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Message ID: 14120     Entry time: Tue Jul 31 22:50:18 2018
 Author: aaron Type: Update Category: OMC Subject: OMC Expected Refl Signal

I learned a lot about lasers this week from Siegman. Here are some plots that show the expected reflectivity off of the OMC for various mode matching cases.

The main equation to know is 11.29 in Siegman, the total reflection coefficient going into the cavity:

$R=r-\frac{t^2}{r}\frac{g(\omega)}{1-g(\omega)}$

Where r is the mirror reflectivity (assumed all mirrors have the same reflectivity), t is the transmissivity, and g is the complex round-trip gain, eq 11.18

$g(\omega)=r_1r_2(r_3...)e^{-i\phi}e^{-\alpha_0p}$

The second exponential is the loss; in Siegman the \alpha_0 is some absorption coecfficient and p is the total round trip length, so the product is just the total loss in a round trip, which I take to be 4*the loss on a single optic (50ppm each). \phi is the total round trip phase accumulation, which is 2\pi*detuning(Hz)/FSR. The parameters for the cavity can be found on the wiki.

I've added the ipynb to my personal git, but I can put it elsewhere if there is somewhere more appropriate. I think this is all OK, but let me know if something is not quite right.

 Attachment 1: omcRefl.pdf  21 kB  Uploaded Wed Aug 1 13:43:48 2018
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