I computed the occurrence of higher-order modes up to order *m* + *n* = 20 as a function of *g* factor for a ring cavity.
In the first set of plots of plots, I've fixed the cavity half-length *L* and chosen several values of modulation frequency *f*_{PDH}. In the second set of plots, I've fixed *f*_{PDH} and chosen several values of *L*. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that
- there are two or three "best" regions to place
*g*: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability);
- the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and
- a lower modulation frequency widens these best regions.
So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is. |