Theory Of Noncollinear Ultra-fast Frequency Doubling Based On BBO Crystal

The output wavelengths of solid laser are almost in the range of near-infrared and infrared.However,the application in the field of spectroscopy,Laser induced nuclear fusion and Laser lithography need short wavelength laser pulses which often obtained by frequency conversion.So it is must to study frequency conversion.The frequency conversion of ultrashort pulses different with that of cw laser need to reach phase matching and group velocity matching simultaneously,which make frequency conversion complicated.In this dissertation,non-collinear second harmonic generation of ultrashort pulse is studied.The analytic solution is obtained and the variation of second harmonic wave with frequency-doubling parameter is discussed.Firstly,the domestic and foreign research status of ultrashort pulse and laser frequency doubling are briefly reviewed.And then the basic knowledge of the ultrashort pulse frequency doubling is introduced,including coupled wave equation,phase matching,effective nonlinear coefficient,accepted angle,band width of frequency-doubling.Secondly,according to theory of frequency doubling,coupled wave equations for non-collinear frequency doubling of type I and condition of phase matching are derived.For BBO nonlinear crystal,the numeric solution for phase matching angle is obtained.For transformation-limited Gaussian pulses pumping,the analytic solution is obtained in pump undepleted approximation.The results shows that second harmonic waves have a broadening which is related to interaction length and temporal walk-off length.In the case of interaction length less than crystal,the harmonic pulses have an ideal Gaussian shape.It is also found that spatial distribution of second harmonic pulses is related with pulse width which can be used to measure sub-100 fs pulses.For chirped Gaussian pulses pumping,second harmonic wave ischirped Gaussian pulses,too.And the chirp can’t be used to compress pulse.Simultaneously,the chirp is linked with spatial distribution of second harmonic pulse.Then the quantity of chirp which have few effect on pulse width is analyzed.This study is of benefit to theory of frequency-doubling.