Theoretical Study On Phase Matching Conditions Of Nonlinear Optical Conversions In Coupled Optical Waveguide Structures

Acting as a major driving force behind modern optics and due to its advantages such as high integration,tight confinement of photons and providing high-power light,micro-nano photonics has attracted great attention in optical signal generation,optical information transmission/communication,biological and chemical sensing,light field regulaton/imaging and so on.Nonlinear optical conversion plays an essential role in expanding laser spectrum and it has a wide range of applications in information science and materials science.In addition,phase matching condition is the key to achieving highly-efficient nonlinear optical conversion.Due to its tight confinement of photons,micro and nano-scale optical waveguides are ideal devices for low power and high integrated nonlinear optical conversion devices in the future.However,in the nonlinear optical conversion of waveguide devices,due to the material dispersion,it is difficult for a single waveguide to achieve phase matching between fundamental waveguiding modes of light waves.Taking second harmonic generation（ω₂=2₁）as an example,by applying the conventional modal dispersion method,a higher-order mode of second-harmonic wavelength is usually found to match a fundamental mode of pump.However,the spatial distribution of fundamental mode and high-order mode in waveguide is very different,which results in poor modal overlap of nonlinear optical conversion and low nonlinear optical conversion efficiency.In this paper,the phase matching between fundamental modes of pump and second-harmonic wavelength is innovatively proposed by using coupled nonlinear optical waveguide structure,which greatly increases the mode overlap integral,and thus significantly improves the efficiency of nonlinear optical conversion.Taking the second-order nonlinear optical conversion as an example,the phase matching conditions in coupled nonlinear optical waveguides are clarified by establishing the coupled mode equation.The phase matching conditions and their influencing factors in second harmonic generation of coupled nonlinear optical waveguides are studied in depth.In this paper,a complete set of theory for phase matching of nonlinear optical conversion in coupled nonlinear optical waveguide structure is constructed.The specific work is as follows:1.Six phase matching schemes for second-order nonlinear optical conversion are for the first time identified and well understood according to the supermode theory.2.Under the weak coupling approximation,the coupled mode equation of second harmonic generation in coupled nonlinear optical waveguides is established.When the nonlinear optical conversion efficiency is low,the equation is solved and three phase matching conditions for second harmonic generation in symmetrically coupled optical waveguides are obtained.Based on the above physical model,the effects of waveguide coupling coefficient,phase factor and amplitude factor of pump waves on second harmonic generation in coupled nonlinear optical waveguides are studied in detail.3.In this paper,the fourth-order Runge-Kutta method is used to solve the coupled-mode equation of second harmonic generation in coupled nonlinear optical waveguides with high conversion efficiency.The numerical results are discussed in depth and the validity of the theoretical model is verified.4.Taking zinc oxide micro-nano waveguide structure as an example,the phase matching conditions of second-order nonlinear optical conversion in single waveguide structure and coupled nonlinear optical waveguide structure are studied comparatively.In this paper,it is found that the single waveguide can only realize the phase matching between the fundamental mode of pump and the high-order mode of second-harmonic and its mode overlap integral is extremely small.However,based on the coupled nonlinear optical waveguide structure,the phase matching can be realized between the fundamental modes of pump and the second-harmonic waves,and its mode overlap integral is six larger than that of the single waveguide structure.Based on the coupled nonlinear optical waveguide structure,the phase matching between the fundamental modes of pump and second harmonic waves is realized,which breaks the limitation of the great difference of spatial distribution between fundamental and higher order mode in the traditional mode dispersion method.Therefore,in coupled nonlinear optical waveguides,the effective mode overlap between fundamental and second harmonic waves is greatly improved.In this paper,we have developed a set of integrated,low energy consumption and high efficiency photonic devices for nonlinear optical conversion,which greatly improves the efficiency of nonlinear conversion,and would be helpful for constructing future high-efficient nonlinear optical conversion devices.