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Library of Congress Cataloging-in-Publication Data Soskind, Yakov. Field guide to Diffractive Optics / Yakov Soskind. p. cm. -- (The field guide series ; 21) Includes bibliographical references and index. ISBN 978-0-8194-8690-5 1. Diffraction. 2. Optics. I. Title. QC415.S67 2011 535'.42–dc23 2011018209 Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1.360.676.3290 Fax: +1.360.647.1445 Email: books@spie.org Web: http://spie.org The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America. First printing
Introduction to the SeriesWelcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org. John E. Greivenkamp, Series Editor Optical Sciences Center The University of Arizona The Field Guide SeriesKeep information at your fingertips with all of the titles in the Field Guide Series: Field Guide to Adaptive Optics, Tyson & Frazier Atmospheric Optics, Andrews Binoculars and Scopes, Yoder, Jr. & Vukobratovich Diffractive Optics, Soskind Geometrical Optics, Greivenkamp Illumination, Arecchi, Messadi, & Koshel Infrared Systems, Detectors, and FPAs, Second Edition, Daniels Interferometric Optical Testing, Goodwin & Wyant Laser Fiber Technology, Paschotta Laser Pulse Generation, Paschotta Lasers, Paschotta Microscopy, Tkaczyk Optical Fabrication, Williamson Optical Lithography, Mack Optical Thin Films, Willey Polarization, Collett Special Functions for Engineers, Andrews Spectroscopy, Ball Visual and Ophthalmic Optics, Schwiegerling Field Guide to Diffractive OpticsRecent advancements in microfabrication technologies as well as the development of powerful simulation tools have led to a significant expansion of diffractive optics and the commercial availability of cost-effective diffractive optical components. Instrument developers can choose from a broad range of diffractive optical elements to complement refractive and reflective components in achieving a desired control of the optical field. Material required for understanding the diffractive phenomenon is widely dispersed throughout numerous literature sources. This Field Guide offers scientists and engineers a comprehensive reference in the field of diffractive optics. College students and photonics enthusiasts will broaden their knowledge and understanding of diffractive optics phenomena. The primary objectives of this Field Guide are to familiarize the reader with operational principles and established terminology in the field of diffractive optics, as well as to provide a comprehensive overview of the main types of diffractive optics components. An emphasis is placed on the qualitative explanation of the diffraction phenomenon by the use of field distributions and graphs, providing the basis for understanding the fundamental relations and the important trends. I would like to thank SPIE Press Manager Timothy Lamkins and Series Editor John Greivenkamp for the opportunity to write a Field Guide for one of the most fundamental physical optics phenomena, as well as SPIE Press Senior Editor Dara Burrows for her help. My endless gratitude goes to my family: to my wife Eleanora, who had to bear additional duties during my work on this book, as well as to my children, Rose and Michael, who learned the material while helping with proofreading the manuscript. Yakov G. Soskind August 2011 Table of ContentsGlossary of Symbols xi Diffraction Fundamentals 1 The Diffraction Phenomenon 1 Scalar Diffraction 2 Paraxial Approximation 3 Fresnel Diffraction 4 Fresnel Diffraction 4 Apertures with Integer Number of Fresnel Zones 5 Fresnel Zone Plates 6 Fresnel Zone Plate Properties 7 Fresnel Phase Plates 8 Comparing Fresnel Plates and Ideal Lenses 9 Efficiency of Fresnel Plates and Ideal Lenses 10 Talbot Effect 11 Fractional Talbot Distributions 12 Fraunhofer Diffraction 13 Fraunhofer Diffraction 13 Diffraction of Waves with Finite Sizes 14 Diffraction on Ring-Shaped Apertures 15 Energy Redistribution within Diffraction Rings 16 Diffraction on Noncircular Apertures 17 Rectangular and Diamond-Shaped Apertures 18 Apodized Apertures 19 Apodized Apertures 19 Apodized Apertures with Central Obscuration 20 Field