# finesse.thermal.hello_vinet¶

Hello-Vinet equations for thermal lenses in cylindrical mirrors. Higher order mode thermal effects are not implemented here. Therefore all the functions return some axially symmetric data.

Equations all based on :

Jean-Yves Vinet, “On Special Optical Modes and Thermal Issues in Advanced Gravitational Wave Interferometric Detectors” Living Review 2009

Functions

 eval_p_n_s_numerical(result) Evaluates a Fourier-Bessel decomposition fit performed with get_p_n_s_numerical(). get_p_n_s(a, w, n, m, chi, eta_n_s, eta_n_s_sq) Returns beam intensity overlap coefficients as calculated by Eq 3.33 in . get_p_n_s_numerical(I, a, s_max, material[, ...]) Performs a Fourier-Bessel decomposition of some axisymmetric irradiance distribution. ring_radiator_intensity(r, a, b_c, D_c, P_c) Calculates the intesity of incident on a mirror surface from an ideally thin ring radiator. substrate_temperatures(data, z, h) Computes the 2D substrate temperature distribution per Watt of absorbed power in each of the coating and substrate for an arbitrary axisymmetric heating irradiance computed with p_n_s_numerical(). substrate_temperatures_HG00(r, z, a, h, w, ...) Computes the 2D substrate temperature distribution per Watt of absorbed power in each of the coating and substrate from a HG00 beam. substrate_thermal_expansion_depth(data, z, h) Computes the depth displacements throughout the bulk of an optic due to coating absorption. Computes the depth displacements throughout the bulk of an optic due to coating absorption. Computes the depth displacement change of the surface of an optic due to coating absorption. Computes the depth displacement change of the surface of an optic due to coating absorption. Computes the depth displacement change of the surface of an optic due to bulk absorption from a generic axisymmetric heating profile. Computes the depth displacement change of the surface of an optic due to bulk absorption from a HG00 beam. thermal_lenses(data, h) Computes the substrate thermal lens per Watt of absorbed power in each of the coating and substrate for an arbitrary axisymmetric heating irradiance computed with get_p_n_s_numerical(). thermal_lenses_HG00(r, a, h, w, material[, ...]) Computes the substrate thermal lens per Watt of absorbed power in each of the coating and substrate from a HG00 beam. zeros_of_xjn_1_chi_jn(double chi, int n_max, ...) Compute the roots of the equation