## Question: Regarding parameters of the PRC.

We are trying to get the parameters of the PRC so that it is mode matched with the FPMi. But there are so many parameters that need to be considered at once here. Is there a way to determine them numerically or on paper and not by iterating over all the variables? Iterating over them just seems like a trial and error way to do it and it won’t tell us what exactly is happening in the cavity.

## One comment on “Question: Regarding parameters of the PRC.”

1. Sean Leavey says:

Hi Sagar,

If you look at the simplified Advanced LIGO file provided for Option B, you’ll see that it defines cavities using the cav command. What this does is tell Finesse that the mirrors and nodes specified in the command form cavity, and Finesse should automatically match the incoming beam to the cavity basis (i.e. it makes it perfectly match the cavity mode). This gets a little more complicated if you have multiple cavities (see this cheatsheet for more information), but that’s the basic principle of operation. The key thing to know is that you can view the results of this automatic beam tracing by using the trace command (you’ll have to read the documentation for this command to understand which options to use). This command can tell you the beam size, Rayleigh range, etc. at each node in the perfectly mode matched arm cavities case, if you define cav commands for your arm cavities. Can you then use the information for the beam at your PRM using the trace command to decide how you must set its radius of curvature to match the laser transmitting through the PRM to the (identical) arm cavity eigenmodes? Remember that in the option description you are told to place a lens in front of each arm cavity which should significantly simplify the number of radii of curvatures you must set elsewhere.