The diffraction problem of a plane wave impinging on a grating formed by nested cavities is solved by means of the modal method, for $s$ and $p$ polarization modes. The cavities are formed by perfectly conducting sheets that describe rectangular profiles. The electromagnetic response of the grating is analyzed, paying particular attention to the generation of resonances within the structure. The dependence of the resonances on the geometrical parameters of the grating is studied, and results of far and near field are shown. The results are checked and compared with those available in the literature for certain limit cases.
We discuss the applicability of holographically recorded gratings in photopolymers and holographic polymer-dispersed liquid crystals as neutron optical elements. An experimental investigation of their properties for light and neutrons with different grating spacings and grating thicknesses is performed. The angular dependencies of the diffraction efficiencies for those gratings are interpreted in terms of a rigourous coupled wave analysis. Starting from the obtained results we work out the lines for the production of an optimised neutron optical diffraction grating, i.e., high diffraction effi…
We derive from first principles the expression for the angular/wavelength distribution of the intensity diffracted by a blazed reflective grating, according to a scalar theory of diffraction. We considered the most common case of a groove profile with rectangular apex. Our derivation correctly identifies the geometric parameters of a blazed reflective grating that determine its diffraction efficiency, and fixes an incorrect but commonly adopted expression in the literature. We compare the predictions of this scalar theory with those resulting from a rigorous vector treatment of diffraction fro…
The optical characterization of dielectric periodic line-gratings for which the period of the grating is significantly larger than the probing wavelength is investigated experimentally, numerically, and analytically. The experimental diffraction efficiencies are analyzed in transmission with the help of a closed-form approximate solution within a single scattering picture. In particular, the angular width of significant scattering and the haze are analyzed for samples of increasing grating profile amplitude.
A diffractive arrangement that allows imaging of an object without any intermediate or complementary element is presented. This optical system with only two diffraction gratings forms color images with white light.
Measurement and analysis of diffraction parameters of thick transmission holographic phase gratings recorded on PHC-488 photopolymer are presented. Precision determination of the spatial grating period is executed by Bragg angle measurement for two precisely known wavelengths in the first diffraction order and also by Bragg angle measurement on one wavelength in the first and second diffraction orders. Determination of actual grating thickness and depths of spatial modulation of a holographic recording, which are responsible for their main optical characteristics, is carried out with the appli…
The increase of cell efficiency resulting from using a diffraction grating as a back reflector is investigated. An enhancement coefficient is introduced as a figure of merit that accounts for the ability of the rear grating to increase the generation of electric carriers. According to results in this paper, a diffraction-grating-like relief on the rear face of the photovoltaic cell may reduce the intensity of the specular reflection while favouring the intensity of high-angle rays. In this way, the path-length of reflected rays increases, and so does the efficiency of the cell.
Periodically patterned columnar thin films (PP-CTFs) were made by evaporating CaF2 and directing the vapor flux obliquely towards lithographically fabricated micrometer/sub-micrometer gratings. The growth of the PP-CTFs was controlled by the deposition rate to form prismatic air cavities within them and they function like blazed diffraction gratings with asymmetric diffraction patterns and diffraction efficiencies upto 52% in transmission at visible wavelengths. Scalar diffraction theory qualitatively explained the measured diffraction efficiencies.
We experimentally characterize the positions of the diffraction maxima of a phase grating on a screen, for laser light at oblique incidence (so-called off-plane diffraction or conical diffraction). We discuss the general case of off-plane diffraction geometries and derive basic equations for the positions of the diffraction maxima, in particular for their angular dependence. In contrast to previously reported work [Jetty et al., Am. J. Phys. 80, 972 (2012)], our reasoning is solely based on energy- and momentum conservation. We find good agreement of our theoretical prediction with the experim…
Resonance diffraction of THz HCN laser radiation on a semiconductor (InSb) grating is studied both experimentally and theoretically. The specular reflectivity suppression due to the resonance excitation of the THz surface plasmon-polariton is observed on a pure semiconductor grating and on semiconductor gratings covered with a thin striped layer of the residual photoresist. Presence of a thin dielectric layer on the grating surface leads to the shift and widening of the plasmon-polariton resonance. A simple analytical theory of the resonance diffraction on a shallow grating covered with a diel…
We propose an Adaptive Perfectly Matched Layer (APML) to be used in diffraction grating modeling. With a properly tailored co-ordinate stretching depending both on the incident field and on grating parameters, the APML may efficiently absorb diffracted orders near grazing angles (the so-called Wood's anomalies). The new design is implemented in a finite element method (FEM) scheme and applied on a numerical example of a dielectric slit grating. Its performances are compared with classical PML with constant stretching coefficient.
