Grating Profiles Research Articles

Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings

Abstract We consider the inverse elastic scattering problem of determining a three-dimensional diffraction grating profile from scattered waves measured above the structure. In general, a grating profile cannot be uniquely determined by a single incoming plane wave. We completely characterize and classify the bi-periodic polyhedral structures under the boundary conditions of the third and fourth kinds that cannot be uniquely recovered by only one incident plane wave. Thus we have global uniqueness for a polyhedral grating profile by one incident elastic plane wave if and only if the profile belongs to neither of the unidentifiable classes, which can be explicitly described depending on the incident field and the type of boundary conditions. Our approach is based on the reflection principle for the Navier equation and the reflectional and rotational invariance of the total field.

Mueller polarimetry as a tool for detecting asymmetry in diffraction grating profiles

Reflected Mueller matrix spectra were measured and simulated for asymmetrical photoresist master diffraction gratings in conical mounting (i.e., the direction of grating grooves was not perpendicular to the plane of light incidence). From the electromagnetic reciprocity theorem, Mueller matrix of symmetric grating (composed of only reciprocal materials, and operating in zeroth-order diffraction) is invariant under transposition (M=Mt). For zeroth-order diffraction of asymmetric gratings, the lack of profile rotational symmetry violates this reciprocity and, consequently, breaks the symmetry of the above-mentioned matrix. This property of the Mueller matrix of asymmetric gratings was experimentally observed and numerically modeled at all experimental illumination conditions with the exception of planar mounting (the direction of grating grooves was perpendicular to the plane of light incidence), where there is no cross-polarization effect for the gratings composed of isotropic materials. It was demonstrated that optical nonreciprocity of diffraction gratings can be used for unambiguous detection of grating profile asymmetry. In addition, choosing optimal measurement configuration (i.e., azimuthal angles) considerably increases the sensitivity of the detection technique.

Design and fabrication of a microspectrometer based on silicon concave micrograting

The conventional planar grating (CPG) system has a complicated optical structure, which causes complexities in various aspects, e.g., a variety of processes such as fabrication, assembly, and alignment. The size of the CPG cannot be further reduced due to the minimum optical path length requirement imposed by the spectral resolution. This paper proposes an ultracompact grating system that is turned into a reality by a shorter optical path length through a specified grating profile. Our proposed microphotolithographic inductive coupled plasma - reactive ion etching process demonstrates that an arbitrary grating profile with high aspect ratio and small surface roughness can be achieved. The aberrations of different wavelengths are greatly reduced or eliminated. An etching depth of 30 to 60 μm is achieved. The surface roughness meets the requirement of λ/10 (50 nm). The size of the grating system is 30 × 30 × 2 mm. The resolving power R reaches 600 to 700 in the visible region.

Short period resonant dual-grating structures for applications to anisotropic color change securities

A subwavelength grating with resonant behaviors can be used to exploit security productions with characteristics of anisotropic color variation, i.e., its color has been changed when the grating is rotated on its own plane. In this paper, a novel grating structure with potentials of broadening its spectral bandwidths and improving its color aspects is proposed and its design principles and fabrication methods are also provided. The design of it is completely based on rectangular gratings with a filling factor of 0.5, but the grating regions of fabricated structures have profiles of sinusoidal gratings. Reflection spectra of such two structures are simulated and compared using vector diffraction methods and compared. Moreover, a security grating with unique characteristics of color change has been successfully designed and fabricated, and the changes of color aspects of it have also been verified from both theory and experiment. The proposed structure and its related fabrication methods are feasible in practical application of security and have better values and potentials for mass productions through holographic embossing equipments.

Mixed metal dielectric gratings for pulse compression.

We report on manufacturing and testing results of high efficiency mixed metal dielectric gratings (MMLD) for high power pulse compression applications. The gratings with 1780 l/mm are etched in the top low index layer of a Au-(SiO2/HfO2)4-SiO2 mirror stack. Various grating profiles manufactured in order to modify the near electric field distribution are damage tested on a facility operating at 1.053 µm, 500 fs pulse duration. We evidence that damage threshold is governed by the value of the maximum electric field intensity inside the grating pillar. Moreover thresholds close to 3 J/cm2 beam normal are obtained with this new MMLD grating being thus an interesting alternative to gold and pure dielectric gratings for pulse compression applications.

