I use COMSOL to simulate the temperature distribution inside the mirror.
The mirrors are separate into 3 regions for different meshing quality see attached figures.
This model assume 0.95 emissivity on the surface, and 310 K at the surface between the mirror and the spacer.
The temperature between 10 mW and 10mW + RIN*10mW is plotted and fitted with polynomial function of order 9.
*the unit of y axis on fig3 is Kelvin
The Temperature difference will be applied to the coating surface and calculated the upper limit for photo thermal noise.
The function is
T = p1*z.^9 + p2*z.^8 + p3*z.^7 + p4*z.^6 +
p5*z.^5 + p6*z.^4 + p7*z.^3 +
p8*z.^2 + p9*z + p10;
where
p1 = -5.335e-10 ; %(-5.806e-10, -4.864e-10)
p2 = 1.602e-08 ;% (1.474e-08, 1.731e-08)
p3 = -2.041e-07 ;% (-2.188e-07, -1.894e-07)
p4 = 1.438e-06 ;% (1.347e-06, 1.528e-06)
p5 = -6.144e-06 ;%(-6.47e-06, -5.818e-06)
p6 = 1.645e-05 ;%(1.576e-05, 1.715e-05)
p7 = -2.773e-05 ;%(-2.858e-05, -2.687e-05)
p8 = 2.912e-05 ;%(2.857e-05, 2.967e-05)
p9 = -1.893e-05 ;%(-1.908e-05, -1.877e-05)
p10 = 7.548e-06 ;% (7.534e-06, 7.562e-06)
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