The sizes of the symbols represent the magnitude of one component of the electric
field (usually, E_z). These wavefunctions represent solutions of the
two-dimensional Helmholtz equation, which is the wave equation under the assumption
of exponential time dependence like
Psi(x,y,t) = psi(x,y) * exp(-i*omega*t)
The wave equation being solved looks like
Laplacian * Psi - (n/c)^2 * Psi = 0
where the Laplacian is the sum of squared partial derivatives w.r.t. x and y, and n is the index of refraction, c is the speed of light in vacuum. It is assumed that n is much larger than the index of refraction n' existing outside the cavity being studied, which leads to the possibility of modes being confined in the cavity by total internal reflection.
These solutions assume the so-called Dirichlet boundary conditions, meaning, psi = 0 on the geometrical boundary being used. This is a reasonable approximation so long as the mode is undergoing total internal reflection, which may or may not be the case! TIR confinement depends on the ratio of index of refraction inside the cavity compared to outside the cavity, (n/n'); larger ratio improves the possibility for TIR for some of the modes.
The modes were tested for TIR confinement by looking at their Fourier transforms. Modes whose Fourier transforms only have intensity above a non-zero incident angle to the faces, can be TIR confined.