Both the magnitude and sign of the change depend on the velocity of the object, as well as on its... more Both the magnitude and sign of the change depend on the velocity of the object, as well as on its shape, orientation, and composition. In some cases, the change in total scattered energy is greatest when the object is moving transversely to the propagation direction of the interrogating signal, even though the Doppler effect is strongest when the motion is parallel or antiparallel to the propagation direction.
The energy absorption and energy extinction cross sections of an object in uniform translational ... more The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for co-moving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-co-moving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).
The energy extinction cross section of a concentrically layered sphere varies with velocity as th... more The energy extinction cross section of a concentrically layered sphere varies with velocity as the Doppler shift moves the spectral content of the incident signal in the sphere's co-moving inertial reference frame toward or away from resonances of the sphere. Computations for hollow gold nanospheres show that the energy extinction cross section is high when the Doppler shift moves the incident signal's spectral content in the co-moving frame near the wavelength of the sphere's localized surface plasmon resonance. The energy extinction cross section of a three-layer sphere consisting of an olivine-silicate core surrounded by a porous and a magnetite layer, which is used to explain extinction caused by interstellar dust, also depends strongly on velocity. For this sphere, computations show that the energy extinction cross section is high when the Doppler shift moves the spectral content of the incident signal near either of olivine-silicate's two localized surface phonon resonances at 9.7 µm and 18 µm.
IEEE Transactions on Antennas and Propagation, 2019
As vector wavefunctions are available to represent incident and scattered fields in an isotropic ... more As vector wavefunctions are available to represent incident and scattered fields in an isotropic dielectric-magnetic medium endowed with magnetoelectric gyrotropy, a transition matrix can be conceptualized to relate the scattered field coefficients to the incident field coefficients for scattering by an arbitrary scatterer composed of a linear medium. The elements of the transition matrix must satisfy certain conditions for zero backscattering. For a scatterer composed of a uniaxial dielectricmagnetic medium endowed with magnetoelectric gyrotropy, the extended boundary condition method can be formulated to determine the transition matrix. Numerical results obtained thereby lead to the formulation of a sufficient set of three zerobackscattering conditions: (i) The scatterer is a body of revolution with the incident plane wave propagating along the axis of revolution. (ii) The impedances of both mediums are identical. (iii) The magnetoelectric-gyrotropy vectors of both mediums are aligned along the axis of revolution, whether or not both magnetoelectric-gyrotropy vectors are co-parallel.
The simplest Lorentz-nonreciprocal medium has the constitutive relations (D = ε 0 E -Γ × H and B ... more The simplest Lorentz-nonreciprocal medium has the constitutive relations (D = ε 0 E -Γ × H and B = µ 0 H + Γ × E). Scattering by a three-dimensional object composed of this medium was investigated using the extended boundary condition method. Scattering by this object in free space must be attributed to non-zero Γ = |Γ|. The differential scattering efficiency is immune to the transformation of the incident toroidal electric field phasor into a poloidal electric field phasor, or vice versa, and a consequence of this source-invariance is the polarization-state invariance of the differential scattering efficiency when the irradiating field is a plane wave. Both the total scattering and forward-scattering efficiencies of an ellipsoid composed of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is incident in a direction coparallel (but not antiparallel) to Γ, and the backscattering efficiency is minimum when Γ is parallel to the incidence direction. The total scattering and the forward-scattering efficiencies are maximum when the incidence direction is parallel to the largest semi-axis of the ellipsoid if the incidence direction is coparallel (but not antiparallel) to Γ. Lorentz nonreciprocity in an object is thus intimately connected to the shape of that object in affecting the scattered field.
