  We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome
cavity resonator that owe their shape and character entirely to the
Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM
polarization, are well described by a 2D billiard map with the Goos-Haenchen
shift included. A phase space plot of this augmented billiard map reveals a
saddle-node bifurcation; the stable periodic orbit that is created in the
bifurcation corresponds to the numerically calculated eigenmode, dictating the
angle of its "V". A transition from a fundamental Gaussian to a TM V mode has
been observed as the cavity is lengthened to become nearly hemispherical.
