Matlab script

% caculates the cavity spectrum and the frequency distance between TEM_00 % and higher order modes m+n. Two curved mirrors possible. % % 1. Vers.: 14.03.12 , T.Legero % Revised : 19.11.13 , T. Legero , Two curved mirrors possible.

clear all; clc;

Len = 0.48; % cavity length in [m] Curv1 = 1000000000; % mirror no. 1 curvature in [m] Curv2 = 1; % mirror no. 2 curvature in [m] Refl = 0.99998; % reflectivity of mirrors c = 299792458; % speed of light [m/s]

FSR = c /(2*Len); % Free-Spectral-Range Gouy = FSR/pi*acos(sqrt¹⁾); % Gouy-Phase

% Finesse = pi*sqrt(Refl)/(1-Refl); % linewidth = FSR/Finesse;

fprintf('Cavity length L = %g m ⇒ FSR = %g MHz\n', Len, FSR/1E6); fprintf('Radius of Curvature R1 = %g m and R2 = %g m ⇒ Gouy = %g MHz\n\n', Curv1, Curv2, Gouy/1E6);

%fprintf('Reflectivity R = %g ⇒ Finesse F = %d \n ⇒ Linewidth d = %g MHz \n\n' , Refl, round(Finesse),linewidth/1E6);

mn_max = 100; w_max = 100;

delta = zeros(mn_max,w_max);

for w = 1:w_max

  for mn = 1:mn_max
      delta(mn,w) = w*FSR - mn*Gouy; % Freq.Diff. von (q-w)ter höherer 
                                     % Mode mn zu q-ter TEM_00-Mode 
      if (abs(delta(mn,w)) < 10E6)
         fprintf('Freq. diff. of m+n = %g higher order mode to 00-mode is %g MHz\n', mn, delta(mn,w)/1E6); 
      end
                                         
  end

end

%% plot

mn = 4; % Modenumber of Higher-Order-Mode to plot R = 0.95:0.01:1.05; % Vary Mirror-Curvature

G = FSR./pi*acos(sqrt(1-Len./R)); % Gouy-Phase %G = FSR./pi*acos(sqrt²⁾); % Gouy-Phase d = FSR - mn*G; % Difference between TEM_00 and TEM_mn

plot(R,G);