Obstruction by an Opaque Semiplane 21 Apodization with Serrated Edges 22 Serrated Apertures as Apodizers 23 Diffraction by Multiple Apertures 24 Diffraction by Multiple Apertures 24 Effects of Aperture Spacing 25 Aperture Fill Factor 26 Aperiodically Spaced Apertures 27 Resolution Limit in Optical Instruments 28 Resolution Limit in Optical Instruments 28 Superresolution Phenomenon 29 Superresolution with Two-Zone Phase Masks 30 Point Spread Function Engineering 31 Adjusting Diffraction-Ring Intensity 32 Amplitude and Phase Filter Comparison 33 Vortex Phase Masks 34 Combining Amplitude and Vortex Phase Masks 35 Diffractive Components 36 Diffraction Gratings 36 Volume Bragg Gratings 37 Polarization Dependency of Volume Bragg Gratings 38 One-Dimensional Surface-Relief Gratings 39 GRISM Elements 40 Two-Dimensional Diffractive Structures 41 Holographic Diffusers 42 Multispot Beam Generators 43 Design of Fan-Out Elements 44 Diffractive Beam-Shaping Components 45 Digital Diffractive Optics 46 Three-Dimensional Diffractive Structures 47 Grating Properties 48 Grating Equation 48 Grating Properties 49 Free Spectral Range and Resolution 50 Grating Anomalies 51 Polarization Dependency of Grating Anomalies 52 Gratings as Angular Switches 53 Gratings as Optical Filters 54 Gratings as Polarizing Components 55 Blazing Condition 56 Blazing Condition 56 Blazed Angle Calculation 57 Optimum Blazed Profile Height 58 Scalar Diffraction Theory of a Grating 60 Scalar Diffraction Theory of a Grating 60 Diffraction Efficiency 61 Blaze Profile Approximation 62 Extended Scalar Diffraction Theory 63 Extended Scalar Diffraction Theory 63 Duty Cycle and Ghost Orders 64 Extended Scalar versus Rigorous Analysis 65 Gratings with Subwavelength Structures 66 Gratings with Subwavelength Structures 66 Blazed Binary Gratings 67 Relative Feature Size in the Resonant Domain 68 Effective Medium Theory 69 Scalar Diffraction Limitations and Rigorous Theory 70 Rigorous Analysis of Transmission Gratings 71 Analysis of Blazed Transmission Gratings 71 Polarization Dependency and Peak Efficiencies 72 Peak Efficiency of Blazed Profiles 73 Wavelength Dependency of Efficiency 74 Efficiency Changes with Incident Angle 75 Diffraction Efficiency for Small Feature Sizes 76 Polychromatic Diffraction Efficiency 77 Polychromatic Diffraction Efficiency 77 Monolithic Grating Doublet 78 Spaced Grating Doublet 79 Monolithic Grating Doublet with Two Profiles 80 Diffractive and Refractive Doublets: Comparison 81 Efficiency of Spaced Grating Doublets 82 Efficiency of Spaced Grating Doublets 82 Sensitivity to Fabrication Errors 83 Facet Width and Polarization Dependency 84 Sensitivity to Axial Components Spacing 85 Frequency Comb Formation 86 Diffractive Components with Axial Symmetry 87 Diffractive Components with Axial Symmetry 87 Diffractive Lens Surfaces 88 Diffractive Kinoforms 89 Binary Diffractive Lenses 90 Optical Power of a Diffractive Lens Surface 91 Diffractive Surfaces as Phase Elements 92 Stepped Diffractive Surfaces 93 Properties of Stepped Diffractive Surfaces 94 Multi-order Diffractive Lenses 95 Diffractive Lens Doublets 96 Diffractive Surfaces in Optical Systems 97 Diffractive Lens Surfaces in Optical Systems 97 Achromatic Hybrid Structures 98 Opto-thermal Properties of Optical Components 99 Athermalization with Diffractive Components 100 Athermalization with SDSs 101 Appendix: Diffractive Raytrace 102 Equation Summary 105 Bibliography 111 Index 114 Glossary of Symbols and AcronymsASMA aperiodically spaced multiple apertures B base length of a PRISM CR incident wave obliquity factor CS diffracted wave obliquity factor CGH computer-generated hologram d diameter of central obscuration dB Bragg plane spacing dg grating period or groove spacing di step width of ith zone D aperture diameter or lateral size DA Airy disk diameter Dn material dispersion D0 lens clear aperture diameter DC duty cycle DDO digital diffractive optics DLS diffractive lens surface e aperture obscuration E(ρ, φ) complex electric field in polar coordinates E⊥ electric field normal to the grating grooves E∥ electric field parallel to the grating grooves f focal length of a lens nominal