Electromagnetic wave propagation through doubly dispersive subwavelength metamaterial hole

The characteristics of the guided electromagnetic wave propagation through a subwavelength hole surrounded by a doubly dispersive metamaterial are investigated. Characteristic equations are derived for the surface polariton modes related to the subwavelength hole and mode classifications established. The surface polariton modes for two different hole-radii are numerically obtained and their electromagnetic dispersion curves and power flux characteristics analyzed and compared with each other. In particular, it was found that the border of the counterpropagation between the forward and backward Poynting vectors was located within the metamaterial, rather than at the interface between the metamaterial and the free space. ©2005 Optical Society of America OCIS codes: (130.2790) Guided waves; (240.5420) Polaritons; (240.6680) Surface plasmons; (260.2030) Dispersion; (350.5500) Propagation. References and links 1. T. Thio, K. M. Pellerin, R. A. Linke. H. J. Lezec, and T. W. 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Introduction
Unusual electromagnetic wave transmission though subwavelength aperture has been one of the important present research subjects of current electromagnetics and optics [1].Usually, these subwavelength apertures in the novel metals and the incident electromagnetic waves are in the region of visible and infrared wavelengths.In these wavelengths, the materials can be viewed as plasma media.Excitation and de-excitations of plasma waves at both ends of the subwavelength apertures can be an explanation of a principle of the extraordinary transmission through subwavelenth apertures [2].These plasma waves can also propagate through the subwavelength hole which is surrounded by the metamaterial.The study on the metamaterials is another hot topic in various microwave / optical device applications as well as in fundamental electromagnetics.In our present work, we investigate the electromagnetic wave propagation along the subwavelength hole which is surrounded by doubly dispersive metamaterials.We consider the electromagnetic dispersion of the waveguiding systems and the propagating power along the subwavelength hole.Some of newly obtained physical effects are addressed and discussed.

Characteristics Equation of Doubly Dispersive Metamaterial Hole
Fig. 1 shows the schematic view of the doubly dispersive circular metamateria hole with its diameter 2a .The inner region of the hole is free space and the surrounding region is composed of the doubly dispersive metamaterial.The dielectric and magnetic constants of the metamaterial can be given by .Fig. 2 shows the plots of the material expressions.The characteristic equation of the metamterial hole waveguide can be derived as follows from the standard steps of deriving procedure of conventional dielectric rod waveguides.Axial field component of the inner region of the hole is governed by Subscripts 1 and 2 represent the free space ( ) r a < and metamaterial ( ) is the propagation constant in the radial direction.0 k is the free space wave number.
-781 - β is the propagation constants in the axial direction.m is the azimuthal eigen value.The discrete eigenvalue solution of (1) forms the guided modes of the metamaterial hole and their normalized energy flux can be defined as ( ) ( )

Numerical Results
Fig. 3 shows the dispersion characteristics and their corresponding normalized energy flux for the TE-like modes.

Conclusions
In this work, we investigated the electromagnetic dispersion characteristics and power distributions on the subwavelength hole which is surrounded by the doubly dispersive metmaterials.Two kinds of hole radii are considered.Both TE-like and TM-like surface guided modes are existed only in principal mode and their higher order modes are not existed.In any case, TM 01 and TE 01 modes support only backward waves and higher order modes can support forward and backward wave modes in certain situations.We have also found that all the fractional power flows are positive below certain frequency due to the negative power cancellation in metamaterial regions.

Fig. 3 (Fig. 4 .Fig. 5 .
Fig. 3 (a) is the dispersion characteristics in the case of 10.0 mm a = .Dispersion curves are existed above the