Identification of Plasmonic Modes in Parabolic Cylinder Geometry by Quasi-Separation of Variables.

Kazuyoshi Kurihara,Fumiyoshi Kuwashima,Junichi Takahara,Masahiko Tani,Akira Otomo,Kazuhiro Yamamoto

doi:10.1007/s11468-014-9791-3

Abstract

This paper describes the plasmonic modes in the parabolic cylinder geometry as a theoretical complement to the previous paper (J Phys A 42:185401) that considered the modes in the circular paraboloidal geometry. In order to identify the plasmonic modes in the parabolic cylinder geometry, analytic solutions for surface plasmon polaritons are examined by solving the wave equation for the magnetic field in parabolic cylindrical coordinates using quasi-separation of variables in combination with perturbation methods. The examination of the zeroth-order perturbation equations showed that solutions cannot exist for the parabolic metal wedge but can be obtained for the parabolic metal groove as standing wave solutions indicated by the even and odd symmetries.

Highlights

Metallic tapered waveguides have attracted considerable attention as a possible experimental structure for the waveguides in achieving deep subwavelength confinement in optical region [1, 2] and in terahertz (THz) region [3,4,5]
Superfocusing in metallic tapered waveguides originates from two remarkable theoretical papers [9, 10] in 1997 regarding the peculiarities of surface plasmon polaritons (SPPs) [11, 12] known as electromagnetic waves propagating along a metal-dielectric interface
We describe a theoretical investigation of plasmonic modes in a parabolic cylinder geometry by solving the wave equation for the magnetic field by means of the quasiseparation of variables (QSOV) in combination with perturbation methods

Summary

Introduction

Metallic tapered waveguides have attracted considerable attention as a possible experimental structure for the waveguides in achieving deep subwavelength confinement in optical region [1, 2] and in terahertz (THz) region [3,4,5]. Ð58Þ which is a special case of the parabolic cylinder Eq (A.1) corresponding to the parameter values z 1⁄4 2qffiπffiffijffiffiεffiffimffiffijffiffi1ffi=ffiffi2ffiffiηffiffi≡umÀpffiηffiÁ; ð59Þ n o a 1⁄4 ζsuð0ÞðξÞ þ λ20β2mξ =4πjεmj1=2≡vsmðξÞ: Characteristic Equations for Determining the Unified Separation Quantity of the Zeroth-Order for the Parabolic Metal Groove. By using (A.19), we find that the asymptotic behaviors of the the tawmopsliotuludteiovnasryinin(g79a)saηr−e1o/4scfoilrlathtoerylimasitaoffupncffiηtffii→onÆof∞η, with ; this behavior is similar to those exhibited by the outgoing and incoming solutions of the unified radial equation for ξ→∞ in (75), respectively This clearly indicates that the two linearly independent solutions in (79) are unsuitable for the composition of interval tÆhepzffiηffie∈roÂtph-ffiηffioffi0ffir;d∞erÁ extended because angular function in their behavior does the not belong to localization but to propagation.

Tables and

Conclusions