Showing papers on "Diffraction efficiency published in 1993"
TL;DR: In this paper, a numerically stable method for the analysis of diffraction gratings of arbitrary profile, depth, and in conical mountings is presented based on the classical modal method and uses a stack of lamellar gratittivity to approximate an arbitrary profile.
Abstract: A numerically stable method is presented for the analysis of diffraction gratings of arbitrary profile, depth, and in conical mountings. It is based on the classical modal method and uses a stack of lamellar gratpermittivity to approximate an arbitrary profile. A numerical procedure known as the R-matrix propagation aling layers gorithm is used to propagate the modal fields through the layers. This procedure renders the implementation of this new method completely immune to the numerical instability that is associated with the conventional algorithm. Numerical examples including diffraction efficiencies of both dielectric and metallic propagation gratings of depths that range from subwavelength to hundreds of wavelengths are presented. Information about the convergence and the computation time of the method is also included.
361 citations
TL;DR: In this article, it was shown that the coupled-wave method converges slowly for metallic lamellar gratings in TM polarization, and the reason for the slow convergence was attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region.
Abstract: Numerical evidence is presented that shows that, for metallic lamellar gratings in TM polarization, the coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am. A3, 1780 ( 1986)] converges slowly. (In some cases, for achieving a relative error of less than 1% in diffraction efficiencies, the number of spatial harmonics retained in the computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct categories, the cause for the slow convergence is analyzed and attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region. The eigenvalues and the eigenfunctions of the modal fields in the grating region, whose accurate determination is crucial to the success of the coupled-wave method, are shown to converge slowly as a result of the use of these Fourier expansions. Despite its versatility and simplicity, the coupled-wave method should be used with caution for metallic surface-relief gratings in TM polarization.
221 citations
TL;DR: In this paper, a transmission phase grating was used to write a 94% reflectivity in-fibre index grating in a photosensitive optical fiber with a single UV laser beam at 242 nm.
Abstract: A transmission phase grating was used to write a 94% reflectivity in-fibre index grating in a photosensitive optical fibre with a single UV laser beam at 242 nm. This method offers the possibility of high-volume production of in-fibre gratings.
190 citations
TL;DR: In this paper, a rigorous modal analysis of lamellar gratings with rectangular grooves in conical mountings is presented, which is an extension of the analysis of Botten et al. which considered non-conical gratings.
Abstract: A rigorous modal analysis of lamellar gratings, i.e. gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.
150 citations
TL;DR: In this paper, the authors apply the rigorous electromagnetic grating theory and an electromagnetic wave propagation model with Kirchhoff boundary conditions to analyze and optimize the performance of arrays of cylindrical dielectric multilevel diffractive lenses.
Abstract: We apply the rigorous electromagnetic grating theory and an electromagnetic wave-propagation model with Kirchhoff boundary conditions to analyze and optimize the performance of arrays of cylindrical dielectric multilevel diffractive lenses. We show that the diffraction efficiency of a high-numerical-aperture lens array can be improved if the surface-relief profile is constructed with the use of rigorously optimized grating groove structures, which differ significantly from a multilevel approximation of a triangular profile.
110 citations
TL;DR: A new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface based on a high-order rigorous perturbative technique is presented.
Abstract: We present a new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface. This method is based on a high-order rigorous perturbative technique, whose application to singly periodic gratings was treated in the first two papers of this series [ J. Opt. Soc. Am. A10, 1168, 2307 ( 1993)]. We briefly discuss the theoretical basis of our algorithm, namely, the property of analyticity of the diffracted fields with respect to variations of the interfaces. While the algebraic derivation of some basic recursive formulas is somewhat involved, it results in expressions that are easy to implement numerically. We present a variety of numerical examples (for bisinusoidal gratings) in order to demonstrate the accuracy exhibited by our method as well as its limited requirements in terms of computing power. Generalization of our computer code to crossed gratings other than bisinusoidal is in principle immediate, but the full domain of applicability of our algorithm remains to be explored. Comparison with results presented previously for actual experimental configurations shows a substantial improvement in the resolution of our numerics over that given by other methods introduced in the past.
107 citations
TL;DR: An echelle polychromator for inductively coupled plasma optical emission spectroscopy (ICP-OE9) was designed for use with the multichannel solid-state detector described in the companion article as discussed by the authors.
