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Entry  Fri Feb 8 18:23:32 2013, Jamie, Summary, General, arbcav of half PRC with flipped PR2 prm23t-modes.pdfprm23t-geometry.pdf
    Reply  Fri Feb 8 19:29:44 2013, yuta, Summary, General, arbcav of half PRC with flipped PR2 
       Reply  Mon Feb 11 17:17:30 2013, Jamie, Summary, General, more analysis of half PRC with flipped PR2 foo.pdf
          Reply  Tue Feb 12 18:25:43 2013, Jamie, Summary, General, half PRC with astigmatic PR2/3 
Message ID: 8059     Entry time: Mon Feb 11 17:17:30 2013     In reply to: 8041     Reply to this: 8068
Author: Jamie 
Type: Summary 
Category: General 
Subject: more analysis of half PRC with flipped PR2 


We need expected finesse and g-factor to compare with mode-scan measurement. Can you give us the g-factor of the half-PRC and what losses did you assumed to calculate the finesse?

This is exactly why I added the higher order mode spacing, so you could calculate the g parameter.  For TEM order N = n + m with spacing f_N, the overall cavity g parameter should be:

g = (cos( (f_N/f_FSR) * (\pi/N) ))^2

The label on the previous plat should really be f_N/FSR, not \omega_{10,01}

BUT, arbcav does not currently handle arbitrary ABCD matrices for the mirrors, so it's going to be slightly less accurate for our more complex flipped mirrors.  The affect would be bigger for a flipped PR3 than for a flipped PR2, because of the larger incidence angle, so arbcav will be a little more correct for our flipped PR2 only case (see below).


Also, flipped PR2 should have RoC of - R_HR * n_sub (minus measured RoC of HR surface multiplied by the substrate refractive index) because of the flipping.

This is not correct.  Multiplying the RoC by -N would be a very large change.  For an arbitrary ABCD matrix:

R_eff = -2 / C

When the incident angle in non-zero:

tangential: R_eff = R_eff / cos(\theta)
sagittal:   R_eff = R_eff * cos(\theta)

For flipped PR2, with small 1.5 degree incident angle and RoC of -706 at HR:

M_t = M_s = [1.0000, 0.0131; -0.0028, 1.0000]
R_eff = 705.9

For flipped PR3, with large 41 degree incident angle and RoC of -700 at HR:

M_t = [1.0000, 0; 0.0038, 1.0000]
M_s = [1.0000, 0; 0.0022, 1.0000]
R_eff = 592.4

The affect of the substrate is negligible for flipped PR2 but significant for flipped PR3.

The current half-PRC setup

OK, I have now completely reconciled my alamode and arbcav calculations.  I found a small bug in how I was calculating the ABCD matrix for non-flipped TTs that made a small difference.  I now get the exact same g parameter values with both with identical input parameters.


According to Jenne dictionary, HR curvature measured from HR side is;

PRM: -122.1 m
PR2: -706 m
PR3: - 700 m
TM in front of BS: -581 m

Sooooo, I have redone my alamode and arbcav calculations with these updated values.  Here are the resulting g parameters

  arbcav a la mode measurement
g tangential 0.9754 0.9753 0.986 +/- 0.001
g sagital 0.9686 0.9685 0.968 +/- 0.001

So the sagittal values all agree pretty well, but the tangential measurement does not.  Maybe there is an actual astigmatism in one of the optics, not due to angle of incidence?

arbcav HOM plot:


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