Effective index dispersion account in the cold model of disk resonator with uniform gain

Semiconductor microdisk lasers with whispering-gallery (WG) modes attract much attention since the early, 1990´s, as sources of infrared and optical radiation having worked on building theoretical description of the optical modes of microdisks. This was done either with rough analytical or through FDTD simulations. In these papers, a 3-D problem for a finite thickness disk was approximately reduced to the 2-D one based on the effective index method developed earlier for layered media, however, the dependence of the effective index on frequency was neglected. Our paper presents a study of a 2-D lasing eigenvalue problem for a microdisk, based on the complete Maxwellian formulation with transmission condition at the disk boundary and radiation condition at infinity.