focal length of a diffractive surface FDTD finite difference time domain FWHM full width at half maximum FPP Fresnel phase plate FZP Fresnel zone plate h grating profile depth or height hi step height of ith zone hm profile height of a multi-order diffractive lens hopt optimum grating profile depth (height) hSDS step height of SDS HOE holographic optical element unit vector codirectional with x axis I(r) radial intensity distribution IR infrared unit vector codirectional with y axis J0(ρ) Bessel function of the first kind of the zero order J1(ρ) Bessel function of the first kind of the first order unit vector codirectional with z axis k(x, y) wave vector of the propagating wavefront k0 wavenumber L observation distance Talbot distance of order m LED light-emitting diode m diffraction order n refractive index of optical material n1 refractive index before optical interface n2 refractive index after optical interface nd refractive index of diffraction grating layer np refractive index of prism material effective index for the electric field effective index for the electric field N number of binary levels NF Fresnel zone number Ng number of grating (groove) facets Nk number of kinoform zones OPD optical path difference PSF point spread function vector orthogonal to the grating plane of symmetry at the point of intersection Q grating “thickness” parameter vector normal to the grating surface at the incoming ray intersection point vector connecting points in two lateral planes R0 substrate radius of curvature propagation direction vector before diffractive surface propagation direction vector after diffractive surface SDS stepped diffractive surface SPDT single point diamond turning t axial spacing of a grating doublet T effective thickness of volume phase grating tb thickness of a binary lens level Tg geometrical transmission pattern of a facet TE transverse electric TM transverse magnetic U(x, y, z) complex field amplitude UV ultraviolet VBG volume Bragg grating VLSI very large-scale integration W(x, y) propagating wavefront Wg grating width vector normal to the two reference planes α coefficient of thermal expansion αB angle of the incident light after refraction into the volume phase medium αd deflection angle β diffracted angle inside the volume phase medium γ angle between the Bragg planes and the incident light δ minimum feature size of the diffractive component ε grating minor (secondary) facet angle ζ fill factor of radiation η normalized diffraction efficiency ηm diffraction efficiency in mth diffraction order ηM diffraction efficiency of a grating with M facets ηP diffraction efficiency of P-polarized light ηS diffraction efficiency of S-polarized light θd diffraction angle θi angle of incidence θm mth order diffraction angle
mth order diffraction angle in Littrow mount mth order diffraction angle of the wavelength λl mth order diffraction angle of the wavelength λs θφ incidence angle with respect to the grating facet λ wavelength of light λb blazing wavelength
blazing wavelength in Littrow configuration (mount) λs the shortest wavelength within the spectral range λl the longest wavelength within the spectral range λ0 design wavelength ξ opto-thermal coefficient of a surface ρ radial coordinate υ volume phase grating parameter φ grating primary facet angle φb grating facet blaze angle φi facet angle of ith kinoform zone φp grating passive facet angle φmax maximum value of facet blazed angle ϕ optical path difference ΦAH optical power of an achromatic hybrid ΦD optical power of a diffractive surface or lens ΦH optical power of a hybrid surface or lens ΦR optical power of a refractive surface or lens ΦSDS optical power of SDS
effective optical power of SDS ψ(r) radial phase profile of a diffractive surface ψ(x, y) phase profile of a diffractive surface Δfchr axial or longitudinal chromatic aberration ΔHchr lateral or transverse chromatic aberration Δλ spectral bandwidth ΔλFSR free spectral range of a grating Δn refractive index modulation Λ grating parameter |
CITATIONS
Diffraction
Diffraction gratings
Geometrical optics
Energy efficiency
Adaptive optics
Atmospheric optics
Visual optics