Abstract: An echelle polychromator for inductively coupled plasma optical emission spectroscopy (ICP-OE9) was designed for use with the multichannel solid- state detector described in the companion article. The optical system has separate output sections for the UV and visible wavelength ranges, which permit high spectral resolution and high optical throughput nahile covering the spectral range from 167 to 782 nm. A novel component in the UV section corrects spherical aberration, cross-disperses the spectrum, and separates the UV and risible beams. A large-area echelle grating has been ruled for this system which has high diffraction efficiency and constant blaze angle across the spectrum and low stray light
93 citations
TL;DR: In this paper, the fixed holograms can be read out directly or after a positive-voltage pulse is applied that can dramatically enhance the diffraction efficiency, and single gratings as well as images are recorded and fixed.
Abstract: Photorefractive holograms stored in Sr0.75Ba0.25Nb2O6 crystals are electrically fixed at room temperature. The fixed holograms can be read out directly or after a positive-voltage pulse is applied that can dramatically enhance the diffraction efficiency. Single gratings as well as images are recorded and fixed.
91 citations
TL;DR: In this paper, a method of variation of boundaries for the solution of diffraction problems was introduced, which is based on a theorem of analyticity of the electromagnetic field with respect to variations of the interfaces.
Abstract: We recently introduced a method of variation of boundaries for the solution of diffraction problems [ J. Opt. Soc. Am. A10, 1168 ( 1993)]. This method, which is based on a theorem of analyticity of the electromagnetic field with respect to variations of the interfaces, has been successfully applied in problems of diffraction of light by perfectly conducting gratings. We continue our investigation of diffraction problems. Using our previous results on analytic dependence with respect to the grating groove depth, we present a new numerical algorithm that applies to dielectric and metallic gratings. We also incorporate Pade approximation in our numerics. This addition enlarges the domain of applicability of our methods, and it results in computer codes that can predict more accurately the response of diffraction gratings in the resonance region. In many cases results are obtained that are several orders of magnitude more accurate than those given by other methods available at present, such as the integral or differential formalisms. We present a variety of numerical applications, including examples for several types of grating profile and for wavelengths of light ranging from microwaves to ultraviolet, and we compare our results with experimental data. We also use Pade approximants to gain insight into the analytic structure and the spectrum of singularities of the fields as functions of the groove depth. Finally, we discuss some connections between Pade approximation and another summation mechanism, enhanced convergence, which we introduced in the earlier paper. It is argued that, provided that certain numerical difficulties can be overcome, the performance of our algorithms could be further improved by a combination of these summation methods.
90 citations
TL;DR: In this article, a continuous surface-relief diffractive optical element for two-dimensional array generation (fan-out) is designed and fabricated, and the phase-grating microstructures are generated by laser-beam writing lithography in a single exposure step and converted to nickel shims by electroplating.
Abstract: Continuous surface-relief diffractive optical elements for two-dimensional array generation (fan-out) are designed and fabricated. Separable and nonseparable solutions for the two-dimensional element design are compared. The phase-grating microstructures are generated by laser-beam writing lithography in a single exposure step and converted to nickel shims by electroplating, enabling low-cost replicas to be produced by using laboratory and commercial replication processes. Results are presented for a 9 x 9 fan-out diffractive optical element with a measured efficiency of 94% and an overall uniformity within +/-8%; replicas in epoxy have the same efficiency and a uniformity of +/-15%.
88 citations
TL;DR: Experimental results obtained by use of a magneto-optic SLM are presented and diffraction-free beams are generated by the use of diffractive optical elements written on a spatial light modulator.
Abstract: Diffraction-free beams are generated by the use of diffractive optical elements written on a spatial light modulator (SLM). By alteration of the pattern placed on the SLM, the axis of propagation can be both shifted laterally and rotated. We present experimental results obtained by use of a magneto-optic SLM.
TL;DR: A volume holographic storage scheme, spatioangular multiplexed, which is a hybrid of both angular and spatial multiplexing is proposed, which reports the successful replay of all images with negligible cross talk and with an average diffraction efficiency of 0.5%.
Abstract: We propose a volume holographic storage scheme, spatioangular multiplexing, which is a hybrid of both angular and spatial multiplexing. We describe the recording procedure, for a preliminary experiment in which 750 holograms were recorded (at room temperature) in a single photorefractive crystal of iron-doped lithium niobate and report the successful replay of all images with negligible cross talk and with an average diffraction efficiency of 0.5%.
