ELECTRO-OPTICS
`HANDBOOK
`
`Ronald W. Waynant Editor
`
`Marwood N. Ediger Editor
`Food and Drug Administration
`Rockville, Maryland
`
`Second Edition
`
`McGRAW-HILL, INC.
`New York San Francisco Washington, D.C. Auckland Bogota´
`Caracas Lisbon London Madrid Mexico City Milan
`Montreal New Delhi San Juan Singapore
`Sydney Tokyo Toronto
`
`ASML 1122
`
`

`
`Library of Congress Cataloging-in-Publication Data
`
`Electro-optics handbook / Ronald W. Waynant, editor, Marwood N. Ediger, editor.—2nd ed.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 0-07-068716-1 (hc)
`1. Electrooptical devices—Handbooks, manuals, etc.
`II. Ediger, Marwood N., date.
`TA1750.E44
`2000
`621.36—dc21
`
`I. Waynant, Ronald W.
`
`99-044081
`
`Copyright 䉷 2000 by The McGraw-Hill Companies, Inc. All rights reserved.
`Printed in the United States of America. Except as permitted under the United
`States Copyright Act of 1976, no part of this publication may be reproduced
`or distributed in any form or by any means, or stored in a data base or
`retrieval system, without the prior written permission of the publisher.
`
`1 2 3 4 5 6 7 8 9 0 DOC / DOC 0 5 4 3 2 1 0
`
`ISBN 0-07-068716-1
`
`The sponsoring editor for this book was Stephen S. Chapman and the
`production supervisor was Sherri Souffrance. It was set in Times Roman
`by Pro-Image Corporation.
`
`Printed and bound by R. R. Donnelley & Sons Company.
`
`McGraw-Hill books are available at special quantity discounts to use as
`premiums and sales promotions, or for use in corporate training programs.
`For more information, please write to the Director of Special Sales,
`Professional Publishing, McGraw-Hill, Two Penn Plaza, New York, NY
`10121-2298. Or contact your local bookstore.
`
`Information contained in this work has been obtained by The
`McGraw-Hill Companies, Inc. (McGraw-Hill) from sources be-
`lieved to be reliable. However, neither McGraw-Hill nor its au-
`thors guarantee the accuracy or completeness of any information
`published herein, and neither McGraw-Hill nor its authors shall
`be responsible for any errors, omissions, or damages arising out
`of use of this information. This work is published with the un-
`derstanding that McGraw-Hill and its authors are supplying in-
`formation but are not attempting to render engineering or other
`professional services. If such services are required, the assistance
`of an appropriate professional should be sought.
`
`

`
`CONTENTS
`
`xv
`Contributors
`Preface to Second Edition
`Preface to First Edition
`Acronyms
`xxi
`
`xvii
`
`xix
`
`Chapter 1. Introduction to Electro-Optics Ronald W. Waynant and
`Marwood N. Ediger
`
`1.1 Introduction / 1.1
`1.2 Types of Light Sources / 1.1
`1.3 Materials / 1.4
`1.4 Detectors / 1.5
`1.5 Current Applications / 1.6
`1.6 References / 1.7
`
`Chapter 2. Noncoherent Sources Sharon Miller
`
`2.1 Introduction / 2.1
`2.2 Definition of Terms / 2.1
`2.3 Characteristics / 2.6
`2.4 Measurements and Calibration / 2.10
`2.5 Sources of Noncoherent Optical Radiation / 2.21
`2.6 References / 2.35
`
`Chapter 3. Ultraviolet, Vacuum-Ultraviolet, and X-Ray Lasers
`Roland Sauerbrey
`
`3.1 Lasers in the Electromagnetic Spectrum / 3.1
`3.2 Principles of Short-Wavelength Laser Operation / 3.4
`3.3 Ultraviolet and Vacuum Ultraviolet Lasers / 3.11
`3.4 X-Ray Lasers and Gamma-Ray Lasers / 3.36
`3.5 References / 3.43
`
`1.1
`
`2.1
`
`3.1
`
`vii
`
`

`
`viii
`
`CONTENTS
`
`Chapter 4. Visible Lasers William T. Silfvast
`
`4.1
`