Diffraction Efficiencies by Electromagnetic Wave Scattering from Holographic Fourier Gratings

This article describes a new closed form of the matrix elements in scattering from holographic Fourier gratings by using the T-matrix method. This formulation is useful because the T-matrix element is presented in the analytical form of the Bessel function series. The energy convergence does supply a numerical consistency check at less than 1% in percentage power error. Numerical examples are illustrated for diffraction efficiencies with various incident angles and profiles for holographic Fourier gratings. If the profile of a grating is chosen appropriately, the diffraction efficiency can be more than 80% at TE- and TM-polarization.

Illumination artifacts in hyper-NA vector imaging

Off-axis polarized monopole illumination is applied to a hyper-numerical-aperture (NA) (NA>1) microscopic system. Illumination artifacts due to vector effects are observed, which are asymmetric and depend on illumination conditions. A model based on rigorous coupled wave theory is used to simulate image profiles for dielectric, semiconductor, and metal gratings with different monopole locations and polarization states. A solid immersion lens microscope is used to image different types of samples including MoSi photomask, patterned silicon wafer, and chrome photomask. The experimental images are in good agreement with simulation results.

Fast numerical method for modelling one-dimensional diffraction gratings

Based on the generalised source method, a new method for calculating the light diffraction on one-dimensional dielectric diffraction gratings with an arbitrary profile is proposed. The method is an alternative to the widely used Fourier modal method because it possesses the same possibilities in defining different grating profiles; however, it has a significant advantage in calculating complex-shaped gratings because it requires many fewer mathematical operations. The applicability of the method is shown by comparing the calculation results by this method with the results obtained by the conventional methods of light diffraction calculation on the gratings.

Design and fabrication of a polarization-independent wideband transmission fused-silica grating

A fused-silica polarization-independent wideband transmission grating used in the -1st order (Littrow mounting) for chirped-pulse-amplification, high-power lasers is designed and manufactured. An approximate grating profile can be obtained by using the simplified modal method with consideration for the corresponding accumulated phase difference of two excited propagating grating modes. An exact grating profile is optimized by using the rigorous coupled-wave analysis. With the optimized profile parameters, the gratings can theoretically exhibit diffraction efficiencies of greater than 97% at a wavelength of 800 nm for both of TE- and TM-polarized waves. Diffraction efficiencies of greater than 92% can be obtained in a 100 nm bandwidth (from 750 to 850 nm) for both TE- and TM-polarized waves. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results agree well with the theoretical values.

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500–1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.

Long-wave infrared surface plasmon grating coupler

We present a simplified analytic formula that may be used to design gratings intended to couple long-wave infrared radiation to surface plasmons. It is based on the theory of Hessel and Oliner (1965). The recipe is semiempirical, in that it requires knowledge of a surface-impedance modulation amplitude, which is found here as a function of the grating groove depth and the wavelength for silver lamellar gratings at CO(2) laser wavelengths. The optimum groove depth for photon-to-surface-plasmon energy conversion was found by experiment and calculation to be approximately 10%-15% of the wavelength. This value is about twice what has been reported previously in the visible spectral range for sinusoidal grating profiles.

Effect of fabrication errors on the diffraction pattern produced by sawtooth gratings

In this work we investigate, analytically and numerically, the effect on the diffracted field produced by typical fabrication errors in sawtooth gratings. The analysis is carried out for the near and far field, showing the effects on the intensity and on the diffraction orders efficiency. When the grating profile is not perfect but presents a curved profile or overdevelopment error, some different diffraction orders appear, changing the intensity and the efficiency of each order. In addition, when roughness is present, a decreasing of efficiency is produced, but without generating different diffraction orders than the first one. We show the analytical dependence of these modifications in terms of the profile of the grating, corroborating the results with numerical methods.

Numerical investigation of the impact of reflectors on spectral performance of Raman fibre laser

Using a cavity mode model we study numerically the impact of bandwidth and spectral response profile of fibre Bragg gratings on four-wave-mixing-induced spectral broadening of radiation generated in 6 km and 22 km SMF-based Raman fibre lasers.

