Hong Hong(洪丽红), and Zhi-Yuan Li(李志远). Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface[J]. 中国物理B, 2023, 32(5): 50301-050301.

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Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface

Rigorous solution to second harmonic generation considering transmission and reflection of light at air-crystal interface

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