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Showing papers on "Diffraction efficiency published in 1999"


Journal ArticleDOI
TL;DR: A new, to the knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light.
Abstract: We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.

452 citations


Journal ArticleDOI
TL;DR: In this article, the theoretical performance of blazed binary diffractive elements composed of pillars carefully arranged on a two-dimensional grid whose period is smaller than the structural cutoff was investigated through electromagnetic theories.
Abstract: We report here on the theoretical performance of blazed binary diffractive elements composed of pillars carefully arranged on a two-dimensional grid whose period is smaller than the structural cutoff. These diffractive elements operate under unpolarized light. For a given grating geometry, the structural cutoff is a period value above which the grating no longer behaves like a homogeneous thin film. Because the grid period is smaller than this value, effective-medium theories can be fully exploited for the design, and straightforward procedures are obtained. The theoretical performance of the blazed binary elements is investigated through electromagnetic theories. It is found that these elements substantially outperform standard blazed echelette diffractive elements in the resonance domain. The increase in efficiency is explained by a decrease of the shadowing effect and by an unexpected sampling effect. The theoretical analysis is confirmed by experimental evidence obtained for a 3λ-period prismlike grating operating at 633 nm and for a 20°-off-axis diffractive lens operating at 860 nm.

346 citations


Journal ArticleDOI
TL;DR: Bragg diffractive gratings recorded in the volume of photosensitive silicate glasses doped with silver, cerium, fluorine, and bromine recorded with photothermorefractive process observedabsolute diffraction efficiency of as much as 93% was observed for 1-mm-thick gratings with spatial frequencies up to 2500 mm(-1).
Abstract: Photosensitive silicate glasses doped with silver, cerium, fluorine, and bromine were fabricated at the Center for Research and Education in Optics and Lasers. Bragg diffractive gratings were recorded in the volume of these glasses with a photothermorefractive process (exposure to UV radiation of a He–Cd laser at 325 nm is followed by thermal development at 520 °C). Absolute diffraction efficiency of as much as 93% was observed for 1-mm-thick gratings with spatial frequencies up to 2500 mm-1. No decreasing of diffraction efficiency was detected at low spatial frequencies. Original glasses were transparent (absorption coefficient less than 1 cm-1) from 350 to 4100 nm. Induced losses in exposed and developed glass decreased from 0.3 to 0.03 cm-1 between 400 and 700 nm, respectively, and did not exceed 0.01–0.02 cm-1 in the IR region from 700 to 2500 nm. Additional losses caused by parasitic structures recorded in the photosensitive medium were studied.

288 citations


Journal ArticleDOI
TL;DR: In this article, permanent birefringent structures with controllable microscopic dimensions are inscribed in pure fused silica platelets, and the bireringence properties of transmission gratings and of a quasi-uniform layer have been established.

252 citations


Journal ArticleDOI
TL;DR: A simple technique for simultaneously imaging multiple layers within an object field onto a single camera using a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order.
Abstract: We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front-sensing system.

190 citations


Journal ArticleDOI
TL;DR: A precision laser pattern generator for writing arbitrary diffractive elements was developed and two resistless technologies of writing on chromium and on amorphous silicon films were developed and implemented and limit characteristics were investigated by writing special test structures.
Abstract: A precision laser pattern generator for writing arbitrary diffractive elements was developed as an alternative to Cartesian coordinate laser/electron-beam writers. This system allows for the fabrication of concentric continuous-relief and arbitrary binary patterns with minimum feature sizes of less than 0.6 µm and position accuracy of 0.1 µm over 300-mm substrates. Two resistless technologies of writing on chromium and on amorphous silicon films were developed and implemented. We investigated limit characteristics by writing special test structures. A 58-mm f/1.1 zone plate written directly is demonstrated at a λ/50 rms wave-front error corresponding to a 0.06-µm pattern accuracy. Several examples of fabricated diffractive elements are presented.

176 citations


Journal ArticleDOI
TL;DR: In this paper, an efficient finite-difference time-domain algorithm for the analysis of axially symmetric diffractive optical elements is proposed. But the algorithm is not suitable for focusing planar and Gaussian beams.
Abstract: We formulate and apply an efficient finite-difference time-domain algorithm to the analysis of axially symmetric diffractive optical elements. We discuss aspects relating to minimizing numerical dispersion in the incident field, application of absorbing boundary conditions in the radial direction, convergence to a steady state, and propagation of the steady-state electromagnetic fields from the finite-difference time-domain region to the plane of interest. Incorporation of these aspects into a single finite-difference time-domain algorithm results in an extremely efficient and robust method for diffractive optical element analysis. Application to the analysis of subwavelength and multilevel lenses, both with and without loss, for focusing planar and Gaussian beams is presented.

