## 1. Introduction

[2] Considerable attention has been devoted to the analysis of radiation from open-ended waveguides [*Gardiol*, 1985; *Bird*, 1996] because they are widely used in various applications, such as nondestructive measurement [*Mosig*, 1981] and space communication systems. Many methods have been proposed to analyze the radiation for open-ended waveguides, such as the correlation matrix method [*MacPhie and Zaghloul*, 1980], the complexification and extrapolation method [*Shen and MacPhie*, 1997], the Kobayashi potential method [*Serizawa and Hongo*, 2005], and the matrix pencil method [*Tan and Shen*, 2008]. On the other hand, the problem of wave propagating in a multilayer structure has been intensively studied for several decades [*Hansen*, 1989; *Chew*, 1990; *Wait*, 1996]. The superstrate effects on printed antennas were studied by *Alexopoulos and Jackson* [1984], and an approximate transmission line model was adopted by *Jackson and Alexopoulos* [1985] and *Yang and Alexopoulos* [1987] to analyze the high-directive radiation of a printed antenna embedded in a multilayer structure. The radiation of a horizontal dipole embedded in multilayer structure was studied by *Kipp and Chan* [1994] using the complex image method. The admittance of an open-ended waveguide radiating into layered medium was studied by *Galejs* [1965] decades ago. Open-ended waveguides radiating through a one-layer superstrate were studied by many researchers such as *Crosswell et al.* [1967], *Wu* [1969], *Chow et al.* [1991], *Li and Chen* [1995], and *Panariello et al.* [2001]. The multilayer effects on cavity-backed slot antennas were studied by *Vouvakis et al.* [2004] using the hybrid finite element method/method of moments (FEM/MoM) approach. A simple transmission line model was proposed by *Tan et al.* [2008] to investigate the radiation from an aperture antenna through a two-layer superstrate. In the work of *Teodoridis et al.* [1985], the method of characteristic mode was used to calculate the reflection from an open-ended waveguide terminated by a multilayer medium numerically.

[3] In this paper, an efficient full-wave analysis of the radiation from an open-ended waveguide through a two-layer superstrate is presented. Contributions are made in the following aspects. Firstly, the spectral dyadic Green's function in a multilayer superstrate is formulated so that it can be derived through cascaded matrices, each of which represents one layer of the superstrate independently. Therefore, it is very convenient to be modified for arbitrary superstrate configurations. Secondly, the generalized pencil of function (GPOF) [*Hua and Sarkar*, 1989] method and Gaussian quadrature are employed to accelerate the computation of reflection coefficient matrix. The convergence behavior of this efficient method is also investigated. Thirdly, the influence of the superstrate dimensions on the high antenna directivity are examined to show the properties of radiation through the two-layer medium.

[4] The rest of the paper is organized as follows. Formulations of the efficient full-wave analysis method are given in section 2. In section 3, numerical results of an open-ended WR-90 waveguide radiating through a two-layer superstrate are provided. The efficiency and convergence behavior of our method as well as the high directive radiation from open-ended waveguides are also examined. Conclusions are given in section 4.