## 1. Introduction

[2] The permeability and permittivity of materials are two fundamental parameters of the constitutive relations which determine how the media interact with electromagnetic (EM) waves propagating in the materials. In 1968, *Veselago* [1968] theoretically studied wave characteristics in a special medium whose permittivity and permeability are both negative simultaneously. These hypothetical materials exhibit a left-handed rule defining the polarizations of electric and magnetic fields and the propagation vector constant and the media are thus referred to as left-handed materials (LHM) in literature [*Chen et al.*, 2004; *Grbic and Eleftheriades*, 2004; *Katsarakis et al.*, 2004; *Ziolkowski and Kipple*, 2003; *Panoiu and Osgood*, 2003; *Kuzmiak and Maradudin*, 2002; *Markos and Soukoulis*, 2002; *Yao et al.*, 2005a, 2005b]. The double negative (DNG) material has shown special optical properties, and could lead to a perfect lens [*Pendry*, 2000; *Zhang et al.*, 2002; *Pendry and Ramakrishna*, 2003; *Pendry*, 2003; *Ye*, 2003; *Ramakrishna and Pendry*, 2004].

[3] For EM waves propagating through a stratified DNG medium, reflection and refraction of the waves were formulated by *Kong* [2002]. The objective of this paper is to extend the existing application from planar structures to cylindrical structures, so as to gain more insight into the hybrid effects of metamaterials and cylindrical curvature. Potential applications of the results in this work include the conformal antenna radome analysis and design, two-dimensional microwave and optical imaging, etc. In this paper, we first derive a general formula of EM fields in all regions of a multilayered cylinder with DNG and DPS materials in this paper. The eigenfunction expansion method is applied to express the EM fields in this structure. To verify our formulations and validate our analysis, the distant scattering sections for a two-layered cylinder with double positive medium are first shown. Next, we consider some special cases to characterize the DNG materials. The first example that we consider is a dielectric cylinder with (−ɛ_{0}, −*μ*_{0}) which has a refractive index of *n* = −1. For the incidence wave of transverse magnetic polarization, the reflection visibly diminishes when the electric size of the cylinder is increased. When a parallel line source is placed nearby, focus phenomenon is observed clearly inside the cylinder, provided that the electric size of the cylinder is much larger than the wavelength. Finally, distributions of field components are shown to confirm applicability of these formulas.