Graded index optical microresonators: analytical and numerical analyses

It is known that the spectra of optical modes supported by microresonators are shape and size dependent. We have introduced an additional parameter, i.e., spatially varying refractive index, to tailor the spectra of optical modes in a microdisk resonator while keeping size and shape intact. A new class of whispering gallery mode microresonators, referred to as graded index (GRIN) microresonators, is proposed. The GRIN profile belongs to a special inhomogeneous medium known as Maxwell's fish eye. The modal analysis of the structure is investigated both analytically and numerically. Solution of the Helmholtz equation is attempted under the spatially varying refractive index scenario and numerical verification of the analytical findings is tested by the finite-difference time-domain method. It is found that the two approaches support each other. It is expected that the findings of the GRIN microresonator may open up new research and device opportunities in photonics.