Goos-Hänchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Hänchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Hänchen 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.