A. V. Konyashkin

Piezoelectric resonance calorimetry of nonlinear-optical crystals under laser irradiation

Novel method is proposed for determination of nonlinear-optical crystal both heat transfer and optical absorption coefficients by measuring kinetics of the laser-irradiated crystal temperature-dependent piezoelectric resonance frequency. When laser radiation propagates through the crystal its temperature evaluation with time is directly determined from crystal piezoelectric resonance frequency shift, which is precisely measured by analyzing crystal response to the applied ac electric voltage. Heat transfer and optical absorption coefficients are obtained using measured characteristic time of crystal laser heating kinetics by solving nonstationary heat conduction equation. Experiments were performed with nonlinear-optical α-quartz, lithium triborate (LBO) and periodically poled lithium niobate (PPLN) crystals.

Impedance spectroscopy for measuring low optical absorption coefficients of nonlinear optical crystals

Novel piezoelectric resonance laser calorimetry technique, based on impedance spectroscopy, is introduced for measuring low optical absorption coefficients of nonlinear-optical crystals. This method exploits dependence of crystal piezoelectric resonance frequencies on its temperature. Nonuniform temperature of the crystal heated by laser radiation is characterized by equivalent temperature that is directly determined by measuring frequency shift of certain piezoelectric resonance calibrated on temperature. Kinetics of crystal equivalent temperature during its interaction with laser radiation is obtained by measuring frequency kinetics of piezoelectric resonance. It is demonstrated that optical absorption coefficient can be determined from the linear slope of initial part of temperature kinetics. Basing on experiments with LiB3O5 and LiNbO3 crystals it was proved that values of optical absorption coefficients determined from initial part and full time kinetics of equivalent temperature have almost the same values.

Equivalent temperature of nonuniformly heated nonlinear-optical crystals in course of laser radiation frequency conversion

Novel method of piezoelectric resonance spectroscopy is introduced for nonlinear-optical crystals equivalent temperature measurement during frequency conversion of laser radiation. Equivalent temperature of the crystal heated by laser radiation is directly determined from its strongly temperature sensitive piezoelectric resonance frequencies. Method was applied for PPLN crystal temperature measurement during second harmonic generation of CW ytterbium fiber laser radiation. Temperature tuning curves of PPLN and its phase matching temperature dependence on pump power were precisely measured using concept of the equivalent temperature. Hysteresis of PPLN temperature and optical bistability of second harmonic power in respect to pump power were observed.

Resonant acoustic spectroscopy of the interaction of the single-mode high-power laser radiation with crystals

Resonant acoustic spectroscopy technique gives the opportunity to measure the crystal temperature during linear and nonlinear interaction of the laser radiation with crystals. It is based on the registration of the crystal piezoelectric or acoustical resonance frequency change caused by the interaction of the laser radiation with crystals. Piezoelectric resonance is observed by measuring the dependence of the sample electrical impedance on the external electric field frequency. It is shown that inhomogeneous crystal heating can be characterized by the equivalent crystal temperature depending on the influence laser power. Equivalent crystal temperature can be directly determined from the measured piezoelectric resonance frequency.

Model of resonant acoustic spectroscopy of interaction of high power single-mode laser radiation with crystals

Every nonlinear optical laser frequency conversion process is accompanied by the crystal heating due to the absorption of some part of the radiation energy. Optical absorption coefficients and internal crystal temperature distribution during interaction with the high-power laser radiation are directly determined from modelling the experimentally obtained stationary and kinetics data of the radiation-induced frequency shifts of the crystal piezoelectric resonances.

Self-Action of Second Harmonic Generation and Longitudinal Temperature Gradient in Nonlinear-Optical Crystals

Model of second harmonic generation with thermal self-action was developed. Second harmonic generation temperature phase matching curves were measured and calculated for periodically polled lithium niobate crystal. Both experimental and calculated data show asymmetrical shift of temperature tuning curves with pump power.

