Complex Space Source Research Articles

Image Solution for the 3-D Static Green’s Function of a Vertically Stratified Two-Layer Half-Space

The general form of 3-D static Green’s function for a general structure consisting of ${N}$ arbitrary adjacent dielectric wedges is derived using the Kontorovich-Lebedev and Fourier transforms. It consists of several point sources in physical space and a line image source in complex space for each region of the problem geometry. While the point sources can be treated conventionally, the line image distributions are obtained by extracting a proper asymptotic behavior of the solution, which can be numerically computed. As an example, the case of a vertically stratified two-layer half-space is investigated and the respective point and line image sources are obtained. The efficiency of the proposed solution method is demonstrated by comparing the computational time for a given structure with that required by a commercially available numerical code using the finite integration technique.

Complex space source theory of partially coherent light wave

The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.

Basic full-wave generalization of the real-argument Hermite–Gauss beam

The linearly polarized real-argument Hermite-Gauss beam is investigated by the Fourier transform method. The complex power is obtained and the reactive power of the paraxial beam is found to be zero. The complex space source required for the full-wave generalization of the real-argument Hermite-Gauss beam is deduced. The resulting basic full real-argument Hermite-Gauss wave is determined. The real and the reactive powers of the full wave are evaluated. The reactive power of the basic full real-argument Hermite-Gauss wave is infinite, and the reasons for this singularity are described. The real power depends on kw(0), m, and n, where k is the wavenumber, w(0) is the e-folding distance of the Gaussian part of the input distribution, and m and n are the mode numbers. The variation in the real power with respect to changes in kw(0) for specified m and n as well as with respect to changes in m and n for a specified kw(0) is examined.

Time-Domain Green Function Corresponding to a Time-Harmonic Point Source in Complex Space

ABSTRACT The time-domain counterpart of the scalar field arising from a time-harmonic point source in the complex space is derived. The solution corresponds to the complex-space source Green function, which has grown very important in various electromagnetic problems, because it can be applied to approximate the narrow radiation of the Gaussian beam type. The time-domain counterpart presented in the present paper is seen to be real and causal. The solution is demonstrated to an asymptotic case of the Sommerfeld half-space problem in time domain.

Exact image theory for the Sommerfeld half-space problem, part I: Vertical magnetic dipole

Applying the Laplace transform, the exact distributed image current function is obtained for the classical Sommerfeld half-space problem with vertical magnetic current source. The resulting field integral is well behaved when the image current is situated in complex space. Unlike previous approximate images, the present theory is valid for any distance, height of the source, frequency, and half-space parameters. It is demonstrated that the present image theory reduces to the well-known dipole image at complex depth for large dielectric parameters of the half-space. Also, the reflection-coefficient method is obtained as a farfield approximation. Calculation of fields through exact image integration is seen to be simple and accurate and require modest computer capacity and time. In an appendix, some properties of the multivalued Green's function arising from a dipole source in complex space are also studied.