Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1605.04540

Analytical Solutions for Beams Passing Apertures with Sharp Boundaries

Eitam Luz·Er'el Granot·Boris A. Malomed
View original source ↗Read source document ↗Export metadata ↓

Abstract

An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.

Explore related subjects

physics.opticsnlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Eitam Luz, Er'el Granot, Boris A. Malomed. 2016-05-15. Analytical Solutions for Beams Passing Apertures with Sharp Boundaries. https://doi.org/10.1088/2040-8978%2F18%2F7%2F075607

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Paraxial diffusion-field retrieval. II. Fokker-Planck generalization of the transport-of-intensity equation

The transport-of-intensity equation (TIE), namely the continuity equation associated with a coherent paraxial optical wavefield, is widely used for phase retrieval. It is a second-order partial differential equation which may be solved for the phase of a coherent paraxial field such as a monochromatic scalar optical beam, given the intensity and longitudinal intensity derivative in a plane perpendicular to the optical axis. We show how the coherent flow associated with the TIE may be augmented by a diffusive flow associated with a scalar or tensor diffusion field. Such diffusive flow can arise via scattering from unresolved spatially random microstructure in an illuminated sample, blurring effects of an extended chaotic source that illuminates the sample, the resolution-reducing effect of shot noise in detected intensity images of the sample, and the sharpening effect (negative diffusion) associated with scattering from sharp sample edges. Augmenting the TIE's modeling of coherent flow with a diffuse-flow channel leads to a Fokker-Planck extension to this equation. Two different augmentations are obtained, using several complementary derivations. The inverse problems of phase retrieval and diffusion-field retrieval are then considered, for defocus-based imaging and mask-based imaging. When symmetric overfocus and underfocus images are used for phase retrieval, the diffusive term drops out and our Fokker-Planck formalism implies that any ensuing TIE-based phase-retrieval method needs no modification in light of our formalism. However, the same focal-series dataset---typically an infocus image, a weakly overfocused image, and a weakly underfocused image---may also be employed to access the additional channel of information associated with the Fokker-Planck diffusion field. Our formalism is applicable to visible light, x-ray, electron, and neutron imaging.

physics.optics↗
arXiv2026

Robust multichannel bulk transport in a time-reversal-invariant insulator-free photonic waveguide array

Ultracompact cladding-free waveguide arrays with zero inter-channel spacing and negligible crosstalk open a new avenue for high-density integrated photonic circuits. However, existing cladding-free waveguide arrays typically rely on conventional trivial bulk modes, making them highly susceptible to scattering losses at sharp bends or in the presence of obstacles and defects. To overcome this limitation, we theoretically propose and experimentally demonstrate a robust, crosstalk-free, and cladding-free photonic waveguide array based on chiral anomaly bulk states (CABSs) in photonic crystals. By interfacing distinct Dirac photonic crystals that host Dirac cones at different high-symmetry points (Γ and K) in the Brillouin zone and carefully engineering the boundary conditions, the boundary-induced CABSs in adjacent channels become effectively decoupled due to a large momentum separation, thereby eliminating inter-channel crosstalk. More importantly, we experimentally demonstrate that these crosstalk-free CABSs are robust to perturbations, including metallic obstacles, air defects, and sharp bends. We further extend the CABS-based waveguide array to two dimensions and demonstrate a cladding-free triangular resonator and a crosstalk-free waveguide crossing, both of which are previously unattainable. Our work establishes a new design paradigm for cladding-free, crosstalk-free, and ultracompact topological photonic devices, paving the way for robust, highly integrated photonic circuits.

physics.optics↗
arXiv2026

A conformally-Euclidean Line Element for evaluating color differences

Starting from our previously proposed line element and considering more ``surface color'' datasets, we derive a simplified version which matches experimental datasets equally well and resulted into a conformally-Euclidean line element, which is conceptually much simpler than any existing color difference metrics. The color difference is written as an Euclidean difference multiplied with a simple factor which depends on the luminance only. In a subspace with constant luminance, as considered by MacAdam, this factor becomes constant and the subspace is flat. The same holds for sufficiently large luminances. Based on this LE we derive perceptual coordinates $\left(A,l_{c},s_{c}\right)$ very similar to the CIELab $\left(L^{*},a^{*},b^{*}\right)$.

physics.optics↗