# Determine laser cavity modal content from beating / interference?

I'm trying to better understand the modal content and dynamics of laser cavities. I'm specifically interested in mode-locking, although this question is pretty general and applies to CW lasers too.

I understand that the modal spacing, Δf, in a cavity is set by cavity geometry and the gain bandwidth, ΔF, is set by the gain medium. Therefore, the maximum number of modes that can oscillate is ΔF/Δf.

However, what determines how many modes will actually be excited, and when some are (i.e. standard lasing operation), which modes dominate?

To quantify the modal content of a laser, I appreciate you can using a scanning Fabry perot interferometer connected to an oscilloscope and visualise each mode, providing the resolution and free spectral range are selected carefully.

However, I wonder if there are any easier ways of interfering this, say electrically? For example, I wonder if shining the laser onto a photodetector (with bandwidth ~ 1 GHz say) will cause interference between modes, creating difference frequencies, which can then be visualised on an electrical spectrum analzyer.

So, if I had 3 excited modes in my cavity, spaced by 10 MHz, then would I see 2 peaks on the electrical signal analyzer: one at 10 MHz (for the difference 30-20 MHz and 20-10 MHz) and a lower amplitude peak at 20 MHz (for the difference 30-10 MHz)? And similarly, if my laser were single-frequency, could we deduce that there is no interference on the photodetector as there is only one incident mode, so the only signal generated is in the THz regime (due to the wavelength of visile light, say), which can't be detected by the photodetector. Hence, we'd see no signal on the electrical spectrum analyzer?

Any guidance / references much appreciated. Thanks