`4.1 Introduction / 4.1
`4.2 Visible Lasers in Gaseous Media / 4.2
`4.3 Visible Lasers In Liquid Media—Organic Dye Lasers / 4.14
`4.4 Visible Lasers in Solid Materials / 4.18
`4.5 References / 4.21
`
`Chapter 5. Solid-State Lasers Georg F. Albrecht and Stephen A. Payne
`
`5.1
`
`5.1 Introduction / 5.1
`5.2 Solid-State Laser Devices / 5.2
`5.3 Solid-State Laser Materials / 5.34
`5.4 Future Directions / 5.56
`5.5 References / 5.57
`
`Chapter 6. Semiconductor Lasers James J. Coleman
`
`6.1
`
`6.1 Compound Semiconductors and Alloys / 6.1
`6.2 Energy Band Structure / 6.3
`6.3 Heterostructures / 6.6
`6.4 Double Heterostructure Laser / 6.7
`6.5 Stripe Geometry Lasers / 6.10
`6.6 Index-Guided Stripe Geometry Lasers / 6.12
`6.7 Materials Growth / 6.13
`6.8 Quantum Well Heterostructure Lasers / 6.14
`6.9 Vertical Cavity Surface Emitting Lasers / 6.17
`6.10 Laser Arrays / 6.18
`6.11 Modulation of Laser Diodes / 6.21
`6.12 Reliability / 6.23
`6.13 References / 6.25
`
`Chapter 7. Infrared Gas Lasers Michael Ivanco and Paul A. Rochefort
`
`7.1
`
`7.1 Introduction / 7.1
`7.2 Gas Laser Theory / 7.1
`7.3 Specific Gas Lasers / 7.12
`7.4 Conclusions / 7.30
`7.5 References / 7.30
`
`Chapter 8. Free-Electron Lasers John A. Pasour
`
`8.1
`
`8.1 Introduction / 8.1
`8.2 FEL Theory / 8.3
`8.3 FEL Components / 8.8
`8.4 FEL Devices / 8.14
`8.5 Future Directions / 8.17
`8.6 Conclusions / 8.20
`8.7 References / 8.20
`
`

`
`Chapter 9. Ultrashort Optical Pulses: Sources and Techniques Li Yan,
`P.-T. Ho, and Chi. H. Lee
`
`9.1
`
`CONTENTS
`
`ix
`
`9.1 Principles of Ultrashort Pulse Generation / 9.1
`9.2 Methods of Generation / 9.5
`9.3 Ultrashort Pulse Laser Systems / 9.18
`9.4 Methods of Pulse Width Measurements / 9.26
`9.5 Conclusions / 9.31
`9.6 References / 9.32
`
`Chapter 10. Optical Materials—UV, VUV Jack C. Rife
`
`10.1
`
`10.1 Fundamental Physical Properties / 10.3
`10.2 Transmissive UV Optics / 10.7
`10.3 Reflective UV Optics / 10.16
`10.4 Damage and Durability / 10.26
`10.5 Fabrication / 10.31
`10.6 References / 10.37
`
`Chapter 11. Optical Materials: Visible and Infrared W. J. Tropf, T. J. Harris,
`and M. E. Thomas
`
`11.1
`
`11.1 Introduction / 11.1
`11.2 Types of Materials / 11.1
`11.3 Applications / 11.2
`11.4 Material Properties / 11.5
`11.5 Property Data Tables / 11.9
`11.6 References / 11.71
`
`Chapter 12. Optical Fibers Carlton M. Truesdale
`
`12.1
`
`12.1 Theory of Fiber Transmission / 12.1
`12.2 Materials for the Fabrication of Optical Fiber / 12.10
`12.3 Fabrication Methods / 12.12
`12.4 Fiber Losses / 12.16
`12.5 Pulse Broadening / 12.19
`12.6 References / 12.26
`
`Chapter 13. Nonlinear Optics Gary L. Wood and Edward J. Sharp
`
`13.1
`
`13.1 Introduction / 13.1
`13.2 Linear Optics: The Harmonic Potential Well / 13.1
`13.3 Nonlinear Optics: The Anharmonic Potential Well / 13.4
`13.4 Second-Order Nonlinearities: ␹ / 13.7
`13.5 The Third-Order Susceptibilities: ␹ / 13.9
`13.6 Propagation Through Nonlinear Materials / 13.12
`13.7 Acknowledgments / 13.27
`13.8 References / 13.27
`
`

`
`x
`
`CONTENTS
`
`Chapter 14. Phase Conjugation Gary L. Wood
`
`14.1
`
`14.1 Phase Conjugation: What It Is / 14.1
`14.2 Phase Conjugation: How to Generate It / 14.5
`14.3 Applications / 14.30
`14.4 References / 14.34
`
`Chapter 15. Ultraviolet and X-Ray Detectors George R. Carruthers
`
`15.1
`
`15.1 Overview of Ultraviolet and X-Ray Detection Principles / 15.1
`15.2 Photographic Film / 15.1
`15.3 Nonimaging Photoionization Detectors / 15.2
