Electromagnetic source transformations and scalarization in stratified gyrotropic media

Progress In Electromagnetics Research B 06/2009; 18(18). DOI: 10.2528/PIERB09070904
Source: arXiv


It is known that with restrictions on the type of the constitutive equations, Maxwell's equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have previously been obtained in two quite different ways. Either by a ``scalarization of the sources'', where the relevant scalar quantities are essentially vector potential components and where the derivation was limited to isotropic media; or alternatively by using the ``scalar Hertz potentials'', and this method has been applied to more general media. In this paper it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional definition of the vector potentials, can also be obtained using the traditional definition provided a proper gauge condition is applied and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the first method and therefore are the natural potentials for obtaining scalarization. Finally it is shown that both methods are also equivalent with a much older third method based on Hertz vectors. Comment: 20 pages, 0 figures

Download full-text


Available from: Patrick M. De Visschere, Apr 07, 2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: We present a simulation method for light emitted in uniaxially anisotropic light-emitting thin film devices. The simulation is based on the radiation of dipole antennas inside a one-dimensional microcavity. Any layer in the microcaviy can be uniaxially anisotropic with an arbitrary orientation of the optical axis. A plane wave expansion for the field of an elementary dipole inside an anisotropic medium is derived from Maxwell's equations. We employ the scattering matrix method to calculate the emission by dipoles inside an anisotropic microcavity. The simulation method is applied to calculate the emission of dipole antennas in a number of cases: a dipole antenna in an infinite medium, emission into anisotropic slab waveguides and waveguides in liquid crystals. The dependency of the intensity and the polarization on the direction of emission is illustrated for a number of anisotropic microcavities.
    No preview · Article · Sep 2011 · Optics Express
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A scalar potential formulation for a homogeneous uniaxial bianisotropic medium is derived through the use of Helmholtz's theorem and operator orthogonality and compared with prior findings. It is shown that an expected and unexpected depolarizing dyad appears in the development. Using a spectral domain analysis and Leibnitz's rule in the field recovery process, it is shown the unexpected depolarizing dyad is canceled. Thus, a mathematically and physically consistent scalar potential theory is confirmed.
    Preview · Conference Paper · Sep 2013