# Gaussian beam in a Fabry-Perot interferometer

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## Main Question or Discussion Point

Hello I am reading some introductory laser cavity stuff and I am a bit confused about the existence of gaussian beams in the Fabry-Perot interferometer. If you solve the stability condition for a cavity (i.e. asking for the q parameter to reproduce itself after one round trip) you get that in order to obtain a stable cavity you need that the radius of curvature of the gaussian beam at each of the 2 mirrors should be the same as the radius of the mirrors. In general this is easily achievable (for stable cavities) by placing the beam waist at the right place. However in the case of Fabry-Perot interferometer, the radius would be infinity, while the gaussian beam has radius infinity just at the waist, and it is not possible to make it has infinite radius at 2 points. Does this mean that Fabry-Perot interferometer is not stable for gaussian beams? Yet it appears on the list of stable resonators. Can someone explain this to me? (I am sorry if the question is dumb, it is my first encounter with the topic). Thank you!

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I suppose that the stable FP cavity mentioned in the list refers to the one using curved coupling mirrors, whose radius is finite.

I suppose that the stable FP cavity mentioned in the list refers to the one using curved coupling mirrors, whose radius is finite.
Yes, I understand that case. But FP cavities with flat mirrors (i.e. almost infinite radius) exist in practice. I am not sure I understand how does the field looks inside the cavity, as a Gaussian beam doesn't make sense.

Andy Resnick