147 citations


Journal ArticleDOI
TL;DR: In this paper, the authors have coupled a liquid crystal display (LCD) to an optically addressed parallel-aligned nematic liquid crystal spatial light modulator (PAL-SLM) with a set of lenses.
Abstract: To realize a high efficiency electrically addressable phase-only modulator, we have coupled a liquid crystal display (LCD) to an optically addressed parallel-aligned nematic liquid crystal spatial light modulator (PAL-SLM) with a set of lenses. Phase modulation exceeding 3ϖ at 532 nm wavelength was obtained. We obtained linear transfer characteristics for phase modulation at various desired phase levels after calibration and adjustment of the transfer characteristics of the PAL-SLM and the LCD. Diffraction efficiency of 40% for binary phase grating and of 90% for 8-level blazed phase grating, which were very close to the simulation values, were observed. The power loss of the readout light was caused when passed through a half mirror, therefore, we examined a setup using an oblique readout light at the modulator. Very high diffraction efficiency was obtained from the setup by optimizing the polarization direction and optical path for this light, and the orientation of liquid crystals. Since the modulator can perform at better than 90% diffraction efficiency and at nearly 100% reflectivity, various high efficiency systems utilizing such modulators are expected.

139 citations


Journal ArticleDOI
TL;DR: Reflection gratings produced entirely of dielectric materials give the opportunity to enhance the laser damage threshold over that occurring in conventional metal gratings used for chirped-pulse-amplification, high-power lasers.
Abstract: We report on reflection gratings produced entirely of dielectric materials. This gives the opportunity to enhance the laser damage threshold over that occurring in conventional metal gratings used for chirped-pulse-amplification, high-power lasers. The design of the system combines a dielectric mirror and a well-defined corrugated top layer to obtain optimum results. The rules that have to be considered for the design optimization are described. We optimized the parameters of a dielectric grating with a binary structure and theoretically obtained 100% reflectivity for the -1 order in the Littrow mounting for a 45° angle of incidence. Subsequently we fabricated gratings by structuring a low-refractive-index top layer of a multilayer stack with electron-beam lithography. The multilayer system was fabricated by conventional sputtering techniques onto a flat fused-silica substrate. The parameters of the device were measured and controlled by light scatterometer equipment. We measured 97% diffraction efficiency in the -1 order and damage thresholds of 4.4 and 0.18 J/cm2 with 5-ns and 1-ps laser pulses, respectively, at a wavelength of 532 nm in working conditions.

136 citations


Journal ArticleDOI
TL;DR: A theoretical study of one-dimensional blazed-binary gratings shows that the reason for this high efficiency is a waveguiding effect as mentioned in this paper. But this is not the case with standard echelette diffractive elements.
Abstract: Recent experimental and numerical results clearly show that blazed-binary diffractive elements outperform their standard blazed-echelette counterparts in the resonance domain. A theoretical study of one-dimensional blazed-binary gratings shows that the reason for this high efficiency is a waveguiding effect. The electromagnetic study supports the idea that, through waveguiding, a reduction of the shadowing zone is achieved, and thus the efficiency is increased. This is intrinsic to high-frequency binary structures and cannot be achieved with standard echelette diffractive elements.

117 citations


Journal ArticleDOI
TL;DR: In this article, a fluid mechanics model for photoinduced surface relief grating (SRG) formation on azopolymer films is discussed precisely using a fluid dynamics model which takes depth dependence of photoinduced driving force and velocity distribution in the film surface into account.
Abstract: Photoinduced surface relief grating (SRG) formation on azopolymer films is discussed precisely using a fluid mechanics model which takes depth dependence of photoinduced driving force and velocity distribution in the film surface into account. Formulation for the SRG dynamics is derived analytically as a function of film thickness and interference wave number. The film thickness dependence of diffraction efficiency, which is observed experimentally, agrees well with the theoretical value in the entire range of film thickness. The dependence of SRG driving force on interference wave number is also discussed in terms of the experimental data using proposed model.

