Aeu Archiv Fur Elektronik Und Ubertragungstechnik, 1988
The well known method of moments is transformed into a very general iterational form called momen... more The well known method of moments is transformed into a very general iterational form called moment iteration method (MIM), which can be applied to problems involving large or complicated bodies. It is shown that other iterational methods applied in the literature can be conceived as special cases of MIM. The convergence of MIM is not automatic, but it is obtained through acceptance of only such iterational steps which reduce the residual norm. The generality of the method gives possibilities for different strategies of computation. Two examples are considered with two different strategies: one applying zooming expansion functions whose scale decreases during the iteration process, the other one applying statistical method of choosing the expansion functions. Since MIM does not involve orthogonalization processes for choosen expansion functions, the method is simpler and suitable to small computers for which the computing time requirement is not of prime importance.
Introducing a class of metamaterial, labeled as wave-guiding anisotropic media, it shown that giv... more Introducing a class of metamaterial, labeled as wave-guiding anisotropic media, it shown that given impedance boundary conditions can be exactly realized by a slab of such a material when backed by a PEC plane. An analytic relation is derived between the surface admittance dyadic of the boundary and the parameters of the material slab and verified with non-trivial special cases of the theory.
A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarte... more A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarter-wave transformer with interesting properties. By increasing the transverse permittivity and permeability the transformer becomes a thin sheet. It is shown that the recently introduced SHDB boundary conditions, generalizing the soft-and-hard and DB conditions, realized by the interface of a skewon-axion medium, can be transformed to form a novel class of SHD'B' boundary conditions which generalizes the soft-and-hard and D'B' boundary conditions. Reflection of a plane wave from a planar SHD'B' boundary is considered by numerical examples revealing an interesting narrow beam with radical change of reflection for certain values of parameters and incidence angles.
The Maxwell-Garnett mixing formula, previously well-known for dielectric mixtures, is generalized... more The Maxwell-Garnett mixing formula, previously well-known for dielectric mixtures, is generalized for the first time to cover chiral materials. The mixing formula expresses the permittivity, permeability, and chirality of a two-component mixture with spherical inclusions as functions of the material parameters of the components. The result gives the classical Maxwell-Garnett formula as a special case.
A new variational functional is introduced for the analysis of curved open and closed waveguides.... more A new variational functional is introduced for the analysis of curved open and closed waveguides. The theory is based on variational principle for nonstandard eigenvalue problems, recently applied for straight anisotropic fibers. The present method does not set any restrictions to the shape of the waveguide or to the radius of the bend. The dielectric function can be homogeneous or nonhomogeneous with transverse and/or longitudinal anisotropy. As an example of the method a curved isotropic and anisotropic single mode fiber with two different kinds of anisotropy models are studied. The analysis includes field distributions, changes in the dispersion curves due to reformed geometry, and birefringence properties in the curved anisotropic fibers.
Electrostatic image theory for a point charge on the axis of a perfectly conducting prolate spher... more Electrostatic image theory for a point charge on the axis of a perfectly conducting prolate spheroid is formulated. The exact image expression is found using the Havelock identity, according to which the external harmonics of the potential solution emanate from a system of continuous image sources distributed along the focal line. Many tests for the theory are performed and graphical examples given. In the case of a slightly prolate sphere, the first correction to the image solution for the conducting sphere by Lord Kelvin is developed. An expression for the image polarization density function is derived for the dipolar source.
The dyadic Green's function for an unbounded nonreciprocal uniaxial bianisotropic medium is deriv... more The dyadic Green's function for an unbounded nonreciprocal uniaxial bianisotropic medium is derived in explicit form. Such uniaxial bianisotropic media can be realized by randomly dispersing uniaxial metallic inclusions with parallel orientations into an isotropic host medium. The availability of an analytic solution for the dyadic Green's function marks therefore an important step towards an understanding of radiation from sources and propagation of waves in composite materials.
