Theodoros D. Tsiboukis

Eddy currents: theory and applications

The theory and applications of eddy currents induced in conducting materials by time-varying magnetic fields are reviewed. The mathematical methods employed in solving the relevant problems are presented. Both analytical and numerical methods are described. Applications based on effects arising from eddy currents are discussed in detail. These applications are to magnetic levitation, electromagnetic launching, hyperthermia treatment of cancer, and nondestructive testing. >

Reduction of numerical dispersion in FDTD method through artificial anisotropy

In this paper, a simple and computationally low-cost modification of the standard finite-difference time-domain (FDTD) algorithm is presented to reduce numerical dispersion in the algorithm. Both two- and three-dimensional cases are considered. It is shown that the maximum error in phase velocity can be reduced by a factor of 2-7, depending on the shape of the FDTD cell. Although the reduction procedure is optimal for only single frequency, numerical examples show that the proposed method can also improve the accuracy significantly in wide-band inhomogeneous problems.

Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance

The dispersive characteristics of a photonic crystal fiber enhanced with a liquid crystal core are studied using a planewave expansion method. Numerical results demonstrate that by appropriate design such fibers can function in a single-mode/single-polarization operation, exhibit high- or low- birefringence behavior, or switch between an on-state and an off-state (no guided modes supported). All of the above can be controlled by the application of an external electric field, the specific liquid crystal anchoring conditions and the fiber structural parameters.

Optimal Modeling of Infinite Graphene Sheets via a Class of Generalized FDTD Schemes

The accurate and fully 3-D analysis of graphene surface conductivity models by means of a frequency-dependent finite-difference time-domain method is introduced in this paper. For the infinite sheet to be consistently simulated, the novel technique uses a set of periodic boundary conditions that lead to a unit cell excited with a spectral scheme in terms of a total-field/scattered-field formulation. On the other hand, graphene itself is modeled through a subcell approach and a complex surface conductivity concept defined by quantum mechanical equations. This conductivity model is next converted to a volume one in order to permit a realistic time-domain study. Numerical outcomes, addressing a variety of applications, reveal a promising coincidence with those acquired from analytical closed-form expressions.

Low-dispersion algorithms based on the higher order (2,4) FDTD method

This paper discusses the enhancement of numerical dispersion characteristics in the context of the finite-difference time-domain method based on a (2,4) computational stencil. Rather than implementing the conventional approach-based on Taylor analysis-for the determination of the finite-difference operators, two alternative procedures that result in numerical schemes with diverse wide-band behavior are proposed. First, an algorithm that performs better than the standard counterpart over all frequencies is constructed by requiring the mutual cancellation of terms with equal order in the corresponding dispersion relation. In addition, a second method is derived, which is founded on the separate optimization of the spatial and temporal derivatives. In this case, analysis proves that significant error compensation is accomplished around a specific design frequency, while reduced errors are obtained for higher frequencies, thus enabling the reliable execution of wide-band simulations as well. The quality and efficiency of the proposed techniques, which exhibit the same computational requirements as the standard (2,4) approach, are investigated theoretically, and subsequently, validated by means of numerical experimentation.

Tunable highly birefringent bandgap-guiding liquid-crystal microstructured fibers

A new type of nematic liquid-crystal infiltrated photonic bandgap-guiding fiber for single polarization or high-birefringence guidance is proposed. Numerical studies demonstrate that modal birefringence can be tuned by proper selection of the structural and material parameters as well as by the application of an external electric field in conjunction with the specific liquid-crystal anchoring conditions

Inverse scattering using the finite-element method and a nonlinear optimization technique

A new spatial-domain technique for the reconstruction of the complex permittivity profile of unknown scatterers is proposed in this paper. The technique is based on a combination of the finite-element method (FEM) and the Polak-Ribiere nonlinear conjugate gradient optimization algorithm. The direct scattering problem is explicitly dealt with by means of the differential formulation and it is solved by applying the FEM. The inversion methodology is oriented to minimizing a cost function, which consists of a standard error term and regularization term. A sensitivity analysis, which is carried out by an elaborate finite-element procedure, results in the determination of the direction required for correcting the profile. Significant reduction of the computation time is obtained by introducing the adjoint state vector methodology. The efficiency of the presented inversion technique is validated by applying it to the inversion of synthetic scattered far-field measurements, which are corrupted by additive noise.

Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects

The tuning properties of two-dimensional dielectric and metallic photonic crystals, which contain nematic liquid crystal materials as defect elements or layers, are thoroughly analyzed using appropriate formulations of the finite difference time domain (FDTD) method. Our methodology correctly incorporates the anisotropy introduced by the liquid crystal materials together with the dispersive properties of the metallic elements; it is used for calculating both the dispersion diagrams of the defect-free photonic crystal as well as the device response in the presence of the defect elements. Numerical simulations reveal that defect states originating from the liquid crystal impurities can be effectively tuned by the application of a local static electric field. Indeed, tuning ranges up to almost 100 nm can be achieved requiring operating voltages lower than 4 V. It is also concluded that the placement of a defect mode relative to the bandgap edges greatly influences both its linewidth as well as its tuning range.

A finite element based technique for microwave imaging of two-dimensional objects

In this paper, a microwave imaging technique for estimating the spatial distributions of the permittivity and the conductivity of a scatterer, by post-processing electromagnetic scattered field data, is presented. For the description of the direct scattering problem, the differential formulation is applied. This allows the use of the finite element method. During the inversion, the computation of the derivative of the finite element solution with respect to the parameters, which describe the scatterer, is required. This task is performed by a finite element-based sensitivity analysis scheme, which is enhanced by applying the adjoint state vector methodology. The merits of the proposed technique are examined by applying it to both transverse magnetic and transverse electric polarization cases. Finally, the technique is adopted by a frequency-hopping approach to cope with multifrequency inverse scattering problems.

Constitutive inconsistency: rigorous solution of Maxwell equations based on a dual approach

A dual scheme is proposed, that correctly represents the electromagnetic fields as differential forms. A rigorous solution of Maxwells equations is obtained that satisfies both Amperes and Faradays laws. The solution of Maxwells equations derived from the numerical discretization of two complementary formulations is inconsistent with the constitutive laws. This inconsistency is used as an error estimator in a 3D adaptive refinement procedure resulting in very accurate solutions and reduced computational cost. A new error criterion, the dual constitutive error, consisting of two components: the electric error and the magnetic error, is introduced. Edge elements with tangential continuity are used giving no spurious solutions. The validity of the proposed technique is illustrated by an application to a loaded cavity. >