IMAGE-FORMING BY MEANS OF AXICON

A theoretical analysis of the image-forming properties of the conical axicon in the scalar diffraction Kirchhoff-Fresnel approximation within the framework of the theory of linear systems revealed that the classical concept of the point spread function is not applicable to axicon images. In the near diffraction zone, a point light source is imaging by a conical axicon in the form of a segment along a straight line connecting the source and the center of the axicon. Moreover, different annular areas of the axicon form different sections on this segment. When used in tandem with a lens, the axicon can allow to increase the depth of focus. Preliminary experimental data have been obtained, which confirm the theoretical conclusions.

Quasi-Continuous Metasurface Beam Splitters Enabled by Vector Iterative Fourier Transform Algorithm

Quasi-continuous metasurfaces are widely used in various optical systems and their subwavelength structures invalidate traditional design methods based on scalar diffraction theory. Here, a novel vector iterative Fourier transform algorithm (IFTA) is proposed to realize the fast design of quasi-continuous metasurface beam splitters with subwavelength structures. Compared with traditional optimization algorithms that either require extensive numerical simulations or lack accuracy, this method has the advantages of accuracy and low computational cost. As proof-of-concept demonstrations, several beam splitters with custom-tailored diffraction patterns and a 7 × 7 beam splitter are numerically demonstrated, among which the maximal diffraction angle reaches 70° and the best uniformity error reaches 0.0195, showing good consistency with the target energy distribution and these results suggest that the proposed vector IFTA may find wide applications in three-dimensional imaging, lidar techniques, machine vision, and so forth.

Slit homogenizer introduced performance gain analysis based on Sentinel-5/UVNS spectrometer

The spectral accuracy of high resolution Earth observation spectrometer missions is affected by the impact of spatially heterogeneous Earth radiance scenes on the instrument spectral response function (ISRF). As the ISRF is the direct link between the forward radiative transfer model and the spectra measured by the instrument, distortions of the iSRF owing to radiometric inhomogeneity of the imaged Earth scene will degrade the precision of the Level-2 retrievals. Therefore, the spectral requirements of an instrument are often parametrized in the knowledge of the ISRF over non-uniform scenes in terms of shape, centroid position of the spectral channel and the Full Width at Half Maximum (FWHM). The Sentinel-5/UVNS instrument is the first push-broom spectrometer that makes use of a concept referred as slit homogenizer (SH) for the mitigation of spatially non-uniform scenes. This is done by employing a spectrometer slit formed by two parallel mirrors, scrambling the scene in along track direction (ALT) and hence averaging the scene contrast only in the spectral direction. The flat mirrors do not affect imaging in the across track direction (ACT) and thus preserve the spatial information in that direction. The multiple reflections inside the SH act as coherent virtual light sources and the resulting interference pattern at the SH exit plane can be described by simulations using scalar diffraction theory. By homogenizing the slit illumination, the SH moreover strongly modifies the spectrograph pupil as a function of the input scene. In this work we investigate the impact and strength of spectrograph pupil variations for different scene cases and quantify the impact on the ISRF stability for different type of aberrations present in the spectrograph optics.

“Perfect” Terahertz Vortex Beams Formed Using Diffractive Axicons and Prospects for Excitation of Vortex Surface Plasmon Polaritons

Transformation of a Bessel beam by a lens results in the formation of a “perfect” vortex beam (PVB) in the focal plane of the lens. The PVB has a single-ring cross-section and carries an orbital angular momentum (OAM) equal to the OAM of the “parent” beam. PVBs have numerous applications based on the assumption of their ideal ring-type structure. For instance, we proposed using terahertz PVBs to excite vortex surface plasmon polaritons propagating along cylindrical conductors and the creation of plasmon multiplex communication lines in the future (Comput. Opt. 2019, 43, 992). Recently, we demonstrated the formation of PVBs in the terahertz range using a Bessel beam produced using a spiral binary silicon axicon (Phys. Rev. A 2017, 96, 023846). It was shown that, in that case, the PVB was not annular, but was split into nested spiral segments, which was obviously a consequence of the method of Bessel beam generation. The search for methods of producing perfect beams with characteristics approaching theoretically possible ones is a topical task. Since for the terahertz range, there are no devices like spatial modulators of light in the visible range, the main method for controlling the mode composition of beams is the use of diffractive optical elements. In this work, we investigated the characteristics of perfect beams, the parent beams being quasi-Bessel beams created by three types of diffractive phase axicons made of high-resistivity silicon: binary, kinoform, and “holographic”. The amplitude-phase distributions of the field in real perfect beams were calculated numerically in the approximation of the scalar diffraction theory. An analytical expression was obtained for the case of the binary axicon. It was shown that a distribution closest to an ideal vortex was obtained using a holographic axicon. The resulting distributions were compared with experimental and theoretical distributions of the evanescent field of a plasmon near the gold–zinc sulfide–air surface at different thicknesses of the dielectric layer, and recommendations for experiments were given.

Spacetime Paths as a Whole

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman’s original derivation of the path integral formulation of non-relativistic quantum mechanics uses time-slicing to calculate amplitudes as sums over all possible paths through space, but along a definite curve through time. Here, a 3+1D spacetime wave distribution and its 4-momentum dual are formally developed which have no external time parameter and therefore cannot change or evolve in the usual sense. Time is thus seen “from the outside”. A given 3+1D momentum representation of a system encodes complete dynamical information, describing the system’s spacetime behavior as a whole. A comparison is made to the mathematics of holograms, and properties of motion for simple systems are derived.

The photonic nanojets formation by two-dimensional microprisms

Using the finite difference method implemented in the COMSOL Multiphysics software package, the focusing of laser radiation by dielectric prisms with a triangular profile was numerically investigated. It was shown that two-dimensional triangular prisms make it possible to focus light in free space into spots with dimensions smaller than the scalar diffraction limit. In particular, a silica glass prism with a base width of 60 μm and a height of 28.5 μm forms a photonic nanojet with a maximum intensity of 6 times the intensity of the incident radiation and a width of FWHM=0.38λ. A prism from barium titanate with a base width of 60 μm and a height of 20 μm allows to obtain a photonic nanojet with the same width (0.38λ) and a maximum intensity 5 times the intensity of the incident radiation. The size of the focal spot can be reduced further if the height of the prism is selected so that the maximum intensity is located inside the material of the prism. For example, a barium titanate prism with a height of 21 μm and a base width of 60 μm forms a focal spot with a width of FWHM=0.25λ.

Focusing of Light Pulses by Different Types of Wavy Parabolic Mirrors

The propagation of an ultra-short light pulse is studied in the framework of scalar diffraction theory. Light pulses are focused by different types of wavy parabolic surfaces. The temporal-spatial behavior of the two-dimensional wave field is computed in the vicinity of the focal plane. It is shown that the slightly perturbation from the perfect parabolic shape leads a space-time dispersion of the pulse in the neighborhood of the focus.