Handbook of optical engineering

Handbook of Optical Engineering edited by Daniel Malacara Centro de Investigaciones en Optica, A.C León, Mexico Brian J Thompson University of Rochester Rochester, New York Marcel Dekker, Inc New York • Basel TM Copyright © 2001 by Marcel Dekker, Inc All Rights Reserved ISBN: 0-8247-9960-7 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http//www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Sales/Professional Marketing at the headquarters address above Copyright # 2001 by Marcel Dekker, Inc All Rights Reserved Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit): 10 PRINTED IN THE UNITED STATES OF AMERICA OPTICAL ENGINEERING Founding Editor Brian J Thompson University of Rochester Rochester, New York Editorial Board Toshimitsu Asakura Hokkai-Gakuen University Sapporo, Hokkaido, Japan Nicholas F Borrelli Corning, Inc Corning, New York Chris Dainty Imperial College of Science, Technology, and Medicine London, England Bahram Javidi University of Connecticut Storrs, Connecticut Mark Kuzyk Washington State University Pullman, Washington Hiroshi Murata The Furukawa Electric Co., Ltd Yokohama, Japan Edmond J Murphy JDS/Uniphase Bloomfield, Connecticut Dennis R Pape Photonic Systems Inc Melbourne, Florida Joseph Shamir Technion–Israel Institute of Technology Hafai, Israel David S Weiss Heidelberg Digital L.L.C Rochester, New York Electron and Ion Microscopy and Microanalysis: Principles and Applications, Lawrence E Murr Acousto-Optic Signal Processing: Theory and Implementation, edited by Nor man J Berg and John N Lee Electro-Optic and Acousto-Optic Scanning and Deflection, Milton Gottlieb, Clive L M Ireland, and John Martin Ley Single-Mode Fiber Optics: Principles and Applications, Luc B Jeunhomme Pulse Code Formats for Fiber Optical Data Communication: Basic Principles and Applications, David J Morris Optical Materials: An Introduction to Selection and Application, Solomon Musikant Infrared Methods for Gaseous Measurements: Theory and Practice, edited by Joda Wormhoudt Laser Beam Scanning: Opto-Mechanical Devices, Systems, and Data Storage Optics, edited by Gerald F Marshall Opto-Mechanical Systems Design, Paul R Yoder, Jr 10 Optical Fiber Splices and Connectors: Theory and Methods, Calvin M Miller with Stephen C Mettler and Ian A White 11 Laser Spectroscopy and Its Applications, edited by Leon J Radziemski, Richard W Solarz, and Jeffrey A Paisner 12 Infrared Optoelectronics: Devices and Applications, William Nunley and J Scott Bechtel 13 Integrated Optical Circuits and Components: Design and Applications, edited by Lynn D Hutcheson 14 Handbook of Molecular Lasers, edited by Peter K Cheo 15 Handbook of Optical Fibers and Cables, Hiroshi Murata 16 Acousto-Optics, Adrian Korpel 17 Procedures in Applied Optics, John Strong 18 Handbook of Solid-State Lasers, edited by Peter K Cheo 19 Optical Computing: Digital and Symbolic, edited by Raymond Arrathoon 20 Laser Applications in Physical Chemistry, edited by D K Evans 21 Laser-Induced Plasmas and Applications, edited by Leon J Radziemski and David A Cremers 22 Infrared Technology Fundamentals, Irving J Spiro and Monroe Schlessinger 23 Single-Mode Fiber Optics: Principles and Applications, Second Edition, Re vised and Expanded, Luc B Jeunhomme 24 Image Analysis Applications, edited by Rangachar Kasturi and Mohan M Trivedi 25 Photoconductivity: Art, Science, and Technology, N V Joshi 26 Principles of Optical Circuit Engineering, Mark A Mentzer 27 Lens Design, Milton Laikin 28 Optical Components, Systems, and Measurement Techniques, Rajpal S Sirohi and M P Kothiyal 29 Electron and Ion Microscopy and Microanalysis: Principles and Applications, Second Edition, Revised and Expanded, Lawrence E Murr 30 Handbook of Infrared Optical Materials, edited by Paul Klocek 31 Optical Scanning, edited by Gerald F Marshall 32 Polymers for Lightwave and Integrated Optics: Technology and Applications, edited by Lawrence A Hornak 33 Electro-Optical Displays, edited by Mohammad A Karim 34 Mathematical Morphology in Image Processing, edited by Edward R Dougherty 35 Opto-Mechanical Systems Design: Second Edition, Revised and Expanded, Paul R Yoder, Jr 36 Polarized Light: Fundamentals and Applications, Edward Collett 37 Rare Earth Doped Fiber Lasers and Amplifiers, edited by Michel J F Digonnet 38 Speckle Metrology, edited by Rajpal S Sirohi 39 Organic Photoreceptors for Imaging Systems, Paul M Borsenberger and David S Weiss 40 Photonic Switching and Interconnects, edited by Abdellatif Marrakchi 41 Design and Fabrication of Acousto-Optic Devices, edited by Akis P Goutzoulis and Dennis R Pape 42 Digital Image Processing Methods, edited by Edward R Dougherty 43 Visual Science and Engineering: Models and Applications, edited by D H Kelly 44 Handbook of Lens Design, Daniel Malacara and Zacarias Malacara 45 Photonic Devices and Systems, edited by Robert G Hunsberger 46 Infrared Technology Fundamentals: Second Edition, Revised and Expanded, edited by Monroe Schlessinger 47 Spatial Light Modulator Technology: Materials, Devices, and Applications, edited by Uzi Efron 48 Lens Design: Second Edition, Revised and Expanded, Milton Laikin 49 Thin Films for Optical Systems, edited by Francoise R Flory 50 Tunable Laser Applications, edited by F J Duarte 51 Acousto-Optic Signal Processing: Theory and Implementation, Second Edition, edited by Norman J Berg and John M Pellegrino 52 Handbook of Nonlinear Optics, Richard L Sutherland 53 Handbook of Optical Fibers and Cables: Second Edition, Hiroshi Murata 54 Optical Storage and Retrieval: Memory, Neural Networks, and Fractals, edited by Francis T S Yu and Suganda Jutamulia 55 Devices for Optoelectronics, Wallace B Leigh 56 Practical Design and Production of Optical Thin Films, Ronald R Willey 57 