Time domain born type formulation for low frequency scattering

Abstract

1. Introduction For past decades many numerical methods have been developed in electromagnetics for time and frequency domains. The capability of individual method has continuously been improved, and these techniques have been successfully applied to a wide range of applications from a calculation of radar cross section of a complicated object to a RF circuit optimization. However, due to computing capability numerical methods have been usually used for a moderate frequency range and/or scatterers of a moderate size. In very high or low frequencies, analytical techniques may have advantages over numerical methods yet. Low frequency band has been widely used in many applications such as medical imaging since the band provides specific advantages, for example good penetration through highly lossy media such as human body. At very low frequencies, however, it is well known that the conventional numerical methods fail to generate correct results, and as a result to solve the problem a special basis function such as loop-star basis function has to be used [1]. In this frequency range, any time domain technique such as finite difference time domain (FDTD) also may fail since to accurately model a scatterer, a very small cell should be used and so the time step is automatically very small, but global simulation time may be very large. Therefore, due to the dispersion error of FDTD algorithm, the overall simulation accuracy may not be sufficient. Since in very low frequencies a scatterer may be electrically very small, interactions inside the scatterer may be very weak, and thus negligible. Hence in frequency domain, (distorted) Born approximation has been widely used for the frequencies [2]. To calculate time domain response for a complex scatterer, a frequency domain response is computed first and then using Fourier transform, the desired time domain solution can be constructed. However, this procedure is not computationally efficient. Therefore, in this paper, an efficient time domain Born type approximation is formulated, based on sampling theorem to maximize the time step.