Gaussian beam in a Fabry-Perot interferometer

[Malamala]

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!

 

[wcghha]

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

 

[Malamala]

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]

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.

Interesting point. If you have seen a 'resonator stability diagram', you will find that planar resonators are "conditionally stable", but it's unclear if there are Gaussian modes for a planar resonator. Here's a link to the worked-out problem:

(Abstract):
The transmission of a Gaussian beam through a Fabry–Perot interferometer (FPI) has been investigated. The equation for the electric field of the transmitted beam was derived and then the transmitted irradiance was numerically calculated for different selected parameters of both the FPI and the beam. The results show that the energy profile of the transmitted beam has been distorted to different degrees depending on the various parameters of the Gaussian beam and the FPI. Moreover the results show that the positions of the peaks of the transmitted beam are shifted, especially for intermediate waists for which the arctan term is nonlinear. The results also show that for nonnormal incidence successive transmitted beams are spatially separated and are not interfering appreciably with each other.

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-33-18-3805