Temperature distributions and thermal deformations of mirror substrates in laser resonators

Abstract

For finite-thickness media with convective surface losses, the three-dimensional temperature distributions and thermal deformations of mirror substrates in laser resonators that are due to absorption of laser light with a Gaussian power-density profile are calculated by use of the well-known Green's function methods. Some expressions and theoretical profiles of the temperature distributions and thermal deformations as functions of the radius and the thickness of a mirror substrate are obtained. The results of the calculations show that the rise in temperature is closely related to the absorption coefficient of the medium as well as to the convective heat-transfer coefficient, that the initial thermal deformations of mirror surfaces increase quickly at the beginning of laser heating and that then the thermal deformations are insensitive to laser heating times. Meanwhile, thermal deformations of a silicon mirror are experimentally demonstrated by use of CO(2) laser irradiation. The experimental trends of thermal deformations are in agreement with the theoretical profiles.

Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals

“…By considering a Gaussian source term and longitudinal absorption, Usivich et al could present an analytical solution for the time-independent heat equation in the cylindrical coordinates [27]. Peng et al solved the 3D steady-state heat equation for a cylindrical laser mirror by use of the Green's function method [28]. By considering a rectangular Nd:YVO 4 crystal as an anisotropic one and imposing the constant temperature condition for six sides, Shi et al could solve the heat equation semianalytically [11].…”

“…The rearrangement of Eq. (13) gives us the f lmn t equation as df lmn t dt Γ lmn ρC f lmn t ηE abs Q 0 ρCτ p q l s m t n εt: (28) The equation above can be solved simply with the help of the following formula:…”

Irradiation effects in CaF2 probed by Raman scattering

“…A broad transmission window as a result of a wide band gap of 11 eV and a low refractive index are some of the optical properties that make calcium fluoride (CaF 2 ) one of the most versatile ionic insulators. CaF 2 is found in numerous technological applications including lenses for infrared spectroscopy, thin‐film optical coats, insulating layers on top of semiconductor microstructures, as well as deep UV or high‐power laser windows . However, CaF 2 is sensitive to ionizing radiation.…”

In situ Resonant Ultrasound Spectroscopy during irradiation of solids with relativistic heavy ions

“…is a widely used material. Recently, its application as windows for high-power lasers had been studied [10]. Upon ion irradiation a-SiO 2 usually densifies, which is explained by a rearrangement of the ring network into smaller, compacter rings [11].…”