Finally, in the space spanned by the wave functions of the SU(2) harmonic oscillator, we find that the discrete normalized Bargmann transform commutes with the fractional Fourier-Kravchuk transform.We present an experimental and numerical study of the optical properties of nanofabricated samples with layered dielectric structures. The samples, which contain periodic arrays of silicon disks over a flat layer of silicon dioxide on a silicon substrate, present diffraction and thin film interference effects. Well-defined circular fringes that modulate the intensity of the diffraction orders are observed in the far-field angular distribution of scattered light. We also find that although the angle of incidence modulates the intensity of the observed circular ring patterns, it has little or no effect on their angular position. The problem is modeled theoretically through numerical calculations based on a Rayleigh method.In the present work, diffraction of a Gaussian source beam by a perfect electromagnetic conductor (PEMC) semi-screen is investigated. Due to the special property of the PEMC sheet, which is a combination of perfect electric conductor and perfect magnetic conductor surfaces, the reflected wave from the PEMC surface has a cross-polarized component in addition to the co-polarized component. For an electric line source illumination, the diffracted fields are derived by considering the analogy between the transition boundaries and scattered geometric optics fields. Later, the complex point source technique is applied for evaluation of Gaussian beam diffraction. The finite magnitude values of fields are derived with the aid of an improved version of the well-known uniform theory of diffraction for evanescent plane waves. Also, the resultant waves are plotted and discussed for different groups of parameters.We introduce a very efficient noniterative algorithm to calculate the signed area of a spherical polygon with arbitrary shape on the Poincaré sphere. The method is based on the concept of the geometric Berry phase. It can handle diverse scenarios like convex and concave angles, multiply connected domains, overlapped vertices, sides and areas, self-intersecting polygons, holes, islands, cogeodesic vertices, random polygons, and vertices connected with long segments of great circles. A set of MATLAB routines of the algorithm is included. FTI 277 inhibitor The main benefits of the algorithm are the ability to handle all manner of degenerate shapes, the shortness of the program code, and the running time.Diffractive shearing interferometry (DSI) is a method that has recently been developed to perform lensless imaging using extreme ultraviolet radiation generated by high-harmonic generation. In this paper, we investigate the uniqueness of the DSI solution and the requirements for the support constraint size. We find that there can be multiple solutions to the DSI problem that consist of displaced copies of the actual object. These alternative solutions can be eliminated by enforcing a sufficiently tight support constraint, or by introducing additional synthetic constraints. We furthermore propose a new DSI algorithm inspired by the analogy with coherent diffractive imaging (CDI) algorithms the original DSI algorithm is in a way analogous to the hybrid input-output algorithm as used in CDI, and we propose a new algorithm that is more analogous to the error reduction algorithm as used in CDI. We find that the newly proposed algorithm is suitable for final refinement of the reconstruction.When a target is embedded in random media, the quality of optical imaging can be improved by actively controlling the illumination and exploiting vector wave properties. A rigorous description, however, requires expensive computational resources to fully account for the electromagnetic boundary conditions. Here, we introduce a statistically equivalent scaling model that allows for reducing the complexity of the problem. The new scheme describes the entanglement between the local wave vector and the polarization state in random media and also accounts for cumulative properties such as geometric phase. The approach is validated for different scenarios where the coherent background noise alters substantially the performance of active imaging.A wavelength demultiplexing (WDM) structure based on graphene nanoribbon resonators is proposed and simulated using the finite-difference time-domain (FDTD) method. Based on a simple structure, the demultiplexing wavelength and transmission characteristics of the WDM can be tuned by adjusting the length of the resonator, the nanoribbon width, or the chemical potential of graphene within a relative broadband frequency range. Moreover, the mechanism of the proposed WDM structure is analyzed in detail using the theory of Fabry-Perot (F-P) resonance and temporal coupled-mode theory. The proposed structure has promising potential in the field of ultracompact WDM systems in highly integrated optical circuits.Snapshot channeled polarimeters forgo temporal modulation in favor of modulating polarization information in either space or wavenumber. We have recently introduced methodologies for describing both channeled and partial polarimeters. In this paper, we focus on the nine-reconstructables design, which limits the resolution loss by reducing the number of carriers. The architecture offers a number of favorable trade-offs a factor of 5.44 increase in spatial bandwidth or a factor of 3.67 increase in spectral bandwidth, for a smaller amount of temporal bandwidth loss as dictated by the number of snapshots taken. The multi-snapshot structured decomposition given here allows one to analytically shape the measured space with optimal noise characteristics and minimum system complexity. A two-snapshot system can measure a premeditated set of 14 reconstructables; we provide the null space for the subset of optimal systems that also achieve better SNR than the baseline single-snapshot system. A three-snapshot system can measure all 16 Mueller elements while offering an overall 26.3% or 50.4% better bandwidth-SNR figure of merit for the spectral and spatial systems, respectively. Finally, four-snapshot systems provide diminishing returns, but may be more implementable.