Patent•
03 Dec 1993
TL;DR: An optical memory diffraction grating having a plurality of spaced ridges each having an optically reflective facet has been proposed in this paper, where information can be stored in the optical memory by locally changing the optical properties of the grating.
Abstract: An optical memory diffraction grating having a plurality of spaced ridges each having a plurality of optically reflective facets. When illuminated with an incident light beam the grating produces a number of diffracted beams corresponding to the number of facets. The diffracted beams can be machine read by a reading device which produces a reading light beam directed at the grating. The reading device has a plurality of detectors positioned to be illuminated by the diffracted light beams. Information can be stored in the optical memory by locally changing the optical properties of the grating. The grating may be employed in security cards and documents. The grating may be arranged as a bar code or as a pixelgram. Reading, writing and erasing devices are also claimed.
TL;DR: An experimental study of the photorefractive effect in a polymeric material containing carbazole and the second-order tricyanovinylcarbazole moieties as a side chain is presented, investigating the electric-field dependence of the diffraction efficiency.
Abstract: An experimental study of the photorefractive effect in a polymeric material containing carbazole and the second-order tricyanovinylcarbazole moieties as a side chain is presented. This polymeric system exhibits intrinsically both photoconductivity and the electro-optic effect. Absorptive and photorefractive gratings have been evidenced by four-wave-mixing experiments and electro-optic measurements. The properties of the photorefractive gratings are studied by investigating the electric-field dependence of the diffraction efficiency. The dynamics of the erase-write behavior of the gratings, as well as permanent photobleaching of the polymer, are described.
TL;DR: Second order diffraction has been observed from Bragg gratings written within germanosilicate glass fibres as discussed by the authors, which is consistent with a saturation in the photo-induced change in refractive index.
TL;DR: P polarization-selective computer-generated holograms with independent phase profiles for the two orthogonal linear polarizations with first-order diffraction efficiency varied from 6% to 25%, with as much as 40:1 contrast between polarizations.
Abstract: We demonstrate polarization-selective computer-generated holograms with independent phase profiles for the two orthogonal linear polarizations The holograms are made of two surface-relief-etched birefringent substrates joined face to face We describe their design and fabrication and present experimental results for dual binary-phase computer-generated holograms fabricated in lithium niobate The first-order diffraction efficiency varied from 6% to 25%, with as much as 40:1 contrast between polarizations Such elements can be used in compact optoelectronic systems or combined with electro-optic polarization rotators to make electrically controlled optical elements
Patent•
15 Dec 1993
TL;DR: In this article, a method of writing plane holographic gratings Bragg-matching for reflection in the infrared in a photorefractive material using shorter wavelength light through a face perpendicular to the grating planes is presented.
Abstract: A method of writing plane holographic gratings Bragg-matched for reflection in the infrared in a photorefractive material using shorter wavelength light through a face perpendicular to the grating planes. The writing beam wavelength is selected to be within the photorefractive sensitivity range of the crystal and the angles are chosen relative to the wavelength to define a reflection grating with a period such that counter-propagating reflection occurs at the desired IR wavelength. For reflection gratings at different wavelengths, either the transmission or the reflection mode geometry may be used. In the transmission mode, the writing beams are incident on the same side face while in the reflection made the writing is on opposite faces in an off-axis (non-counter-propagating) configuration. Anti-reflection coatings of the appropriate wavelengths are used on the crystal surfaces to reduce reflection losses and improve the diffraction efficiency of the grating.
TL;DR: The optothermal expansion coefficient is used to design athermalized lenses that combine refractive and diffractive surfaces and useful design equations are presented that describe focal length, phase coefficients, and diffraction efficiency as functions of temperature.
Abstract: The thermal properties of lenses play an important role in the performance of optical systems. We discuss the effects of uniform temperature changes and thermal gradients on diffractive lens performance. Comparisons are made between the thermal sensitivity of refractive and diffractive lenses. Useful design equations are presented that describe focal length, phase coefficients, and diffraction efficiency as functions of temperature. We present important thermal data for a number of lens materials. The optothermal expansion coefficient is used to design athermalized lenses that combine refractive and diffractive surfaces.
