A Mode matching to an optical cavity

[kelly0303]

Hello! I need to mode match a laser light to an optical cavity and I am a bit unsure what is the most time efficient way of doing so. The cavity is a symmetrical bow-tie and I inject the light from one of the flat mirrors (the other 2 are concave). In this case, I want the shape of the gaussian beam after passing through the mode matching lenses, to have the waist right in between the 2 flat mirrors. Doing ABCD matrix formalism I know the expected waist in the steady state inside the cavity. I can also calculate the waist after the beam passes through the lenses (given my setup it turns out I need first a divergent than a convergent lens). However, for this latter case, there are several unknowns, for example, I can use the formula for the ABCD formalism for a thin lens, but how do I account for the thickness of the lenses? Or, the light passes through an EOM, do I just assume that is a block of glass of a given index of refraction? Overall, I might get an estimate, but I can't precisely calculate the needed lenses focal lenses and distance between them. What is the best way, starting from the calculations, to optimize in practice the mode matching?