和频、差频共存的太赫兹波上转换探测理论分析

Theoretical Analysis of Terahertz-Wave Frequency Up-Conversion Detection Based on Coexisting Difference-and Sum-Frequency Generation

基于非线性频率上转换的太赫兹波探测技术具有灵敏度高、响应速度快、可室温操作等优点,现有理论研究中仅考虑了差频转换或和频转换,而这与实验中观察到的二者共存的物理现实并不一致。本文提出了在非线性频率转换过程中差频与和频共存时的理论方程,并以DAST晶体为例模拟分析了不同晶体厚度及泵浦强度下的太赫兹波探测情况。理论计算表明:和频、差频共存下各波变化趋势与单差频或单和频情况有所不同;和频过程的存在会降低差频过程的效率,若只考虑差频,则结果将有所偏差。在特定实验条件下,同时利用差频光与和频光,总信号输出强度更大,其探测效率高于单差频的情况;存在一个最佳的晶体厚度,使得总信号输出最强。进一步计算表明,基于非线性频率上转换的太赫兹单光子探测有可能实现。

Objective Terahertz technology is developing rapidly and is widely used in various basic scientific research and application fields such as biology,industrial nondestructive evaluation,environment monitoring,and security.Among the various applications,high-sensitivity detection of terahertz waves has attracted considerable attention.Terahertz-wave detection technology based on nonlinear frequency up-conversion is a promising technique owing to its decent performance in terms of high sensitivity,fast response,and room-temperature operation.Based on the second-order nonlinear effect in crystals,a new near-infrared(NIR)signal light is obtained via the interaction of NIR pumping laser and terahertz wave.High-sensitivity detection of terahertz waves can be achieved with the assistance of signal light detection using mature NIR detection technology.In experiments,difference-frequency generation(DFG)and sum-frequency generation(SFG)exist together.In previous studies,only DFG or SFG process was considered,both of which possess some limitations.Therefore,the coexistence of DFG and SFG demands prompt investigation.In this study,theoretical nonlinear frequency conversion equations that contain both DFG and SFG are proposed.The detailed situations of terahertz-wave detection based on DAST crystals were simulated and analyzed under different setting conditions.Such a theoretical study of terahertz wave detection under the coexistence of DFG and SFG will be helpful in future experiments.Methods In this study,four-wave interaction equations considering the coexistence of DFG and SFG are proposed,derived from the improvement and further deduction of classical three-wave coupling equations.Considering the nonlinear organic crystal DAST as an example,a series of simulations and analyses were performed based on the four-wave interaction equations using MATLAB software and conclusions were drawn.To illustrate lightwave conversion in different nonlinear processes,an ideal case of ignoring the light absorption and phase mismatching was first analyzed.In the next step,considering the typical wavebands commonly used for nonlinear frequency upconversion with DAST crystals,4.3THz and 1395nm were respectively chosen as the frequency of terahertz wave and corresponding pumping wavelength in further simulations.To optimize the terahertz detection more practically,the difference-and sum-frequency processes under different pumping intensities and DAST crystal thicknesses were calculated.In addition,the simulation of terahertz single-photon detection based on the coexistence of DFG and SFG was performed.Results and Discussions The theoretical calculation results based on the four-wave interaction equations are as follows.For the evolution of terahertz waves and up-converted signal light,three nonlinear processes(DFG,SFG,and coexistence situation)showed different characteristics.The terahertz optical intensity slightly changed with the coexistence of DFG and SFG;it neither rose rapidly in the single difference-frequency process nor did it decrease rapidly in the single sum-frequency process(Fig.2).Considering the absorption and phase mismatching in simulations,the calculation results were more helpful in experiments.At the beginning of the interaction,the conversion efficiency of the sum-and difference-frequency processes were similar,but the terahertz intensity declined quickly under the combined action of the conversion and crystal absorption after a certain distance.When the pumping intensity was weak,the terahertz photons generated by the difference-frequency process were insufficient for continuing the sum-frequency conversion,which led to the reversion of the sum-frequency process.In addition,the signal light of the difference-frequency process increased slowly,so the total signal photon number had a maximum value corresponding to the optimal crystal thickness;the maximum output was larger than that when only the difference-frequency process was considered(Fig.3).However,when the pumping intensity became larger,the generated terahertz wave was sufficient for maintaining the sum-frequency process and the signal light continued to increase.The efficiency of the difference-frequency conversion further decreased owing to the sumfrequency conversion.The total signal photon number was still smaller than that in the single difference-frequency process,indicating that the existence of the sum-frequency process significantly affected the difference-frequency conversion(Fig.4).Therefore,we can choose different pumping wavelengths to change the phase matching of the two processes and improve the detection efficiency by using or suppressing the sum-frequency process.Conclusions In terahertz-wave detection through nonlinear frequency up-conversion,the difference-and sumfrequency processes coexist.The lightwave conversion between the pumping laser,terahertz wave,and signal light satisfies the Manley-Rowe relations.The nonlinear optical evolution under the coexistence of DFG and SFG differed from that of the case where only either was considered.The existence of the sum-frequency process reduced the difference-frequency conversion efficiency.Thus,the results obtained by ignoring the concurrent sum-frequency conversion may be inaccurate.Further,both pumping intensity and crystal thickness had a significant impact on the frequency up-conversion process.The total signal intensity of DFG and SFG was higher than that when only DFG was considered,leading to a higher detection efficiency under certain experimental conditions.In addition,there was an optimal crystal thickness corresponding to the maximum total signal output.Further theoretical simulations showed that terahertz-wave single-photon detection through nonlinear optical frequency up-conversion could be realized using an NIR single-photon detector.