槽型衍射光栅结构参数优化设计研究

槽型衍射光栅结构参数优化设计研究

Analysis of the focal pattern distortion of a cylindrical concave micro-grating in a slab waveguide and the mechanism of spatial resolution recovery

With modern lithographic technology, a compact spectrometer is designed to include a blazed micro-grating with cylindrical concave grating profile. In order to restrict the sagittal beam divergence and to reduce the size of the spectrometer, the micro-grating is embedded inside a pair of planar mirrors used as a slab waveguide. In the simulations for the effect of the waveguide, we discover that the focal pattern distortion introduced by the waveguide causes a blunted and side-tailed peak in the spectrum. The distortion can be managed by allowing some gap between the edge of the waveguide and the image sensor. Such a configuration has greatly improved the resolving power of the micro-grating in this compact system.

Asymmetrisation of the profile of a thin dynamic holographic grating in a TV-locked optical feedback loop

A system for recording a dynamic holographic grating in an optically addressed liquid-crystal spatial light modulator is studied. The system provides the asymmetrisation of the grating profile by using a TV-locked optical feedback loop (nonlinear or adaptive interferometer).

Design and fabrication of a polarization-independent two-port beam splitter

We design and manufacture a fused-silica polarization-independent two-port beam splitter grating. The physical mechanism of this deeply etched grating can be shown clearly by using the simplified modal method with consideration of corresponding accumulated phase difference of two excited propagating grating modes, which illustrates that the binary-phase fused-silica grating structure depends little on the incident wavelength, but mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These analytic results would also be very helpful for wavelength bandwidth analysis. The exact grating profile is optimized by using the rigorous coupled-wave analysis. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results agree well with the theoretical values.

Photo-induced gratings in thin color center layers on lithium fluoride

We study the recording of permanent Bragg gratings on surface-colored lithium fluoride (LiF) crystals by using the interference pattern of a continuous-wave UV argon-ion laser operating at 244 nm. Gratings with spatial periodicity ranging from 400 to 1000 nm are written by using a phase-mask interferometer and are stable for several months after the writing process. Absorption and photoluminescence spectra show the bleaching of primary F and F -aggregate laser-active color centers as a result of the process. Confocal microscopy is used to determine the pitch and the profile of the fluorescent gratings. The UV laser-induced optical bleaching in highly colored LiF ultrathin layers is responsible for the periodic spatial modulation of absorption and photoemission properties that characterize the gratings. In the colored surface layer, a reduction of as much as 50% of the initial color-center-induced refractive-index increase has been estimated in the bleached areas.

Bragg reflector by means of the form birefringence effect in dielectric rings

In this work, form birefringence physics and the mechanisms of Si/SiO2 dielectric concentric optical rings are investigated. The optical rings are modeled by means of a Bragg reflector. Similarly to a negative uniaxial crystal, the dielectric concentric pattern admits two preferred propagation directions defined by an extraordinary and an ordinary refractive index representing two field polarizations. The circular grating profile splits the electromagnetic field into a radial (extraordinary field) and a tangential (ordinary field) component which represent two modes of the periodic structure. These two modes are characterized by the refractive index ellipse obtained by the Huygens principle. The model is developed through the wave front propagation inside the anisotropic structure. The Bragg theory and conservation of momentum vectors provide the Bragg angles of the ordinary and extraordinary rays for different optical wavelengths. The Bragg theoretical model is validated by the finite difference time domain (FDTD) approach for a wavelength of λ=0.98μm.

Optically addressed high-resolution liquid crystal spatial light modulator with a diffraction efficiency above 50%

An optically addressed liquid crystal spatial light modulator (SLM) with a photosensitive amorphous hydrogenated silicon carbide (a-SiC:H) layer has been studied using holographic techniques. The maximum diffraction efficiency (DE) of the device amounted to ηmax = 50.5%. A decrease in the DE to a level of 0.5ηmax was observed at a spatial frequency of 75 mm−1. The high resolution and DE of the proposed SLM are due to features in the formation of an asymmetric grating line profile in the given structure.