When a cavity is defined and with one or two objects of the class Mirror, it is possible to define an etalon effect in the input or end mirrors. For that we should add 2 ingredients:

• we need to give a certain AR reflectivity for the AR coating, for example a transmission of 1 – 0.001, to give a reflectivity of 0.1%
• specify the number of round trip in the substrate to simulate a very loss finesse cavity.

One example of such code is give in the OSCAR repository: Example_Mirror_as_input.m

But how to choose the right number of round trip in the substrate ? If it is too low, it will not account for all the reflections and so the energy will not be preserved. So the higher the reflectivity of the AR side, the higher the number of round trip necessary. Here a code to test that:

• define a flat – flat substrate without any loss
• try different numbers of round trip inside the substrate
• and the check of round trip when the loss is below 0.001 ppm (1E-9)

E_input = E_Field(G1,'w0', 0.001);

HR = Interface(G1,'RoC',inf,'CA',CA,'T',1E-3,'L',0);
AR = Interface(G1,'RoC',inf,'CA',CA,'T',1-1E-2,'L',0);


for ii=1:15  % try different number of round trips
        
    MI = Mirror(HR,AR,6.35e-3);
    MI.RT_inside = ii;
    
    [E_ref, E_trans] = Transmit_Reflect_Mirror(E_input,MI,'AR');
    
    Loss(ii) = abs(1 - (Calculate_Power(E_ref) + Calculate_Power(E_trans)));
    
end
ind_x_loss_inf = find(Loss < 1E-9);
semilogy(Loss)
ind_x_loss_inf(1)

Which give the following results (for a HR reflectivity of 99.9%):

AR reflectivity	Nb of round trip in substrate required
2% (very bad AR)	11
1%	10
0.5%	8
0.1%	7
500 ppm	6
100 ppm	5
50 ppm	5
10 ppm	4