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Wed Jan 27 11:02:30 2010
PRC Cavity Length
I fitted the data from scanning the PRC by changing the beat frequency of the auxiliary laser beam with the PSL beam.
The data points that I've taken so far over the entire frequency range (0-300 MHz) are not continuous. For several reasons the PLL was unable to maintain lock for such a large range and I had to break it into smaller segments. The measurements to acquire them stretched over a too long period of time during which the status of the PRC changed.
Because of that, before I get a continuous set of data points (perhaps normalized by the circulating power inside of the cavity), I restricted the fit to a 55MHz range around 100MHz. I obtained the following numbers for the fit parameters:
Length PRC = 2.169 +/- 0.007 m
Schnupp Asymmetry: 0.471+/- 0.006 m
The fit is shown in the attached plot:
When I fit over the entire set of data I get this:
Length PRC = 2.224 +/- 0.005 m
Schnupp Asymmetry: 0.457+/- 0.005 m
The results are different.
Evidently I have to improve the measurement.
I'm working on it.
The function I used to fit the transmitted beat power vs. frequency is the following:
E_trans = - t_prm * r_itm * exp(1i*2*wb*l_prc/c) .* sin(wb*l_/c) ./ ( 1 + r_prm * r_itm * exp(1i*2*wb*l_prc/c) .* cos(wb*l_/c)
Where wb is the angular frequency of the beat, l_prc and l_ are the length of the PRC and the Schnupp asymmetry, respectively; r_itm, t_itm, r_prm, t_prm are reflectances and transmittances of PRM and ITM; c is the speed of light.