The extended boundary condition method (EBCM) can be used to study planewave scattering by an ell... more The extended boundary condition method (EBCM) can be used to study planewave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The scattering, absorption, and extinction efficiencies were calculated thereby in relation to the propagation direction and the polarization state of the incident plane wave, the constitutive-anisotropy parameters, and the nonsphericity parameters of the ellipsoid, when the eigenvectors of the real permittivity dyadic are aligned along the three semi-axes of the ellipsoid. As the electrical size of the ellipsoid increases, multiple lobes appear in the scattering pattern. The total scattering efficiency can be smaller than the absorption efficiency for some configurations of the incident plane wave but not necessarily for others. The nonsphericity of the object has a stronger influence on the total scattering efficiency than on the absorption efficiency. The forward-scattering efficiency increases monotonically with the electrical size for all configurations of the incident plane wave, and so does the backscattering efficiency for some configurations. For other configurations, the backscattering efficiency has an undulating behavior with increase in electrical size, and is highly affected by the shape and the constitutive anisotropy of the ellipsoid. Even though the ellipsoid is not necessarily a body of revolution, it is anisotropic, and it is not impedance matched to free space, the backscattering efficiency can be minuscule but the forward-scattering efficiency is not. This feature can be useful for harvesting electromagnetic energy.
Over time the account of how the Kramers-Kronig (dispersion) relations between the real and imagi... more Over time the account of how the Kramers-Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather than to the general arguments about linearity, causality and analyticity in modern model-independent derivations. Kramers merely speculated on whether the specific results he obtained might have a more general validity. Neither author showed that a signal cannot travel faster than cin any medium for which the dispersion relations are satisfied. Indeed, they did not mention, even obliquely, signal speeds and causality. Despite their magical aura, Kramers-Kronig relations are translations into somewhat cryptic frequency language of statements clearer in time language.
The original Bruggeman and Maxwell Garnett formulas for the average dielectric function of a comp... more The original Bruggeman and Maxwell Garnett formulas for the average dielectric function of a composite medium satisfy a scaling law: if the dielectric functions of both components are scaled by the same factor, the average dielectric function scales by this factor. These formulas are independent of the size of polarizable elements. Extended formulas explicitly account for size, but at least one formula fails to satisfy the scaling law, a likely failing of all such formulas.
Both the magnitude and sign of the change depend on the velocity of the object, as well as on its... more Both the magnitude and sign of the change depend on the velocity of the object, as well as on its shape, orientation, and composition. In some cases, the change in total scattered energy is greatest when the object is moving transversely to the propagation direction of the interrogating signal, even though the Doppler effect is strongest when the motion is parallel or antiparallel to the propagation direction.
The energy absorption and energy extinction cross sections of an object in uniform translational ... more The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for co-moving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-co-moving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).
The energy extinction cross section of a concentrically layered sphere varies with velocity as th... more The energy extinction cross section of a concentrically layered sphere varies with velocity as the Doppler shift moves the spectral content of the incident signal in the sphere's co-moving inertial reference frame toward or away from resonances of the sphere. Computations for hollow gold nanospheres show that the energy extinction cross section is high when the Doppler shift moves the incident signal's spectral content in the co-moving frame near the wavelength of the sphere's localized surface plasmon resonance. The energy extinction cross section of a three-layer sphere consisting of an olivine-silicate core surrounded by a porous and a magnetite layer, which is used to explain extinction caused by interstellar dust, also depends strongly on velocity. For this sphere, computations show that the energy extinction cross section is high when the Doppler shift moves the spectral content of the incident signal near either of olivine-silicate's two localized surface phonon resonances at 9.7 µm and 18 µm.
IEEE Transactions on Antennas and Propagation, 2019
As vector wavefunctions are available to represent incident and scattered fields in an isotropic ... more As vector wavefunctions are available to represent incident and scattered fields in an isotropic dielectric-magnetic medium endowed with magnetoelectric gyrotropy, a transition matrix can be conceptualized to relate the scattered field coefficients to the incident field coefficients for scattering by an arbitrary scatterer composed of a linear medium. The elements of the transition matrix must satisfy certain conditions for zero backscattering. For a scatterer composed of a uniaxial dielectricmagnetic medium endowed with magnetoelectric gyrotropy, the extended boundary condition method can be formulated to determine the transition matrix. Numerical results obtained thereby lead to the formulation of a sufficient set of three zerobackscattering conditions: (i) The scatterer is a body of revolution with the incident plane wave propagating along the axis of revolution. (ii) The impedances of both mediums are identical. (iii) The magnetoelectric-gyrotropy vectors of both mediums are aligned along the axis of revolution, whether or not both magnetoelectric-gyrotropy vectors are co-parallel.