Acousto-Optics: Second Edition, Adrian Korpel 58 Diffraction Gratings and Applications, Erwin G Loewen and Evgeny Popov 59 Organic Photoreceptors for Xerography, Paul M Borsenberger and David S Weiss 60 Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, edited by Mark G Kuzyk and Carl W Dirk 61 Interferogram Analysis for Optical Testing, Daniel Malacara, Manuel Servin, and Zacarias Malacara 62 Computational Modeling of Vision: The Role of Combination, William R Uttal, Ramakrishna Kakarala, Spiram Dayanand, Thomas Shepherd, Jagadeesh Kalki, Charles F Lunskis, Jr., and Ning Liu 63 Microoptics Technology: Fabrication and Applications of Lens Arrays and Devices, Nicholas Borrelli 64 Visual Information Representation, Communication, and Image Processing, edited by Chang Wen Chen and Ya-Qin Zhang 65 Optical Methods of Measurement, Rajpal S Sirohi and F S Chau 66 Integrated Optical Circuits and Components: Design and Applications, edited by Edmond J Murphy 67 Adaptive Optics Engineering Handbook, edited by Robert K Tyson 68 Entropy and Information Optics, Francis T S Yu 69 Computational Methods for Electromagnetic and Optical Systems, John M Jarem and Partha P Banerjee 70 Laser Beam Shaping, Fred M Dickey and Scott C Holswade 71 Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition, Revised and Expanded, edited by Michel J F Digonnet 72 Lens Design: Third Edition, Revised and Expanded, Milton Laikin 73 Handbook of Optical Engineering, edited by Daniel Malacara and Brian J Thompson 74 Handbook of Imaging Materials: Second Edition, Revised and Expanded, edited by Arthur S Diamond and David S Weiss 75 Handbook of Image Quality: Characterization and Prediction, Brian W Keelan 76 Fiber Optic Sensors, edited by Francis T S Yu and Shizhuo Yin 77 Optical Switching/Networking and Computing for Multimedia Systems, edited by Mohsen Guizani and Abdella Battou 78 Image Recognition and Classification: Algorithms, Systems, and Applications, edited by Bahram Javidi 79 Practical Design and Production of Optical Thin Films: Second Edition, Revised and Expanded, Ronald R Willey 80 Ultrafast Lasers: Technology and Applications, edited by Martin E Fermann, Almantas Galvanauskas, and Gregg Sucha 81 Light Propagation in Periodic Media: Differential Theory and Design, Michel Nevière and Evgeny Popov 82 Handbook of Nonlinear Optics, Second Edition, Revised and Expanded, Richard L Sutherland Additional Volumes in Preparation Optical Remote Sensing: Science and Technology, Walter Egan Preface This comprehensive and cohesive work includes all the relevant data to allow optical engineers worldwide to meet present and upcoming challenges in their day-to-day responsibilities The thrust of the Handbook of Optical Engineering is toward engineering and technology rather than theoretical science The book has 26 chapters that cover most but not all topics in optics, beginning with a few chapters describing the principles of optics elements These are followed by more technical and applied chapters All authors prepared their chapters with the following criteria in mind: Descriptions are restricted to explaining principles, processes, methods, and procedures in a concise and practical way so that the reader can easily apply the topics discussed Fundamental descriptions and a how-to-do-it approach are emphasized Useful formulas are provided wherever possible, along with step-by-step, worked-out examples, as needed, to illustrate applications and clarify calculation methods Formulas are arranged in the best sequence for use on a computer or calculator The book is replete with tables, flow charts, graphs, schematics and line drawings in the tradition of useful reference books and major handbooks National and ISO standards are included where appropriate, and permitted, in suitable abridgement for useful reference Overlapping among different chapters has been avoided unless absolutely necessary Daniel Malacara Brian J Thompson iii Contents Preface Contributors Basic Ray Optics Orestes Stavroudis 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Introduction Gaussian Optics a` la Maxwell The Eikonal Function and Its Antecedents Ray Tracing and Its Generalization The Paraxial Approximation and Its Uses The Huygens’ Principle and Developments The Aberrations, Seidel and Otherwise References iii xiii 1 15 22 27 30 35 Basic Wave Optics Glenn D Boreman 39 2.1 2.2 2.3 2.4 39 49 66 71 73 Diffraction Interference Coherence Polarization References Basic Photon Optics Sofia E Acosta-Ortiz 75 3.1 3.2 3.3 3.4 75 80 91 99 Nature of Quantum Optics Nonlinear Optics Multiphoton Processes Phase Conjugate Optics v Optical Fibers and Accessories 817 includes a new polishing method called PC (physical contact) The PC uses a curved polishing that dramatically reduces back reflections PC style offers very good performance for single-mode and multimode fiber connectors They are commonly used in analog systems (CATV) and high bit-rate systems The majority of the connectors of the second generation are threaded connectors This is inconvenient and decreases packing density Connectors of the third and fourth generation tend to be push–pull types This type of connector has shorter connection time and allows a significant increase in packing density Since packing density is becoming more important, fourth-generation connectors are focused on ease of use and reduced size One of the new designs is the LC connector This connector offers an easy installation and high pack density because of a reduced connector’s diameter Table 22.4 describes some of the widespread connector types Table 22.4 Connector Types 818 22.4.14 Starodumov Fiber Splicers Splices are permanent connections between fibers Splices are used in two situations: mid-span splices, which connect