I'm currently learning lasers. In my research of mode-locking, I've stumbled across something called a longitudinal mode.
The allowed modes of the cavity are those where the mirror separation distance L is equal to an exact multiple of half the wavelength, λ:
L = (n λ) / 2
where n is an integer known as the mode order.
Does this mean the wavelength, the literal 450 nm length, say, has to be of that criterion? I realize increasing the wavelength will create a completely different sinusoid, and if that doesn't fit in the cavity where its 0 points are at either end, it won't lase? Because what I envision, in the first place, are photons bouncing from the gain medium, off the resonator, back through the gain medium, etc. If this is then an 'information' wave, for lack of a better word -- if its energy fits the criteria, if we took its sinusoid associated with its wavelength and extended it, if it could lase we would have 0 points at either resonator?
I guess what I'm trying to ask is, what is this wavelength in this case, and if it is what I'm thinking, then its wavelength does then have spacial significance? Is that what the wavenumber is, essentially?
What we definitely have in the laser system are photons bouncing off the gain medium to resonators and back. How on earth did this become turned into a standing wave? And how is it supposed to leak out if our abstraction we've made doesn't have nodes at either end of the mirror?
I know this is a mouthful, but I'd really appreciate any help.
Also, how does destructive interference occur if there are no 0 amplitude nodes at either end of the resonator in the first place? Having trouble visualizing that.ie, if our condition with L is not met?