`15.4 Imaging Proportional Counters / 15.7
`15.5 Photoemissive Detectors / 15.9
`15.6 Solid-State Detectors / 15.27
`15.7 Scintillation Detectors / 15.34
`15.8 References / 15.35
`
`Chapter 16. Visible Detectors Suzanne C. Stotlar
`
`16.1
`
`16.1 Introduction / 16.1
`16.2 The Human Eye as a Detector / 16.3
`16.3 Photographic Film / 16.6
`16.4 Photoelectric Detectors / 16.6
`16.5 Thermal Detectors / 16.15
`16.6 Other Detectors / 16.19
`16.7 Detection Systems and Selection Guide / 16.19
`16.8 References and Further Reading / 16.21
`
`Chapter 17. Infrared Detectors Suzanne C. Stotlar
`
`17.1
`
`17.1 Introduction / 17.1
`17.2 Photographic Film / 17.1
`17.3 Photoelectric Detectors / 17.2
`17.4 Thermal Detectors / 17.13
`17.5 Other Detectors / 17.21
`17.6 Detection Systems and Selection Guide / 17.21
`17.7 References and Further Reading / 17.23
`
`Chapter 18. Imaging Detectors Frederick A. Rosell
`
`18.1
`
`18.1 Introduction / 18.1
`18.2 Photosurfaces / 18.2
`18.3 Imaging Tubes / 18.5
`18.4 Solid-State Imaging Devices / 18.10
`18.5 Imaging System Performance Model / 18.13
`18.6 Modulation Transfer Functions / 18.19
`18.7 Applications / 18.22
`18.8 References / 18.23
`
`

`
`Chapter 19. Holography Tung H. Jeong
`
`19.1 Introduction / 19.1
`19.2 Theory of Holographic Imaging / 19.1
`19.3 Volume Holograms—A Graphic Model / 19.6
`19.4 Material Requirements / 19.9
`19.5 General Procedures / 19.12
`19.6 Current Applications / 19.13
`19.7 References / 19.15
`
`CONTENTS
`
`xi
`
`19.1
`
`Chapter 20. Laser Spectroscopy and Photochemistry G. Rodriguez,
`S. B. Kim, and J. G. Eden
`
`20.1
`
`20.1 Introduction / 20.1
`20.2 Laser-Induced Fluorescence and Absorption Spectroscopy / 20.3
`20.3 Photoionization and Photoelectron Spectroscopy / 20.12
`20.4 Multiphoton Spectroscopy / 20.21
`20.5 Nonlinear Laser Spectroscopy / 20.24
`20.6 Photochemistry / 20.39
`20.7 Concluding Comments / 20.45
`20.8 Acknowledgments / 20.46
`20.9 References / 20.46
`
`Chapter 21. Fiber-Optic Sensors Charles M. Davis and Clarence J. Zarobila
`
`21.1
`
`21.1 Introduction / 21.1
`21.2 Fiber-Optic Sensor Transduction / 21.1
`21.3 Fiber-Optic Sensor Components / 21.9
`21.4 Temperature Sensors / 21.13
`21.5 Static and Dynamic Pressure Sensors / 21.15
`21.6 Accelerometers / 21.19
`21.7 Rate-of-Rotation Sensors / 21.21
`21.8 Magnetic / Electric Field Sensors / 21.22
`21.9 References / 21.25
`
`Chapter 22. High-Resolution Lithography for Optoelectronics
`Martin Peckerar, P.-T. Ho, and Y. J. Chen
`
`22.1
`
`22.1 Introduction / 22.1
`22.2 Fundamentals of Lithography / 22.2
`22.3 Lithographic Techniques Useful In Optoelectronic Device Fabrication / 22.6
`22.4 Examples / 22.22
`22.5 Concluding Remarks / 22.33
`22.6 Acknowledgments / 22.34
`22.7 References / 22.34
`
`

`
`xii
`
`CONTENTS
`
`Chapter 23. Laser Safety in the Research and Development Environment
`David H. Sliney
`
`23.1
`
`23.1 Introduction / 23.1
`23.2 Biological Effects / 23.2
`23.3 Safety Standards / 23.4
`23.4 Risk of Exposure / 23.4
`23.5 Laser Hazard Classification / 23.7
`23.6 Laser Hazard Assessment / 23.12
`23.7 Laser System Safety / 23.13
`23.8 The Safe Industrial Laser Laboratory / 23.14
`23.9 Laser Eye Protection / 23.16
`23.10 Laser Accidents / 23.23
`23.11 Electrical Hazards / 23.24
`23.12 Visitors and Observers / 23.24
`23.13 Delayed Effects and Future Considerations / 23.24
`23.14 Conclusions and General Guidelines / 23.25
`23.15 References / 23.26
`
`Chapter 24. Lasers in Medicine Ashley J. Welch and M. J. C. van Gemert
