IEICE TRANS. ELECTRON., VOL.E93–C, NO.1 JANUARY 2010 81 BRIEF PAPER Special Section on Recent Progress in Electromagnetic Theory and Its Application TE Volume Modes in Anisotropic Single-Negative Slab with Negative Component in Permeability Tensor Masashi HOTTA †a) , Member, Ryota OGAWA †* , Nonmember, and Mitsuo HANO † , Member SUMMARY Existence of backward TE volume modes which are to be identified as Magnetostatic Wave (MSW) in anisotropic single-negative slab with partly negative permeability tensor component have already been revealed by present authors. In this paper, detailed modal analysis has been carried out for this kind of TE volume modes to find out their novel and peculiar properties. From these numerical results, it has been clarified that dispersion curve of the lowest order mode for thicker slab has a frequency of turning point below which both forward and backward waves can be simultaneously observed and also there is a critical slab thickness for each order of TE volume modes to exist. key words: volume mode, single-negative, tensor material pa- rameters, metamaterial 1. Introduction Metamaterial with negative material parameters has attracted a great deal of attention due to their eter- nal possibility of a new vista in the field of electromag- netic (EM) applications [1]-[5]. Ordinary material in nature is double-positive media with all positive ma- terial parameters, however, it has been reported that the appropriately constructed metamaterials only with nonmagnetic and non-ionized media show the negative permittivity and/or permeability [5]. The materials with negative parameters can be broadly divided into two categories; one is double-negative media with both permittivity and permeability negative, and the other is single-negative media with either permittivity or per- meability negative which is the intermediate state be- tween the double-positive and the double-negative me- dia. Applying these metamaterials with negative pa- rameters to the novel devices, their modal properties and the peculiar propagation behaviors of the wave in those materials must be revealed in advance. Based on the modal analysis for single-negative slab, the present authors have revealed so far that only TE surface waves can exist on the isotropic single- negative slab with scalar negative permeability and also only TM surface modes on the slab with scalar negative Manuscript received March 24, 2009. Manuscript revised July 30, 2009. † The authors are with the Graduate School of Science and Engineering, Yamaguchi University, Ube-shi, 755-8611, Japan. * Currently with the Canon Co. a) E-mail: hotta@yamaguchi-u.ac.jp DOI: 10.1587/transele.E93.C.81 permittivity [6]. In addition, it has already been pre- sented that backward TE volume modes which are to be identified as the magnetostatic wave can be observed in the anisotropic single-negative slab whose permeability tensor has partly negative component [7]-[9]. In this paper, the detailed modal analysis has been achieved for the anisotropic single-negative slab with the permeability tensor whose x-component is negative and dispersive, in order to pursue the novel and peculiar properties of these TE volume modes. At first, the detailed inspection on the dispersion characteristics of the TE volume modes would be car- ried out for the anisotropic single-negative slab with different thickness. Then, we will estimate the eigen- values for each order TE volume modes as a function of the slab thickness. From these results, the peculiar modal characteristics of the TE volume modes in the anisotropic single-negative slab would be presented. 2. Basic Structure and Eigenvalue Equation We analyze TE volume modes in the anisotropic single- negative slab as shown in Fig.1. The region II whose thickness is set as T is single-negative media and their tensor permittivity and permeability are assumed to be expressed as ˆ ε =   ε x 0 0 0 ε y 0 0 0 ε z   , ˆ μ =   μ x 0 0 0 μ y 0 0 0 μ z   (1) where their components are allowed to be negative. The regions I and III are chosen as the free-space with the Fig. 1 Finite-Thickness single-negative slab with material pa- rameter tensors. Copyright c ⃝ 2010 The Institute of Electronics, Information and Communication Engineers