Interaction of Electromagnetic Waves with a Moving Slab: Fundamental Dyadic Method

Abstract—This paper concerns with the interaction of electromagnetic waves with a moving slab. Consider a homogeneous isotropic slab moving uniformly in an arbitrary direction surrounded by an isotropic medium (free space). In this paper a new simple and systematic method is proposed for analyzing reflection and transmission of obliquely incident electromagnetic waves by a moving slab based on the concept of propagators. In the previous works complex relations were arrived but using this novel method those complexities will not appear thus the method may be extended to more complex structures. In this method, first, electric and magnetic fields are decomposed into their tangential and normal components then each constitutive dyadic is decomposed into a two-dimensional dyadic in transverse plane and two two-dimensional vectors in this plane. Substituting these dyadics into Maxwell’s equations gives a first order differential equation which contains fundamental dyadic of the medium. From the solution of this equation, fields inside the slab may be expressed in terms of fields at the front surface of the slab and the propagator matrix which is an exponential function of fundamental dyadic. Using this method the up-going and down-going tangential electromagnetic fields may be obtained at the same time. As a limiting case a slab with vanishing velocity is discussed using this method, and reflection and transmission coefficients of this slab are derived, which ends in Fresnel’s equations. At last, several typical examples are provided to exemplify the applicability of the proposed method. Moreover, the results are compared with the method of Lorentz transformation. A good agreement is observed between the results which verifies the validity of the proposed method. 1