`
`24.1
`
`24.1 Introduction / 24.1
`24.2 Optical-Thermal Interactions / 24.3
`24.3 Medial Applications / 24.17
`24.4 Ablation / 24.23
`24.5 Photochemical Interactions / 24.26
`24.6 Photoacoustic Mechanisms / 24.27
`24.7 Future Directions / 24.28
`24.8 References / 24.29
`
`Chapter 25. Material Processing Applications of Lasers James T. Luxon
`
`25.1
`
`25.1 Material Processing Lasers / 25.1
`25.2 Laser Characteristics For Material Processing: Advantages and
`Disadvantages / 25.4
`25.3 Laser Surface Modification / 25.6
`25.4 Welding / 25.8
`25.5 Cutting and Drilling / 25.11
`25.6 Marking / 25.12
`25.7 Microelectronics Applications / 25.13
`25.8 Bibliography / 25.14
`
`Chapter 26. Optical Integrated Circuits Hiroshi Nishihara,
`Masamitsu Haruna, and Toshiaki Suhara
`
`26.1
`
`26.1 Features of Optical Integrated Circuits / 26.1
`26.2 Waveguide Theory, Design, and Fabrication / 26.1
`26.3 Grating Components For Optical Integrated Circuits / 26.9
`26.4 Passive Waveguide Devices / 26.17
`26.5 Functional Waveguide Devices / 26.24
`26.6 Examples of Optical Integrated Circuits / 26.31
`26.7 References / 26.35
`
`

`
`Chapter 27. Optoelectronic Integrated Circuits Osamu Wada
`
`27.1
`
`CONTENTS
`
`xiii
`
`27.1 Introduction / 27.1
`27.2 Categories and Features / 27.1
`27.3 Materials, Basic Devices and Integration Techniques / 27.3
`27.4 Optoelectronic Integrated Circuits / 27.15
`27.5 System Applications / 27.27
`27.6 Summary / 27.33
`27.7 References / 27.33
`
`Chapter 28. Optical Amplifiers Beth A. Koelbl
`
`28.1
`
`28.1 Introduction / 28.1
`28.2 Optical Fiber Amplifiers / 28.1
`28.3 Semiconductor Optical Amplifiers / 28.7
`28.4 Planar Waveguide Amplifiers / 28.8
`28.5 Performance Parameters / 28.8
`28.6 Applications / 28.14
`28.7 Conclusions / 28.15
`28.8 References / 28.15
`
`Chapter 29. High-Speed Semiconductor Lasers and Photodetectors
`Thomas Liljeberg and John E. Bowers
`
`29.1
`
`29.1 High-Speed Lasers / 29.1
`29.2 High-Speed Laser Structures / 29.4
`29.3 High-Speed Photodetectors / 29.7
`29.4 Summary / 29.12
`29.5 References / 29.13
`
`Index follows Section 29
`
`

`
`CHAPTER 10
`OPTICAL MATERIALS—UV, VUV
`
`Jack C. Rife
`
`This chapter discusses properties and selection of ultraviolet (uv) window, mirror, and coating
`materials. The uv range of the electromagnetic spectrum extends from energies (wavelengths)
`of about 3 eV (400 nm) just outside the visible to a vague boundary near 6000 eV (0.2 nm),
`the start of the x-ray range. This chapter primarily discusses spectral ranges in terms of
`energy. An energy scale better serves spectroscopy, since prominent spectral features across
`the whole range have the imprint of a relatively narrow range of unoccupied final electronic
`states. A wavelength scale will be used at times, however, to emphasize the longer wave-
`lengths and provide a useful gauge for thin film dimensions. A useful conversion factor is
`that the wavelength ␭ in nm is given by ␭ ⫽ 1239.8/E , where E is the energy in eV.
`The uv and x-ray ranges of the electromagnetic spectrum divide into subregions that are
`overlapping and whose boundaries are not commonly agreed on. Figure 10.1 shows the
`approximate ranges of the various named regimes and physical phenomena that determine
`experimental ranges. The near uv extends from just outside the visible at 3 eV to the begin-
`ning of the vacuum uv at 6.7 eV, where air is no longer transparent and vacuum is required.
