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Entry  Thu Feb 7 12:56:18 2013, Jamie, Summary, General, PRC/arm mode matching calculations 8x
    Reply  Thu Feb 7 17:10:11 2013, Koji, Summary, General, PRC/arm mode matching calculations 
       Reply  Fri Feb 8 00:23:33 2013, rana, Summary, General, PRC/arm mode matching calculations 
          Reply  Fri Feb 8 11:07:07 2013, Jamie, Summary, General, PRC/arm mode matching calculations 
             Reply  Fri Feb 8 12:42:45 2013, nicolas, Summary, General, PRC/arm mode matching calculations 
Message ID: 8022     Entry time: Thu Feb 7 12:56:18 2013     Reply to this: 8025
Author: Jamie 
Type: Summary 
Category: General 
Subject: PRC/arm mode matching calculations 

NOTE: There was a small bug in my initial calculation.  The plots and numbers have been updated with the fixed values.  The conclusion remains the same.

Using Nic's a la mode mode matching program, I've calculated the PRC mode and g-parameter for various PR2/3 scenarios.  I then looked at the overlap of the resultant PRC eigenmodes with the ARM eigenmode.  Here are the results:

NOTE: each optical element below (PR2, ITM, etc.) is represented by a compound M matrix.  The z axis in these plots is actually just the free space propagation between the elements, not the overall optical path length.

ARM

This is the ARM mode I used for all comparisons:

 flat_ARM_t.pdfflat_ARM_s.pdf

  tangential sagittal
gouy shift, one-way 55.63 55.63
g (from gouy) 0.303 0.303
g (product of individual mirror g) 0.303 0.303

PRC, nominal design (flat PR2/3)

This is the nominal "as designed" PRC, with flat PR2/3 folding mirrors.

flat_PRC_t.pdfflat_PRC_s.pdf

  tangential sagittal
gouy shift, one-way 14.05 14.05
g (from gouy) 0.941 0.941
g (product of individual mirror g) 0.942 0.942

 ARM mode matching: 0.9998

PRC, both PR2/3 flipped

This assumes both PR2 and PR3 have a RoC of -600 when not flipped, and includes the affect of propagation through the substrates.

 flipped_PRC_t.pdfflipped_PRC_s.pdf

  tangential sagittal
gouy shift, one-way 19.76 18.45
g (from gouy) 0.886 0.900
g (product of individual mirror g) 0.888 0.902

ARM mode matching: 0.9806

PRC, only PR2 flipped

In this case we only flip PR2 and leave PR3 with it's bad -600 RoC:

flipped_pr2_PRC_t.pdfflipped_pr2_PRC_s.pdf

  tangential sagittal
gouy shift, one-way 18.37 18.31
g (from gouy) 0.901 0.901
g (product of individual mirror g) 0.903 0.903

ARM mode matching: 0.9859

Discussion

I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.

I guess the main take away is that we get slightly better PRC stability and mode matching to the arms by only flipping PR2.

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