Journal ArticleDOI
TL;DR: In this article, the diffraction efficiency, birefringence, and surface relief modulation were investigated on functionalized azopolymer films of p(DR1M-co-MMA) with a 12% mole fraction of DR1M.
Abstract: Dynamical experimental studies of the diffraction efficiency, birefringence, and surface relief modulation were carried out on functionalized azopolymer films of p(DR1M-co-MMA) with a 12% mole fraction of DR1M The gratings were recorded using two linearly polarized pump beams (λ = 5145 nm) either with a parallel configuration (p+p) or (s+(-s)) or with orthogonal polarizations (p+s) A general Jones matricial approach in conjuction with real-time polarization analyses of the first order diffracted beam (S+1) appears to be a quite sensitive method to extract relevant parameters such as birefringence (Δn) and surface relief modulation (2Δd) The phase matrices have been developed considering the pump polarization of the two interfering beams and taking into account the orientational “angular hole-burning” model under low pump irradiances Numerical calculations allow us to extract the time variations of Δn and 2Δd and to compare the various efficiencies in grating formation The obtained values for Δn are

Journal ArticleDOI
TL;DR: In this article, the authors measured and analyzed the temporal behavior of beams diffracted by volume gratings in photopolymer thin films by solution of the diffusion equation for the monomer concentration inside the thin films.
Abstract: The temporal behavior of beams diffracted by volume gratings in photopolymer thin films are measured and analyzed by solution of the diffusion equation for the monomer concentration inside the thin films. Two contributors to the refractive-index change that forms the volume gratings are assumed: One is the phase grating formed by modulation of the monomer concentration, and the other is the phase grating formed by modulation of the density of the polymeric materials. The phase grating that is due to monomer modulation is responsible for the initial fast rise and decay of the diffracted signal, and the phase grating that is due to modulation of density of the polymeric materials is responsible for the slowly rising and then steady signal. The temporal behavior of the diffracted beams is determined by the ratio of magnitudes of the incident beam intensity and the diffusion coefficient.

Journal ArticleDOI
TL;DR: The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.
Abstract: The extraction of the spectrum corresponding to a single extreme-ultraviolet ultrashort pulse embedded in an extended spectrum may alter the duration of the pulse itself. This is due to the spectral filtering of optics and the differences in the optical path of the rays caused by ordinary diffraction when a grating is used. The basic mechanism that leads to the latter effect is the difference of one wavelength of the path length of two rays diffracted at the first order by nearby grating grooves. A study of these effects and some possible solutions obtained from using a pair of diffraction gratings is presented. The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.

Journal ArticleDOI
TL;DR: An azocarbazole-based polyimide was synthesized from an azocarazole diamine monomer and 4,4‘-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) by a two-step polycondensation reaction.
Abstract: An azocarbazole-based polyimide was synthesized from an azocarbazole diamine monomer and 4,4‘-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) by a two-step polycondensation reaction. Birefringence experiments have been performed on the pure polyimide and on the polyimide mixed with small azo chromophores. Because of its high Tg, the polyimide has a very stable induced birefringence (only 14% loss during the relaxation process). The stability of the mixtures is also very high. Surface relief diffraction gratings were inscribed on these systems. The measured diffraction efficiency was about 0.25% for a diamine-doped polyimide exposed for 1 h to an irradiance of 200 mW/cm2. The surface profile studied by atomic force microscopy showed an amplitude of 30 nm and a regular spacing of 700 nm on a 255 nm thick film. The photoinduced gratings had a high stability without further surface deformation after baking at 240 °C for 1 h in air.

Proceedings ArticleDOI
05 Oct 1999
TL;DR: A volume phase grating is an interferometric pattern within the volume of a material which, when suitably processed, becomes a modulation of the material's index of refraction.
Abstract: Volume phase (VP) gratings are now available and being applied to the applications of astronomical spectroscopy, Raman spectroscopy, ultrafast lasers, and wavelength division multiplexers. A volume phase grating results from the recording of an interferometric pattern within the volume of a material which, when suitably processed, becomes a modulation of the material's index of refraction. When a VP grating is substantially illuminated, the light interacts with the material due tot he recorded pattern. Light propagates within and out of the VP grating according to Bragg diffraction. Definitions of various VP gratings designed and fabricated to study performance are provided as relating to the applications listed above. Performance parameters include diffraction efficiency, spectral coverage, and angular coverage. Descriptions of the test methods are given. Performance data is provided and compared to the respective design.

Journal ArticleDOI
TL;DR: In this article, phase-type gratings that were formed in a polymer azobenzene liquid-crystal (PALC) film were confirmed by atomic force microscopy, which revealed that the gratings could not be characterized only as conventional surface-relief gratings.
Abstract: Unique characteristics were observed in phase-type gratings that were formed in a polymer azobenzene liquid-crystal (PALC) film. Generation of sinusoidal variation of the surface of the film was confirmed by atomic force microscopy. However, comparison of the diffraction efficiency with the surface modulation revealed that the gratings could not be characterized only as conventional surface-relief gratings. In the glassy state of the film, moderate efficiency (∼18%) was obtained with large surface modulation (68−76 nm), whereas the gratings recorded in the nematic (N) phase showed high diffraction efficiency (∼28%) with slight surface modulation (33−53 nm). The diffraction efficiency was enhanced in the liquid-crystalline phase. Dynamics of the first-order diffraction beam exhibited that the grating formation was associated with photochemical phase transition of PALC. It was assumed that the isotropic (I) phases were formed by photochemical reaction of azobenzene moieties in the interference pattern at an...

