## 1. Introduction

[2] Analysis of periodic corrugated structures can be performed using several methods such as using the anisotropic surface impedance or by analyzing the corrugated structure with all its details. The surface impedance method requires knowledge of the surface impedance, and can only be used for plane wave incidence with known angle of arrival, which is very rarely present in general field problems. It does not provide any information about the field within the corrugation region. Its accuracy depends on how accurately we predict the surface impedance. Another approach could be using the periodic boundary conditions, but this will force the periodicity to the corrugations and will not allow the study of nonperiodic structures in the presence of the periodic structures. In addition, if the corrugated region is finite, a detailed numerical analysis must be used. In some numerical methods such as the method of moments, such a detailed structure can be very large and require excessive computational resources in terms of memory and run time. If the finite difference time domain (FDTD) method is to be used, the details of the corrugations might require very fine cell sizes to accurately capture all the details of the structure and consequently great amounts of computational resources are required.

[3] Recently, an asymptotic corrugation boundary condition (ACBC) has been used to analyze corrugated structures even if the corrugation depth is varying or the corrugation region is finite. Typically, there should be more than 10 corrugations per wavelength for the asymptotic method to be accurate [*Kishk et al.*, 1998], but it will often work satisfactorily even for 2 or 4 corrugations per wavelength if the corrugation width is smaller than λ/2 in the dielectric material inside the corrugations. The ACBC is able to overcome the limitations in geometry and complexity of the other methods. The ACBC was formulated on the basis of the study of structures that exhibit anisotropic characteristics similar to soft and hard surfaces [*Kildal*, 1990]. It is an anisotropic averaging type of boundary condition, but in the FDTD, certain field behavior is enforced in the corrugated region and on the surface. The ACBC may be mixed with other conventional boundary conditions when dealing with composite materials or structures [*Kishk et al.*, 1998; *Kishk and Kildal*, 1995]. *Kishk et al.* [1998] used an analytical series expansion technique with the ACBC to model corrugations used as hard surfaces and was able to get excellent agreement with a solution based on the exact Floquet mode expansion and the mode matching technique. The comparison also made apparent that the ACBC could be applied in certain cases when there are fewer than 10 corrugations per wavelength. *Kishk* [2004] applied the ACBC in the method of moments for cylinders with arbitrarily cross section.

[4] We applied the ACBC in the FDTD. The updating field expressions are given through the discretized field equations. In addition, the ratio between the corrugation widths to the period width (*w*/*p* factor) is added as a weighting factor that was shown by *Kishk et al.* [1998] to improve the accuracy of the ACBC. It was added intuitively by *Kishk et al.* [1998] by comparing the surface impedance approach that used the factor when analyzing corrugated surfaces. We demonstrate our analysis by an example of a strut with corrugations placed on it to create an artificial hard surface for purposes of reducing the forward scattering [*Kildal et al.*, 1996]. Results using the FDTD simulation for the ACBC cases are compared with their corresponding detailed corrugated cases; simulations that describe the detailed corrugations using dielectric and conducting materials.