Svend Berntsen

Retarded time absorbing boundary conditions

Over the past few years simulations of electromagnetic problems in three dimensions using the finite difference time domain (FDTD) method have become increasingly popular. A major problem in such simulations is the truncation of the computational domain. A formulation of this boundary problem using retarded time values of the field inside the computational domain is suggested, and hence the name retarded time absorbing boundary condition (RT-ABC). This formulation allows the boundary to be situated in the near field of the problem and thereby reduces the necessary computational domain, and the present formulation allows error estimates for the numerically calculated fields. >

Self-consistent model for photon scanning tunneling microscopy: implications for image formation and light scattering near a phase-conjugating mirror

A macroscopic self-consistent model for photon scanning tunneling microscopy with an uncoated fiber tip is developed by use of integral plane-wave representations of the total electric field in two-dimensional geometry. The model framework allows one to treat the incident field with an arbitrary angular spectrum and the presence of a thin-layer medium with a subwavelength structure on the sample surface. Imaging with the photon scanning tunneling microscope and light scattering near a phase-conjugating mirror are considered with our model by use of numerical simulations. We show that the near-field optical images provided by the microscope can be quite different from the light intensity distributions that exist near the sample surface in the absence of the fiber tip. We demonstrate that the self-consistent field at the site of a scatterer placed in front of a phase-conjugating mirror can be significantly enhanced as a result of multiple phase conjugation of the scattered light.

Extension of the macroscopic model for reflection near-field microscopy: regularization and image formation

A macroscopic self-consistent model for external-refraction near-field microscopy is extended to include the consideration of arbitrary fiber tips and the image formation of surface structures. An appropriate regularization procedure is developed to produce a stable solution of the self-consistent equation. This equation is generalized to treat the presence of a thin-layer medium with a subwavelength structure on the sample surface. Numerical results for two trapezium-shaped fiber tips are presented. This modeling confirms that the sharper tip ensures better imaging properties of the microscope but that the lateral resolution is limited by a fraction of the wavelength because of the microscopic sizes of the fiber tips.

Macroscopic self-consistent model for external-reflection near-field microscopy

The self-consistent macroscopic approach based on the Maxwell equations in two-dimensional geometry is developed to describe tip–surface interaction in external-reflection near-field microscopy. The problem is reduced to a single one-dimensional integral equation in terms of the Fourier components of the field at the plane of the sample surface. This equation is extended to take into account a pointlike scatterer placed on the sample surface. The power of light propagating toward the detector as the fiber mode is expressed by using the self-consistent field at the tip surface. Numerical results for trapezium-shaped tips are presented. We show that the sharper tip and the more confined fiber mode result in better resolution of the near-field microscope. Moreover, it is found that the tip–surface distance should not be too small so that better resolution is ensured.

Theoretical model for phase conjugation of optical near fields

A macroscopic self-consistent model for external-reflection near-field microscopy together with a similar model for photon scanning tunneling microscopy is used to describe phase conjugation of light that is emitted by a fiber tip placed near a phase-conjugating mirror. The appropriate relations are obtained for a two-dimensional configuration, and numerical results for various trapezium-shaped fiber tips are presented. This modeling accounts for the main features of recent experiments on phase conjugation of optical near fields and emphasizes the significance of taking into consideration field components that are evanescent in air but propagating in the phase-conjugating mirror. The influence of fiber tip parameters on the spatial confinement of phaseconjugated light is discussed.

A general formulation of applied potential tomography.

Reconstruction of the conductivity of a medium from a set of known values of the boundary potential and boundary normal current is described. The geometry is general, two or three dimensional. The method is applied to two cases, a circular medium and an infinite medium under a plane. In both cases the conductivity is found as an expansion on a system of orthogonal functions. In a linear approximation the conductivity may explicitly be reconstructed. The problem is an ill posed one, the condition numbers are found. Some numerical examples are included.

Comments on "The Foster Reactance Theorem for Antennas and Radiation Q

For original paper by Geyi et al., see IEEE Trans. Antennas Propag., vol.48, no.3, p.401-8 (March 2000)

Quasi-static Profile Reconstruction of a Circular Cylinder

Reconstruction of a radially varying conductivity in a circular cylinder is considered by exciting the cylinder with a quasi-static current and measuring the potential distribution on the surface. A nonlinear integral equation is derived from which the conductivity distribution may be obtained from Fourier harmonics of the surface potential. A linear version is used for studies of uniqueness, resolution and accuracy. Using the orthogonality of shifted Legendre polynomials an explicit solution for the conductivity is given, avoiding numerical inversion problems. The solution is only unique if the conductivity on the axis is known. The resolution is determined by the maximum number N of Fourier harmonics, and the sensitivity of the solution increases rapidly with N. The nonlinear version, although non-unique in principle, is solved numerically by iteration with a considerable improvement of the reconstruction.

Regularization in the macroscopic self-consistent model for near-field microscopy

Abstract The macroscopic self-consistent model for near-field microscopy in two-dimensional geometry is considered. A unified approach for regularization in our macroscopic model is developed and applied to various configurations of the tip-surface system. The configuration with the incoming field being incident from the side of the sample is considered in details. The appropriate regularization parameters are determined and found to be dependent not only on the geometry of the tip-surface system but also on the spatial spectrum of the incident field.

Inverse acoustic problem of N homogeneous scatterers

The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered field at a plane below all scatterers onto the field and the complex wavenumbers is explicitly constructed. Uniqueness theorems for the inverse problem are proven.