Reflection and transmission of a plane wave at the planar interface of isotropic and bi-isotropic... more Reflection and transmission of a plane wave at the planar interface of isotropic and bi-isotropic (BI) media are analyzed. The analysis applies vector transmission line theory, which for the general case is seen to involve both dyadic impedance and dyadic propagation factor quantities. Explicit expressions for the reflection and transmission dyadics are given and their special cases for the Tellegen, nonreciprocal nonchiral, media are obtained and confirmed by previous results. Eigen polarizations for the reflection dyadic are found and conditions for zeros of eigen reflections are worked out to give explicit expressions for Brewster angles corresponding to the BI interface. A new phenomenon is the appearance of two Brewster angles for certain material parameter values of bi-isotropic half space. Also, conditions for zeros of cross-polarized reflections are found for the general case. These nonreciprocal cross Brewster angles for which, a horizontally polarized wave gives no vertically polarized reflection whereas a vertically polarized wave gives nonzero horizontally polarized reflection, may find practical applications because this effect does not appear for special cases of Tellegen and Pasteur media.
The Silberstein wave-field decomposition of electromagnetic fields is applied to the problem of w... more The Silberstein wave-field decomposition of electromagnetic fields is applied to the problem of wave propagation in chiral medium. The problem involving a planar interface between two chiral media is considered and eigensolutions for the reflection and transmission problems are given. Numerical results are calculated for the eigenpolarizations and reflection coefficients with different incident field polarizations, for the problem involving an interface between isotropic and chiral media. Also, the limit cases of reflection from a half space with only small amount of chirality are studied and it is shown that the chirality gives a second-order effect on the co-polarized reflection coefficient and a first-order effect on cross-polarization.
Journal of Electromagnetic Waves and Applications, 2001
ABSTRACT The classical Helmholtz theorem which decomposes a given vector field to curl-free and d... more ABSTRACT The classical Helmholtz theorem which decomposes a given vector field to curl-free and divergence-free components and presents the field in terms of a scalar and a vector potential is reformulated so that the divergence-free part is further decomposed in two parts with respect to either one or two given unit vectors. It is shown that these decompositions follow in a straightforward way from certain operator identities. The field is represented in terms of three scalar potential functions, two of which can be related to Hertzian potentials and TE/TM decomposition when decomposing time-harmonic electromagnetic field vectors outside the source region. Applying the decomposition to time-harmonic sources as well as the fields, equations between scalar source and field potentials can be formulated which gives an alternative method of solving electromagnetic problems.
Journal of Electromagnetic Waves and Applications, 2003
ABSTRACT The classical Helmholtz theorem which decomposes a given vector field in three dimension... more ABSTRACT The classical Helmholtz theorem which decomposes a given vector field in three dimensions to its curl-free and divergence-free components in terms of a scalar and a vector potential is generalized in differential-form formalism to multiform fields in an n-dimensional space. Decomposition of a p-form field follows in a straightforward way from certain operator identities corresponding to the curl-curl formula of the Gibbsian vector analysis in three dimensions. For p ≥ 1, the representation of a given p-form field is given in terms of a (p-1)-form and a (p+1)-form potential field whose respective generalized curl and divergence operations vanish.
ABSTRACT The image principle in electromagnetics replaces a physical structure by an equivalent s... more ABSTRACT The image principle in electromagnetics replaces a physical structure by an equivalent source, the image of the primary source. The number of structures with analytic image expressions is limited but increasing. In finding new image expressions, the Heaviside operational calculus can be applied by first transforming the three-dimensional problem to one concerning transmission lines. The image problem can be reduced to the compact form in terms of a pseudo-differential operator applied to the original source function. To interprete the result in terms of computable functions, approximations can be done at this stage. As a simple example of the theory the interface of two isotropic media with smooth or slightly rough interface is considered. A table of operational formulas is given as an appendix.
