I have defined my cavity but when I do a scan over one FSR, I can see the presence of some second order modes. Or when I look at the reflected power, I can see a mode LG10 or I do not have the maximum power gain. All that may indicate that the mode matching is not optimal.

The parameters of the fundamental mode on the input mirror could be easily calculated, however that is not the mode necessary for the optimal mode matching. The reason is that the input beam in OSCAR is defined at the level of the input mirror but outside the cavity. So the beam must pass through the input mirror which could act a lens if it is not a flat-flat mirror. By default, the substrate of the mirror is assumed to be infinitely thin, with a refractive index of 1.45 and with a second flat surface outside the cavity.

“Thank you, it is all clear but I do not want to do complicated calculation.”, yes and you are right. The optimal input beam parameter can be found with the command;

C1.Check_Stability

With C1, object of class Cavity1 and the last lines in the command window would be something like:

Mode matched input beam parameters:
Beam radius [m]: 0.0205755  	 	 Wavefront curvature [m]: -1724.14  

That is the value of the beam parameters for the optimal mode matching (derive with the ABCD matrix):

E_input = E_Field(G1,'w',0.0205755,'R',-1724.14);

One method has been introduced since the version 3.30 of OSCAR with an automatic mode matching argument for the input laser:

E_input = E_Field(G1,'Optimal_MM',true);