Slow Light in Tapered Negative- Refractive-Index Waveguides Kosmas L. Tsakmakidis and Ortwin Hess Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, GU2 7XH, United Kingdom E-mail address: K.Tsakmakidis@surrey.ac.uk, O.Hess@surrey.ac.uk Abstract: We analytically demonstrate that a lightwave propagating along an adiabatically tapered waveguide with a core of negative refractive index (NRI) material can efficiently be brought to a complete standstill, while allowing for more than 90% in-coupling from an ordinary dielectric waveguide. @2007 Optical Society of America OCIS codes: 230.7400, 130.2790, 060.4510, 230.1150, 240.6680, 310.2790 1. Introduction An important scientific breakthrough in modern electromagnetics and optics has been the conception and practical implementation of materials exhibiting simultaneously negative electric permittivity and magnetic permeability, known also as left-handed metamaterials (LH-MMs). Their conceivable strong economic and social impact, owing to their potential applicability in diverse realms of science, such as telecommunications, radars and defence, nano- lithography with light, microelectronics, medical imaging, and so on, has lately prompted an overwhelming excite- ment within the scientific community [1]. Profiting from the freedom in the design and the materials’ feasible response that MMs provide us with [2], we here report on a novel and auspicious approach for slowing/stopping light. As outlined in the following, this method relies on the use of nonuniform adiabatically tapered LH-MM waveguides, wherein the power-flow direction inside the LH regions is opposite to the one in the RH regions, resulting in a pronounced deceleration of the guided electromagnetic waves. The scheme uses efficiently excitable waveguide oscillatory modes and is remarkably simple, since the slowing of the guided modes is performed solely by sufficient (adiabatic) decrease of the core thickness. In doing so, we are able to allow for extremely large bandwidths over which the slowing or stopping of the incoming optical signals can be achieved, similar to the photonic crystal (PC) technique [3]. However, compared to the PC method, our approach has the advantage that it can facilitate very efficient butt-coupling, directly to a slow mode alone, because: i) it supports single-mode operation in the slow-light regime [4, 5], ii) the characteristic impedance of the LH waveguide can be appropriately adjusted by varying the core thickness (see Fig. 3, below), and iii) the spatial distribution of the slow mode closely matches that of a single-mode fibre [4, 5]. These conclusions are drawn following exact manipulations of Maxwell’s equations, without invoking paraxial or heuristic approximations. Considering that the conception and construction of LH-MMs has progressed to such an extend that wideband, optical, MMs seem within reach [6], it is our view that the present technique could open a new host of applications for slow light and optical metamaterials research. 2. Slowly-varying left-handed waveguides To describe the phenomenon of rapid adiabatic deceleration of light signals guided by a tapered left-handed heterostructure, we here will concisely present the main results of the analytic study. The geometry of the investigated system is illustrated in Fig. 1. Consider a translationally slowly-varying nonuniform waveguide that has a core of negative refractive index (NRI) material (n < 0), bounded asymmetrically by two positive-index media (far right side, Fig. 1). The waveguide is adiabatic to prevent back reflections and scattering, so that we may assume the total, i.e. forward plus (the absolute value of the) backward power of a local mode to be conserved. We note that the principal conclusions of the analysis do not depend on the dimensionality of the problem or on Imn. Clearly, the assumption of slow variation is very accurate provided that the length of each tapered waveguide segment is large compared with the biggest length scale for the fields, i.e. the largest distance over which the total field may change significantly owing to phase differences between the various local modes. In our study, we deploy the eikonal approximation, known also as Wentzel-Kramers-Brillouin (WKB) or quasiclassical approximation in quantum mechanics. The phase of the a214_1.pdf SWB5.pdf © 2007 OSA/SL 2007