Vladimir G. Romanov

IDENTIFICATION OF DIPOLE SOURCES IN A BOUNDED DOMAIN FOR MAXWELL'S EQUATIONS

Abstract The inverse problem of determining the spatial current source distribution in a conducting object is formulated, with an emphasis on the case of a current dipole source. Some uniqueness results are established, and explicit formulas for identification of the location and moment of the dipole source are derived. The static case is considered, as well as the general case of an arbitrary frequency. The formulas are generalized to the case of a current dipole in a chiral object. The case when both a current dipole and a magnetic dipole exist is also considered.

General properties of N x M self-images in a strongly confined rectangular waveguide

General properties of N x M self-images in a strongly confined rectangular waveguide are given. Analytical formulas are derived for the positions, amplitudes, and phases of the N x M images at the end of multimode interference section. The formulas are verified with numerical simulation of a three-dimensional semivectorial beam propagation method.

A Simple and Effective Method for Calculating the Bending Loss and Phase Enhancement of a Bent Planar Waveguide

A simple and effective method is introduced to calculate the bending loss and phase enhancement of a bent planar waveguide. The wave field is represented in terms of Airy functions and an eigenvalue equation is derived by matching the boundary conditions and the radiation condition in the outer cladding layer. The complex propagation constant is obtained by solving the eigenvalue equation with the Newton–Raphson method, and the imaginary part of the propagation constant gives directly the bending loss of the bent waveguide. The results are compared with the previous experimental and numerical results and are shown to be highly accurate and effective. The phase enhancement due to the bending is also studied.

Explicit full identification of a transient dipole source in the atmosphere from measurement of the electromagnetic fields at several points at ground level

Explicit full identification of a transient dipole source in the atmosphere from measurement of the electromagnetic fields at several points at ground level

Analysis of the Green’s function approach to one‐dimensional inverse problems. II. Simultaneous reconstruction of two parameters

The wave‐splitting Green’s function approach to one‐dimensional electromagnetic inverse problems of simultaneous reconstructions with different types of scattering data is analyzed. Theorems of existence, uniqueness, and stability are given for the following types of scattering data: reflection and transmission data for one round trip, two‐sided reflection data for one round trip, reflection data for two round trips.

Some uniqueness theorems for mammography-related time-domain inverse problems for the diffusion equation

Some mammography-related inverse problems for the time-dependent diffusion equation are considered. The extrapolated boundary condition is used and the problem is linearized. Uniqueness theorems for two different types of inverse problems are given, namely the determination of the diffusion or absorption coefficients from the reflection data and the simultaneous determination of the diffusion and absorption coefficients from the transmission data. The inverse problem for the latter is reduced to two tomography problems which can be solved successively.

Identification of small flaws in conductors using magnetostatic measurements

The identification of small flaws in a conducting half-space or rectangular specimen using boundary measurements of the static magnetic field is considered. The perturbed magnetic field due to the presence of a small flaw is assumed to be generated by an equivalent current dipole located at the flaw position. Explicit formulas are given for the identification of a single flaw or a set of flaws in a conducting half-space or rectangular specimen.

Analysis of the Green’s function approach to one‐dimensional inverse problems. I. One parameter reconstruction

An analysis of a Green’s function approach (based on wave splitting) to the one‐dimensional electromagnetic inverse problem is given. The Green’s functions refer to split components of the fundamental solution. The linear system of equations for the Green’s functions is shown to be well‐posed for the inverse problem and stability estimates, theorems on existence, uniqueness, local correctness, and convergence are given.

Explicit formulas for the identification of a small defect in a planar waveguide

Nondestructive testing of a small defect (a dust particle or air void) in a strongly confined planar waveguide is considered. Explicit formulas are given for a quick identification of the small defect by use of the distorted fields measured at the two end faces of the planar waveguide for two frequencies. The explicit identification scheme is verified numerically.

A simple analytical method for calculating the leakage loss of a buried rectangular waveguide

A simple and efficient analytical method is presented for studying leaky modes in a buried rectangular waveguide on a high-refractive-index substrate. The cross-sectional profile of the refractive index for the buried rectangular waveguide is decomposed into three parts. The two main parts correspond to two independent multilayered slab waveguide structures and the remaining part is treated as a small perturbation term. The contributions from all three parts to the leakage loss are given analytically. Numerical results are presented and compared with those calculated with the semi-vectorial finite difference method. Fast speed, satisfactory accuracy and simplicity are the main advantages of the present method.