`This is the region where radiation begins to be energetic enough to be ionizing. The vacuum
`uv extends to the beginning of the x-ray region proper at 2000 to 6000 eV where He and
`other gases become sufficiently transparent. This is also where Be windows are transparent
`and thick enough to support one atmosphere of differential pressure. Other regions include
`the extreme ultraviolet or xuv (sometimes termed euv) that extends from the approximately
`11.9 eV cutoff of the largest bandgap window, LiF, to the x-ray region. The grazing incidence
`region begins at 30 eV where instruments must be designed with grazing incidence optics
`(excluding diffraction spectrometers using multilayers and crystals). Here the normal inci-
`dence reflectance of homogeneous mirror materials falls off approximately as 1/E4. The soft
`x-ray region normally starts at the grazing incidence boundary at 30 eV and extends to 6000
`eV. An additional subregion receiving particular attention now for in vivo soft x-ray mi-
`croscopy is the water window from the carbon K edge at 285 eV to the oxygen K edge at
`540 eV, where water is transparent relative to the absorption in organic materials. This
`chapter emphasizes the spectral region from 3 to 40 eV, which is more likely to be of interest
`for electro-optics. XUV and soft x-ray materials are covered as well, however, in recognition
`of the potential of free electron lasers, laser-driven xuv lasers, and multilayer optics in that
`region.
`Much of the information in this chapter remains unchanged from the 1991 edition, but
`new references to work up to 1998 have been added throughout. UV optical materials are
`fairly standardized with evolutionary improvements coming primarily from reduced impu-
`rities and defects and new developments from microstructuring and new fabrication capa-
`bilities. Optical constants of the elements are well known and the band structure and the
`
`10.1
`
`

`
`10.2
`
`CHAPTER TEN
`
`FIGURE 10.1 Ultraviolet regimes.
`
`thermophysical properties of the elements and most crystalline compounds as well. Surface
`and interfacial properties are generally understood. New uv materials such as fluorides, poly-
`mers, and self-assembled films present unique capabilities and are being rapidly explored.
`Most of the new materials and properties, however, are based on microstructuring. Nano-
`crystalline materials, composite metals, combinations of organic and inorganic materials,
`anti- and high-reflective multilayer coatings, graded index of refraction materials and Bragg
`fiber gratings, and photonic band gap materials offer new optical performance. Some of these
`have been applied extensively in the infrared and visible but have yet to make a large impact
`in the uv.
`The major driving forces for the development of new uv optical materials are the demands
`for higher spatial resolution images, toleration of heat load, damage resistance, and reduced
`cost. Large resources are being applied to maintain the march of integrated circuit lithography
`to smaller submicron linewidths via shorter uv wavelengths to decrease diffraction limited
`image size. In the near uv, transmission optics are being developed successively for the KrF,
`ArF, and F2 excimer wavelengths of 248, 193, and 157 nm, respectively, with little prospect
`of moving to shorter wavelengths because of the lack of transmissive materials. Projection
`lithography at 13 nm pushes to much shorter wavelengths with highly reflective xuv multi-
`layer optics that will have to have beyond state-of-the-art 0.25 nm asphere figure accuracy
`and 0.2 nm surface roughness. The third generation of synchrotron radiation sources requires
`the initial beamline mirror to maintain arcsecond figure accuracy under continuous, nonuni-
`form heat loads of up to 100 W over square millimeters of mirror surface. Applications of
`excimer lasers, free-electron lasers, harmonics of various solid state lasers and, in particular,
`tabletop terrawatt femtosecond lasers and the National Ignition Facility must deal with ra-
`diation damage problems of high fluence and/or high instantaneous uv power. Finally, cost
`is a large driving factor in the development of the replication of expensive aspherical uv
`optics and adaptive optics for synchrotron mirrors and large telescopes.
`Developments in uv optics appear in a variety of conference proceedings; but the national
`and international conferences on Synchrotron Radiation Instrumentation, the Boulder Laser
`Induced Damage in Optical Materials symposia, and many SPIE (International Society for
`Optical Engineering) meetings, in particular, are sources of the latest work.
`Samson1 has written the most frequently used handbook on uv techniques. It provides
`useful graphs of standard uv window and xuv thin film filter transmission, discussion of
`polarization effects, and graphs of standard uv reflective coatings. It has been updated in a
`recent book.2 General information on optics is also contained in the book by Born and Wolf,3
`
`

`
`OPTICAL MATERIALS—UV, VUV
`
`10.3
`
`the AIP4 and the OSA5 Handbooks, or in the series Applied Optics and Optical Engineering
`on instrument design6; but these works are focused on longer wavelengths. Laser-related
`optical materials are covered extensively in a CRC Handbook.7
`This chapter is intended as a guide to fundamental properties, application issues, and
`sources of information on uv optical materials. It is not a collection of graphs and tables
`available elsewhere.
`
`10.1 FUNDAMENTAL PHYSICAL PROPERTIES
`
`10.1.1 Optical Constants
`
`Forms.