two lengths of cable; and pigtails, at the ends of a main cable, when rerouting of optical paths is not required or expected Splices offer lower attenuation, easier installation, lower backreflection, and greater physical strength than connectors, and they are generally less expensive In addition, splices can fit inside cable, offer a better hermetic seal, and allow either individual or mass splicing There are two basic categories of splices: fusion splices and mechanical splices Fusion Splicing The most common type of splice is a fusion splice, formed by aligning and welding the ends of two optical fibers together Usually a fusion splicer includes an electric arc welder to fuse the fibers, alignment mechanisms, and a camera or binocular microscope to magnify the alignment by 50 times or more The fusion parameters can usually be changed to suit particular types of fibers, especially if it is necessary to fuse two different fibers After the splicing procedure, the previously removed plastic coating is replaced with a protective plastic sleeve Fusion splicing provides the lowest connection loss, keeping losses as low as 0.05 dB Also, fusion splices have lower consumable cost per connection than mechanical splices However, the capital investment in equipment to make fusion splices is significantly higher than that for mechanical splices Fusion splices must be performed in a controlled environment, and should not be done in open spaces because of dust and other contamination In addition, fusion splices cannot be made in an atmosphere that contains explosive gasses because of the electric arc generated during this process Mechanical Splices A mechanical splice is a small fiber connector that precisely aligns two fibers together and then secures them by clamping them within a structure or by epoxying the fibers together Because tolerances are looser than in fusion splicing, this approach is used more often with multimode fibers than single-mode fibers Although losses tend to be slightly higher than those of fusion splices and back reflections can be a concern, mechanical splices are easier to perform and the requirements for the environment are looser for mechanical splicing than those for fusion splicing Generally, the consumables for a mechanical splice results in a higher cost than consumables for fusion splices; however, the equipment needed to produce a mechanical splice is much less expensive than the equipment for fusion splices To prepare mechanical splices, the fibers are first stripped of all buffer material, cleaned, and cleaved Cleaving a fiber provides a uniform surface, which is perpendicular to a fiber axis, needed for maximum light transmission to the other fiber Then the two ends of the fibers are inserted into a piece of hardware to obtain a good alignment and to permanently hold the fibers’ ends Many hardware devices have been developed to serve these goals The most popular devices can be divided in two broad categories: capillary splices and V-groove splices Capillary splice is the simplest form of mechanical splicing Two fiber ends are inserted into a thin capillary tube made of glass or ceramic, as illustrated in Optical Fibers and Accessories 819 Figure 22.38 Capillary splice Fig 22.38 To decrease backreflections from the fiber ends, an index-matching gel is typically used in this splice The fibers are held together by compression or friction, although epoxy may be used to permanently secure the fibers The V-groove splice is probably the oldest and still most popular method, especially for multifiber splicing of ribbon cable This type of splice is either crimped or snapped to hold the fibers in place Many types of V-groove splices have been developed using different techniques The simplest technique confines the two fibers between two plates, each one containing a groove into which the fiber fits This approach centers the fiber core, regardless of variation in the outer diameter of the fiber (Fig 22.39(a)) The popular V-groove technique uses three precision rods tightened by means of an elastic band or shrinkable tube (Fig 22.39(b)) The splice loss in this method depends strongly on the fiber size (core and cladding diameter variations) and eccentricity (the position of the core relative to the center of the fiber) V-groove techni- Figure 22.39 V-groove splice cross sections: (a) V-groove using two plates and (b) V-groove using three rods 820 Starodumov ques properly carried out with multimode fibers result in splice losses of the order of 0.1 dB or less Some of them can be applied to single-mode fibers as well The borderline connectors and splices is rather indefinite One example is the rotary mechanical splice (RMS), which is a disconnectable splice made by attaching ferrules to the two fiber ends, joining the ferrules in a housing, and holding the assembly together with a spring clip The assembly can be disconnected by removing the slip and is rated to suvive 250 mating cycles Rotary mechanical splices provide a simple and quick method of joining single-mode and multimode fibers with mean losses less than 0.2 dB without the need for optical or electronic monitoring equipment Splices, once completed, whether fusion or mechanical, are then placed into splicing trays designed to accommodate the particular type of splice in use On the other hand, fiber-optic splices require protection from the environment, so they are stored in a splice enclosure These special boxes are available for indoors as well as outdoor mounting The outdoor type should be weatherproof, with a watertight seal Additionally, splices enclosures protect stripped fiber-optic cable and splices from strain and help organize spliced fibers in multifiber cables REFERENCES Optical Fibers Agrawal, G