Mode Matching

I descirbe what mode matching is in the context of illuminating a Fabry-Perot cavity with a laser beam, why it is necessary, and give one simple way to choose lenses to get close to the ideal mode matching geometry.

[@subhashishbarik4319]

This is really helpful, thanks a ton :) Lot of important information put in a very understandable fashion in a short video.

[@z44eg]

Perfectly useful and simple! Thank you a lot!

[@jiwenguan4604]

thanks a lot.

[@bund008]

Thanks a lot!

[@drbeyersdorf]

If one mirror of a Fabry-Perot is flat, the mode matching condition is that there is a waist at the location of that mirror, and that the waist size be such that by the time the beam gets to the other mirror its curvature matches that of the second mirror. If BOTH mirrors are flat, there is no way to mode match (in theory you could, but you'd need an infinitely large beam waist) such a cavity is unstable.

[@gitu1]

Thanks for the explanation. Could you also please explain the mode matching conditions for a flat mirror Fabry-Perot cavity??

[@PapaMuntz1992]

There is a mistake in your calculations for 'controlling waist size' (around the 10 min mark), right?. The imaginary part of 1/q3 looks different when I calculate it by hand (and additionally with mathematica). The numerator in the imaginary part should be lambda/(pi*w1^2). Maybe my calculations are wrong. Could you comment on that?

[@kingrobert04]

Dear Peter, I have a (probably) stupid question: does the light from the laser reflect from the back of the mirror as it enters the cavity or does all the light from the laser make it into the cavity (ideally)?

[@hjg03]

+kingrobert04 The mirror will probably have an anti-reflection coating on its back side to minimize reflection off of its surface. However, all of the light will be reflected from the cavity if the light is not on resonance. The peaks one sees in transmission are "100%" transmission, whose narrowness is determined by the finesse of the cavity.

[@sruthiv868]

Could you please tell me the mode matching into triangular cavity in which two of them are plane mirrors?

[@drbeyersdorf]

The procedure to mode match into a triangular cavity is the same as a linear cavity, but for calculating the eigenmode of the cavity use half of the cavity perimeter in place of the cavity length (L -> p/2). The other difference is that the reflection at non normal incidence from the curved mirror introduces astigmatism. This is usually dealt with by minimizing the angle of incidence on the curved mirror when building the cavity. Typically a triangular cavity would have two planar mirrors that are partial reflectors and oriented at nearly 45 degrees to the input beam. One is the input coupler, and one is the output coupler. The third mirror is a curved high reflector that forms the third point on the triangle and is at near normal incidence.

[@sruthiv868]

Thank you so much!