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 tem- erature 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.