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08 Jul 2008 (Updated )

An optical FFT code to simulate Fabry Perot cavities with arbitrary mirror profiles

clear all; close all; clear classes

disp('                  OSCAR V3.13                                   ')
disp('  ')

% Define the grid for the simulation: 128 X 128, 40 cm X 40 cm
G1 = Grid(128,0.4);

% Define the incoming beam on the input mirror surface (beam radius 4.3 cm,
% wavefront curvature -1034 m, propagating toward the waist)
E_input = E_Field(G1,'w',0.043,'R',-1034);

% Add the sidebands to the field E1, frequency of modulation 6.7 MHz,
% modulating index 0.3
E_input = Add_sidebands(E_input,6.7234E6,0.3);

% Define the 2 mirrors, RofC_IM = 1500m, RofC_IM = 1700m, 30 cm in
% diameter, transmission 5% for the input mirror and 0.5% for the end
% mirror.

IM = Interface(G1,'RoC',1500,'CA',0.35,'T',0.05);
EM = Interface(G1,'RoC',1700,'CA',0.35,'T',0.005);

% Use the 2 previous Interfaces and the input beam to defing a cavity 3000
% meter long
C1 = Cavity1(IM,EM,3000,E_input);
C1.Laser_start_on_input = false ;

Nb_point = 200;                                     % Number of points for the scan

Phase_scan = zeros(Nb_point,1);           % Phase shift used to scan the cavity
Sig.p = zeros(Nb_point,1);                      % Demodulated signal in phase in reflection from the cavity
Sig.q = zeros(Nb_point,1);                      % Demodulated signal in quadrature in reflection from the cavity = zeros(Nb_point,1);               % Circulating power of the carrier in the cavity
Power.SBl = zeros(Nb_point,1);               %  Circulating power of the lower sideband in the cavity
Power.SBu = zeros(Nb_point,1);              %  Circulating power of the upper sideband in the cavity

for i=1:Nb_point
    Phase_scan(i) = i*(2*pi)/Nb_point;          % Scan the round trip phase shift from 0 to 2 pi
    C1.Resonance_phase = exp(1i*Phase_scan(i));         % Set the round trip phase shift for the cavity
    C1 = Calculate_fields(C1);                  
    [Sig.p(i) Sig.q(i)] = Demodulate_SB(C1.Field_ref);       % Demodule the carrier with the sidebands in reflection
 = Calculate_power(C1.Field_circ);           % calculate also the power of the carrier circulating in the cavity                       
     [Power.SB1(i) Power.SB2(i)] = Calculate_power_SB(C1.Field_circ);   % and the sidebands

% Plot all the results

hold all
hold off
legend('Signal in phase','Signal in quadrature')
title('Demodulated PDH signal in reflection')
xlabel('Cavity round trip phase shift')
ylabel('Signal [a.u.]')

hold all
hold off
legend('Carrier','Lower sideband','Upper sideband')
title('Power of the fields circulating inside the cavity')
xlabel('Cavity round trip phase shift')
ylabel('Power [W]')


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