An efficient algorithm to restore the actual surface potential image from Kelvin probe force microscopy measurements of semiconductors is presented. The three-dimensional potential of the tip-sample system is calculated using an integral equation-based boundary element method combined with modeling the semiconductor by an equivalent dipole-layer and image-charge model. The derived point spread function of the measuring tip is then used to restore the actual surface potential from the measured image, using noise filtration and deconvolution algorithms. The model is then used to restore high-resolution Kelvin probe microscopy images of semiconductor surfaces.

A novel algorithm for fast computation of tomographic image projections is presented. The method comprises a decomposition of an image into subimages followed by an aggregation of projections computed for the subimages. The multilevel domain decomposition algorithm is formulated as a recursive procedure. The computational cost of the proposed algorithm is comparable to that of FFT-based techniques while it appears to be more flexible than the latter. Numerical results demonstrate the effectiveness of the method.

Photonic crystal microcavities, formed by local defects within an otherwise perfectly periodic structure, can be used as narrowband optical resonators and filters. The coupled-cavity waveguide (CCW) is a linear array of equally spaced identical microcavities. Tunneling of light between microcavities forms a guiding effect, with a central frequency and bandwidth controlled by the local defects’ parameters and spacing, respectively. We employ cavity perturbation theory to investigate the sensitivity of microcavities and CCWs to random structure inaccuracies. For the microcavity, we predict a frequency shift that is due to random changes in the lattice structure and show an approximate linear dependence between the standard deviation of the structure inaccuracy and that of the resonant frequency. The effect of structural inaccuracy on the CCW devices, however, is different; it has practically no effect on the CCW performance if it is below a certain threshold but may destroy the CCW if this threshold is exceeded.

A generalized equivalence integral equation (GEIE) approach to formulating scattering from essentially convex closed surfaces is proposed. The GEIE approach invokes the generalized surface field equivalence to partially fill the volume originally occupied by the scatterer with judiciously selected materials, as opposed to the conventional replacement of the scatterer by the free space. The type and shape of the material inclusions can be selected to allow for a numerically efficient construction of the modified Green's function. Introduction of impenetrable and lossy materials confines the field interaction along the scatterer surface and reduces the coupling between the distant parts of the scatterer, which essentially makes the impedance matrix banded. The presence of lossy materials also resolves the nonuniqueness problem of the electric and magnetic field integral equations by eliminating the internal resonances. The formulation provides a pathway for developing fast iterative and direct electromagnetic integral equation solvers.

A class of inherently compressible integral equation formulations for problems of scattering by impenetrable objects, which makes use of generalized directional sources, is presented. The new formulation effectively reduces the problem’s dimensionality and, thus, allows for efficient low-rank compression of moment matrices’ off-diagonal blocks. When the formulation is used with a hierarchical matrix compression and factorization algorithm, a fast direct solver is obtained. The computational bottlenecks introduced by the proposed generalized formulation, in both the matrix-fill and matrix compression stages, are alleviated by using non-uniform sampling-based techniques. These techniques are described in detail for one choice of generalized sources, which use absorbing equivalent source shields, and can be extended to other shield types. The formulation’s properties and limitations are studied and its enhanced compressibility is used for the development of a fast direct solver.

A concept for an optical holographic security tag is proposed and demonstrated. When illuminated with a laser beam, the image scattered from the tag projects a Quick Response code which encodes identifying information. The image also carries pseudorandom speckle noise, from which a unique speckle pattern “fingerprint” is derived. We show numerically that the tag is unclonable without access to a secret key - the starting conditions of the design algorithm. However, given the key, it is straightforward to reproduce a tag exhibiting the expected fingerprint. Several tags have been realized, implemented as plasmonic meta-holograms, and characterized experimentally. The robustness of the tag to fabrication error and its resilience to counterfeiting are studied in detail and demonstrated experimentally.