P., Nonlinear Fiber Optics, 2nd edn, Academic Press, San Diego, 1995 Ghatak, A and K Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, Cambridge, 1998 Goff, D R., Fiber Optic Reference Guide, Focal Press, Boston, 1996 Hecht, J., Understanding Fiber Optics, SAMS, Indiana, 1987 Keiser, G., Optical Fiber Communications, McGraw-Hill, Singapore, 1991 Midwinter, J., Optical Fibers for Transmission, John Wiley and Sons, New York, 1979 Wilson, J and J F B Hawkes, Optoelectronics: An Introduction, Prentice Hall, London, 1983 Yeh, C., Handbook of Fiber Optics: Theory and Applications, Academic Press, San Diego, 1990 Special Fibers Agrawal, G P., Nonlinear Fiber Optics, 2nd edn, Academic Press, San Diego, 1995 10 Armitage, J R., R Wyatt, B J Ainslie, and S P Craig-Ryan, ‘‘Highly Efficient 980 nm Operation of an Yb3þ -Doped Silica Fiber Laser,’’ Electron Lett., 25, 298–299 (1989) 11 Artjushenko, V G., L N Butvina, V V Vojtsekhovsky, E M Dianov, and J G Kolesnikov, ‘‘Mechanisms of Optical Losses in Polycrystalline Fibers,’’ J Lightwave Technol., LT-4, 461–464 (1986) 12 Berman, I E., ‘‘Plastic Optical Fiber: A Short-Haul Solution,’’ Optics & Photonics News, 9, 29 (1998) 13 Bornstein, A and N Croitoru, ‘‘Experimental Evaluation of a Hollow Glass fiber,’’ Appl Opt., 25, 355–358 (1986) 14 Desurviere, E., Erbium-Doped Fiber Amplifiers, John Wiley and Sons, New York, 1994 15 DiGiovanni, D J and M H Muendel, ‘‘High Power Fiber Lasers,’’ Optics & Photonics News, 26–30 (January 1999) 16 Drexhage, M G and C T Moynihan, ‘‘Infrared Optical Fibers,’’ Scientific American, 259, 76–81 (November 1988) Optical Fibers and Accessories 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 821 France, P W., S F Carter, M W Moore, and C R Day, ‘‘Process in Fluoride Fibers for Optical Communications,’’ British Telecom Technology Journal, 5(2), 28–44 (1987) in Selected Papers on Infrared Fiber Optics, SPIE, MS 9, 59–75 (1990) Garmire, E., T McMahon, and M Bass, ‘‘Flexible Infrared Waveguides for HighPower Transmission, ’’ IEEE J Quantum Electron., QE-16(1), 23–32 (1980) Ghatak, A and Thyagarajan, K., Introduction to Fiber Optics, Cambridge University Press, New York, 1998 Harrington, J A., A G Standlee, A C Pastor, and L G DeShazer, ‘‘Single-Crystal Infrared Fibers Fabricated by Traveling-Zone Melting,’’ Infrared Optical Materials and Fibers III, Proc SPIE, 484, 124–127 (1984) Hecht, J., Understanding Fiber Optics, 1st edn, SAMS, Carmel, Indiana, 1992 Hecht, J., ‘‘Perspectives: Fiber Lasers Prove Versatile,’’ Laser Focus World, 73–77 (1998) Ikedo, M., M Watari, F Ttateishi, and H Ishiwatari, ‘‘Preparation and Characteristics of the TlBr-TlI Fiber for a High Power CO2 Laser Beam,’’ J Appl Phys., 60(9), 3035– 3039 (1986) Kaminov, I P and T L Koch, Optical Fiber Telecommunications IIIB, Academic Press, San Diego, 1997 Katsuyama, T and H Matsumura, ‘‘Low-Loss Te-Based Chalcogenide Glass Optical Fibers,’’ Appl Phys Lett., 49(1), 22–23 (1986) Katsuyama, T and H Matsumura, Infrared Optical Fibers, Adam Hilger, Bristol, 1989 Katzir, A., Lasers and Optical Fibers in Medicine, Academic Press, San Diego, 1993 Keiser, G E., ‘‘A Review of WDM Technology and Applications,’’ Optical Fiber Technology, 5, 3–39 (1999) Klocek, P and G H Sigel, Jr., Infrared Fiber Optics, SPIE Optical Engineering Press, Bellingham, 1989 Lu¨thy, W and H P Weber, ‘‘High-Power Monomode Fiber Lasers,’’ Opt Eng., 34(8), 2361–2364 (1995) Matsuura, Y., M Saito, M Miyagi, and A Hongo, ‘‘Loss Characteristics of Circular Hollow Waveguides for Incoherent Infrared Light,’’ JOSA A, 6(3), 423–427 (1989) Minelly, J D and P R Morkel, ‘‘320-mW Nd3þ -Doped Single-Mode Fiber Superfluorescent Source,’’ CLEO’93, CFJ6, 624–626 (1993) Miyashita, T and T Manabe, ‘‘Infrared Optical Fibers, IEEE J Quantum Electron., QE-18(10), 1432–1450 (1982) Ono, T., ‘‘Plastic Optical Fiber: The Missing Link For Factory, Office Equipment,’’ Photonics Spectra, 29, Issue 11, 88–91 (1995) Optical Fiber Lasers and Amplifiers, France, P W., ed., Blackie and Son, Glasgow, 1991 Pask, H M., R J Carman, D C Hanna, et al., ‘‘Ytterbium-Doped Silica Fiber Lasers: Versatile Sources for the 1–1.2 mm Region,’’ IEEE J Selected Topics in Quantum Electron., 1(1), 2–13 (1995) Sa’ar, A and A Katzir, ‘‘Intrinsic Losses in Mixed Silver Halide Fibers,’’ Infrared Fiber Optics, Proc SPIE, 1048, 24–32 (1989) Sa’ar, A., N Barkay, F Moser, I Schnitzer, A Levite, and A Katzir, ‘‘Optical and Mechanical Properties of Silver Halides Fibers,’’ Infrared Optical Materials and Fibers V, Proc SPIE, 843, 98–104 (1987) Saito, M and M Takizawa, ‘‘Teflon-Clad As-S Glass Infrared Fiber with LowAbsorption Loss,’’ J Appl Phys., 59(5), 1450–1452 (1986) Sakaguchi, S and S Takahashi, ‘‘Low-Loss Fluoride Optical Fibers for Midinfrared Optical Communication,’’ J Lightwave Technol., LT-5(9), 1219–1228 (1987) Tran, D C., G H Sigel, Jr., and B Bendow, ‘‘Heavy Metal Fluoride Glasses and Fibers: A Review,’’ J Lightwave Technol., LT-2(5), 566–586 (1984) 822 Starodumov 42 Vasil’ev, A V., E M Dianov, L N Dmitruk, V G Plotnichenko, and V K Sysoev, ‘‘Single-Crystal Waveguides for the Middle Infrared Range,’’ Soviet Journal of Quantum Electronics, 11(6), 834–835 (1981) 43 Worrell, C A., ‘‘Infra-Red Optical Properties of Glasses and Ceramics for Hollow Waveguides Operating at 10.6 mm Wavelength,’’ Infrared Optical Materials and Fibers V, Proc SPIE, 843, 80–87 (1987) 44 Wysocki, J A., R G Wilson, A G Standlee, et al., ‘‘Aging Effects in Bulk and Fiber TlBr-TlI,’’ J Appl Phys., 63(9), 4365–4371 (1988) 45 Zyskind, J L., Nagel, J A., and H D Kidorf, ‘‘Erbium-Doped Fiber Amplifiers for Optical Communications,’’ in Optical Fiber Telecommunications IIIB, Kaminov, I P and T L Koch, eds, Academic Press, San Diego, 1997 Fiber Optic Components 46 Agrawal, G P., Nonlinear