A multi-reflection model of grating diffraction based on the simplified modal method is proposed. Simulation results for a guided mode resonance Brewster grating using our method and rigorous coupled wave analysis are presented to verify our model. The solution of our method is in good agreement with that of rigorous coupled wave analysis. Benefiting from its clear physical view, this model helps us to better understand the diffraction process inside subwavelength gratings. On the basis of the multi-reflection model, we developed a matrix Fabry-Perot (FP) resonance condition and a single-mode …
We report on the optical characterization of an ultra-high diffraction efficiency grating in 1st order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high reflection mirror. Measurement of the cavity finesse provided precise information about the grating's diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635$\pm$0.016)% and an overall optical loss due to scattering and absorption of just 0.185 %. Such high quality gratings, including the …
This document aims at presenting both theoretical and practical aspects of the grating2D.pro and grating3D.pro [1] ONELAB [2] models. The 2D model grating2D.pro applies to so-called mono-dimensional gratings, i.e. structures having one direction of invariance. Various geometries and materials can be handled or easily added. The two classical scalar polarization cases, denoted here E// and H//, are addressed as well as the conical vector case. The output consists in a full energy balance of the problem computed from the field maps. The 3D vector model grating3D.pro applies to crossed-gratings. …
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions.
Diffraction gratings with large angular dispersion rates are central to obtaining high spectral resolution in grating spectrometers operating over a broad spectral range from infrared to soft-x-ray domains. The greatest challenge is of course to achieve large dispersion rates in the short-wavelength x-ray domain. Here we show that crystals in non-coplanar asymmetric x-ray Bragg diffraction can function as high-reflectance soft-x-ray diffraction gratings with dispersion rates that are at least two orders of magnitude larger than those that are possible with state-of-the-art man-made gratings. T…
Optical gratings are a key component in many spectroscopy, communications, and imaging systems. While initially static elements, advances in optical materials have enabled dynamically tunable gratings to be designed. One common tuning strategy is relying on mechanical deformation of the grating pitch to modify the diffraction pattern. To date, most mechanically adaptive optical gratings consist of a hybrid system where rigid moieties are patterned on an elastomeric substrate. In the present work, we demonstrate an all-polymer tunable grating that is fabricated using replica molding from the po…
The general features of the light scattering resulting in the so-called resonant Wood's anomalies in the reflection and transmission spectra are described using the effective parameters of a quasi-guided mode. The expression determining the spectral angular dependence of Wood's anomaly in the case of plasmonic grating structures is given and compared to the analogous expression for dielectric grating structures. Comparison of the resonant Wood's anomalies (RWA) with the surface plasmon-polariton resonances (SPPRs) is discussed as well.
A single-order transmission diffraction grating based on dispersion engineered all-dielectric metasurfaces is proposed and its wavelength discriminating properties have been theoretically described and confirmed using numerical simulations. The metasurface is designed using a 2D array of all-dielectric resonators, which emulates a Huygens source configuration to achieve a perfect match to free-space in broad bandwidth. Using a holey dielectric nanodisk structure as the unit cell, the resonant wavelength is tapered across the metasurface to engineer the wavelength dependent spatial phase gradie…
Symmetry and reciprocity constraints on polarization state of the field diffracted by gratings of quasi-planar particles are considered. It is shown that the optical activity effects observed recently in arrays of quasi-planar plasmonic particles on a dielectric substrate are due to the reflection of the field at the air-dielectric slab interface and are proportional to this reflection coefficient.
