Linear Optical Analysis of Microdisk Lasers Concentrically Coupled with Microrings

The lasing spectra and thresholds of a microdisk laser concentrically coupled with external microrings are investigated using the recently developed formalism of the lasing eigenvalue problem (LEP). The 3-D boundary problem for the Maxwell equations is reduced to a 2-D one with the effective index method, and the in-plane 2-D problem is then analysed accurately with the aid of separation of variables. The influence of the microrings on the lasing frequencies and threshold values of material gain is studied, and the dependences of frequencies and thresholds on the thickness of rings are presented.