% function used by plot_modes.m to find the waveguide beta and plot the
% modes

function F = disprel(beta)

global h e1 u1 e2 u2 e3 u3  k0 kc ks kf phis phic m 

ks = sqrt(beta^2-(e3*u3)*k0^2);
kc = sqrt(beta^2-(e1*u1)*k0^2);
kf = sqrt(-beta^2+(e2*u2)*k0^2);
phis = atan(ks*u2/kf/u3);
phic = atan(kc*u2/kf/u1);



F = kf*h-phis-phic-m*pi;  % dispersion relation