Analytical analysis of the decrease in the focal intensity of a femtosecond laser pulse caused by an imperfect surface of compressor diffraction gratings
Under white light illumination, gratings produce an angular distribution of wavelengths dependent on the diffraction order and geometric parameters. However, previous studies of gratings are limited to at least one geometric parameter (height, periodicity, orientation, angle of incidence) kept constant. Here, we vary all geometric parameters in the gratings using a versatile nanofabrication technique, two-photon polymerization lithography, to encode hidden color information through 2 design approaches. The first approach hides color information by decoupling the effects of grating height and p…
In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order $J_l(κr)$ on a 2D amplitude grating is presented. The diffraction pattern in the main and fractional Talbot planes under certain conditions is a lattice of annular microbeams, the diameters of which depend on the grating period, the illuminating beam diameter, the number of the Talbot plane, and the topological charge $l$. For the rings near the optical axis, the latter reproduces $l$ of the illuminating beam. Experiments carried out on the Novosibirsk free electron laser at a wavelength $λ= 141$$μ$m us…
We consider the spectral response of moving diffraction gratings, in which the incident light extends over a broad angular range and where the diffracted light is observed from a specific angle. We show that the dispersion relation between the frequency perceived by an observer who is looking at a moving grating and the incident frequency can exhibit some unique features, such as a flat band (i.e., a local minimum). An observer can see the light diffracted into a non-specular diffraction order from a multitude of incident light rays and the angle of incidence of each ray is frequency-dependent…
Diffraction gratings are famous for their ability to exhibit, near a Wood anomaly, an arbitrarily large angular dispersion, e.g., with respect to the incidence angle or wavelength. For a diffraction grating under incidence by a plane wave at a fixed frequency, by rotating the incidence angle at a given angular velocity, the field propagated by a nonzero diffraction order will rotate at increasingly fast angular velocity as the incidence angle approaches the angle where Wood anomaly occurs. Such a fast rotating diffracted field has the potential to generate a substantial Doppler shift. Indeed, …
We analyze the diffraction characteristics of dielectric gratings that feature a high index grating layer, and devise, through rigorous numerical calculations, large bandwidth, highly efficient, high dispersion dielectric gratings in reflection, transmission, and immersed transmission geometry. A dielectric TIR grating is suggested, whose -1dB spectral bandwidth is doubled as compared to its all-glass equivalent. The short wavelength diffraction efficiency is additionally improved by allowing for slanted lamella. The grating surpasses a blazed gold grating over the full octave. An immersed tra…
A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. Discrete sampling and bisection algorithm are applied for finding numerical solution of the diffraction pattern of QD grating. This 2D mathematical model allows the precise design of QD grating and improves the optical performance of simultaneous multiplane imaging system.
Successful phase-matching methods for Third Harmonics Generation (THG) include phase-matching in birefringent crystal and quasi-phase-matching (QPM) in crystal with periodically poled domains. However, these methods are not feasible in some isotropic materials (e.g. fused silica and photosensitive silicate glass). It was known that volume-grating in isotropic materials can independently generate frequency-converted waves. One of disadvantages of single-layer volume-grating is that the brightness of harmonic emission can not be enhanced by increasing the grating thickness. In this paper, a THG …
In the framework of the approximation of slowly varying amplitudes a multiwave dynamical theory of neutron diffraction on a moving phase grating was developed. The influence of the velocity of the grating, its period and height of the slits on the discrete energy spectrum and intensity of various diffraction orders was analyzed.
We theoretically investigate the second harmonic generation and photon drag effect induced by an incident plane wave to a doped graphene placed on a two-dimensional diffraction grating. The relevant nonlinear conductivity of the graphene is obtained by a semi-classical treatment with a phenomenological relaxation. The grating acts not only as a plasmon coupler but also as a dispersion modulator of the graphene plasmon. As a result, the second harmonic generation is strongly enhanced by exciting the graphene plasmon polariton of the first- and/or second-harmonic frequencies. The photon drag eff…
The recent development of phase-grating moiré neutron interferometry promises a wide range of impactful experiments from dark-field imaging of material microstructure to precise measurements of fundamental constants. However, the contrast of 3 % obtained using this moiré interferometer was well below the theoretical prediction of 30 % using ideal gratings. It is suspected that non-ideal aspects of the phase-gratings was a leading contributor to this deficiency and that phase-gratings needed to be quantitatively assessed and optimized. Here we characterize neutron diffraction from phase-grating…
We experimentally demonstrate the phase relations of 3-port gratings by investigating 3-port coupled Fabry-Perot cavities. Two different gratings which have the same 1st order diffraction efficiency but differ substantially in their 2nd order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities we could validate the results of an earlier theoretical description of the phases at a three port grating.
