Electromagnetic theory for optical disc resonators

The electromagnetic properties of optical disc resonators are analysed by the effective dielectric constant method. The assumptions inherent in this method are clearly defined, thus enabling the requirements of a complete electromagnetic model to be stated. The present formalism is applicable to structures where the radial boundary is defined by index and/or gain changes. An eigenvalue equation is obtained for the complex resonant frequency of the structure. Analytic solutions to the eigenvalue equation are obtained using material and device parameters relevant to disc resonators fabricated in III¿¿V heterostructure semiconductor materials. The complex eigenvalue gives not only the resonant frequency (wavelength), but also the Q-factor of that resonant mode. An outline is given of the applicability of the device to optoelectronic integrated circuits, and also a brief discussion is given of a number of methods for tuning the resonator.