Ismo V. Lindell

Soft-and-Hard/DB Boundary Conditions Defined by a Skewon-Axion Medium

A novel set of electromagnetic boundary conditions is defined in terms of an interface of a medium belonging to the class of skewon-axion media. Such a medium class can be introduced in a simple and natural manner applying four-dimensional representation of electromagnetic media. It is shown that the novel boundary conditions generalize soft-and-hard (SH) and DB boundary conditions to SHDB conditions. As an application, reflection of a plane wave from a planar SHDB boundary is studied. It is shown that the two eigenvectors of the reflection dyadic define eigenwaves for which the SHDB boundary can be replaced by equivalent PEC or PMC boundaries. The theory is tested with numerical examples which reveal an interesting narrow-beamed reflection phenomenon associated to the SHDB boundary condition.

Spherical Resonator with dB-Boundary Conditions

A novel set of boundary conditions requiring vanishing of the normal components of the D and B vectors at the boundary surface was introduced recently and labeled as the DB-boundary conditions. Basic properties of a resonator structure defined by the spherical DB boundary are studied in this paper. It is shown that the resonance modes polarized TE and TM with respect to the radial direction coincide with those of the respective PEC and PMC resonators. Modes in the DB resonator show higher degree of degeneracy than those of the PEC resonator which may find application in materials research.

Decomposable Medium Conditions in Four-Dimensional Representation

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. It is shown that the previously known classes of generalized Q-media and generalized P-media are particular cases of the proposed decomposable media (DCM) associated to a quadratic equation for the medium dyadic. As a novel solution, another class of special decomposable media (SDCM) is defined by a linear dyadic equation. The paper further discusses the properties of medium dyadics and plane-wave propagation in all the identified cases of DCM and SDCM.

On the realization of the generalized soft‐and‐hard surface

Boundary conditions generalizing those of the soft-and-hard surface were recently introduced as an example of an ideal boundary on which the complex Poynting vector cannot have a normal component. It was shown that under such conditions a boundary surface can be used as a polarization transformer for a reflected plane wave. The question of how to realize the generalized soft-and-hard surface is considered here. Various possibilities are discussed based on a medium interface, a slab of an anisotropic medium, and a configuration of antennas.

Material realizations of extreme electromagnetic boundary conditions and metasurfaces

The paper discusses the correspondence between electromagnetic boundary conditions and interface conditions. In particular, the focus is on the synthetic approach where the interest is in finding material realizations for given boundary conditions. Material realizations are approximative but not unique because, especially if anisotropic and bianisotropic materials are allowed, there are different material classes with which any given boundary condition can be mimicked. As examples, the PEC, PMC, PEMC, and DB boundary conditions are discussed. By comparing the scattering characteristics, it is demonstrated how well certain extreme-parameter material realizations are able to simulate the boundary effect.

Electromagnetic media with no dispersion equation

Recently, some novel boundary conditions have been observed to arise at interfaces of certain electromagnetic media in which plane waves are not restricted by a dispersion equation. In the present study an attempt is made to define most general media in which dispersion equations are identically satisfied for any plane wave. Applying four-dimensional formalism, it is shown that there are three classes of media satisfying this requirement.

Realization of spherical D′B′ boundary by a layer of wave-guiding medium

Abstract In this paper the concept of wave-guiding medium, recently introduced for planar structures, is defined for the spherically symmetric case. It is shown that a quarter-wavelength layer of such a medium serves as a transformer of boundary conditions between the two interfaces. As an application, the D′B′-boundary condition, requiring vanishing of normal derivatives of the normal components of D and B field vectors, is realized by transforming the DB-boundary conditions. To test the theory, scattering from a spherical DB object covered by a layer of wave-guiding material is compared to the corresponding scattering from an ideal D′B′ sphere, for varying medium parameters of the layer.

Generalized Soft-and-Hard/DB Boundary

A novel class of boundary conditions is introduced as a generalization of the previously defined class of soft-and-hard/DB (SHDB) boundary conditions. It is shown that the conditions for the generalized SHDB (GSHDB) boundary arise most naturally in a simple and straightforward manner by applying 4-D differential-form and dyadic formalism. At a given boundary surface, the GSHDB conditions are governed by two one-forms. In terms of Gibbsian 3-D vector and dyadic algebra, the GSHDB conditions are defined in terms of two vectors tangential to the boundary surface and two scalars. Considering plane-wave reflection from the GSHDB boundary, for two eigenpolarizations, the GSHDB boundary can be replaced by the perfect electric conductor or perfect magnetic conductor boundary. Special attention is paid to the problem of plane waves matched to the GSHDB boundary, defined by a 2-D dispersion equation for the wave vector, making the reflection dyadic indeterminate. Examples of dispersion curves for various chosen parameters of the GSHDB boundary are given. Conditions for a possible medium, whose interface acts as a GSHDB boundary, are discussed.

Electromagnetic Boundaries with PEC/PMC Equivalence

The most general electromagnetic boundary, deflned by linear and local boundary conditions, is deflned in terms of conditions which can be called generalized impedance boundary conditions. Requiring that the boundary be equivalent to PEC and PMC boundaries for its two eigen- plane waves, which property is known to exist for many of its special cases, it is shown that the recently introduced Generalized Soft-and-Hard/DB (GSHDB) boundary is the most general boundary satisfying this property.

SHDB Boundary Conditions Realized by Pseudochiral Media

A novel set of SHDB boundary conditions, generalizing those of the soft-and-hard boundary and the DB boundary, was recently introduced in terms of an interface of a medium belonging to the class of skewon-axion media. In this letter, the same boundary conditions are shown to arise at the interface of certain bi-anisotropic pseudochiral media. Realization of such a medium in terms of helical and metamaterial inclusions or omega-shaped particles is suggested. Plane-wave propagation in the pseudochiral medium is analyzed in terms of wavefield expansions.