Showing papers on "Diffraction grating published in 1980"

Electromagnetic theory of gratings

Abstract: 1 A Tutorial Introduction- 11 Preliminaries- 111 General Notations- 112 Time-Harmonic Maxwell Equations- 113 Boundary Conditions- 114 Electromagnetism and Distribution Theory- 115 Notations Used in the Description of a Grating- 12 The Perfectly Conducting Grating- 121 Generalities- 122 The Diffracted Field- 123 The Rayleigh Expansion and the Grating Formula- 124 An Important Lemma- 125 The Reciprocity Theorem- 126 The Conservation of Energy- 127 The Littrow Mounting- 128 The Determination of the Coefficients Bn by the Rayleigh Method- 129 An Integral Expression of ud in P Polarization- 1210 The Integral Method in P Polarization- 1211 The Integral Method in S Polarization- 1212 Modal Expansion Methods- 1213 Conical Diffraction- 13 The Dielectric or Metallic Grating- 131 General i ti es- 132 The Diffracted Field Outside the Groove Region- 133 Maxwell Equations and Distributions- 134 The Principle of the Differential Method (in P Polarization)- 14 Miscellaneous- References- Appendix A: The Distributions or Generalized Functions- AI Preliminaries- A2 The Function Space R- A3 The Space R1- A31 Definitions- A32 Examples of Distributions- A4 Derivative of a Distribution- A5 Expansion with Respect to the Basis ej(x) =exp [i (nK+k sine) x] = exp (i?n x)- A51 Theorem- A 52 Proof- A53 Application to deltaR- A6 Convolution- A61 Memoranda on the Product of Convolution in D'1- A62 Convolution in R1- 2 Some Mathematical Aspects of the Grating Theory- 21 Some Classical Properties of the Helmholtz Equation- 22 The Radiation Condition for the Grating Problem- 23 A Lemma- 24 Uniqueness Theorems- 241 Metallic Grating, with Infinite Conductivity- 242 Dielectric Grating- 25 Reciprocity Relations- 26 Foundation of the Yasuura Improved Point-Matching Method- 261 Definition of a Topological Basis- 262 The System of Rayleigh Functions is a Topological Basis- 263 The Convergence of the Rayleigh Series A Counterexample- References- 3 Integral Methods- 31 Development of the Integral Method- 32 Presentation of the Problem and Intuitive Description of an Integral Approach- 321 Presentation of the Problem- 322 Intuitive Description of an Integral Approach- 33 Notations, Mathematical Problem and Fundamental Formulae- 331 Notations and Mathematical Formulation- 332 Basic Formulae of the Integral Approach- 34 The Uncoated Perfectly Conducting Grating- 341 The TE Case of Polarization- 342 The TM Case of Polarization- 35 The Uncoated Dielectric or Metallic Grating- 351 The Mathematical Boundary Problem- 352 Vital Importance of the Choice of a Well-Adapted Unknown Function- 353 Mathematical Definition of the Unknown Function and Determination of the Field and Its Normal Derivative Above P- 354 Expression of the Field in M2 as a Function of ?- 355 Integral Equation- 356 Limit of the Equation when the Metal Becomes Perfectly Conducting- 36 The Multiprofile Grating- 37 The Grating in Conical Diffraction Mounting- 38 Numerical Application- 381 A Fundamental Preliminary Choice- 382 Study of the Kernels- 383 Integration of the Kernels- 384 Particular Difficulty Encountered with Materials of High Conductivity- 385 The Problem of Edges- 386 Precision on the Numerical Results- References- 4 Differential Methods- 41 Introductory Remarks- 411 Historical Survey- 412 Definition of Problem- 42 The E,, Case- 421 The Reflection and Transmission Matrices- 422 The Computation of Transmission and Reflection Matrices- 423 Numerical Algorithms- 424 Al ternative Matching Procedures for Some Grating Profiles- 425 Field of Application- 43 The H Case- 431 The Propagation Equation- 432 Numerical Treatment- 433 Field of Application- 44 The General Case (Conical Diffraction Case)- 441 The Reflection and Transmission Matrices- 442 The Differential System- 443 Matching with Rayleigh Expansions- 444 Field