Fiber Optics, 2nd edn, Academic Press, San Diego, 1995 47 Allard, F C., Fiber Optics Handbook: for Engineers and Scientists, McGraw-Hill, New York, 1990 48 Azzam, R M A and N M Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1989 49 Bergh, R A., M J F Digonnet, H C Lefevre, S A Newton, and H J Shaw, ‘‘Single Mode Fiber Optic Components,’’ Fiber Optics-Technology, Proc SPIE, 326, 137–142 (1982) 50 Born, M and E Wolf, Principles of Optics, 6th edn, Cambridge University Press, Cambridge, 1997 51 Calvani, R., R Caponi, and F Cisternino, ‘‘Polarization Measurements on SingleMode Fibers,’’ J Lightwave Technol., 7(8), 1187–1196 (1989) 52 Chomycz, B., Fiber Optic Installations, McGraw-Hill, New York, 1996 53 Culshaw, B., C Michie, P Gardiner, and A McGown, ‘‘Smart Structures and Applications in Civil Engineering,’’ Proc IEEE, 84(1), 78–86 (1996) 54 Ghatak, A and K Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, Cambridge, 1998 55 Goff, D R., Fiber Optic Reference Guide, Focal Press, Boston, 1996 56 Hayes, J., Fiber Optics Technician’s Manual, International Thomson Publishing Company, New York, 1996 57 Huard, S., Polarization of Light, John Wiley and Sons, Masson, Belgium, 1997 58 Kaminov, I P., ‘‘Polarization in Optical Fibers,’’ IEEE J Quantum Electron., QE17(1), 15–22 (1981) 59 Kashyap, R., ‘‘Photosensitive Optical Fibers: Devices and Applications,’’ Optical Fiber Technology, 1, 17–34 (1994) 60 Keiser, G., Optical Fiber Communications, McGraw-Hill, Singapore, 1991 61 Keiser, G E., ‘‘A Review of WDM Technology and Applications,’’ Optical Fiber Technology, 5, 3–39 (1999) 62 Kersey, A D., ‘‘A Review of Recent Developments in Fiber Optic Sensor Technology,’’ Optical Fiber Technology, 2, 291–317 (1996) 63 Miller, C., Optical Fiber Splicers and Connectors, Marcel Dekker, New York, 1986 64 Murata, H., Handbook of Optical Fibers and Cables, Marcel Dekker, New York, 1996 65 Noda, J., K Okamoto, and I Yokohama, ‘‘Fiber Devices Using PolarizationMaintaining Fibers,’’ Reprinted from Fiber and Integrated Optics, 6(4), 309–330 (1987) in On Selected Papers on Single-Mode Optical Fibers, Brozeit, A., K D Hinsch, and R S Sirohi, eds, SPIE, MS 101, 23–33 (1994) 66 Pearson, E R., The Complete Guide to Fiber Optic Cable System Installation, Delmar Publishers, Albany, New York, 1997 Optical Fibers and Accessories 67 68 69 70 71 823 Rashleigh, S C., ‘‘Origins and Control of Polarization Effects in Single-Mode Fibers,’’ J Lightwave Technol., LT-1(2), 312–331 (1983) Sirkis, J S., ‘‘Unified Approach to Phase-Strain-Temperature Models for Smart Structure Interferometric Optical Fiber Sensors: part 1, Development,’’ Optical Engineering, 32(4), 752–761 (1993) Stolen, R H and R P De Paula, Proceeding of the IEEE, 75(11), 1498–1511 (1987) Todd, D A., G R J Robertson, and M Failes, ‘‘Polarization-Splitting Polished Fiber Optic Couplers,’’ Opt Eng., 32(9), 2077–2082 (1993) Yariv, A., Optical Electronics in Modern Communications, 5th edn, Oxford University Press, New York, 1997 Erbium-Doped Fibers 72 73 74 75 76 Agrawal, G P., Nonlinear Fiber Optics, 2nd edn, Academic Press, San Diego, 1995 Desurviere, E., ‘‘Erbium-Doped Fiber Amplifiers,’’ John Wiley and Sons, New York, 1994 Ghatak, A and K Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, New York, 1998 Keiser, G E., ‘‘A Review of WDM Technology and Applications,’’ Optical Fiber Technology, 5, 3–39 (1999) Zyskind, J L., J A Nagel, and H D Kidorf, ‘‘Erbium-Doped Fiber Amplifiers for Optical Communications,’’ in Optical Fiber Telecommunications IIIB, Kaminov, I P and T L Koch, eds, Academic Press, San Diego, 1997 Double-Clad Fiber Lasers 77 78 79 80 81 82 83 84 Armitage, J R., R Wyatt, B J Ainslie, and S P Craig-Ryan, ‘‘Highly Efficient 980 nm Operation of an Yb3þ -Doped Silica Fiber Laser,’’ Electron Lett., 25(5), 298–299 (1989) Bell Labs Ultra-High-Power, ‘‘Single-Mode Fiber Lasers,’’ Technical Information DiGiovanni, D J and M H Muendel, ‘‘High Power Fiber Lasers,’’ Optics & Photonics News, 26–30 (1999) Hecht, J., ‘‘Perspectives: Fiber Lasers Prove Versatile,’’ Laser Focus world, 73–77 (1998) Kaminov, L P and T L Koch, Optical Fiber Telecommunications IIIB, Academic Press, San Diego, 1997 Lu¨thy, W and H P Weber, ‘‘High-Power Monomode Fiber Lasers,’’ Opt Eng., 34(8), 2361–2364 (1995) Minelly, J D and P R Morkel, ‘‘320-mW Nd3þ -Doped Single-Mode Fiber Superfluorescent Source,’’ CLEO’93, CFJ6, 624–626 (1993) Pask, H M., R J Carman, D C Hanna, et al., ‘‘Ytterbium-Doped Silica Fiber Lasers: Versatile Sources for the 1–1.2 mm Region,’’ IEEE J Selected Topics in Quantum Electron., 1(1), 2–13 (1995) Infrared Fibers 85 86 87 Artjushenko, V G., L N Butvina, V V Vojtsekhovsky, E M Dianov, and J G Kolesnikov, ‘‘Mechanisms of Optical Losses in Polycrystalline Fibers,’’ J Lightwave Technol., LT-4(4), 461–464 (1986) Drexhage, M G and C T Moynihan, ‘‘Infrared Optical Fibers,’’ Scientific American, 110–115 (1988) France, P W., S F Carter, M W Moore, and C R Day, ‘‘Progress in Fluoride Fibers for Optical Communications,’’ British Telecom Technology Journal, 5(2), 28–44 (1987) in Selected Papers on Infrared Fiber Optics, SPIE, MS 9, 59–75 (1990) 824 Starodumov 88 Harrington, J A., A G Standlee, A C Pastor, and L G DeShazer, ‘‘Single-Crystal Infrared Fibers Fabricated by Traveling-Zone Melting,’’ Infrared Optical Materials and Fibers III, Proc SPIE, 484, 124–127 (1984) 89 Kedo, M., M Watari, F Ttateishi, and H Ishiwatari, ‘‘Preparation and Characteristics of the TlBr-TlI Fiber for a High Power CO2 Laser Beam,’’ J Appl Phys., 60(9), 3035– 3039 (1986) 90 Kaminov, I P and T L Koch, Optical Fiber Telecommunications IIIB, Academic Press, San Diego, 1997 91 Kanamori, T., Y Terunuma, S Takahashi, and T Miyashita, J Lightwave Technol., LT-2, 607 (1984) 92 Katsuyama, T and H