I calculated the frequency for other higher Hermite-Gaussian modes, (n+m up to 20) to make sure that there is no overlap between these frequencies
and our choice of sideband frequency.
The beam frequency for higher order modes will be different from that of fundamental mode because of the phase shift. The frequency shift can be found in
Siegman, p 762 (Thanks Zach for pointing me to this). The phase shift from TEM00 will be multiples of 258.29 MHz. To find 20 possible lines, we use
N* 258.9 mod 737 , N = 1,2,3....20 (the free spectral range is 737 MHz), This will be the contribution from left side of the interested peak. To find the contribution from the right side we use,
737 - N*258.9 mod 737.
The plot below show the allowed frequency for higher order TEM (from the closest fundamental mode at f=0 and 737 MHz) on x axis, the FWHM is exaggerated for clarity. They are smaller in real life. The side bands at 21.5 and 35.5 MHz (our EOMs) are plotted in red.
I only plot from -100 to 100 MHz. |