Ultralow Lasing Thresholds of$pi $-Type Supermodes in Cyclic Photonic Molecules Composed of Submicron Disks With Monopole and Dipole Modes

Cyclic photonic molecules (CPMs) composed of an even number of identical submicron-size circular-disk active resonators in free space are studied in two dimensions. Cold-cavity lasing frequencies and threshold values of material gain are extracted from an electromagnetic eigenvalue problem with exact boundary and radiation conditions. We show that assembling several small cavities in a tightly packed CPM efficiently lowers the thresholds of optically coupled nonwhispering-gallery modes of the lowest values (i.e., 0 and 1) of the azimuth index in each cavity provided that high antisymmetry is arranged