Journal ArticleDOI
TL;DR: Efficient surface gratings are UV imprinted in an acrylate-rich hybrid solgel glass that is resistant to temperature and to solvent effects, and could have useful applications in sensor and spectroscopic devices.
Abstract: Efficient surface gratings are UV imprinted in an acrylate-rich hybrid solgel glass. Structural changes occurring in the material upon exposure to light are investigated. Large amplitude modulation (700 nm) and low surface roughness (0.2 nm) were measured by atomic force microscopy. Diffraction efficiencies were found to be close to theoretical predictions. The method of fabrication does not involve any etching step, and an all-UV process is proposed. The gratings are resistant to temperature and to solvent effects. These devices could have useful applications in sensor and spectroscopic devices.

Journal ArticleDOI
TL;DR: In this article, the authors measured the diffraction efficiency of two-dimensional photonic-bandgap lattices consisting of a triangular array of circular air holes etched in a semiconductor waveguide.
Abstract: We report on the measurement of the diffraction efficiency of two-dimensional photonic-bandgap lattices consisting of a triangular array of circular air holes etched in a semiconductor waveguide. We use the spontaneous emission of the material as an internal point source. Combined with previous reflectivity and transmission measurements, the diffraction data allow us to assess the total amount of out-of-plane losses experienced by a guided wave traversing the dielectric lattice, as a function of the lattice pitch. We found that these losses are particularly weak for some range of parameters, especially in the photonic bandgap of interest. We discuss the reasons why they can be substantial with other parameters.

Journal ArticleDOI
TL;DR: In this article, the authors reported on the fabrication of diffraction gratings in photosensitive sol-gel thin films by direct contact printing using a UV-mercury lamp.

Journal ArticleDOI
TL;DR: In this article, a technique was developed to fabricate surface-relief gratings using photosensitive gel films, which were derived from metal-alkoxides chemically modified with β-diketones.

Journal ArticleDOI
TL;DR: In this article, a vertical-cavity surface-emitting laser (VCSEL) with a monolithically integrated diffractive optical element (DOE) was demonstrated for advanced beam shaping.
Abstract: We have demonstrated a vertical-cavity surface-emitting laser (VCSEL) with a monolithically integrated diffractive optical element (DOE) for advanced beam shaping. The DOE is a two-level surface relief, etched into the GaAs substrate beneath a bottom-emitting VCSEL. The combination generates a 4/spl times/4 array of focused spots 10 mm from the substrate with spot sizes down to less than 400 /spl mu/m, almost at the diffraction limit. Diffraction efficiencies of 29% and uniformity errors of 14% were measured.

Journal ArticleDOI
Lifeng Li1
TL;DR: In this paper, a formulation of the Chandezon method for modeling one-dimensionalally periodic, multilayer, inhomogeneous, anisotropic diffraction gratings is presented.
Abstract: A formulation of the Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic diffraction gratings is presented. The formulation is based on an oblique Cartesian coordinate system so that blazed surface-relief profiles and slanted volume permittivity variations can be treated simultaneously. The permittivity tensors of the anisotropic materials can be arbitrary, but their spatial variations are assumed to have the same period as the surface corrugations. Some of the previous authors’ works in the above individual aspects of the subject are improved on in regard to clarity, simplicity, and generality. Most important, the theory of Fourier factorization is applied throughout the analysis to ensure fast convergence of the numerical method when the permittivity tensors or the derivatives of the grating’s surface-profile functions have discontinuities. Numerical examples, including those of two types of multilayer magneto-optic gratings, are provided.

