REGULAR PAPER Repeated passing principle for propagation in optical resonators Tatjana P. Kec ˇa 1,2 • William R. Headley 3 • Goran Z. Mashanovich 4 • Petar S. Matavulj 1 Received: 19 November 2015 / Accepted: 3 February 2016 Ó The Optical Society of Japan 2016 Abstract In this paper we make comparison between a well-known theoretical model of light propagation through racetrack resonator and experimentally obtained results. Observed differences are studied and some original modi- fications are made in the existing model so as to achieve better alignment with experiment. The influence of several geometric parameters on racetrack’s response is used for further adjustments to be performed. This procedure opens up the possibility to estimate the free spectral range and resonant wavelength for different geometric parameters and consequently to predict resonator functionality and working conditions, as well as functionality of complex photonic devices based on resonant structures. Keywords Coupled-mode theory Á Racetrack resonators Á SOI structures Á Spectral response 1 Introduction Practical mathematical models which explain propagation of electromagnetic waves and their interaction within guided wave optics have been developing since 1970s. One such model is the conventional coupled-mode theory (CMT), based on propagation through single independent waveguide [1]. According to the CMT, propagation mode and propa- gation constant have to be determined for unperturbed waveguides. Then systems of coupled-mode equations are used to describe processes occurring in perturbed waveg- uides [2–6]. The coupled-mode theory was applied to optical resonators and curved waveguides by several authors. Very useful transfer matrices and functions which entirely describe propagation have been derived [7–9]. Optical resonators, their design, functions, fabrication, and materials used, have been studied intensively for a few decades. Resonators can function as modulators, filters and routers. The authors have investigated different structures fabricated in various materials, and have determined their working conditions, Q-factors, polarization-independent and single-mode conditions [10, 11]. Also devices com- prising resonators, such as filters and gratings, have been discussed in literature in detail (e.g. [12, 13]). This paper is focused on silicon-on-insulator (SOI) racetrack resonators. The main advantages of SOI struc- tures are versatile fabrication, high refraction index con- trast between silicon and silica, and possibility of integrating associated electronics in a single platform. SOI racetrack or ring resonators in photonic circuits can operate as efficient optical filters, switches, modulators, detectors & Tatjana P. Kec ˇa tatjana.keca@ict.edu.rs William R. Headley w.headley@surrey.ac.uk Goran Z. Mashanovich g.mashanovich@soton.ac.uk Petar S. Matavulj matavulj@etf.bg.ac.rs 1 Faculty of Electrical Engineering, University of Belgrade, Room 87, Bulevar kralja Aleksandra 73, P.O. Box 35-54, Belgrade 11120, Serbia 2 ICT College of Vocational Studies, Zdravka C ˇ elara 16, Belgrade 11060, Serbia 3 Centre for Communications Systems Research, University of Surrey, Room 45 BA 01, Guildford GU2 7XH, UK 4 Optoelectronics Research Centre, University of Southampton, Highfield, Southampton, Hampshire SO17 1BJ, UK 123 Opt Rev DOI 10.1007/s10043-016-0195-9