Ebook Topic:
Front Matter
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This section contains the preface, the table of contents, and the glossary of symbols.

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

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Introduction to the Series

Welcome 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 Series

Keep 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 Optics

Recent 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 Contents

Glossary 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 Acronyms

ASMA

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

f0D

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

i

unit vector codirectional with x axis

I(r)

radial intensity distribution

IR

infrared

j

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

k

unit vector codirectional with z axis

k(x, y)

wave vector of the propagating wavefront

k0

wavenumber

L

observation distance

LTm

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

n

effective index for the electric field E

n

effective index for the electric field E

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

q

vector orthogonal to the grating plane of symmetry at the point of intersection

Q

grating “thickness” parameter

r

vector normal to the grating surface at the incoming ray intersection point

r12

vector connecting points in two lateral planes

R0

substrate radius of curvature

S

propagation direction vector before diffractive surface

S'

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

z

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

θmL

mth order diffraction angle in Littrow mount

θmλl

mth order diffraction angle of the wavelength λl

θmλs

mth order diffraction angle of the wavelength λs

θφ

incidence angle with respect to the grating facet

λ

wavelength of light

λb

blazing wavelength

λbL

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

ΦeffSDS

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

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