`In the uv, the dominant photon-material interactions are bound-to-bound and ion-
`izing transitions of atomic electrons. These interactions lead to incoherent photoabsorption
`or photoemission and associated coherent, elastic Rayleigh scattering and reflection. Phonon
`processes or lattice vibration effects modify band to band transitions in this spectral region
`slightly and are usually neglected. For solids and molecular systems, the atoms are considered
`frozen on the time scale of absorption or scattering. In absorption measurements, the intensity
`transmitted I through a sample of thickness x of an incident beam of intensity I0 is given by
`I ⫽ I e
`0
`
`(10.1)
`
`⫺␮ x
`
`where ␮ is the absorption coefficient most often known by ␣ at longer wavelengths. ␮ is
`given by ␳␴, the product of the number density of atoms/molecules and the atomic cross
`section. Typical absorption cross sections per atom are 10⫺15 to 10⫺18 cm2. Inelastic processes
`such as the Raman and Compton effects are less likely. Raman cross sections are about 10⫺29
`cm2, and the Compton effect begins to be significant only above 2000 eV.8
`Bulk optical properties are determined by Maxwell’s equations, where the photon-solid
`interaction is incorporated in the displacement field D ⫽ ⑀E, the product of the complex
`dielectric coefficient and the applied electric field. The complex dielectric coefficient is di-
`rectly connected to atomic polarizability and oscillator strengths of atomic transitions. The
`dielectric coefficient ⑀ is given by the density of atoms ␳ and the atomic polarizability ␣ as
`
`⑀ ⫽ 1 ⫹ 4␲␳␣
`
`(10.2)
`
`The atomic polarizability can be approximated on the basis of a collection of Lorentz os-
`cillators
`
`ƒ
`j
`(␻ ⫺ ␻ ) ⫺ i␻⌫
`2
`2
`j
`j
`
`(10.3)
`
`冘
`
`j
`
`␣ ⫽
`
`2
`
`e
`m
`
`where ƒj, ␻j, and ⌫
`
`j are the oscillator strength, frequency, and half width of the jth transition.
`For solids, a correction needs to be made to account for the polarization of the surrounding
`medium. In addition, the band structure will spread out the distribution of atomic oscillator
`strength for bound transitions.
`Optical constants of the various elements and solid materials completely determine ideal,
`linear transmittance and reflectance. Formulas and characteristic behavior in transmission
`and reflection are discussed more extensively in Secs. 10.2 and 10.3, respectively. The com-
`plex constants represent the real and imaginary parts of the linear response of the medium
`or polarization and scattering and absorption. Various interrelated forms in the uv are used
`depending on the spectral region and physical processes of interest.
`⫹ i⑀
`In the visible and near uv, the complex dielectric coefficient ⑀ ⫽ ⑀
`2 is directly
`1
`related to internal fields and band structure calculations, as indicated above. The complex
`index of refraction N ⫽ n ⫹ ik, where n is the index of refraction and k the extinction
`
`

`
`10.4
`
`CHAPTER TEN
`
`coefficient, makes a clearer connection with physical measurements. The phase velocity in
`
`
`the medium is c/n, the wavelength in the medium is ␭0/n (␭0 in vacuum), and the absorption
`coefficient is given by
`
`␮ ⫽
`
`4␲k
`␭
`0
`
`(10.4)
`
`The index of refraction takes the form N ⫽ 1 ⫺ ␦ ⫺ i␤ in the soft x-ray region, where n is
`very close to one and k very close to zero.
`⫹ ƒ2 is more often used in the
`The complex atomic scattering factor or amplitude ƒ ⫽ ƒ1
`x-ray region, where ƒ1 is proportional to Thomson scattering off of the Z atomic electrons,
`as if they were free, plus a term due to scattering associated with ionizing transitions or
`‘‘anomalous’’ dispersion.9,10
`The forms of optical constants are related by the formulae
`
`⑀ ⫽ N
`
`2
`
`⑀ ⫽ n ⫺ k
`2
`2
`1
`
`⑀ ⫽ 2nk
`2
`
`␦ ⫽
`
`␤ ⫽
`
`r ␭
`2
`e
`2␲ q
`
`r ␭
`2
`e
`2␲ q
`
`冘 q 1q
`冘 q 2
`
`␳ ƒ
`
`␳ ƒ q
`
`(10.5)
`
`(10.6)
`
`(10.7)
`
`(10.8)
`
`(10.9)
`
`where re is the classical radius of the electron e2/mc 2 and ␳
`q is the number of atoms per
`unit volume of type q. The real and imaginary parts of the optical constants are rigorously
`related via a Kramers-Kronig integral.11 For the index of refraction
`
`(10.10)
`
`(10.11)
`
`n(␻) ⫺ 1 ⫽ P 冕
`k(␻) ⫽ ⫺ P 冕
`
`2
`␲
`
`⬁
`
`0
`
`␻ ⬘k(␻ ⬘)
`␻/2 ⫺ ␻
`2
`
`d␻⬘
`
`2␻
`␲
`
`⬁
`
`0
`
`n(␻⬘) ⫺ 1
`␻/2 ⫺ ␻
`2
`
`d␻⬘
`
`where P stands for the principal value integral.
