Theoretical Analysis Of The Cascaded Optical Parametric Oscillator Based On Periodic Polarized Crystals

Since the first observation of the second harmonic generation of the ruby laser by quartz crystal in 1961 by P.A.Franken et al.,people have realized the potential of new optical wavelengths generated by nonlinear optical technology,and quickly formulated the nonlinear frequency conversion criteria through the nonlinear medium,also promoted the development of various second-order nonlinear frequency conversion processes such as second harmonic generation(SHG),sum frequency generation(SFG),difference frequency generation and optical parameter generation,amplification,and oscillation,etc..In order to extend the spectral range of the laser towards a new wavelength band,the optical parametric oscillation(OPO)technique generating the wide tuning wavelength is particularly important,especially the development and extension of continuous-wave singly resonant optical parametric oscillators(SRO)such as cascaded frequency multiplication and sum-frequency etc.However,its development relied heavily on suitable nonlinear crystals.Since the first periodic-polarized crystal was developed in 1995,a continuous-wave high-power tunable laser from ultraviolet to mid-infrared has been achieved with nonlinear frequency conversion technology.As a key crystal medium in second-order nonlinear frequency conversion technology,quasi-phase-matched periodic-polarized crystals are important nonlinear crystal materials,and they play a pivotal role in the achieving continuously tunable laser sources.Quasi-phase-matched periodic-polarized crystals can be divided into single-grating,multiple-grating,cascaded-grating,fan-out grating and chirp grating crystals according to the different grating distribution.According to the type of polarized crystals,crystals materials such as PPLN,PPLT,MgO:PPLN,MgO:sPPLT and PPKTP are often used for realizing continuous-wave high-power tunable laser sources in experiments.The second-order nonlinear frequency conversion technology was once limited by the lack of suitable crystals.With the continuous development of nonlinear crystal materials,the OPO output spectral range has been able to cover the UV to mid-infrared radiation nowadays.In nonlinear frequency conversion devices based on periodically poled crystals,up until now,SRO which is pumped by green light at 532 nm and chooses MgO:sPPLT as nonlinear crystal can generate continuous laser radiation from red to near-infrared light;SRO with MgO:PPLN as nonlinear crystal which is pumped by 1064 nm infrared light,can obtain continuous laser radiation from the near-infrared to mid-infrared(4-5 ?m)waveband;Through frequency multiplication operation of resonant signal laser where is in SRO pumped by 532 nm with MgO:sPPLT as nonlinear crystal,namely intracavity frequency doubled in SRO(IFD-SRO),continuous laser radiation in visible light band can be obtained.Through intracavity SFG between the pump and resonant signal where are in the SRO pumped by 532 nm with MgO:sPPLT as nonlinear crystal,namely intracavity sum frequency generation in SRO(IC-SFG-SRO),a continuous ultraviolet radiation can be generated.The IC-SFG-SRO can provide shorter wavelengths than that of the IFD-SRO.In this paper,we develop the following three parts of research work on the theoretical analysis of the cascaded optical parametric oscillator based on periodic polarized crystals.The main contents are as follows:Firstly,the improvement of the Sellmeier formula about the periodic polarized crystals and the research of quasi-phase-matching(QPM)properties of second-order nonlinear processes based on these crystals.In the second-order nonlinear process,the momentum conservation satisfied by the interaction laser is closely related to the refractive index of the nonlinear crystal.The refractive index of the nonlinear crystal depends on the Sellmeier formula of the crystal,for example,the tuning characteristics of the output wavelength in SRO are closely related to the Sellmeier dispersion equation.However,the current coverage of Sellmeier equation is relatively narrow.First of all,we have fitted out the dispersion equation with wider coverage based on previous formulae and experimental results(mainly for PPLN,MgO:PPLN and MgO:sPPLT crystals).Meanwhile we also predicted the tuning characteristics of the nonlinear frequency conversion device based on the periodically poled crystal,for example,the tuning characteristics of IFD-SRO and IC-SFG-SRO process based on PP-crystals are predicted.And we have made a theoretical analysis of the broadband phase matching characteristics,so that these features provide important references for designing and tunning broadband mid-infrared lasers.Secondly,the output characteristics of the IFD-SRO are studied under plane-wave approximation and Gaussian beam approximation respectively.The output characteristics of IFD-SRO pumped by 532 nm green with MgO:sPPLT as nonlinear crystal and IFD-SRO pumped by 1064 nm infrared laser with MgO:PPLN as nonlinear crystal are fitted under plane-wave approximation and Gaussian beam approximation respectively.The theoretical calculation results are in good agreement with the experimental results.For the plane-wave approximation,some important fitting parameters are obtained,and the output characteristics of other IFD-SROs can be predicted based on these theories and parameters.For a collimated Gaussian beam approximation,the output characteristics can be calculated directly with the experimental known parameters.The relationship between the SH out-put power and SHG crystal length in IFD-SRO is predicted under two approximations.Two theoretical calculations show that when the pump power is given,the crystal is not selected as long as possible,but there is an optimal SHG crystal length to maximize the output power of the frequency-doubled laser,which will provide an important guidance on the selection of SHG crystal length optimization in the IFD-SRO.Through these theory,the output characteristics of the 397.5 nm laser radiation which are generated in IFD-SRO pumped by 532 nm with MgO:sPPLT are predicted.These laser are used to prepare for non-classical field about Rb atomic transition line in quantum optics.Thirdly,the output characteristics of the IC-SFG-SRO are studied under plane-wave approximation and Gaussian beam approximation respectively.After considering the different spatial sequences of SRO process and SFG process,the output characteristics of the IC-SFG-SRO are studied by using plane-wave approximation and Gaussian beam approximation respectively.The theoretical calculation results are in good agreement with the experimental results.Subsequently the relationship between the output characteristics of the IC-SFG-SRO and the SFG crystal length were calculated with two different theories,respectively.For the case of SRO+SFG,the optimal SFG crystal length is 0.5 times the length of the threshold,and for the case of SFG+SRO,the best SFG crystal length is 0.7 times the threshold length.Theoretical results show that there are optimal SFG crystal lengths at different pump powers.These results provide important guidance for the design and optimization of IC-SFG-SRO.And we can further theoretically predict the output characteristics about 323 nm generated in IC-SFG-SRO pumped by 532 nm with MgO:sPPLT,which is used to cool Li atoms in ultra-cold atomic physics experiments.