of Application- 45 Stratified Media- 451 Stack of Gratings- 452 Plane Interfaces Between Homogeneous Media- 46 Infinitely Conducting Gratings: the Conformai Mapping Method- 461 Method- 462 Determination of the Conformai Mapping- 463 Field of Application- References- 5 The Homogeneous Problem- 51 Historical Summary- 52 Plasmon Anomalies of a Metallic Grating- 521 Reflection of a Plane Wave on a Plane Interface- 522 Reflection of a Plane Wave on a Grating- 53 Anomalies of Dielectric Coated Reflection Gratings Used in TE Polarization- 531 Determination of the Leaky Modes of a Dielectric Slab Bounded by Metal on One of Its Sides- 532 Reflection of a Plane Wave on a Dielectric Coated Reflection Grating Used in TE Polarization- 54 Extension of the Theory- 541 Anomalies of a Dielectric Coated Grating Used in TM Polarization- 542 Plasmon Anomalies of a Bare Grating Supporting Several Spectral Orders- 543 General Considerations on Anomalies of a Grating Supporting Several Spectral Orders- 55 Theory of the Grating Coupler- 551 Description of the Incident Beam- 552 Response of the Structure to a Plane Wave- 553 Response of the Structure to a Limited Beam- 554 Determination of the Coupling Coefficient- 555 Application to a Limited Incident Beam- References- 6 Experimental Verifications and Applications of the Theory- 61 Experimental Checking of Theoretical Results- 611 Generalities- 612 Microwave Region- 613 On the Determination of Groove Geometry and of the Refractive Index- 614 Infrared- 615 Visible Region- 616 Near and Vacuum UV- 617 XUV Domain- 618 X-Ray Domain- 62 Systematic Study of the Efficiency of Perfectly Conducting Gratings- 621 Systematic Study of Echelette Gratings in -1 Order Littrow Mount- 622 An Equivalence Rule Between Ruled, Holographic, and Lamel1ar Gratings- 623 Systematic Study of the Efficiency of Holographic Gratings in -1 Order Littrow Mount- 624 Systematic Study of the Efficiency of Symmetrical Lamellar Gratings in -1 Order Littrow Mount- 625 Influence of the Apex Angle- 626 Influence of a Departure from Littrow- 627 Higher Order Use of Gratings- 63 Finite Conductivity Gratings- 631 General Rules- 632 Typical Efficiency Curves in the Visible Region- 633 Influence of Dielectric Overcoatings in Vacuum UV- 634 The Use of Gratings in XUV and X-Ray Regions (?<1000 A)- 635 Conical Diffraction Mountings- 64 Some Particular Applications- 641 Simultaneous Blazing in Both Polarizations- 642 Spectrometers with Constant Efficiency- 643 Grating Bandpass Filter- 644 Reflection Grating Polarizer for the Infrared- 645 Transmission Gratings as Masks in Photolithography- 646 Gratings Used as Beam Sampling Mirrors for High Power Lasers- 647 Gratings as Wavelength Selectors in Tunable Lasers- 648 Transmission Dielectric Gratings used as Color Filters- Concluding Remarks- References- 7 Theory of Crossed Gratings- 71 Overview- 72 The Bigrating Equation and Rayleigh Expansions- 73 Inducti ve Gri ds- 731 Grids with Rectangular Apertures- 732 Numerical Tests and Applications- 733 Inductive Grids with Circular Apertures- 74 Capacitive and Other Grid Geometries- 741 High-Pass Filters- 742 Low-Pass Filters- 743 Bandpass Filters- 744 Bandstop Filters- 75 Spatially Separated Grids or Gratings- 751 The Crossed Lamellar Transmission Grating- 752 The Double Grating- 753 Symmetry Properties of Double Gratings- 754 Multielement Grating Interference Filters- 76 Finitely Conducting Bigratings- 761 A Short Description of the Method- 762 The Coordinate Transformation- 763 Integral Equation Form- 764 Iterative Solution of the Integral Equations- 765 Total Absorption of Unpolarized Monochromatic Light- 766 Reduction of Metallic Reflectivity: Plasmons and Moth-Eyes- 767 Equivalence Formulae Linking Crossed and Classical Gratings- 768 Coated Bigratings- References- Additional References with Titles

Linewidth measurement on IC masks and wafers by grating test patterns.