TL;DR: Scalar diffraction theory and electromagnetic vector theory are compared by analyzing plane-wave scattering by a perfectly conducting, rectangular-grooved grating and one general conclusion is that, depending on polarization, scalar theory should not be used when the grating period becomes smaller than ten wavelengths.
Abstract: Scalar diffraction theory and electromagnetic vector theory are compared by analyzing plane-wave scattering by a perfectly conducting, rectangular-grooved grating. General field solutions for arbitrary angles of incidence are derived by using scalar and vector theories. Diffraction efficiencies for the scalar and the vector cases as functions of wavelength, grating period, and angles of incidence are determined numerically and plotted. When the wavelength of the incident field is much shorter than the grating period, the diffraction efficiencies match. But when the wavelength is of the order of the grating period, large differences between the scalar and the vector solutions emerge. One general conclusion is that, depending on polarization, scalar theory should not be used when the grating period becomes smaller than ten wavelengths.
TL;DR: In this article, the stationary coupled differential equations of two recording beams that are polarized perpendicular to the plane of incidence are derived and solved analytically for the beam intensities and the phase changes.
Abstract: A theoretical study is presented that describes the recording and the readout of transmission volume holograms in dynamic photoanisotropic organic materials. The stationary coupled differential equations of two recording beams that are polarized perpendicular to the plane of incidence are derived and solved analytically for the beam intensities and the phase changes. These equations self-consistently satisfy the recording dynamics of the hologram formation including the effects of fringe curvature and energy transfer. Analytic formulas for the diffraction efficiency are obtained from the readout equations under the assumption of a Bragg-matched weak probe beam of arbitrary polarization and in the small fringe curvature regime. Previously measured parameters of Methyl Orange–polyvinyl alcohol holograms indicate that the optimal hologram thickness is approximately 0.2 mm and predict the decrease of diffraction efficiency with an increase of beam ratio.
TL;DR: The design theory presented in this paper describes characteristic features of thin diffractive elements and permits the derivation of upper bounds of the diffraction efficiency of diffraction elements. But these bounds are independent of the calculation method used to obtain the diffractive element.
Abstract: The design theory presented describes characteristic features of thin diffractive elements. In particular it permits the derivation of upper bounds of the diffraction efficiency of diffractive elements. These bounds are independent of the calculation method used to obtain the diffractive elements. The consequences of the results for diffractive optics are briefly discussed.
TL;DR: Good-agreement-between the predictions of the-error analysis and the performance of the fabricated components is observed.
Abstract: The effects of mask alignment and etch-depth errors in the array uniformity error U and diffraction efficiency η of multilevel-grating array illuminators are evaluated numerically. Also demonstrated are 16-level fan-out elements with array size up to 32 × 16, with U = 5%–10% and η = 83%–92%. These are fabricated with electron-beam-written binary masks, optical alignment and contact copying, and reactive ion etching. Good agreement between the predictions of the error analysis and the performance of the fabricated components is observed.
TL;DR: In the latest optical switching network, binary phase gratings were used to generate arrays of uniformintensity beams to illuminate modulators in the processor array and space-invariant binary phase grating designs were integral in forming the Banyan interconnection network used to link arrays in the system.
Abstract: Free-space photonic switching systems that optically interconnect large arrays of simple processing elements have already been demonstrated [ IEEE Photon. Technol. Lett.2, 438, 600 ( 1990); Appl. Opt.31, 5431 ( 1992); Electron. Lett.27, 1869 ( 1991)]. In these system experiments, diffractive optical elements served as critical components that provided functionality not easily assumed by conventional optics. In the latest optical switching network, binary phase gratings were used to generate arrays of uniform-intensity beams to illuminate modulators in the processor array. In addition, space-invariant binary phase grating designs were integral in forming the Banyan interconnection network used to link arrays in the system. Here we discuss the function, design, and performance of these diffractive elements.
TL;DR: The temporal holographic response was found to depend strongly on optical recording configurations and on the recording beam intensities, and all-optical modulation of the holographic gratings with 2000 lines/mm is possible by modulation of a separate excitation beam of incoherent UV radiation.
