Perezpearce9523

This paper addresses a number of approximate, analytically invertible solutions of the scalar Helmholtz equation. Primary attention is devoted to the Glauber approximation (GA) derived for the far-field pattern. It is shown that the GA has the form of a nonlinear Radon-to-Helmholtz (RtH) mapping, which transforms a sinogram of the scattering potential into an approximate solution of the Helmholtz equation. A proposal of how to construct a position space counterpart of the GA is formulated. Also, it is established that a paraxial version of the Glauber model coincides, up to an inessential constant factor, with a momentum-space representation of the Mazar-Felsen propagator, which describes forward-scattered waves. For weakly scattering objects, these solutions are reduced to the conventional Born/Rytov approximations, which may, however, preserve the parametrization and sampling formats of the original nonlinear models. Since all RtH mappings are analytically invertible, they can be applied to the (nonlinear) diffraction tomography of penetrable objects. In particular, the Glauber model, which has been largely ignored for years, is shown to provide efficient inversion of synthetic data. The resulting tomograms clearly outperform the Born inversions, even for moderately scattering potentials.The aim of this paper is to describe and demonstrate what should be done to the measured Zernike coefficients when conjugating the pupil and wavefront sensor planes with a 4f system. I provide theoretical and experimental evidence. The experimental setup consisted of two 4f systems of magnifications 1 and 1/3 with their corresponding wavefront sensors at their ends. Spherical and cylindrical trial lenses were measured. In addition, I measured a phase plate with high-order aberrations. I show that the Zernike coefficients of the wavefront expansion at two planes conjugated by a 4f system are related independently of the magnification of the 4f system by the following equation bi=(-1) n ai, with n being the order of the radial Zernike polynomial.A systematic and formal study of the global and elemental properties of the propagating-order scattering matrix of conically mounted and crossed gratings is presented. G140 concentration The most general formulation of the scattering matrix is established. Expressions of the global properties (reciprocity and unitarity) of the scattering matrix (S matrix) in the general form previously not available in the literature are presented in the main text, and their full mathematical derivations are given in two appendices. The distinctive contribution of this work is an exposition of the elemental properties of the S matrix. The elemental S tensor and the elemental S matrix, the latter being the linear-space representation of the former, for a pair of an incident plane wave and a diffracted order are defined and studied. The key results of the exposition are two sum rules of diffraction efficiencies and a dot-product-free, vectorial reciprocity theorem.A structured optical field with controllable three-dimensional intensity and multiple polarization singularities is demonstrated by utilizing a combination of a radially polarized (RP) beam, a designed phase mask, and a high numerical aperture lens. Owing to the tight focusing property of RP beams as well as the interference of multiple linearly polarized non-coplanar plane waves, various lattice-like optical structures can emerge at the focal plane with multiple structured singularities in the transverse plane and optical needle array along with propagation. Compared with recently proposed phase and polarization engineering methods with spatial light modulators, the method presented here is convenient and flexible, and can easily realize the generation of V-point and C-point lattices. More importantly, a structured longitudinal field, namely, an optical needle array, with steerable positive and reverse energy flows may be extensively applied in multi-particle acceleration and trapping, optical microscopes, and second-harmonic generation.In this paper, a tunable plasmon-induced transparency (PIT) structure based on a monolayer black phosphorus metamaterial is designed. In the structure, destructive interference between the bright and dark modes produces a significant PIT in the midinfrared band. Numerical simulation and theoretical calculation methods are utilized to analyze the tunable PIT effect of black phosphorus (BP). Finite-difference-time-domain simulations are consistent with theoretical calculations by coupled mode theory in the terahertz frequency band. We explored the anisotropy of a BP-based metasurface structure. By varying the geometrical parameters and carrier concentration of the monolayer BP, the interaction between the bright and dark modes in the structure can be effectively adjusted, and the active adjustment of the PIT effect is achieved. Further, the structure's group index can be as high as 139, which provides excellent slow-light performance. This study offers a new possibility for the practical applications of BP in micro-nano slow-light devices.In this paper, some explicit analytical solutions for single-scattered radiance in a half-space medium under consideration of a reflecting boundary are derived. We consider both a unidirectional beam source as well as an isotropic point source. In addition to direct applications within optical tomography and computer graphics, the obtained solutions are also needed when solving the radiative transport equation after the separation of the unscattered and single-scattered contribution. Comparisons between the derived analytical solutions and the Monte Carlo method display excellent agreement.An improved algorithm for numerical evaluation of the Hankel transform is developed. The algorithm originally proposed by Yu et al. [Opt. Lett.23, 409 (1998)OPLEDP0146-959210.1364/OL.23.000409] uses the quadrature in which the nodes are zeros of the Bessel function. In this work, it is shown that the accuracy of the algorithm can be significantly improved, with virtually no increase in computation time, via two steps. One is to halve the weight of the last node, and the other is to extrapolate a function tail using the modified Bessel function of the second kind, which gives the analytical estimation of the integral remainder.