Linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide Ilias Tsopelas * , Yannis Kominis, Kyriakos Hizanidis National Technical University of Athens, 157 73 Zografou, Athens, Greece Received 10 November 2006; received in revised form 25 January 2007; accepted 26 January 2007 Abstract In this work we investigate the linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide. The pro- posed device consists of a circular central core and many circular sectoral cores at the periphery, while the whole structure can be con- sidered as a nonlinear multicore composite optical coupler. Hybrid guided modes in a circular sectoral dielectric waveguide are derived using circular harmonic expansion for the electromagnetic fields and the Point Matching Method (PMM) for the application of bound- ary conditions. Several cases are investigated varying some of the parameters of the geometry and the optical frequency in order to pro- duce dispersion diagrams. In advance, the electric and magnetic field distributions for the fundamental guided modes are produced, while linear and nonlinear coupling coefficients as well as the sectoral waveguide mode effective area are derived. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Coupler; Sectoral waveguide; Effective area; Guided modes 1. Introduction During the last decades, optical couplers were studied extensively in the framework of all-optical processing and WDM technology, as they constitute an essential compo- nent of lightwave technology. Different classes of coupling devices, such as symmetric and asymmetric, dual-core and multicore, active or passive, composite and birefringent optical couplers, as well as combinations of them, exhibit remarkable optical properties in linear and nonlinear regime [1]. More specifically, directional dual-core symmet- ric fiber couplers are the most commonly used for a variety of applications related to fiber optics, exhibiting nonlinear optical pulse switching, symmetric and anti-symmetric bright soliton formation [2–4], while asymmetric dual cou- plers have attracted increasing attention during last years, as they open a new potential in photon management appli- cations offering logic gate operation [5], switching power reduction [6], bound soliton formation [7], as well as robust bistability [3]. Furthermore, dual-core birefringent optical couplers exhibit also remarkable nonlinear optical perfor- mance, such as symmetric and anti-symmetric soliton for- mation [8,9], rocking filter behavior [10], all-optical switching [4], and polarization selectivity [11]. On the other hand, in the context of all-optical data pro- cessing and semiconductor laser applications, last years, multicore circular optical couplers–amplifiers have attracted considerable attention by many researchers [12– 19], as they seem to be more controllable that their planar counterparts [20–25]. Modeling a nonlinear multicore opti- cal coupler–amplifier, researchers very often use coupled Discrete Nonlinear Schro ¨ dinger (DNLS) and Ginzburg- Landau (DGL) equations in which coupling phenomena are represented usually by linear and nonlinear coefficients [2,12,15–18,20–26]. As many works have proved, the knowledge of the range of the value of coupling coeffi- cients, which are mainly determined by the form of the cross-section of the coupler, play an important role over the device linear and nonlinear overall performance. The purpose of this work is the investigation of the linear and nonlinear coupling properties of a novel 0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.01.065 * Corresponding author. Tel.: +30 2107722469; fax: +30 2107723513. E-mail address: itsop@central.ntua.gr (I. Tsopelas). www.elsevier.com/locate/optcom Optics Communications 274 (2007) 85–93