Concept of equivalent temperature of the nonlinear-optical crystal interacting with nonuniform laser radiation

Experimental criterion was determined for application of equivalent temperature of nonlinear-optical crystal heated both uniformly and nonuniformly by laser radiation with known spatial distribution of intensity. Novel coefficients are introduced in laser physics that characterize thermal response of crystal to the laser radiation propagating through it. Theoretical model is proposed for calculation of these coefficients. Physical parameters of nonlinear-optical crystals were determined that have significant influence upon correspondence between calculated and measured values of introduced coefficients.

Equivalent temperature of nonlinear-optical crystals in process of laser frequency conversion

Summary form only given. For more than fifty years numerous experimental and theoretical works give evidence of the crucial functional role of the nonlinear-optical crystal heating in various processes of laser frequency conversion including second harmonic generation. However to the present day no precise methods have been proposed for the determination of the true crystal temperature in processes of nonlinear-optical frequency conversion [1]. To our belief the notion of the “Equivalent temperature of the non-uniformly heated nonlinear-optical crystal” that was recently introduced in laser physics [2] can help in solving such problems. It is well known that nonlinear-optical crystals possess piezoelectric properties. If crystal is placed inside the capacitor then acoustical vibrations are excited in crystal when low amplitude voltage at the frequency f from the radiofrequency (rf) generator is applied to the capacitor plates. At the certain frequency Rf piezoelectric resonance between the external electric field and one of the crystal internal vibration modes can be observed. Signal voltage UR that is measured on the load resistor R, connected in series with the capacitor, has specific peculiarity in the vicinity of the piezoelectric resonance (see Fig. 1 (a)). Piezoelectric resonance frequencies are strongly temperature sensitive. In case of the uniform crystal heating frequency shift of the certain piezoelectric mode is governed by the piezoelectric resonance thermal coefficient Kprt of this mode: ΔRf(ΔTcr)=Kprt ΔTcr where ΔTcr is crystal temperature change in respect to the initial temperature T0 [2]. When crystal is non-uniformly heated by laser radiation its resonance frequency shift depends on laser power Pp. In this case equivalent crystal temperature Θeq is directly determined from the piezoelectric resonance frequency shift as follows: Θeq(Pp)=T0+[Rf(Pp) - Rf(0)]/Kprt, where T0 is crystal temperature at Pp=0. Periodically poled lithium niobate crystal (PPLN) was used in experiment of the CW polarised single-mode Yb-doped fiber laser (λ1=1064 nm, Δλ1=0.1 nm) second harmonic generation (SHG) (λ2=532 nm). Laser radiation is focused into the PPLN (beam waist is 30 μm), placed in unclamped manner between strip electrodes in thermostat. Figure 1 (b) shows dependencies on Pp of both the PPLN equivalent temperature measured using resonance (Rf(0)=2024.0 kHz at Tcr=20 °C, Kprt= -179 Hz/°C) and generated second harmonic power Psh. Thermostat temperature is fixed (T0 = 20 °C) and PPLN equivalent temperature in each Pp point is measured after reaching stationary temperature state. At low Pp values PPLN is linearly heated with coefficient β=1.68 °C/W. Nonlinear Θeq and Psh rise is observed as PPLN temperature approaches phase matching temperature. Point Pp=13.4 W is unstable and subsequent Pp increase leads to considerable Psh rise from Psh=90 mW at Pp=13.4 W to Psh=570 mW at Pp=13.5 W. Crystal temperature change during SHG is precisely measured. PPLN phase matching temperature measured for Pp=13.5 W is Tpm=52.2 °C and crystal temperature acceptance bandwidth is ΔTpm=6 °C. PPLN crystal true phase matching temperature dependence on pump power is determined to be dTpm/dPp= -0.11 °C/W.

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 hT 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. PRs are observed in radiofrequency spectra of the crystal response to the applied probe electric field (see Fig. 1 (a)). PRs 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 ǻt 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.

Temperature determination of nonlinear optical crystals heated by laser radiation

Nonuniform temperature distribution inside the nonlinear-optical crystal heated by the high-power laser radition is characterised by the equivalent crystal temperature, which is directly determined from the measured frequency of the crystal piezoelectric resonance.