c=3e8;          %speed of light
lambda = 1064e-9;

Finesse = 1e4;
L=0.2035;       %cavity length

%adjustable parameters
f=10;           %Let's look at 10 Hz
Pin= 10e-3;     % power input 10 mW
RIN= 1e-4;      % RIN level at 10 Hz
Abs= 5e-6;      %absorption level 5ppm

%%coating properties
alpha= 1.8e-6;        %effective thermal expansion coeff of the coatings
beta = 4.47e-6;       %effective dndt of the coatings
d= 4.4e-6;            %coatings thickness, 16doublets 300 ppm Transmission

%%substrate properties
Cap= 1.6e9;     %SiO2 heat capacity per volume J/(m^3.K)
kappa= 1.38;    %SiO2 thermal conductivity W/(m.K)

rt= sqrt( kappa/(2*pi*Cap*f) ); %thermal diffusion length inside SiO2
rg= 292e-6;                     %spotsize on the mirror
Volume= pi*rg*rg*rt;            %volume that is heat up from thermal fluctuation


 
%First, let's calculate dzdt = alpha*d - beta*lambda
%Result from M. Evans et.al. PHYSICAL REVIEW D 78, 102003 (2008)
%this is the combined thermoelastic and thermorefractive mechanisms
dzdT= alpha*d - beta*lambda; 


%Area under sine curve, 1/2 cycle, with amplitude A, frequency f, is A/2f
%Then heat absorbed from half cycle of fluctuation is
Q = Pin*RIN*Abs*Finesse/(pi*pi*f); %.

%To find dT, 
% Q = Volume * Cap *dT

dT = Q/(Volume * Cap);
dz = dzdT*dT;

%to calculate frequency noise, use dz/L = df/f

df = (dz/L)*(c/lambda);
df

% Freq noise is 1.4 mHz/rtHz at 10 Hz, from this calculation.