`
`Connection with Electronic Structure.
`In the regions of transitions from the valence band
`or core levels to bound final states or the conduction band, the optical constants are sensitive
`to bonding in the material. Band structure calculations predict the magnitude and shape of
`spectral features relatively well but do not predict energy locations accurately. Lynch has
`summarized interband phenomena such as critical points, discontinuities in the joint density
`of states, and excitons at the fundamental edge.12 For theoretical verification, band to band
`transitions can be located very accurately at critical points by modulation spectroscopy. Just
`above core level edges, structure in the optical constants primarily map the densities of
`conduction band states of appropriate atomic symmetry, since the core levels are well defined
`in energy. Near-edge structure may also be analyzed with the aid of molecular orbital and
`cluster calculations.13 Above threshold regions, the spectral dependences of the optical con-
`stants of materials are fairly well understood in terms of atomic processes. The strongest
`electronic features in n and k occur in the valence to conduction band transitions below 30
`eV. The bunching of oscillator strength in this region leads to values of n less than one
`above about 30 eV. At higher energies, n rises toward one as 1/(ប␻)2 with the entries of
`further absorption edges appearing as perturbations. Absorption rises abruptly at core level
`
`

`
`OPTICAL MATERIALS—UV, VUV
`
`10.5
`
`edges and then falls to zero toward higher energy approximately as 1/(ប␻)7 / 2, considerably
`above the edges.14 The distribution of oscillator strength above each absorption edge is also
`strongly affected by overlap of initial and final state wavefunctions leading to delayed onset
`of higher angular momenta transitions and the Cooper minimum.15,16,17 Additional modifi-
`cations of the expected distribution of oscillator strength include shape resonances and au-
`toionization.18 More than 30 eV above core level edges, backscattering of the outgoing
`photoelectron from nearby atoms and interference at the absorption site or extended absorp-
`tion fine structure (EXAFS) modulates the absorption by several percent over a few hundred
`eV. Inversion of the EXAFS modulations yields nearest-neighbor distances to an accuracy
`as good as 0.001 nm.19
`The integrity of a set of optical constants covering the entire range of electronic transitions
`is often verified by applying a form of the Thomas-Reiche-Kuhn sum rule for atomic oscil-
`lator strength. The most commonly used sum rule is
`
`冕 ␻⬘⑀ (␻⬘) d␻⬘
`
`n (␻) ⫽
`eff
`
`m
`2␲ ␳e
`2
`
`2
`
`␻
`
`0
`
`2
`
`(10.12)
`
`where neff is the number of effective electrons contributing at each frequency per atom or
`molecule and ␳ is the atomic or molecular number density. Here neff must equal the total
`number of electrons per atom or molecule at energies above the 1s edge.11
`
`Sources. Palik20,21 gives optical constants for a variety of often used metals, semiconduc-
`tors, and insulators for infrared to x-ray energies. In particular, the source provides fine
`energy scale constants in the valence band to conduction band region, and some critical
`analysis of the measurement sources. Chapters are included on the origins and measurement
`of optical constants and the optical constants are available on CD-ROM as well. Optical
`properties of materials include treatment of two-photon absorption by Nikogoian.22
`The compilation of Henke et al.23,24 of the atomic scattering factors for the elements
`above 30 eV provides data to determine reasonably well the optical properties of any ma-
`terial, given the density, at energies away from the absorption edges. The data do not give
`a good picture at the edges of bound unoccupied states that are sensitive to the chemical
`environment. The constants have been derived from absorption measurements, theoretical
`extrapolations, and the Kramers-Kronig relations. The data are also available on the Internet25
`with revisions of the 1993 data and software to calculate the soft x-ray transmission or
`reflectivity of any material.
