The Semiclassical Laser-Equations (also called "Laser Self-Consistancy Equations" ) are used to model a classical EM-Field that is driven by a given Polarisation in an active medium.
In Order to derive these equations, one chooses a full set of orthonormal functions $U_m(x,y,z)$ and expands the electric Field $E$ as a superposition of these functions. Each of the $u_m$ solves the wave equation, and is asigned to a specific frequency, which will then appear in the time evolution equation for the amplitude, by which the mode $u_m$ oscillates.
Now my question is: Why do we choose the set of $U_m$ in a way that the $U_m$ are eigenmodes of the laser cavity? Couldn't I choose abitrarily functions, as long as they form a full set, and satisfy the wave equations? And if I did so, wouldn't I see that off resonant modes are amplified less than resonant modes?