[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. |