`The state of xuv optical constant theory, measurement, and databases has been covered
`by a variety of SPIE papers.26 Soft x-ray electron binding edges, characteristic x-rays, and
`standard filter transmissions and mirror reflectivities along with useful constants and formulas
`have been collected in a handy pocket guide issued by the Center for X-ray Optics.27
`
`Measurement Techniques. UV optical constants are experimentally determined by mea-
`surements of absorption, reflectance, ellipsometry, or direct refraction and Kramers-Kronig
`inversion of the data where needed. Ward has recently surveyed the techniques for bulk and
`thin-film materials.28
`Absorption is measured via transmission, primarily. Corrections for reflectance, thickness,
`and oxide or contaminating layers can present problems for accurate measurements. Use of
`the Kramers-Kronig relations to obtain the index of refraction depends on careful extrapo-
`lation of the absorption to low and high energies. Errors will not appreciably affect the shape
`of optical constant structure but will alter the magnitude. Sum rules such as Eq. (10.12) are
`helpful in gauging the suitability of extrapolations. Weak absorption in transparent materials
`is measured by laser calorimetry29 or photoacoustic methods. Multiphoton processes put a
`limit on sensitivity, however.
`Optical constants can also be determined from reflectance measurements. Below the start
`of the grazing incidence regime at 40 eV, reflectance measurements can be made with tol-
`erable flux in normal incidence. Beyond 40 eV, grazing incidence must be used for reasonable
`
`

`
`10.6
`
`CHAPTER TEN
`
`signal levels, and measurements must be made in orthogonal directions to the incident photon
`beam to determine polarization effects. Measurements made at a variety of grazing angles
`at a single energy can be used to derive the optical constants by intersection of isoreflector
`curves in n and k space or by simultaneous solution.30 Alternatively, reflectance data over a
`wide energy range at normal incidence or a given grazing angle with a highly polarized
`source can be Kramers-Kronig inverted to obtain both optical constants.31 The surface sen-
`sitivity of reflectivity measurements limits the accuracy of optical constants. In the region
`below 20 eV the reflectivity sampling depth is typically 10 to 50 nm, so that a monolayer
`can have 1 percent effects. Aspnes has observed a surface sensitivity of 1 percent in the
`polarized reflectance of (110) Si in the near uv.32 Optical constants based on thin film mea-
`surements should often be called pseudo-optical constants because they can vary significantly
`with deposition conditions owing to roughness, oxide or other overlayers, and void fraction
`or packing density. Aspnes has discussed effective medium approximations for dealing with
`the analysis of measurements of imperfect films.33 Scattering from rough surfaces can remove
`light from the specularly reflected beam and alter measured values. Scattering has a greater
`effect at normal angles and shorter wavelengths, and is discussed more extensively in Secs.
`10.3 and 10.5. For critical telescope applications, measurement of the pseudo-optical con-
`stants of a witness plate near the grazing angle of use is desirable for instrument performance
`predictions.
`Ellipsometry provides a way to simultaneously determine both optical constants in an
`intensity independent way.33 Quick determinations can be made of ideal specimens, but
`correcting for overlayers requires careful work. Accurate uv measurements have been made
`using polarized synchrotron radiation by Johnson et al.34 using MgF2 prisms or three-mirror
`polarizers as analyzers. The measurements lose accuracy at energies larger than 20 to 30 eV,
`however, owing to the constraints of polarizers and the fact that the optimum specimen
`grazing angle for maximum phase shift moves to 45⬚ at higher energies where p-polarized
`reflectance is very small.
`Direct refraction measurements on transparent specimens can be made in the visible and
`near uv by measuring deviation angles or phase shifts interferometrically.35 In the xuv, the
`index of refraction can be determined by refractive corrections to Bragg angles of multilayer
`coatings36 and by direct measurement of the phase shift with x-ray interferometers.37,38 Op-
`tical constants have also been determined, in the xuv, from the diffraction efficiency of
`transmission gratings.39
`There are a number of facilities to measure the transmission, reflectance and optical
`constants of optical materials. These include reflectometers on synchrotrons at the National
`Institute of Standards and Technology (NIST),40,41 on the NRL X24C beamline at the Na-
`tional Synchrotron Light Source at Brookhaven National Laboratory,42 and at the Advanced
`Light Source at Lawrence Berkeley Laboratory.43 NIST also has facilities for diffuse reflec-
`tance44 and index of refraction measurements.
`
`10.1.2 Structure and Thermophysical Properties
`
`Bulk physical properties of materials are often limiting factors in selection. Standard texts
`on solid state physics by Kittel45 and materials science by Van Vleck46 are useful for general
`data and background. Lattice structures of inorganic crystals are available in the series Crys-
`tal Structures.47 Thermal radiation, conductivity, diffusivity, and expansion, together with
`specific heat and viscosity of materials, are available from the national source CINDAS and
`its compilation of material properties.48 Reference 4 is a useful condensed guide to a wide
`range of thermal and mechanical properties. Reference 7 lists thermal properties and elasti