Journal ArticleDOI
TL;DR: In this article, surface-relief diffractive cylindrical mirrors are designed for on-axis and off-axis focusing and incidence configurations, and the diffractive structures are analyzed by both rigorous and scalar integral methods.
Abstract: Metallic surface-relief diffractive cylindrical mirrors are designed for on-axis and off-axis focusing and incidence configurations. These diffractive structures are analyzed by both rigorous and scalar integral methods. Two design methods, based on initial assumptions of zero-thickness and finite-thickness structures, are presented for determining the zone-boundary locations and the surface-relief mirror profiles for the general case of an off-axis incident plane wave and off-axis focusing. With the use of these methods, continuous diffractive, multilevel diffractive, and continuous nondiffractive mirrors were designed. Rigorous analysis is performed for both TE and TM polarizations by using an open-region formulation of the boundary element method (BEM) suitable for regions of complex refractive index such as finite-conductivity metals. Three scalar integral methods corresponding to Dirichlet, Neumann, and Kirchhoff boundary conditions are also used to analyze the diffractive mirrors. The diffracted fields from both the rigorous BEM and the scalar methods of analysis are used to calculate a number of performance metrics including diffraction efficiency, sidelobe power, total reflected power, and focal spot size. The performance of the mirrors is evaluated, and the accuracy of the various scalar methods is determined.

Journal ArticleDOI
TL;DR: In this paper, a procedure for designing binary diffractive lenses by use of pulse-width-modulated subwavelength features is discussed, based on the combination of two approximate theories, effective medium theory and scalar diffraction theory, and accounts for limitations on feature size and etch depth imposed by fabrication.
Abstract: A procedure for designing binary diffractive lenses by use of pulse-width-modulated subwavelength features is discussed. The procedure is based on the combination of two approximate theories, effective-medium theory and scalar diffraction theory, and accounts for limitations on feature size and etch depth imposed by fabrication. We use a closed-form expression based on zeroth-order effective-medium theory to map the desired superwavelength phase to the width of a binary subwavelength feature and to examine the requirements imposed by this technique on fabrication and on analysis. Comparisons are also made to more rigorous approaches. In making these comparisons, we show that a trade-off exists between the exactness of the mapping and the fabrication constraints on the minimum feature.

Journal ArticleDOI
TL;DR: It was found that gratings with larger periods (approximately 1.4 microm) are susceptible to erasure effects with postexposure laser illumination, and crossed gratings were found to have an extended dynamic range.
Abstract: Hologram formation and diffusion reactions in photopolymer films are examined at different stages of exposure and at different spatial frequencies. Different properties of the grating formation process are evaluated from efficiency data, including the relative rates of diffusion and photoinitiated polymerization, dye absorption, and residual efficiency enhancement after UV curing. It was also found that gratings with larger periods (approximately 1.4 microm) are susceptible to erasure effects with postexposure laser illumination. In addition, crossed gratings were found to have an extended dynamic range. This effect can have a significant impact on the number of holograms formed with rotational or peristrophic multiplexing.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate the rotation of multimodel Gauss-Laguerre beams generated with a binary-phase diffractive element, which is designed with the use of an iterative procedure and quantized in two levels after adding a carrier frequency to the phase.
Abstract: We demonstrate the rotation of multimodel Gauss—Laguerre beams generated with a binary-phase diffractive element. The element is designed with the use of an iterative procedure and quantized in two levels after adding a carrier frequency to the phase. The fabrication technology of the diffractive element involves e-beam lithography and reactive ion etching. Experimental and theoretical results are shown to be in good conformity.

Journal ArticleDOI
TL;DR: The principle of polarization multiplexing by use of metal-stripe subwavelength period gratings is described for a diffractive element that has a binary amplitude transmission per polarization channel and is demonstrated by experimental results.
Abstract: Diffractive elements with polarization multiplexing for the visible spectral region are demonstrated. The polarization-multiplexing property of the element is based on the polarization-dependent transmission characteristics of metal-stripe subwavelength period gratings. The proper dimensions of these gratings are estimated by rigorous calculations. The principle of polarization multiplexing by use of metal-stripe subwavelength period gratings is described for a diffractive element that has a binary amplitude transmission per polarization channel and is demonstrated by experimental results.

Journal ArticleDOI
TL;DR: In this article, the performance of diffractive optical elements implemented with pixelated spatial light modulators is investigated and the relation between the maximum diffraction efficiency, the fill factor and the desired diffraction pattern is investigated.

Journal ArticleDOI
TL;DR: In this paper, the effects of the zeroth-order diffraction of a phase mask on the creation of Bragg gratings using the mask technique were theoretically and experimentally investigated.
Abstract: The effects of the zeroth-order diffraction of a phase mask on the creation of Bragg gratings using the mask technique were theoretically and experimentally investigated. Experimental results showed that the zeroth-order diffraction of 1% total power, while in interference with the first-order diffraction of 44% each, dramatically affected the structure of the gratings in a polymer optical preform, including their period. Theoretical analysis by taking the zeroth-order diffraction into account predicted that a very small part of the zeroth-order component (0.1%) would have substantial effects on the gratings, which will be no longer uniform along both the directions of the incident laser beam propagation and the groove array. Theoretical calculation agrees well with the experimental results.