Aeu Archiv Fur Elektronik Und Ubertragungstechnik, 1988
The well known method of moments is transformed into a very general iterational form called momen... more The well known method of moments is transformed into a very general iterational form called moment iteration method (MIM), which can be applied to problems involving large or complicated bodies. It is shown that other iterational methods applied in the literature can be conceived as special cases of MIM. The convergence of MIM is not automatic, but it is obtained through acceptance of only such iterational steps which reduce the residual norm. The generality of the method gives possibilities for different strategies of computation. Two examples are considered with two different strategies: one applying zooming expansion functions whose scale decreases during the iteration process, the other one applying statistical method of choosing the expansion functions. Since MIM does not involve orthogonalization processes for choosen expansion functions, the method is simpler and suitable to small computers for which the computing time requirement is not of prime importance.
Introducing a class of metamaterial, labeled as wave-guiding anisotropic media, it shown that giv... more Introducing a class of metamaterial, labeled as wave-guiding anisotropic media, it shown that given impedance boundary conditions can be exactly realized by a slab of such a material when backed by a PEC plane. An analytic relation is derived between the surface admittance dyadic of the boundary and the parameters of the material slab and verified with non-trivial special cases of the theory.
A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarte... more A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarter-wave transformer with interesting properties. By increasing the transverse permittivity and permeability the transformer becomes a thin sheet. It is shown that the recently introduced SHDB boundary conditions, generalizing the soft-and-hard and DB conditions, realized by the interface of a skewon-axion medium, can be transformed to form a novel class of SHD'B' boundary conditions which generalizes the soft-and-hard and D'B' boundary conditions. Reflection of a plane wave from a planar SHD'B' boundary is considered by numerical examples revealing an interesting narrow beam with radical change of reflection for certain values of parameters and incidence angles.
The Maxwell-Garnett mixing formula, previously well-known for dielectric mixtures, is generalized... more The Maxwell-Garnett mixing formula, previously well-known for dielectric mixtures, is generalized for the first time to cover chiral materials. The mixing formula expresses the permittivity, permeability, and chirality of a two-component mixture with spherical inclusions as functions of the material parameters of the components. The result gives the classical Maxwell-Garnett formula as a special case.
A new variational functional is introduced for the analysis of curved open and closed waveguides.... more A new variational functional is introduced for the analysis of curved open and closed waveguides. The theory is based on variational principle for nonstandard eigenvalue problems, recently applied for straight anisotropic fibers. The present method does not set any restrictions to the shape of the waveguide or to the radius of the bend. The dielectric function can be homogeneous or nonhomogeneous with transverse and/or longitudinal anisotropy. As an example of the method a curved isotropic and anisotropic single mode fiber with two different kinds of anisotropy models are studied. The analysis includes field distributions, changes in the dispersion curves due to reformed geometry, and birefringence properties in the curved anisotropic fibers.
Electrostatic image theory for a point charge on the axis of a perfectly conducting prolate spher... more Electrostatic image theory for a point charge on the axis of a perfectly conducting prolate spheroid is formulated. The exact image expression is found using the Havelock identity, according to which the external harmonics of the potential solution emanate from a system of continuous image sources distributed along the focal line. Many tests for the theory are performed and graphical examples given. In the case of a slightly prolate sphere, the first correction to the image solution for the conducting sphere by Lord Kelvin is developed. An expression for the image polarization density function is derived for the dipolar source.
The dyadic Green's function for an unbounded nonreciprocal uniaxial bianisotropic medium is deriv... more The dyadic Green's function for an unbounded nonreciprocal uniaxial bianisotropic medium is derived in explicit form. Such uniaxial bianisotropic media can be realized by randomly dispersing uniaxial metallic inclusions with parallel orientations into an isotropic host medium. The availability of an analytic solution for the dyadic Green's function marks therefore an important step towards an understanding of radiation from sources and propagation of waves in composite materials.
