Kinetics of equivalent temperature of nonlinear-optical crystals

Summary form only given. Conventional method for the precise determination of optical absorption coefficients of nonlinear-optical crystals is laser calorimetry [1]. It is based on measurements of the heating kinetics of air near crystal surface during and after laser irradiation. Both optical absorption α and heat transfer h^T coefficients are then calculated by solving non-stationary heat conduction equation taking into account boundary conditions. However to the present day crystal temperature during interaction with laser radiation in such techniques is measured indirectly.We propose novel approach for crystal true temperature kinetics measurement employing crystal equivalent temperature directly determined from the crystal piezoelectric resonance (PR) frequency Rf shift. PR´s are observed in radiofrequency spectra of the crystal response to the applied probe electric field (see Fig. 1 (a)). PR´s frequencies are strongly temperature sensitive. Frequency shift of the certain PR is governed by the PR thermal coefficient Kprt: ǻRf(ǻT)=KprtǻT where ǻT=T2-T1 is crystal temperature change [2]. When crystal is nonuniformly heated by laser radiation the Rf depends on laser power P. For linear case Rf shift is ǻRf(P)=KproP, where Kpro is PR optical coefficient. Thus for the certain P value the crystal equivalent temperature change can be determined as ǻĬeq(P)=ǻRf(P)/Kprt [2]. In linear case ǻĬeq(P)=P where =(Kpro/Kprt) is PR light-thermal coefficient. Crystal equivalent temperature kinetics is directly measured using ǻRf dependence on time t when the laser power is switched on. As it is shown in Fig. 1 (b) the RF generator frequency is changed stepwise (step ǻf) and phase response (Ph) minimum that corresponds to Rf at moment ti is measured in each ǻ- t interval. Characteristic Rf kinetics time constant IJ is obtained by fitting Rf(t)=[Rf(0)-Rf(P)]exp(-t/IJ)+Rf(P). Obviously crystal equivalent temperature kinetics IJ value is identical to that of Rf kinetics. Then heat transfer coefficient is obtained hT=(mc)/(SIJ) where m is crystal mass, c is specific heat capacity, S is crystal surface area. Optical absorption coefficient is also calculated: L=hTS where L is crystal length. PR frequency kinetics were measured for LBO and PPLN crystals using CW Yb-doped fiber laser (=1064 nm). For these crystals results obtained from Rf kinetics measurements using concept of the equivalent temperature are presented in Fig. 1 (c). Novel method of piezoelectric resonance calorimetry allows to measure precisely nonlinear-optical crystal true temperature kinetics during its laser heating and to determine both heat transfer and optical absorption coefficients.