## 1. Introduction

[2] Electromagnetic Band-Gap (EBG) structures [*Yablonovitch*, 1993] are made periodic structures artificially which possess the capability to forbid electromagnetic propagation in either all or selected directions to realize spatial filters. They originated from optical regime and have been applied extensively in the microwave region, including the suppression of surface waves [*Gonzalo et al.*, 1999], the construction of Perfect Magnetic Conducting (PMC) planes [*Zhan and Samii*, 2000] and antenna gain enhancement [*Shum et al.*, 2000].

[3] More electromagnetic band gap (EBG) structures have received considerable attentions in recent years, several kinds of planar EBG structures have been suggested, one of them is comprised of a square lattice of holes etched in the grounded plane of a dielectric slab [*Radisic et al.*, 1998], and another is consisted of planar periodic metal patches over a grounded dielectric slab [*Hung-Yu et al.*, 1998], Uniplanar Compact EBG (UC-EBG) structures introduced by *Yang et al.* [1999] are realized with square metallic pads connected by narrow strips to form a distributed LC network mounted on a bare or grounded dielectric slab. All kinds of planar EBG structures are particularly attractive and investigated intensively because of their easy fabrication, low cost, and compatibility with standard planar circuit technology. UC-EBG are more interesting because of being smaller in terms of wavelength, and they have been demonstrated in a variety of applications including, for instance, broadband low-pass, spurious-free band-pass filters [*Yang et al.*, 1999] and harmonic-tuned power amplifiers [*Hang et al.*, 1998].

[4] The planar EBG structures mounted on isotropic dielectric slabs have been computed using MoM [*Hung-Yu et al.*, 1998] or FDTD [*Coccioli et al.*, 1999; *Yang et al.*, 2005], while these structures with anisotropic slab are analyzed infrequently. The purpose of this paper is investigating the effect of electrical and magnetic anisotropy on the band structure of planar EBG. A full-wave analysis is presented for planar EBG mounted on an anisotropic slab which is characterized by tensors [*ɛ*] and [*μ*] simultaneously, and the off-diagonal elements of the tensors also exist because of the misalignment of the material and structure coordinates systems in the transverse plane. Present analysis is performed in the spectral domain, and the periodic dyadic Green's function of the considered structure is obtained from Maxwell's equations directly. The Galerkin's procedure along with Parseval's theorem is applied in succession to obtain the band structure of these planar EBG structures. UC-EBG as one kind of complicated planar EBG structure is analyzed numerically. As the numerical results, the band structure of an UC-EBG with different medium parameters are computed efficiently, and the effects of the material axes' rotation in the transverse plane on the band gap are examined.