Spherical Wave Expansion of the Time Domain Free-Space Dyadic Green’s Function

Azizoglu, S. Alp; Koc, Sencer; Buyukdura, O. Merih

doi:10.1007/0-306-47948-6_10

Cited by 2 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be noted that the (14) is not new; it was first presented in [40] when the authors tried using this expression to derive analytical expression for the coefficients.…”

Section: Spherical Expansion For Time-domain Scalar Green's Functionmentioning

confidence: 99%

“…In [39], timedomain acoustic scattering from a sphere is studied with the help of time-dependent wave functions (inverse Fourier transform of the frequency domain spherical wave functions). The same idea is also extended to two-sphere case [40]. Considering the fact that mode matching concept is used to extract the time-domain signatures, this type of approach is direct time-domain variant of conventional LorentzMie-Debye approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

Shanker²

2015

PIER

View full text Add to dashboard Cite

Abstract-Canonical solutions to frequency domain Maxwell's equations, in the spherical coordinate system, have found extensive use as is evident from citations in the scientific literature. What is conspicuous by its absence is lack of such expressions for transient Maxwell systems. The existence of such expressions or approximations, provide the means to glean interesting physics in a variety of applications as well as validate existing numerical fullwave solvers. However, developing these expressions is beset with challenges; direct inverse Fourier transforms of frequency domain expressions are unstable. Successful approaches that ameliorate this instability are more recent endeavor. In this paper, we generalize our earlier contribution to this effort by exploiting a novel representation of the retarded potential to derive expressions for scattering from a dielectric sphere. Several results are provided that demonstrate the stability and accuracy of the method.

show abstract

“…It should be noted that the (14) is not new; it was first presented in [40] when the authors tried using this expression to derive analytical expression for the coefficients.…”

Section: Spherical Expansion For Time-domain Scalar Green's Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

Shanker²

2015

PIER

View full text Add to dashboard Cite

show abstract

“…A more recent paper examined the causes of instability, errors in the extent literature, and presented a recursive convolution approach that is stable for both late time and high order harmonics [28] for scalar fields. Extension of classical Fourier methods to electromagnetic fields is significantly more complicated [29], and given the instability for scalar fields, it is not clear that this will be stable for vector fields. It is possible that the method developed in [28] may be extended to the vector case.…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Debye–Mie Series Solutions for Electromagnetic Scattering

Shanker

2015

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analog is a challenge, as it involves an inverse Fourier transform of the spherical Hankel functions (and their derivatives) that are convolved with inverse Fourier transforms of spherical Bessel functions (and their derivatives). Series expansion of these convolutions is highly oscillatory (therefore, poorly convergent) and unstable. Indeed, the literature on numerical computation of this convolution is very sparse. In this paper, we present a novel quasi-analytical approach to compute transient Mie scattering that is both stable and rapidly convergent. The approach espoused here is to use vector tesseral harmonics as basis function for the currents in time-domain integral equations (TDIEs) together with a novel addition theorem for the Green's functions that render these expansions stable. This procedure results in an orthogonal, spatially meshfree, and singularity-free system, giving us a set of one-dimensional (1-D) Volterra Integral equations. Timedependent multipole coefficients for each mode are obtained via a time-marching procedure. Finally, several numerical examples are presented to show the accuracy and stability of the proposed method. Index Terms-Time-dependent Mie series, time-domain integral equations (TDIEs), Volterra integral equation.

show abstract

Spherical Wave Expansion of the Time Domain Free-Space Dyadic Green’s Function

Cited by 2 publications

References 4 publications

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

Time-Dependent Debye–Mie Series Solutions for Electromagnetic Scattering

Contact Info

Product

Resources

About