Temperature variation in the process of terahertz wave generation by intense laser pulses

To reach satisfactory energy efficiency of the optical-to-terahertz frequency conversion, femtosecond and nanosecond pulsed periodic lasers are used. This considerably affects the lattice temperature and can lead to the dramatic decrease in conversion efficiency. Nevertheless, the calculations done during the development of a conversion method are often based on the parameters of the non-linear medium taken without an account for its heating up by focused laser radiation. This can result in unpredicted effects. We have developed a method for the account for non-linear medium heating based on first-principle analytical study of thermo-optical processes that take place in nonlinear-optical crystal structures under periodic femtosecond or nanosecond pumping. The developed approach will allow the experimentalists evaluate the temperature and thermo-optical anomalies just inside a pumped volume in every particular case. It is generally considered that the refractive index of a crystal is uniquely defined by the crystal temperature and its stress-strain state. In case of short laser pulses, the situation is more complicated: 1) for times less than the highest relaxation time of photo-excited carriers and phonon subsystem, the concept of crystal temperature cannot be defined. In this time interval, even if the dielectric constant can be correctly defined at each moment, the computation of the refraction coefficient is a kinetics-type problem; 2) if the time interval exceeds the relaxation time, but is shorter than the sound propagation time, it is necessary to take into account the temperature waves; 3) if the time interval exceeds the sound propagation time, the standard parabolic equation for temperature is quite correct. We demonstrate that with a short pump pulse and a high pulse repetition frequency, the parabolic equation gives the correct results. We have developed analytical and numerical methods for calculating the temperature for pulsedperiodic pumping. Numerical methods are not considered here. For the established periodic regime, an analytical solution for a specific experimental scheme can be obtained using known solutions from existing reference materials, replacing the time dependence. In experiments for measuring dn/dT in some cases it is not this value that is directly determined, but the temperature coefficient of the optical path length change ds/dT, which describes the thermally induced distortion of a beam during its passing through a sample. Transversal inhomogeneity of crystal heating will lead to variation in change of optical path length for radiation propagating at different distances from the pumping beam optical axis. In turn, this will result in inclination, spherical deformation (“thermooptical lens” effect) or more complicated distortion of optical pumping wave front. Spatially inhomogeneous depolarization of radiation is also possible

To reach satisfactory energy efficiency of the optical-to-terahertz frequency conversion, femtosecond and nanosecond pulsed periodic lasers are used. This considerably affects the lattice temperature and can lead to the dramatic decrease in conversion efficiency.
Nevertheless, the calculations done during the development of a conversion method are often based on the parameters of the non-linear medium taken without an account for its heating up by focused laser radiation. This can result in unpredicted effects.
We have developed a method for the account for non-linear medium heating based on first-principle analytical study of thermo-optical processes that take place in nonlinear-optical crystal structures under periodic femtosecond or nanosecond pumping. The developed approach will allow the experimentalists evaluate the temperature and thermo-optical anomalies just inside a pumped volume in every particular case.
It is generally considered that the refractive index of a crystal is uniquely defined by the crystal temperature and its stress-strain state. In case of short laser pulses, the situation is more complicated: 1) for times less than the highest relaxation time of photo-excited carriers and phonon subsystem, the concept of crystal temperature cannot be defined. In this time interval, even if the dielectric constant can be correctly defined at each moment, the computation of the refraction coefficient is a kinetics-type problem; 2) if the time interval exceeds the relaxation time, but is shorter than the sound propagation time, it is necessary to take into account the temperature waves; 3) if the time interval exceeds the sound propagation time, the standard parabolic equation for temperature is quite correct. We demonstrate that with a short pump pulse and a high pulse repetition frequency, the parabolic equation gives the correct results.
We have developed analytical and numerical methods for calculating the temperature for pulsedperiodic pumping. Numerical methods are not considered here. For the established periodic regime, an analytical solution for a specific experimental scheme can be obtained using known solutions from existing reference materials, replacing the time dependence.
In experiments for measuring dn/dT in some cases it is not this value that is directly determined, but the temperature coefficient of the optical path length change ds/dT, which describes the thermally induced distortion of a beam during its passing through a sam-ple. Transversal inhomogeneity of crystal heating will lead to variation in change of optical path length for radiation propagating at different distances from the pumping beam optical axis. In turn, this will result in inclination, spherical deformation ("thermooptical lens" effect) or more complicated distortion of optical pumping wave front. Spatially inhomogeneous depolarization of radiation is also possible Some concrete results (LiNbO3 crystals) [1]. Case A. A cylinder-shaped crystal with radius 0.5 cm,

Fig.1a
much smaller than its doubled length ( Fig.1(a)). Pumping radiation with Gaussian profile of diameter 100 m propagates along the cylinder axis. On the crystal surface the heat exchange with air at 300 K Fig.1(b) temperature takes place according to Newton's law. The heat exchange coefficient is taken 8 W/m 2 K. The graph of the corresponding dependence on the transversal coordinate r is shown in Fig.1(b). With an increase in the repetition period of the pump pulses from 10 -8 seconds to 10 -3 seconds, the width of the profile of the temperature distribution increases approximately twice.