Abstract: Polymers doped with photochromic spirooxazine and spiropyran dyes have been investigated for real-time holographic recording. The temporal holographic response was found to depend strongly on optical recording configurations and on the recording beam intensities. The exposure sensitivities that were required for maximal diffraction efficiency were 250 mJ/cm2 for the polymers doped with spirooxazine and 650 mJ/cm2 for those doped with spiropyran. All-optical modulation of the holographic gratings with 2000 lines/mm is possible by modulation of a separate excitation beam of incoherent UV radiation. The modulated gratings can be stored for relatively long times or erased immediately.
TL;DR: In this paper, the phase conjugate reflectivity and diffraction efficiency were measured for both the reflection and transmission grating cases for a Nd:YAG amplifier using orthogonally polarised pump beams of pulse duration 16 ns.
Patent•
17 Nov 1993TL;DR: In this paper, a scanning system and a novel method for compensating for the variations in the output power of the beam from an A-O cell was proposed. But the system and method of the present invention sets the output output power from the AO cell to a desired value.
Abstract: The present invention is a scanning system and a novel method for compensating for the variations in the output power of the beam from an A-O cell. The novel method involves varying the amount of drive current through the laser diode in such a fashion as to compensate for the loss of power due to diffraction inefficiencies. The amount of driving current is dependent upon the amount of power desired in the output beam from the A-O cell. The system and method of the present invention sets the output power from the A-O cell to a desired value. As the diffraction efficiency increases at other portions of the scan, the drive current is cut appropriately to compensate for the increased efficiency; thus keeping the output spot power at the desired value. Likewise, as the diffraction efficiency decreases at other portions of the scan, the drive current should be increased to compensate for the decrease in efficiency; thereby maintaining the desired value.
TL;DR: It is shown that, theoretically, the diffraction efficiency can reach 100% for both TE and TM polarizations that are incident at the Bragg angle, and simple criteria are suggested for the design of the grating structures for both polarizing and nonpolarizing beam splitters.
Abstract: We present a theoretical and experimental study on the diffraction characteristics of gratings, with particular attention focused on the effects of polarization. The goal of our study is to develop multifunctional devices for use in a pickup head for optical storage systems. Experiments and numerical calculations are carried out systematically to determine the effects of the grating parameters of depth, period, and duty cycle and also the effects of the incident-wave parameters of incident angle, wavelength, and polarization. It is shown that, theoretically, the diffraction efficiency can reach 100% for both TE and TM polarizations that are incident at the Bragg angle. The simple dispersion characteristics of the Floquet modes are invoked to explain the different diffraction behaviors between the two polarizations. We conclude that a suitably designed grating may split an incident light beam of mixed polarizations into two beams of the opposite polarizations, each propagating in a different direction. Based on the numerical results, simple criteria are suggested for the design of the grating structures for both polarizing and nonpolarizing beam splitters.
TL;DR: In this paper, a surface normal optical interconnect with a 1-to-12 collinear fan-out was presented, which greatly enhanced the optical signal processing capability of the guided wave interconnects.
Abstract: We present a surface normal optical interconnect with a 1‐to‐12 collinear fan‐out. Two types of polymer‐based holograms were fabricated to provide a collinear 1‐to‐12 fan‐out from guided mode to substrate modes and twelve 1‐to‐1 surface normal interconnects. Fluctuation of up to 7.2 dB for the 1‐to‐12 fan‐out hologram was observed due to the oscillating and the film saturation effects of the transmission hologram. Diffraction efficiency better than 70% was observed for all the total internal reflection holograms. The result reported herein greatly enhanced optical signal processing capability of guided wave optical interconnects. The advantages of free space optical interconnect, such as global interconnect, three dimension, massive fan‐out/fan‐in capabilities, and surface normal optical interconnect, can be realized using the demonstrated architecture. The coupling from waveguide to fiber can be realized from the surface rather than the edge of a photonic integrated circuit.
TL;DR: In this article, reversible holographic storage and beam amplification was achieved in a new polymer composite using a low-power semiconductor visible laser diode emitting at 674nm, which showed substantially better performance than the existing photorefractive polymeric materials.
Abstract: Reversible holographic storage and beam amplification has been achieved in a new polymer composite using a low-power semiconductor visible laser diode emitting at 674nm. This material shows substantially better performance than the existing photorefractive polymeric materials. A diffraction efficiency of 5%, a gain coefficient of 30cm−1 and a net gain of 6cm−1 have been measured in 105 μm-thick samples with an applied field of 40V/μm.