This week was another LIGO-Virgo-KAGRA collaboration meeting, and since my work has focused on the detector itself, I tried to attend more of the sessions on instrumentation than I did in my data analysis days. One topic that stuck in my head was a technique for sensing the sizes of the various optical cavities used in the detectors, sidebands. By modulating the frequency of the main laser beam, we can effectively create frequencies on either side of the central one. This is the inverse of the effect I
discussed way back in my PhD work.
"Modulation" simply means we're multiplying two sinusoids together, and we can apply a trigonometry identity to turn that into a sum:
This says that the frequency of the modulated signal is the sum and difference of the two frequencies that went into it. Often we add this modulated signal back to the carrier,
z_1. Then we have three evenly spaced frequencies:
f_1-
f_2,
f_1, and
f_1+
f_2, hence the name "sidebands". What's interesting is the variety of shapes you can get from this simple setup.
As a way to help me get my head around how everything interacts, I put together another doodad (two in a row!) which you can play with below. The top plot shows the timeseries of the signal, and the bottom plot shows the real part of the
Fourier transform, a representation of the relative sizes frequency components. You can control whether we add the carrier to the modulated signal with the checkbox. I realize this is a somewhat obscure topic (and certainly not "everyday") but I hope it's fun to play with even if you're not as crazy as me!
