PHASE-SPACE CONSTRUCTION OF DIFFRACTION-LIMITED FOX-LI RESONATOR MODES

A method is illustrated of constructing Fox-Li modes of a diffraction-limited dual reflector resonator, using first the geometrical optics description of the ray geometry expressed in phase-space as geometrical transformations of Lagrange manifolds, followed by synthesis of a windowed Fourier Transform (WFT), then sampling by means of an orthogonal Wilson basis. This yields a discretely sampled phase-space parameterisation of the field that can be solved for the Wilson coefficients of the Fox-Li modes.