Matsumura, ‘‘Low-Loss Te-Based Chalcogenide Glass Optical Fibers,’’ Appl Phys Lett., 49(1), 22–23 (1986) 93 Katsuyama, T and H Matsumura, Infrared Optical Fibers, Adam Hilger, Bristol, 1989 94 Miyashita, T and T Manabe, ‘‘Infrared Optical Fibers,’’ IEEE J Quantum Electron., QE-18(10), 1432–1450 (1982) 95 Sa’ar, A and A Katzir, ‘‘Intrinsic Losses in Mixed Silver Halide Fibers,’’ Infrared Fiber Optics, Proc SPIE, 1048, 24–32 (1989) 96 Sa’ar, A., N Barkay, F Moser, I Schnitzer, A Levite, and A Katzir, ‘‘Optical and Mechanical Properties of Silver Halides Fibers,’’ Infrared Optical Materials and Fibers V, Proc SPIE, 843, 98–104 (1987) 97 Saito, M and M Takizawa, ‘‘Teflon-Clad As-S Glass Infrared Fiber with LowAbsorption Loss,’’ J Appl Phys., 59(5), 1450–1452 (1986) 98 Sakaguchi, S and S Takahashi, ‘‘Low-Loss Fluoride Optical Fibers for Midinfrared Optical Communication,’’ J Lightwave Technol., LT-5(9), 1219–1228 (1987) 99 Tran, D C., G H Sigel, Jr., and B Bendow, ‘‘Heavy Metal Fluoride Glasses and Fibers: A Review,’’ J Lightwave Technol., LT-2(5), 566–586 (1984) 100 Vasil’ev, A V., E M Dianov, L N Dmitruk, V G Plotnichenko, and V K Sysoev, ‘‘Single-Crystal Waveguides for the Middle Infrared Range,’’ Soviet Journal of Quantum Electronics, 11(6), 834–835 (1981) 101 Wysocki, J A., R G Wilson, et al., ‘‘Aging Effects in Bulk and Fiber TlBr-TlI,’’ J Appl Phys., 63(9), 4365–4371 (1988) Hollow Waveguides 102 Bornstein, A and N Croitoru, ‘‘Experimental Evaluation of a Hollow Glass Fiber,’’ Appl Opt., 25(3), 355–358 (1986) 103 Garmire, E., T McMahon, and M Bass, ‘‘Flexible Infrared Waveguides for HighPower Transmission,’’ IEEE J Quantum Electron., QE-16(1), 23–32 (1980) 104 Katsuyama, T and H Matsumura, Infrared Optical Fibers, Adam Hilger, Bristol, 1989 105 Klocek, P and G H Sigel, Jr., Infrared Fiber Optics, SPIE Optical Engineering Press, Bellingham, 1989 106 Matsuura, Y., M Saito, M Miyagi, and A Hongo, ‘‘Loss Characteristics of Circular Hollow Waveguides for Incoherent Infrared Light,’’ JOSA A, 6(3), 423–427 (1989) 107 Worrell, C A., ‘‘Infra-Red Optical Properties of Glasses and Ceramics for Hollow Waveguides Operating at 10.6 mm Wavelength,’’ Infrared Optical Materials and Fibers V, Proc SPIE, 843, 80–87 (1987) Plastic Fibers 108 Berman, L E., ‘‘Plastic Optical Fiber: A Short-Haul Solution,’’ Optics & Photonics News, 9(2), 29 (1998) 109 Mitsubishi Rayon Homepage Optical Fibers and Accessories 110 825 Ono, T., ‘‘Plastic Optical Fiber: The Missing Link For Factory, Office Equipment,’’ Photonics Spectra, 29(11), 88–91 (1995) Fiber Bundles 111 112 Hecht, J., Understanding Fiber Optics, 1st edn, SAMS, Carmel, Indiana, 1992 Katzir, A., Lasers and Optical Fibers in Medicine, Academic Press, San Diego, 1993 Polarization Fiber Components 113 114 115 116 117 118 119 120 121 122 123 Azzam, R M A and N M Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1989 Bergh, R A., M J F Digonnet, H C Lefevre, S A Newton, and H J Shaw, ‘‘Single Mode Fiber Optic Components,’’ Fiber Optics-Technology, Proc SPIE, 326, 137–142 (1982) Born, M and E Wolf, Principles of Optics, 6th edn, Cambridge University Press, Cambridge, 1997 Calvani, R., R Caponi, and F Cisternino, ‘‘Polarization Measurements on SingleMode Fibers,’’ J Lightwave Technol., 7(8), 1187–1196 (1989) Huard, S., Polarization of Light, John Wiley and Sons, Masson, Belgium, 1997 Kaminov, I P., ‘‘Polarization in Optical Fibers,’’ IEEE J Quantum Electron., QE17(1), 15–22 (1981) Noda, J., K Okamoto, and I Yokohama, ‘‘Fiber Devices Using PolarizationMaintaining Fibers,’’ Reprinted from Fiber and Integrated Optics, 6(4), 309–330 (1987) in Selected Papers on Single-Mode Optical Fibers, Brozeit, A., K D Hinsch, and R S Sirohi, eds, SPIE, MS 101, 23–33 (1994) Rashleigh, S C., ‘‘Origins and Control of Polarization Effects in Single-Mode Fibers,’’ J Lightwave Technol., LT-1(2), 312–331 (1983) Stolen, R H and R P De Paula, Proceeding of the IEEE, 75(11), 1498–1511 (1987) Todd, D A., G R J Robertson, and M Failes, ‘‘Polarization-Splitting Polished Fiber Optic Couplers,’’ Opt Eng., 32(9), 2077–2082 (1993) Yariv, A., Optical Electronics in Modern Communications, 5th edn, Oxford University Press, New York, 1997 Bragg Gratings 124 125 126 127 128 129 130 Agrawal, G., Nonlinear Fiber Optics, 2nd edn, Academic Press, San Diego, USA, 1995 Culshaw, B., C Michie, P Gardiner, and A McGown, ‘‘Smart Structures and Applications in Civil Engineering,’’ Proc IEEE, 84(1), 78–86 (1996) Ghatak, A and K Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, New York, 1998 Kashyap, R., ‘‘Photosensitive Optical Fibers: Devices and Applications,’’ Optical Fiber Technology, 1, 17–34 (1994) Keiser, G E., ‘‘A Review of WDM Technology and Applications,’’ Optical Fiber Technology, 5, 3–39 (1999) Kersey, A D., ‘‘A Review of Recent Developments in Fiber Optic Sensor Technology,’’ Optical Fiber Technology, 2, 291–317 (1996) Sirkis, J S., ‘‘Unified Approach to Phase-Strain-Temperature Models for Smart Structure Interferometric Optical Fiber Sensors: Part 1, Development,’’ Opt Eng., 32(4), 752–761 (1993) 23 Isotropic Amorphous Optical Materials LUIS EFRAIN REGALADO and DANIEL MALACARA Centro de Investigaciones en Optica, Leo´n, Mexico 23.1 INTRODUCTION The materials used in optical instruments and research can be characterized by many physical and chemical properties [1, 6, 9, 18, 27, 31, 32] The ideal material is determined by the specific intended application Optical materials can be crystalline or amorphous Crystalline materials can be isotropic or anisotropic, but amorphous materials can only be isotropic In this chapter some of the main isotropic amorphous materials used to manufacture optical elements are described The optical materials used to make optical elements such as lenses or prisms have several