We consider the design of cascaded phase diffractive optical elements (DOEs) operating at several different wavelengths. The problem of DOE design is formulated as the problem of minimizing a certain error functional that depends on the functions of diffractive microrelief height of the cascaded DOE and evaluates its performance at different design wavelengths. Explicit expressions are obtained for the Fréchet derivatives of the error functional. The presented expressions for the derivatives of the error functional constitute the basis for gradient design of cascaded multiwavelength DOEs in various problems including the beam shaping and optical classification problems. As particular example, we consider the calculation of cascaded DOEs focusing radiation of three different wavelengths into different letter-shaped areas.
We propose a spatiotemporal optical differentiator of the first order based on a three-layer metal-dielectric-metal (MDM) structure operating in reflection. For describing the transformation of the incident spatiotemporal optical signal, we apply the transfer function formalism of the theory of linear systems. We demonstrate that the differentiator based on the proposed MDM structure enables generating a reflected optical pulse possessing an optical vortex in the spatiotemporal domain (referred to as the spatiotemporal optical vortex, STOV). The MDM differentiator can also be used for high-quality edge detection of the incident spatiotemporal optical signal. Moreover, we investigate a “double” MDM structure consisting of two single (three-layer) MDM structures separated by a dielectric layer, which implements the operation of spatiotemporal differentiation of the second order. By considering the generation of a reflected optical pulse with several phase singularities and studying the edgedetection operation, we show that the operation of second-order spatiotemporal differentiation is implemented with high accuracy. We also investigate the possibility of obtaining an STOV in asymmetric and symmetric dielectric slab waveguides and demonstrate that an STOV can be generated upon reflection of a spatiotemporal optical pulse propagating in the waveguide from an integrated metal-dielectric structure consisting of a few metal strips “buried” in the waveguide core layer. The obtained theoretical results are in good agreement with the results of rigorous numerical simulations of the spatiotemporal differentiation and STOV generation using metal-dielectric structures in both free-space and integrated geometries. We believe that the obtained results may find application in the creation of analog optical computing and optical information processing systems.
Photonic devices performing required temporal and spatial transformations of optical signals are of great interest for a wide range of applications including all-optical information processing and analog optical computing. Among the most important operations of analog optical processing are the operations of temporal and spatial differentiation. Various types of resonant photonic structures performing these operations were previously proposed, such as phase-shifted Bragg gratings and other multilayer structures, resonant diffraction gratings, and nanoresonators.
In the current work, we present an overview of our recent results dedicated to the design of resonant nanophotonic structures for optical implementation of various differential operators including integrated structures for Bloch surface waves and guided modes. A special attention is paid to a simple planar (integrated) optical differentiator consisting of two identical grooves on the surface of a dielectric slab waveguide (the details are presented in our recently published work [L. L. Doskolovich, E. A. Bezus, N. V. Golovastikov, D. A. Bykov, and Victor A. Soifer, “Planar two-groove optical differentiator in a slab waveguide,” Opt. Express 25(19), 22328–22340 (2017)]). The studied planar differentiator operates in reflection and enables temporal and spatial differentiation of optical pulses and beams propagating in the waveguide. The differentiation is associated with the excitation of an eigenmode localized at the ridge cavity located between the grooves. We show that by changing the groove length one can choose the required quality factor of the resonance (and, consequently, the linearity interval of the transfer function of the differentiator) in accordance with the width of the frequency or spatial (angular) spectrum of the incident pulse or beam. The presented numerical simulation results demonstrate high-quality spatial, temporal and the so-called spatiotemporal differentiation. The proposed differentiator may find application in the design of on-chip all-optical analog computing and signal processing systems.