Abstract: Test patterns in the form of diffraction gratings are used for testing and monitoring linewidths on integrated circuit structures. The first and second diffraction orders produed by a laser beam are evaluated to give the width of the grating lines. Measurements on chrome masks show that this technique is accurate to 5% down to linewidths of 0.5 μm. The design of a test set for factory type mask testing is presented. Also, experiments are reported on the testing of patterns on Si wafers directly after. photoresist development and after various etching steps, and an automatic setup for rapid testing of wafers is described.

Bragg diffraction of finite beams by thick gratings

Abstract: The theory of Bragg diffraction of finite beams by thick planar gratings is developed, using coupled-wave theory. Simple analytical expressions for the profiles of the transmitted and diffracted beams in the near field are obtained. Detailed diffraction characteristics for the important case of Gaussian-profile beams are presented. It is shown that the diffraction characteristics depend only on two normalized parameters, the grating strength, and a geometry parameter. The diffraction efficiency and the profiles of the transmitted and diffracted beams are calculated as functions of these two controlling parameters.

Optical demultiplexer using a silicon echelette grating

Abstract: An echelette grating is fabricated on a silicon surface by anisotropic etching. A five channel demultiplexer using this grating for a wavelength-division-multiplexing system is developed in the 0.8-μm wavelength region. The wavelength spacings are 250 A. This system's insertion loss for five channels is 1.4, 1.1, 1.1, 1.1, and 1.2 dB, respectively, and crosstalk levels are <-30 dB.

Holographic method for producing desired wavefront transformations

Abstract: The method utilizes a multi-faceted holographic optical element, the various individual diffraction gratings of each facet collectively functioning to effect a desired wavefront transformation. In this way, a laser beam can be transformed into a specific pattern, permitting unusually shaped objects to be efficiently illuminated with laser light.

Method and apparatus for shaping electromagnetic beams

Abstract: The intensity profile of a beam of electromagnetic waves such as a laser beam is shaped by means of a diffraction grating and/or prism in the beam path. In one embodiment, beams exhibiting Gaussian energy intensity profiles undergo an energy redistribution to approximately uniform profiles. A reflective or transmissive surface relief grating is employed with phase steps generally periodic except at the pattern center where a pattern phase reversal occurs. Prisms are cut and oriented relative to the incoming beam to operate at the Brewster's angle for compressing or expanding the beam with minimum losses.

Diffraction‐grating‐enhanced light emission from tunnel junctions

Abstract: We report the observation of highly polarized, angle‐tunable visible light emission from Al‐AlOx‐Ag tunnel junctions fabricated on holographic gratings. From the angular dependence of the emission frequency we identify the electromagnetic mode responsible for the emission. The mode is surface plasmonlike with a dispersion that closely follows the light line. This is in contrast to the much lower phase velocity ’’junction’’ mode believed responsible for the light emission on surface‐roughened tunnel junctions. We argue that both modes should be considered in describing the emission from these devices.

Inverse scattering method in electromagnetic optics: Application to diffraction gratings

Abstract: We present a theoretical and numerical method for solving problems of inverse scattering in optics given data on the far field, find the scattering object. This method is applied to perfectly conducting diffraction gratings. From the efficiency curve in a Littrow mounting and in the TE case, we derive the shape of the grating surface. Two different cases must be distinguished. The first problem, which we call “reconstruction,” is to compute the profile when the efficiency is experimentally known. In the second one, called “synthesis,” we give a priori an efficiency curve and look for the corresponding grating(s), if it actually exists. We show several theoretical reconstructions for various gratings, and present our first results in the very difficult field of synthesis. The relevance of this method in the domain of electromagnetic optics is then outlined by its application to two other problems.

