Analysis of resonator modes in two-dimensional laser cavities containing a left-handed material

Resonator modes in two-dimensional laser cavities with curved end mirrors filled with a left-handed material were investigated numerically using the extended Fox-Li mode calculation method. The results reveal that the phase profile on the curved end mirrors of a left-handed cavity is inverted relative to that of a cavity filled with a right-handed material. Furthermore, we show that the phase on the end mirrors takes discrete values of zero and ±π under stable resonator conditions, while it varies continuously under unstable resonator conditions. The differences between stable and unstable resonators significantly alter the far-field patterns of the lowest-loss modes.