We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index central (core) layer surrounded by two identical low-index cladding layers, which acts as an optical differentiator in reflection. If the refractive index of the surrounding medium is greater that the refractive index of the cladding layers, the spectra of the considered structure may exhibit resonant features associated with the excitation of a leaky mode localized at the central layer. At resonant conditions, the reflection coefficient will vanish at certain values of frequency and angle of incidence, which enables the differentiation of the incident optical pulse. We theoretically justify that this three-layer structure can perform temporal differentiation (differentiation of an incident optical pulse envelope), spatial differentiation (differentiation of an optical beam profile) and the so-called “spatiotemporal differentiation” (differentiation of an optical signal envelope along a certain direction in the (x,t)-plane). Rigorous numerical simulation results demonstrate high quality of differentiation. It is shown that the resonance quality factor increases with the increase in the thickness of the cladding layers, which makes it possible to achieve a required linearity interval of the differentiating filter. The proposed differentiator is more compact than Fourier correlators containing graded-index lenses and substantially easier to fabricate than metasurface-based devices incorporating periodically arranged nanoresonators and may find application in ultrafast analogue computing and signal processing systems.
In this work, we study numerically and theoretically phase-shifted Bragg gratings (PSBG) for Bloch surface waves (BSW) propagating along the interfaces between a 1D photonic crystal and a homogeneous medium. The studied on-chip structure consists of a set of dielectric ridges located on the photonic crystal surface constituting two symmetrical onchip Bragg gratings separated by a defect layer. Rigorous simulation results demonstrate that the surface wave diffraction on the proposed on-chip PSBG is close to the diffraction of plane electromagnetic waves on conventional PSBG. For the considered examples, the correlation coefficient between the spectra of conventional PSBG and on-chip PSBG exceeds 0.99 near the resonance corresponding to the excitation of the eigenmodes localized in the defect layer. Conventional PSBG are widely used for spectral filtering as well as for temporal and spatial transformations of optical pulses and beams including differentiation and integration of pulse envelope or beam profile. In the present work, we discuss the capability of on-chip PSBG to implement the operations of temporal and spatial differentiation of BSW pulses and beams. The presented examples demonstrate the possibility of using the proposed structure for high-quality differentiation. The obtained results can be applied for the design of the prospective integrated systems for on-chip alloptical analog computing.
In the present work, on-chip dielectric diffraction gratings for steering the propagation of surface plasmon polaritons (SPP) are theoretically, numerically and experimentally studied. The investigated plasmonic gratings consist of dielectric ridges located on the SPP propagation surface (on the metal surface). In contrast to Bragg gratings, at normal incidence the periodicity direction of the grating is perpendicular to the SPP propagation direction. The studied gratings are designed using a simple plane-wave grating model and rigorously simulated using the aperiodic Fourier modal method for numerical solution of Maxwell’s equations. In particular, plasmonic grating-based beam splitter with subwavelength footprint in the propagation direction is presented. Along with the theoretical and numerical results, proof-of-concept experimental results are presented. The investigated grating-based plasmonic gratings were fabricated from resist on a silver film using electron beam lithography and characterized using the leakage radiation microscopy technique. The obtained experimental results are in good agreement with the performed numerical simulations. The proposed on-chip gratings may find application in the design of systems for optical information transmission and processing at the nanoscale.
The fabrication of submicron-height sine-like relief of a trifocal diffractive zone plate using a nanoimprinting technique is studied. The zone plate is intended for use in combined trifocal diffractive–refractive lenses and provides the possibility to form trifocal intraocular lenses with predetermined light intensity distribution between foci. The optical properties of the designed zone plate having the optical powers 3 D, 0, −3 D in the three main diffraction orders are theoretically and experimentally investigated. The results of the theoretical investigations are in good agreement with experimental measurements. The effects of the pupil size (lens diameter) as well as the wavelength-dependent behavior of the zone plate are also discussed.
Magnetooptical effects in the metal/dielectric heterostructure, consisting of a thin metallic layer with the array of
parallel subwavelength slits and a uniform dielectric layer magnetized perpendicular to its plane, are investigated.
Calculations, based on the rigorous coupled-wave analysis of Maxwell's equations, demonstrate that in such structures
the Faraday and Kerr rotation can be significantly enhanced in the near infrared optical range. It is possible by varying
thickness of the magnetic film to make Faraday rotation and transmittance peaks coincident and achieve the increase in
the Faraday effect by more than an order of magnitude at the transmittance of 40-45%. It is shown that the excitation of
the surface plasmon polaritons and quasi-guided TM- and TE- modes in the dielectric layer mostly governs the
enhancement of the Faraday rotation.
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