important properties to be considered, most important of which are described below 23.1.1 Refractive Index and Chromatic Dispersion The refractive index of a transparent isotropic material is defined as the ratio of the speed of light in vacuum to the speed of light in the material With this definition, Snell’s law of refraction gives n1 sin 1 ¼ n2 sin 2 ; ð23:1Þ where n1 and n2 are the refractive indices in two transparent isotropic media separated by an interface The angles 1 and 2 are the angles between the light rays and the normal to the interface at the point where the ray passes from one medium to the other The refractive index for most materials can vary from values close to to values greater than 2, as shown in Table 23.1 827 828 Regalado and Malacara Table 23.1 Refractive Indices of Some Materials Material Refractive index 1.0003 1.33 1.49 1.48–1.70 1.53–1.95 2.42 Air Water Acrylic Crown glass Flint glass Diamond The refractive index n of a given optical material is not the same for all colors: the value is greater for smaller wavelengths The refractive indices of optical materials are measured at some specific wavelengths, as shown in Table 23.2 The chromatic dispersion is determined by the principal dispersion ðnF À nC Þ Another quantity that determines the chromatic dispersion is the Abbe value for the line d, given by Vd ¼ nd À : nF À n C ð23:2Þ The Abbe value expresses the way in which the refractive index changes with wavelength Optical materials are mainly determined by the value of these two constants Two materials with different Abbe numbers can be combined to form an achromatic lens with the same focal length for red ðCÞ and for blue (F) light However, the focal length for yellow ðdÞ can be different This is called the secondary spectrum The secondary spectrum produced by an optical material or glass is Table 23.2 Spectral Lines Used to Measure Refractive Indices Wavelength (nm) 1013.98 852.11 706.52 656.27 643.85 589.29 587.56 546.07 486.13 479.99 435.83 404.66 365.01 Spectral line t s r C C0 D d e F F0 g h i Color Infrared Infrared Red Red Red Yellow Yellow Green Blue Blue Blue Violet Ultraviolet Element Hg Cs He H Cd Na He Hg H Cd Hg Hg Hg Isotropic Amorphous Optical Materials 829 determined by its partial dispersion The partial dispersion Px;y for the lines x and y is defined as nx À ny Px;y ¼ : ð23:3Þ nF À nC An achromatic lens for the lines C and F without secondary spectrum for yellow light d can be made only if the two transparent materials being used have different Abbe numbers Vd but the same partial dispersion number Pd;F 23.1.2 Other Optical Characteristics Spectral Transmission The light transmittance through an optical material is affected by two factors, i.e., the Fresnel reflections at the interfaces and the transparency of the material The Fresnel reflections in a dielectric material like glass are a function of the angle of incidence, the polarization state of the incident light beam, and the refractive index At normal incidence in air the irradiance reflectance  is a function of the wavelength, thus, the irradiance transmittance TR due to the reflections at the two surfaces of the glass plate is TR ¼ ½1 À 2 Š2 : ð23:4Þ The spectral transparency has large fluctuations among different materials and is also a function of the wavelength Any small impurities in a piece of glass with concentrations as small as ten parts per billion can introduce noticeable absorptions at some wavelengths For example, the well-known green color of window glass is due to ion oxides The effect of impurities can be so high that the critical angle for prism-shaped materials can vanish for nonoptical grade materials High-index glasses have a yellowish color due to absorptions in the violet and ultraviolet regions, from the materials used to obtain the high index of refraction At the spectral regions where a material has absorption the refractive index is not a real number but a complex number nà that can be written as nà ¼ nð1 À i Þ; ð23:5Þ where  is the absorption index, which is related to an extinction coefficient  by  ¼ 4n  :   ð23:6Þ If  is the extinction coefficient for the material, the irradiance transmittance TA due to absorption is TA ¼ eÀ t ; ð23:7Þ where t is the thickness of the sample Figure 23.1 shows the typical variations of the absorption index  with the wavelength for metals, semiconductors, and dielectrics [7] Dielectrics have two characteristic absorption bands The absorption in the ultraviolet band is due to the lattice structure vibrations Metals are highly absorptive at long wavelengths, due to their electrical conductivity, but they become transparent at short wavelengths The absorption band in semiconductors is around the visible region 830 Regalado and Malacara Figure 23.1 Absorption index as a function of the wavelength for optical materials (Adapted from Kingery [7].) The total transmittance T of a sample with thickness t talking into consideration surface reflections as well as internal absorption is T ¼ TR TA ¼ ½1 À 2 Š2 eÀ t : ð23:8Þ For dielectric materials far from an absorption region the refractive index n is real and the irradiance reflectance  is given by  ¼ ! n À : n þ ð23:9Þ Optical Homogeneity The degree to which the refractive index varies from point to point within a piece of glass or a melt is a measure of its homogeneity A typical maximum variation of the refractive index in a melt is Æ1  10À4 , but more homogeneous pieces can be obtained For the case of optical glasses the homogeneity is specified in four different groups, as shown in Table 23.3 Table 23.3 Homogeneity Groups for Optical Glasses Homogeneity group H1 H2 H2 H3 Maximum nd variation Æ2  10À5 Æ5  10À6 Æ2  10À6 Æ1  10À6 Isotropic Amorphous Optical Materials 831 Table 23.4 Bubble Classes for Optical Glasses Bubble class Total area of bubbles (mm2 ) B0 B1 B2 B3 0–0.029 0.03–0.10 0.11–0.25 0.26–0.50 Stresses and Birefringence The magnitude of the residual stresses within a piece of glass depends mainly on the annealing of the glass Internal stresses produce birefringence The quality of the optical instrument may depend very much on the residual birefringence Bubbles and Inclusions Bubbles are not frequent in good-quality optical glass, but they are always present in small quantities When specifying bubbles and inclusions, the total percentage covered by them is estimated, counting only those ! 