Broadly tunable picosecond IR source

Abstract: A picosecond traveling-wave parametric device capable of controlled spectral bandwidth and wavelength in the infrared is reported. Intense 1.064 μm picosecond pulses (1) pass through a 4.5 cm long LiNbO 3 optical parametric oscillator crystal (2) set at its degeneracy angle. A broad band emerges, and a simple grating (3) and mirror (4) arrangement is used to inject a selected narrow-band into a 2 cm long LiNbO 3 optical parametric amplifier crystal (5) along a second pump line. Typical input energies at 1.064 μm along both pump lines are 6-8 mJ for the oscillator and 10 mJ for the amplifier. This yields 1 mJ of tunable output in the range 1.98 to 2.38 μm which when down-converted in a 1 cm long CdSe crystal mixer (6) gives 2 μJ of tunable radiation over the 14.8 to 18.5 μm region. The bandwidth and wavelength of both the 2 and 16 μm radiation output are controlled solely by the diffraction grating.

Apparatus for detecting a mutual positional relationship of two sample members

Abstract: An apparatus for detecting a mutual positional relationship of a semiconductor wafer and mask comprises first and second diffraction gratings formed on the wafer and mask and located parallel to each other; a laser source for radiating a coherent light vertically toward the first and second diffraction gratings; a drive mechanism for periodically varying a relative distance between the first and second diffraction gratings; a pair of photosensors for receiving a first interference beam resulting from those +n-order diffracted beams included in said diffracted beams and a second interference beam resulting from those -n-order diffracted beams included in said diffracted beams; and a differential amplifier calculating the difference between the intensities of the first and second interference lights thereby detecting a mutual positional displacement between the first and second diffraction grating.

Coupling device for coupling signals into and out of a transmission glass-fiber

Abstract: PHD. 79-047 ABSTRACT: A device for coupling a first optical signal of a first wavelength into a transmission glass-fibre and for coupling out a second optical signal, which has at least a second wavelength which differs from the first wavelength and which travels in the transmission glass-fibre in a direction opposite to that of the first optical signal, the optical signals to be coupled in and coupled out travelling in spatially separated further glass fibres comprising an imaging device arranged between the transmission glass-fibre and the further glass fibres, in whose pupil a binary optical grating is disposed, further glass fibres receiving the second optical signals which have been diffracted into the diffraction orders of the grating. The grating takes the form of a phase grating and is arranged on an optical axis which it has in common with the imaging device, It has a duty factor of at least substantially 1: 1 as well as an optical path difference of substantially H = (N-1) h = n1 .lambda. I, where nl , 1,2,3,... and in addition substantially complies with the requirement (N-l)h = (m1 + ?) .lambda. k where m1 = 0, 1, 2, ... and k = II, III, ...

Diffraction characteristics of three-dimensional crossed-beam volume gratings

Abstract: The theory of diffraction by gratings formed by the interference of two crossed three-dimensional “arbitrary-profile plane waves” in a photosensitive medium is developed. The detailed diffraction characteristics for the case of crossed-beam gratings formed by two three-dimensional “Gaussian plane waves” are presented. The diffraction efficiencies of these gratings and the profiles of the transmitted and diffracted beams are calculated as functions of the grating strength. The influence of the relative size (the Gaussian beam diameter) of the two writing beams on the diffraction efficiency is determined. Diffraction characteristics for readout with beams of profiles different from those used for writing are presented.

Optical demultiplexer using concave grating in 0.7-0.9 μm wavelength region

Abstract: Experimental results of a demultiplexer using an aberration corrected concave grating for an optical system are described. The demultiplexer has 10 channels and a wavelength spacing of 20 mm from 0.7 to 0.9 μm wavelengths. Insertion losses and crosstalk were less than 2.5 dB and -30 dB, respectively, for all channels.

Interferometric construction of circular gratings

Abstract: Low noise diffraction gratings are constructed with the aid of a circular grating interferometer illuminated with a polychromatic or extended source.

Optical grating multiplexer in the 1.1-1.5 μm wavelength region

Abstract: Experimental results of a multiplexer using a diffraction grating for a wavelength-division-multiplexing transmission system are described. The multiplexer has 10 channels and a wavelength spacing of 36.2 nm in the 1.1-1.5 μm wavelength region. Minimum insertion loss for each channel was less than 2.2 dB.

