Plasmonic crystal waveguides

Plasmonic Crystal Waveguides Slobodan M.Vuković1, Zoran Jakšić2, Ilya V. Shadrivov3 and Yuri S. Kivshar3 1 Institute of Physics, University of Belgrade, 11080 Zemun, Serbia 2 Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Serbia 3 Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australia svukovic@ ipb.ac.rs Abstract- We study the properties of electromagnetic waves propagating along the waveguides with a periodic core created by alternating metal and dielectric layers, the so-called quasi-one-dimensional plasmonic crystal waveguides. Such waveguides can be symmetric or asymmetric depending on the cladding or substrate material properties, as well as on the termination of the periodic structure. We analyze the dispersion characteristics as well as the profiles of the guided modes for several types of the waveguide structures. 1. INTRODUCTION

The increasing development of nanofabrication technologies enabled a qualitatively new step in the exploitation of plasmonic properties of metal-dielectric nanocomposites for new ultra-compact photonic devices. In order to overcome the diffraction limit that prevents confinement and manipulation of light on the scales smaller than a half of the wavelength, various promising designs have been proposed such as hyperlenses [1, 2], hypergratings [3], and planar lenses based on nanoscale slit arrays in metallic films [4, 5]. A possible path toward guiding below diffraction limit is to use the anisotropic metamaterials, such as subwavelength plasmonic crystals (SPC), which ensure ultra-compact dimensions and optical operating frequencies and at the same time enable proper waveguiding through efficient elimination of parasitic conversion of surface plasmon polaritons into free-space modes [6]. A general SPC may have any of various 1D, 2D or 3D geometries, similar to those of photonic crystal guides, and may contain various metal inclusions, e.g. different nanoparticles, nanorods or ultrathin slabs. In fact, SPC represents a periodic nanostructured (super)lattice with alternating metal and dielectric parts. Optical properties of such a planar structure are strongly anisotropic, and similar to uniaxial crystal that supports various types of surface and guided modes [7], and creates plasmonic bandgaps. The relative dielectric permittivity of its metal parts should be below zero in the operating frequency range. Potential application fields for devices based on SPC guides are enormously wide and include among others optical telecommunications, sensors (where plasmonics is already widely applied for chemical/biological sensing), energy harvesting, biomedicine, etc. Maybe the most important envisioned role of plasmon-based subwavelength structures and devices is to serve as a link between electronics and photonics [8, 9] enabling a continuation of Moore's law in micro/nanoelectronics at optical frequencies. The easiest SPC geometry to fabricate is a 1D planar multilayer with alternating metal-dielectric strata having a nanometric thickness (the so-called quasi-one-dimensional SPC). This is the simplest and the oldest plasmonic crystal structure, yet it offers a wealth of effects. Depending on the geometry and the dimensions, as well as on the type of terminating strata, such multilayer guides may be symmetric, antisymmetric or asymmetric [10, 11]. In this paper we study, both theoretically and numerically, propagation of electromagnetic waves along the

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planar waveguides with anisotropic plasmonic crystal core designed with symmetric or asymmetric metal or dielectric claddings. The plasmonic crystal core with binary metal-dielectric unit cell is placed inside the waveguide with the main optical axis either along or normal to the core-cladding interfaces. We obtain the conditions for the existence of TM- and TE-polarized modes, which may appear both above and below the light line. 2. FORMULATION OF THE PROBLEM

r

We consider an electromagnetic wave propagation through a planar SPC waveguide as shown in Fig. 1; k r denotes the wave vector and q is the Bloch vector. The unit cell is binary, consisting of a metal and a dielectric layer with a total thickness L. Each stratum is described by its relative dielectric permittivity, metal with a Drude-type εm(ω) and dielectric with a dispersionless εd, and thickness dm and dd, respectively. The multilayer is sandwiched between thick claddings. In this paper we assume that the cladding material is identical to one of the unit cell constituents. A generalization to other cladding materials is straightforward. The structure represents a r waveguide with an SPC core supporting propagation of both in-plane waves (along the wave vector k in the x-y r plane) and perpendicular ones (along the Bloch vector q in z-direction).

εm y

L

...

k

z q εd Fig. 1. Geometry of a planar multilayer subwavelength plasmonic crystal. Outer gray areas denote cladding which is identical to either metal or dielectric part of the unit cell.

r

For a multilayer with an infinite number of strata Floquet-Bloch dispersion relating frequency ω with k and r q is valid: cos(qL ) = cos(k m d m ) cos(k d d d ) − 1 + α 2s , p sin (k m d m )sin (k d d d ) / 2α 2s , p . Here α s = k d / k m , α p = k d ε m / k m ε d for s and p polarization, respectively and k m,d = (ε m,d − k 2 )1 / 2 . All spatial dimensions are normalized to c/ω and wave numbers to ω/c; c is the speed of light in vacuum. In the uniaxial crystal approximation which implies layers with subwavelength thickness k m d m