The simplest Lorentz-nonreciprocal medium has the constitutive relations (D = ε 0 E -Γ × H and B ... more The simplest Lorentz-nonreciprocal medium has the constitutive relations (D = ε 0 E -Γ × H and B = µ 0 H + Γ × E). Scattering by a three-dimensional object composed of this medium was investigated using the extended boundary condition method. Scattering by this object in free space must be attributed to non-zero Γ = |Γ|. The differential scattering efficiency is immune to the transformation of the incident toroidal electric field phasor into a poloidal electric field phasor, or vice versa, and a consequence of this source-invariance is the polarization-state invariance of the differential scattering efficiency when the irradiating field is a plane wave. Both the total scattering and forward-scattering efficiencies of an ellipsoid composed of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is incident in a direction coparallel (but not antiparallel) to Γ, and the backscattering efficiency is minimum when Γ is parallel to the incidence direction. The total scattering and the forward-scattering efficiencies are maximum when the incidence direction is parallel to the largest semi-axis of the ellipsoid if the incidence direction is coparallel (but not antiparallel) to Γ. Lorentz nonreciprocity in an object is thus intimately connected to the shape of that object in affecting the scattered field.
The extended boundary condition method (EBCM) can be used to study planewave scattering by an ell... more The extended boundary condition method (EBCM) can be used to study planewave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The scattering, absorption, and extinction efficiencies were calculated thereby in relation to the propagation direction and the polarization state of the incident plane wave, the constitutive-anisotropy parameters, and the nonsphericity parameters of the ellipsoid, when the eigenvectors of the real permittivity dyadic are aligned along the three semi-axes of the ellipsoid. As the electrical size of the ellipsoid increases, multiple lobes appear in the scattering pattern. The total scattering efficiency can be smaller than the absorption efficiency for some configurations of the incident plane wave but not necessarily for others. The nonsphericity of the object has a stronger influence on the total scattering efficiency than on the absorption efficiency. The forward-scattering efficiency increases monotonically with the electrical size for all configurations of the incident plane wave, and so does the backscattering efficiency for some configurations. For other configurations, the backscattering efficiency has an undulating behavior with increase in electrical size, and is highly affected by the shape and the constitutive anisotropy of the ellipsoid. Even though the ellipsoid is not necessarily a body of revolution, it is anisotropic, and it is not impedance matched to free space, the backscattering efficiency can be minuscule but the forward-scattering efficiency is not. This feature can be useful for harvesting electromagnetic energy.
Over time the account of how the Kramers-Kronig (dispersion) relations between the real and imagi... more Over time the account of how the Kramers-Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather than to the general arguments about linearity, causality and analyticity in modern model-independent derivations. Kramers merely speculated on whether the specific results he obtained might have a more general validity. Neither author showed that a signal cannot travel faster than cin any medium for which the dispersion relations are satisfied. Indeed, they did not mention, even obliquely, signal speeds and causality. Despite their magical aura, Kramers-Kronig relations are translations into somewhat cryptic frequency language of statements clearer in time language.
The original Bruggeman and Maxwell Garnett formulas for the average dielectric function of a comp... more The original Bruggeman and Maxwell Garnett formulas for the average dielectric function of a composite medium satisfy a scaling law: if the dielectric functions of both components are scaled by the same factor, the average dielectric function scales by this factor. These formulas are independent of the size of polarizable elements. Extended formulas explicitly account for size, but at least one formula fails to satisfy the scaling law, a likely failing of all such formulas.
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