Optical line width measuring apparatus and method

Abstract: Optical monitoring of the lateral dimensions of a pattern disposed on a substrate in the form of a wafer or mask is accomplished by testing for the lateral dimensions of a diffraction grating test pattern disposed adjacent the pattern. A beam of monochromatic light such as from a laser is diffracted by the test pattern and detectors determine the intensity of the diffracted beams. The detectors are disposed in a plane orthogonal to the plane of the test pattern and to the direction of the grating lines. The detectors are selectively spaced from each other according to the periodicity d of the grating and the width of the grating lines a is determined from a relationship of the detected intensities of the beams.

Analysis of the changes in efficiency across the ruled area of a concave diffraction grating.

Abstract: Measurements and calculations have been made to investigate the effects due to the change in groove orientation on efficiencies of gratings ruled on a spherical surface. Typical efficiency maps across the surface are given for various angles of incidence and wavelengths in the VUV and UV regions. Computations based on electromagnetic theory show a good agreement with the experimental data over the 150-2500-A wavelength range. A simple explanation is given to interpret and predict the shape of efficiency maps obtained from both theory and experiments.

Efficiency and resolution measurements of x-ray transmission gratings between 7.1 and 304 A.

Abstract: Efficiency and resolution measurements are reported of an x-ray transmission grating to be flown on board the European X-ray Observatory Satellite (EXOSAT). By optimizing the thickness of the grating bars, very high efficiencies can be obtained over a limited energy range. An absolute efficiency of 20% at 7.1 A decreasing to 10% above 15 A has been achieved, including all effects of support structure and mounting necessary to withstand space qualification. This means that 10% of the incoming radiation at 7.1 A results in the minus first spectral order and 10% in the plus first order. The measured resolution at the short wavelength end of the range (λ < 20 A) is determined by the mirror resolution; at the longer wavelengths (300 A), the effects of coma and astigmatism dominate. The measured resolution at 304 A for the EXOSAT-mirror-grating system is 4.5 A in agreement with theoretical predictions.

Distributed‐feedback dye laser integrated with a channel waveguide formed on silicon

Abstract: Successful operation of an integrated optical distributed‐feedback (DFB) dye laser in which generated light is confined in a V‐groove optical channel waveguide is reported. Both the channel waveguide and second‐order diffraction grating for DFB operation are formed by anisotropic‐etching the silicon substrate. Polyurethane doped with rhodamine 110 dye is used for the laser waveguide region, while undoped polyurethane is used for channel waveguides. Use of an argon laser for pumping yields continuous output at λ=6430 A characterized by a very low threshold and a spectral width less than 2 A. The output wavelength is consistent with the grating period of 4150 A.

A Closed-Form Analysis of Reflective-Array Gratings

Abstract: A new analysis of oblique-incidence reflective array gratings is presented. Gratings with a constant spatial period and with a linear spatial chirp are considered. lutions are derived for the grating waves that incorporate a1 1 orders of ,nul ti ple reflections and power depletion within the gratings. are obtained using coupling-of-modes theory. solutions shed new light on the operation of such grating devices. In particular they permit a more detailed and exact analysis of the reflective-array compressor (RAC) than was previously possible with complex numerical computer analyses. The implications of the new analysis for RAC design are examined in detail and distortions of the device response, caused by previously ignored effects, are elucidated. For the first time exact soThe solutions These

Diffraction based light collector

Abstract: A light collector is provided for collecting light reflected from an information-bearing surface. In one embodiment, used in a flying spot scanning system, a generally cylindrical rod is placed adjacent the information bearing surface, the rod having photodetectors placed at the ends thereof. The rod is of glass construction with a longitudinally-extending portion thereof fabricated as a variable period diffraction grating. This grating is located proximate to the scanned surface so that incident light reflected from the surface strikes the grating and is coupled into the rod via diffraction. The grating periods are selected in conjunction with the light incidence angles as to optimize the amount of light collected by the photodetectors.

