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Entry  Wed Jan 30 11:16:32 2013, Jenne, Update, Locking, Mode spacing calc 
    Reply  Wed Jan 30 15:45:09 2013, Zach, Update, Locking, Mode spacing calc HOM11.pngHOM55.png
       Reply  Thu Jan 31 14:30:50 2013, Jenne, Update, Locking, Mode spacing calc Half_PRC_Configs.pdf
          Reply  Thu Jan 31 15:20:46 2013, Zach, Update, Locking, Mode spacing calc 
Message ID: 7961     Entry time: Wed Jan 30 11:16:32 2013     Reply to this: 7966
Author: Jenne 
Type: Update 
Category: Locking 
Subject: Mode spacing calc 

[Jenne, Jamie]

We did a few pen and paper calculations yesterday to confirm for ourselves that the half PRC should have nicely separated modes.  The half cavity is L=4.34m long, assuming flat mirror is 3.5 inches in front of BS.  That 3.5" is a guess, not a measurement.

Finesse

F = ( pi * sqrt(r1 * r2) ) / (1 - r1*r2) = 111.

Full width at half max

FWHM = c / (2 * L * F) = 311 kHz

FWHM in meters = FWHM * L/f = L*1064nm/c = 4.8 nm

Free spectral range

nu_fsr = F * FWHM = 34.5 MHz

Mode Spacing (eq 19.23 from Siegman)

omega = (n + m) * arccos(\pm sqrt(g1*g2)) / pi     *   (2*pi*c)/(2L)

For our half cavity, g1*g2 = 0.96

For the 01 or 10 modes, n+m = 1

omega = 13.7e6 rad/sec

mode spacing between 00 and 01 = 2.2 MHz

Thus, the modes should be well separated

=>  spacing is 2.2 MHz while FWHM is 0.311 MHz  (cavity fsr = 34.5 MHz)

 

EDIT JCD 31Jan2013:  Fixed mode spacing eqn to be diff between TEM00 mode and HOM, not plane wave and HOM.  Then fixed the factor of 2 error in the mode spacing numbers.

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