Complete anisotropic time-dependent heat equation in KTP crystal under repetitively pulsed Gaussian beams: a numerical approach

Abstract

In this work, a thorough and detailed solution for the time-dependent heat equation for a cylindrical nonlinear potassium titanyl phosphate (KTP) crystal under a repetitively pulsed pumping source is developed. The convection and radiation boundary conditions, which are usually ignored in the literature, have been taken into account, and their importance on the temperature distribution has been discussed in detail. Moreover, the temperature dependence of thermal conductivity of KTP was considered in the calculations, and its impact is discussed. It is shown that the radiation term has a negligible effect and can be dropped safely, while the temperature dependence of thermal conductivity is more influential, such that ignorance of it brings some errors into the modeling. The time evolution of the temperature while the crystal is pumping with a train of successive Gaussian pulses until reaching equilibrium is shown. To accomplish numerical calculations, we developed a homemade code written with the finite difference time domain method in Intel Fortran (ifort) and ran it with the Linux operating system.

Thermal lens analysis in a diode-pumped 10 Hz 100 mJ Yb:YAG amplifier

“…Isotropic and anisotropic crystals were considered in different pumping schemes and boundary conditions. The most complete study, to our knowledge, was performed by Rezaee et al [28] , where a finite difference time domain method was used to solve the equation for an anisotropic crystal and a Gaussian pump profile. Moreover, it presents solutions for nonlinear boundary conditions including convection and radiation.…”

“…where η s is the fraction of power dissipated as heat (normally associated with the quantum defect 1 − λ p /λ l , where λ p and λ l are the pump and lasing wavelengths, respectively), w p is the pumping waist size inside the gain medium, γ is the absorption coefficient and P(t) accounts for the pump temporal profile. The boundary conditions for such a geometry have been intensively studied in previous works [11,24,28] . In the general case, Newton's law of heat transfer governs the boundary conditions.…”