The shot-noise limited sensitivity of Michelson-type laser interferometers with Fabry-Perot arm cavities can be increased by the so-called power-recycling technique. In such a scheme the power-recycling cavity is optically coupled with the interferometer's arm cavities. A problem arises because the central coupling mirror transmits a rather high laser power and may show thermal lensing, thermo-refractive noise and photo-thermo-refractive noise. Cryogenic cooling of this mirror is also challenging, and thus thermal noise becomes a general problem. Here, we theoretically investigate an all-refle…
A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines, and arbitrary complex structure. Conical angles and good conductors are supported.
Color encoding of depth is shown to occur naturally in images of objects observed through diffraction gratings under common white light illumination. A synthetic image is then obtained from a single point of view, a phenomenon that can be applied to stereophotography. The image can be recorded in a common color photograph, providing a simple method of visual decoding by means of ordinary colored 3D spectacles. The fundamental equation and the photographic procedure for maximum fidelity in three-dimensional reproduction are described. The result is a photograph that has the capability of regist…
We theoretically and numerically investigate resonant optical properties of composite structures consisting of several subwavelength resonant diffraction gratings separated by homogeneous layers. Using the scattering matrix formalism, we demonstrate that the composite structure comprising N gratings has a multiple transmittance zero of the order N. We show that at the distance between the gratings satisfying the Fabry-Pérot resonance condition, an (N-1)-degenerate bound state in the continuum (BIC) is formed. The results of rigorous numerical simulations fully confirm the theoretically predict…
We present the design and characterization of waveguide grating devices that couple visible-wavelength light at $λ=674$ nm from single-mode, high index-contrast dielectric waveguides to free-space beams forming micron-scale diffraction-limited spots a designed distance and angle from the grating. With a view to application in spatially-selective optical addressing, and in contrast to previous work on similar devices, deviations from the main Gaussian lobe up to $25$ microns from the focus and down to the $5\times10^{-6}$ level in relative intensity are characterized as well; we show that along…
The generation of induced radiation in volume resonator formed by metal threads is considered. It is shown that using of such volume diffraction grating allows increasing of lasing efficiency in terahertz range. The requirements on beam and grating parameters are obtained.
The equations providing to describe generation process in FEL with varied parameters of diffraction grating (photonic crystal) are obtained. It is shown that applying diffraction gratings (photonic crystal) with the variable period one can significantly increase radiation output. It is mentioned that diffraction gratings (photonic crystal) can be used for creation of the dynamical wiggler with variable period in the system. This makes possible to develop double-cascaded FEL with variable parameters changing, which efficiency can be significantly higher that of conventional system.
High absorption in a wide frequency band has attracted considerable interest since their potential applications in frequency spectrum imaging systems and anti-radar cloaking. In this paper, a polarization-independent, ultra-broadband and omnidirectional terahertz absorber is proposed, fabricated and evaluated. It is experimentally demonstrated that an over 95% absorption can be obtained in the frequency range of 0.75~2.41 THz. Attributing to the multi-frequency destructive interference between the layers and the impedance-matching condition of the grating, five successive absorption peaks at 0…
Synthetic-Aperture Super-Resolution Imaging via Spatial-Frequency Shift in Near-Field Diffraction
School of Electronic Science and Engineering, Southeast University（东南大学电子科学与工程学院）；School of Optoelectronic Engineering, Henan Normal University（河南师范大学光电工程学院）；School of Computer and Electronic Information, Nanjing Normal University（南京师范大学计算机与电子信息学院）；Yangzhou Jinghong Laser Technology Co., Ltd.（扬州景弘激光技术有限公司）
Diffraction gratings with high upward diffraction efficiency and large effective length are required for chip-scale light detection and ranging. In this paper, we propose a diffraction grating based on a multilayer silicon nitride waveguide, which theoretically achieves an upward diffraction efficiency of 92$\%$, a near-field effective length of 376 $μm$ and a far-field divergence angle of 0.105$^{\circ}$ at a wavelength of 850 nm. The diffraction grating has a high tolerance to process variations based on Monte Carlo Analysis. When the conditions are $\pm$5$\%$ layer thickness variation, $\pm…
Spectra of ultracold neutrons that appeared in experiments on neutron diffraction by a moving grating were measured using the time-of-flight Fourier spectrometer. Diffraction lines of five orders were observed simultaneously. The obtained data are in good agreement with the theoretical predictions based on the multiwave dynamical theory of neutron diffraction by a moving grating.
