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
We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation meas...We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.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
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 co...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.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Project supported by the Science and Technology Project of Guangdong(Grant No.2020B010190001)the National Natural Science Foundation of China(Grant No.11974119)+1 种基金the Guangdong Innovative and Entrepreneurial Research Team Program(Grant No.2016ZT06C594)the National Key R&D Program of China(Grant No.2018YFA0306200)。
文摘We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.
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.
基金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)+1 种基金the Science and Technology Project of Guangdong Province,China(Grant No.2020B010190001)the Guangdong Innovative and Entrepreneurial Research Team Program(Grant No.2016ZT06C594)。
文摘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.
