DOI 10.1007/s11082-006-0018-5 Optical and Quantum Electronics (2006) 38:71–81 © Springer 2006 Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity n. sakhnenko 1,2,∗ , t.m. benson 1 , p. sewell 1 and a. nerukh 2 1 George Green Institute for Electromagnetics Research, University of Nottingham, University Park, Nottingham NG7 2RD, UK 2 Kharkov National University of Radio Electronics, 14 Lenin Ave., Kharkov 61166, Ukraine ( ∗ author for correspondence: E-mail: n sakhnenko@yahoo.com) Received 29 September 2005; accepted 31 January 2006 Abstract. This paper considers the switching effects on whispering gallery modes in circular dielectric resonators when their material is subject to abrupt time changes in permittivity. Both the transient response and the new steady-state regime are described in detail by means of an analytical approach. Key words: time-domain analysis, time-varying media, whispering gallery modes (WGM) resonators 1. Introduction Whispering Gallery Mode, WGM, resonators or micro-cavities, have been the subject of significant interest in recent years as they exhibit properties ideal for a wide range of potential applications. These include: optical filter- ing (Little et al. 1997), bio-sensing (Blair and Chen 2001; Boyd and Heebner 2001) and low-threshold micro-lasers (Fujita et al. 1999; Baba et al. 2003). Moreover, arrays of such resonators not only provide more complex optical filtering, but have also led to the observation of the so-called slow and stored light phenomena (Heebner et al. 2002). In addition to the uses of passive resonators, the fabrication of optically active and tuneable devices is of great importance for all-optical data pro- cessing and switching purposes and, generally, active micro-cavities signifi- cant extend the functionality of many devices and enhance their application range. Micro-cavity tuning can be achieved by changing the material refrac- tive index which can be practically realised by varying the input signal in a non-linear micro-cavity (Blom et al. 1997); by voltage control (Savchenkov et al. 2005) or else by free carrier plasma injection (Djordjiev et al. 2002). To date, much of the theoretical work focused upon micro-resonators has concentrated upon prediction of their frequency domain properties, although for applications such as optical memory (Hill et al. 2004) and