Spatial characteristics of the optical-vortex (OV) beams created during the Gaussian beam diffraction by a grating with groove bifurcation are analyzed theoretically and numerically. In contrast to previous works, condition of small-angle diffraction is no longer required and the diffracted beam can be strongly deformed. This causes the intensity profile rotation and the high-order OV decomposition into a set of secondary single-charged OVs. These effects are studied quantitatively and confronted with similar properties of a Laguerre-Gaussian beam that undergoes astigmatic telescopic transform…
We have studied the optical properties of gratings micro-fabricated into semiconductor wafers, which can be used for simplifying cold-atom experiments. The study entailed characterisation of diffraction efficiency as a function of coating, periodicity, duty cycle and geometry using over 100 distinct gratings. The critical parameters of experimental use, such as diffraction angle and wavelength are also discussed, with an outlook to achieving optimal ultracold experimental conditions.
We report on the observation of emerging beam resonances, well known as Rayleigh-Wood anomalies and threshold resonances in photon and electron diffraction, respectively, in an atom-optical diffraction experiment. Diffraction of He atom beams reflected from a blazed ruled grating at grazing incidence has been investigated. The total reflectivity of the grating as well as the intensities of the diffracted beams reveal anomalies at the Rayleigh angles of incidence, i.e., when another diffracted beam merges parallel to the grating surface. The observed anomalies are discussed in terms of the clas…
An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which also go under other names such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identifi…
We consider Wood anomalies in diffraction spectrum from two-dimensional dielectric periodic grid embedded in a surrounding media. The grid is of subwavelength thickness, and diffraction of wave having S-polarization is investigated in the vicinity of the emergence of first diffraction maximum. We reduce Maxwell equations to coupled-mode theory with three parameters, which are integral characteristics of material arrangement in the grid. In particular, we show that such grids are capable to have full reflectance in parametrically narrow frequency bandwidth. The effect is accompanied by a parame…
We performed light optical diffraction experiments on a nanoparticle-polymer volume holographic grating in an angular range including also far off-Bragg replay. A comparison of three diffraction theories - on the same level of complexity - with our experimental results shows that the dynamical theory of diffraction and the first-order two-wave coupling theory using the beta-value method fit the data very well. In contrast, the prevalent two-wave coupling theory using the K-vector closure method yields a poor fit with an order of magnitude worse mean squared error. These findings must be consid…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and its generalized version. The resulting interference patterns exhibit characteristics of the original fractals and their scaling properties.
We introduce a method for using Fizeau interferometry to measure the intrinsic resolving power of a diffraction grating. This method is more accurate than traditional techniques based on a long-trace profiler (LTP), since it is sensitive to long-distance phase errors not revealed by a d-spacing map. We demonstrate 50,400 resolving power for a mechanically ruled XUV grating from Inprentus, Inc.
This work theoretically investigates wide-spectrum and high-resolution diffraction optical elements (DOE) that are made of stacks of low-resolution binary phase gratings, whereby the two-dimensional grids in different grating layers are arranged with specified displacements. We remodel the common Kinoform algorithm for this multi-scale architecture. Numerical computations show that, by increasing the number of stacking layers, the resolution of diffraction fields can be improved and that the stability of optical elements within broad spectrums is significantly enhanced. Practical concern on la…