Spectrum measuring device

Abstract: PURPOSE:To obtain a spectrum measuring device having high image resolution with a low cost by securing such constitution in which the wavelength ranges of the spectrum images of the beams incident to a diffraction grating with different incident angles and through plural slits are consecutively formed into an image on a 1-dimensional image pickup element. CONSTITUTION:The beams of a tungsten electric bulb W and a heavy hydrogen lamp D are successively condensed to slits S1-S4 via a condenser lens L and a sample cell 2 through semitransparent mirrors M1-M4, the aperture N of a shutter 5 and filters f1-f4, respectively. The spectrums incident to a concave diffraction grating 6 through the slits S1-S4 and with different incident angles are formed into an image on a 1-dimensional image pickup element 7 so that the spectrum regions are consecutive to each other. The diffracted beams of different numbers of order are deleted through the filters f1-f4. In such a way, a spectrum measuring device having high image resolution can be obtained with a low cost.

Volume holograms for image restoration

Abstract: The angular selectivity of volume diffraction gratings is exploited to form a spatial-frequency filter. The filter is recorded in a thick recording medium as a superposition of several simple gratings or as a single grating with a modulation that varies in depth. Such a device can have controlled angular selectivity so as to alter the relative amplitude and phase of selected spatial-frequency components. A coupled-wave formalism is used to analyze the angular selectivity of this device and experimental results demonstrate its usefulness in improving motion-blurred images.

Optical detecting, monitoring or measuring arrangements

Abstract: According to the present invention there is provided an optical detecting, monitoring or measuring arrangement, comprising a movable diffraction grating arranged for angular displacement by means responsive for example to changes in one or more parameters, such as temperature or pressure, whereby the color of light being reflected to a light-receiving point from said grating changes and said light is then directed onto a fixed diffraction grating so that the direction of a light beam consequentially reflected from said fixed diffraction grating changes with change in color, such change in direction being dependent upon and providing an indication of the change in said parameter or parameters.

Scattering from high efficiency diffraction gratings

Abstract: This paper has characterized and measured scatter from high efficiency and reflective diffraction gratings. Three major types of scatter are identified: (1) random, which occurs over 2π sr; (2) band or ghost scatter, which occurs in the plane of incidence; and (3) structured scatter, which is a symmetrical pattern repeated about each order. Measurements were taken at 10.6 μm on gratings made by ruling, ion etching, holography, or a combination of these techniques. We found that the characteristic scatter from these high efficiency gratings depends strongly on the way the gratings are fabricated.

Improved holography for chirped gratings.

Abstract: Sources of high propagation loss in holographic gratings on planar waveguides have been identified by viewing the gratings as holograms of the optical exposure apparatus. In order to simplify the optical system and increase the large-area uniformity of the beams, collimating lenses were eliminated and the gratings were formed by interference of spherical wave fronts. In order to define the grating shape without causing mask diffraction patterns, the desired grating region was outlined by negative photoresist over the surface of the exposed and developed grating pattern.

Rectangular-profile diffraction grating from single-crystal silicon.

Abstract: Diffraction gratings having well-shaped rectangular profiles were fabricated by chemical etching of single-crystal silicon oriented in the 〈110〉 direction. The grooves were 2.62 μm deep, 5.4 μm wide, and were separated by 10.2 μm. The diffraction behavior was measured near normal incidence using several laser wavelengths. The specularly reflected (zero-order) beam varied by a factor of at least 140 at different visible wavelengths, thereby demonstrating the excellent geometric form of the structures.

Sound carrier amplitude measurement system

Abstract: Apparatus provides an incident light beam which illuminates the surface of a grooved disc, having signal elements recorded therein in the form of a succession of spaced apart depressions, with a light spot that spans a plurality of convolutions of the groove. The structure of the groove convolutions and signal elements forms a two-dimensional diffraction grating which reflects light into a plurality of diffraction order beams. Photodetectors, respectively positioned to intercept several of the reflected beams provide outputs corresponding to the light power in the respective reflected beams. Estimations of signal element depth in the region illuminated by the light spot may be made from the measured light powers.