0:05 mm Bubble classes are defined as in Table 23.4 23.1.3 Physical and Chemical Characteristics Thermal Expansion The dimensions of most optical materials, increase with temperature The thermal expansion coefficient is also a function of temperature If we plot the natural algorithm of L=L0 vs the temperature T (8C), we obtain a graph (Fig 23.2) for glass Figure 23.2 Thermal expansion of glass BK7 as a function of the temperature [...]... but equivalent ways: As the envelope of an orthotomic system of rays; i.e., rays ultimately from a single object point 1 2 Stavroudis As the cusp locus of a wavefront train, or, equivalently, the locus of points where the element of area of the wavefront vanishes I think the most useful definition is that the caustic is the locus of principal centers of curvature of a wavefront In general, every surface... limits of S at the point P" To best describe the consequences of a discontinuity with mathematical rigor and vigor one should apply the Hilbert integral [13] of the calculus of variations For our purposes a schoolboy explanation is more appropriate Joos [14] uses the definition of the gradient in terms of limits of surface integrals to define a surface gradient as a gradient that straddles a surface of. .. care of the refraction or reflection operation It involves only local properties of the refracting surface: the location of the point of incidence and the unit normal vector N, at that point On the other hand, the transfer operation, by means of which the point of incidence and the surface normal are found, involves the global properties of the surface Suppose the surface is given by a vector function of. .. entirely in optical design which, like all good engineering, remains more of an art even after the advent of the modern computer This brief chapter is intended to convey the basic formulas as well as the flavor of geometrical optics and optical design in a concise and compact form I have attempted to arrange the subject matter logically, although not necessarily in historical order The basic elements of geometrical... us here is the interpretation of his principle in mathematical terms: its representation in terms of the variational calculus which deals specifically with the determination of extrema of functions To set the stage, let us consider an optical medium in which a point is represented by a vector P ¼ ðx; y; zÞ and in which the refractive index is given by a vector function of position: n ¼ nðPÞ We will... equations (Eq (1.38)) describe their rates of change 1 t 0 ¼ n;  1 1 n 0 ¼ À t þ b;   1 b 0 ¼ À n;  ð1:38Þ where 1=, as before, is the curve’s curvature at the point in question and 1= is its torsion These formulas show that the curvature is the rate of change of t and that torsion is the rate of change of the b vector Both these motions are in the direction of n By squaring the expression in Eq (1.37)... rA3 þ sAÞx 0 þ ðqB2 Þy 0 þ ðrC3 þ sCÞz 0 þ rD3 þ sD ¼ 0: Now the coefficient of x 0 must vanish, yielding the last of these conditions, A2 ¼ A3 ¼ A ¼ 0: ð1:7Þ These conditions assure that the coordinate axes in image space are the images of those in object space Nothing has been done to change any of the optical properties of this ideal instrument Substituting these, from Eqs (1.5), (1.6), and (1.7),... media of constant refractive index, dP ¼ S ¼ ð; ; Þ: ds ð1:66Þ Snell’s law, from Eq (1.57), now takes the form n 0 ðS 0  NÞ ¼ nðS  NÞ; ð1:67Þ 16 Stavroudis Figure 1.6 The aplanatic surfaces of a sphere Here k is the radius of the refracting sphere; t ¼ kð1 þ n 0 =nÞ is the radius of the object surface; t ¼ kð1 þ n=n 0 Þ, that of the image surface where S and S 0 are the direction cosine vectors of. .. Fermat’s principle: light consists of a flow of particles, termed corpuscles, the trajectories of which are such that their time of transit from point to point is an extremum, either a maximum or a minimum These trajectories are what we now call rays Fermat’s justification for this principle goes back to observations by Heron of Alexandria, but that is the subject of an entirely different story What... P0 to P If P is the point of incidence, then  must be a solution for the equation fðP0 þ SÞ ¼ 0: ð1:76Þ With the value of  so obtained, Eq (1.75) provides the point of incidence The normal to a surface is best given by the gradient of its equation, rf, so that the unit normal vector is found from rf N ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ðrfÞ2 ð1:77Þ calculated, of course, at the point of incidence But there is ... data to allow optical engineers worldwide to meet present and upcoming challenges in their day-to-day responsibilities The thrust of the Handbook of Optical Engineering is toward engineering and... J Berg and John M Pellegrino 52 Handbook of Nonlinear Optics, Richard L Sutherland 53 Handbook of Optical Fibers and Cables: Second Edition, Hiroshi Murata 54 Optical Storage and Retrieval: Memory,... Third Edition, Revised and Expanded, Milton Laikin 73 Handbook of Optical Engineering, edited by Daniel Malacara and Brian J Thompson 74 Handbook of Imaging Materials: Second Edition, Revised and