Reflection and transmission of a plane wave at the planar interface of isotropic and bi-isotropic... more Reflection and transmission of a plane wave at the planar interface of isotropic and bi-isotropic (BI) media are analyzed. The analysis applies vector transmission line theory, which for the general case is seen to involve both dyadic impedance and dyadic propagation factor quantities. Explicit expressions for the reflection and transmission dyadics are given and their special cases for the Tellegen, nonreciprocal nonchiral, media are obtained and confirmed by previous results. Eigen polarizations for the reflection dyadic are found and conditions for zeros of eigen reflections are worked out to give explicit expressions for Brewster angles corresponding to the BI interface. A new phenomenon is the appearance of two Brewster angles for certain material parameter values of bi-isotropic half space. Also, conditions for zeros of cross-polarized reflections are found for the general case. These nonreciprocal cross Brewster angles for which, a horizontally polarized wave gives no vertically polarized reflection whereas a vertically polarized wave gives nonzero horizontally polarized reflection, may find practical applications because this effect does not appear for special cases of Tellegen and Pasteur media.
The Silberstein wave-field decomposition of electromagnetic fields is applied to the problem of w... more The Silberstein wave-field decomposition of electromagnetic fields is applied to the problem of wave propagation in chiral medium. The problem involving a planar interface between two chiral media is considered and eigensolutions for the reflection and transmission problems are given. Numerical results are calculated for the eigenpolarizations and reflection coefficients with different incident field polarizations, for the problem involving an interface between isotropic and chiral media. Also, the limit cases of reflection from a half space with only small amount of chirality are studied and it is shown that the chirality gives a second-order effect on the co-polarized reflection coefficient and a first-order effect on cross-polarization.
Journal of Electromagnetic Waves and Applications, 2001
ABSTRACT The classical Helmholtz theorem which decomposes a given vector field to curl-free and d... more ABSTRACT The classical Helmholtz theorem which decomposes a given vector field to curl-free and divergence-free components and presents the field in terms of a scalar and a vector potential is reformulated so that the divergence-free part is further decomposed in two parts with respect to either one or two given unit vectors. It is shown that these decompositions follow in a straightforward way from certain operator identities. The field is represented in terms of three scalar potential functions, two of which can be related to Hertzian potentials and TE/TM decomposition when decomposing time-harmonic electromagnetic field vectors outside the source region. Applying the decomposition to time-harmonic sources as well as the fields, equations between scalar source and field potentials can be formulated which gives an alternative method of solving electromagnetic problems.
Journal of Electromagnetic Waves and Applications, 2003
ABSTRACT The classical Helmholtz theorem which decomposes a given vector field in three dimension... more ABSTRACT The classical Helmholtz theorem which decomposes a given vector field in three dimensions to its curl-free and divergence-free components in terms of a scalar and a vector potential is generalized in differential-form formalism to multiform fields in an n-dimensional space. Decomposition of a p-form field follows in a straightforward way from certain operator identities corresponding to the curl-curl formula of the Gibbsian vector analysis in three dimensions. For p ≥ 1, the representation of a given p-form field is given in terms of a (p-1)-form and a (p+1)-form potential field whose respective generalized curl and divergence operations vanish.
ABSTRACT The image principle in electromagnetics replaces a physical structure by an equivalent s... more ABSTRACT The image principle in electromagnetics replaces a physical structure by an equivalent source, the image of the primary source. The number of structures with analytic image expressions is limited but increasing. In finding new image expressions, the Heaviside operational calculus can be applied by first transforming the three-dimensional problem to one concerning transmission lines. The image problem can be reduced to the compact form in terms of a pseudo-differential operator applied to the original source function. To interprete the result in terms of computable functions, approximations can be done at this stage. As a simple example of the theory the interface of two isotropic media with smooth or slightly rough interface is considered. A table of operational formulas is given as an appendix.
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Papers by Ismo Lindell