Phase matching or quasi-phase matching(QPM)is of significant importance to the conversion efficiency of second harmonic generation(SHG)in artificial nonlinear crystals like lithium niobate(LN)crystal or microstructure...Phase matching or quasi-phase matching(QPM)is of significant importance to the conversion efficiency of second harmonic generation(SHG)in artificial nonlinear crystals like lithium niobate(LN)crystal or microstructured nonlinear crystals like periodic-poled lithium niobate(PPLN)crystals.In this paper,we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal,in addition to conventional means of period adjusting or temperature tuning.A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles.The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored.Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory.The results show that the narrow-band tunable SHG output covers a range of 532 nm–552.8 nm at the ideal incident angle from 0°to 90°.This theoretical scheme,fully considering the reflection and transmission at the air-crystal interface,would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal,which would be very helpful for the design of tunable narrow-band pulse nanosecond,picosecond,and femtosecond laser devices via PPLN and other microstructured LN crystals.展开更多
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 ...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.展开更多
基金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)+2 种基金the Guangdong Innovative and Entrepreneurial Research Team Program(Grant No.2016ZT06C594)the National Key Research and Development Program of China(Grant Nos.2018YFA,0306200,and 2019YFB2203500)the Science and Technology Program of Guangzhou City(Grant No.2023A04J1309).
文摘Phase matching or quasi-phase matching(QPM)is of significant importance to the conversion efficiency of second harmonic generation(SHG)in artificial nonlinear crystals like lithium niobate(LN)crystal or microstructured nonlinear crystals like periodic-poled lithium niobate(PPLN)crystals.In this paper,we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal,in addition to conventional means of period adjusting or temperature tuning.A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles.The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored.Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory.The results show that the narrow-band tunable SHG output covers a range of 532 nm–552.8 nm at the ideal incident angle from 0°to 90°.This theoretical scheme,fully considering the reflection and transmission at the air-crystal interface,would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal,which would be very helpful for the design of tunable narrow-band pulse nanosecond,picosecond,and femtosecond laser devices via PPLN and other microstructured LN crystals.
基金the National Natural Science Foundation of China(Grant No.11974119)the Science and Technology Project of Guangdong Province,China(Grant No.2020B010190001)+1 种基金the Guangdong Innovative and Entrepreneurial Research Team Program,China(Grant No.2016ZT06C594)the National Key Research and Development Program of China(Grant No.2018YFA 0306200)。
文摘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.
