ANALOG OPTICAL LINKS Analog Optical Links presents the basis for the design of analog links. Following an introductory chapter, there is a chapter devoted to the de- velopment of the small signal models for common electro-optical com- ponents used in both direct and external modulation. However, this is not adevice book, so the theory of their operation is discussed only insofar as it is helpful in understanding the small signal models that result. These device models are then combined to form a complete link. With these analytical tools in place, a chapter is devoted to examining in detail each of the four primary link parameters: gain, bandwidth, noise figure and dynamic range. Of particular interest is the inter-relation between device and link parameters. A final chapter explores some of the tradeoffs among the primary link parameters. Charles H. Cox, III Sc.D., is one of the pioneers of the field that is now generally referred to as analog or RF photonics. In recognition of this work he was elected a Fellow of the IEEE for his contributions to the analysis, design and implementation of analog optical links. Dr. Cox is President and CEO of Photonic Systems Inc., which he founded in 1998. He holds six US patents, has given 45 invited talks on photonics and has published over 70 papers on his research in the field of phototonics. ANALOG OPTICAL LINKS Theory and Practice CHARLES H. COX, III cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK First published in print format isbn-13 978-0-521-62163-2 isbn-13 978-0-511-19562-4 © Cambridge University Press 2004 2004 Information on this title: www.cambrid g e.or g /9780521621632 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. isbn-10 0-511-19562-1 isbn-10 0-521-62163-1 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Published in the United States of America by Cambridge University Press, New York www.cambridge.org hardback eBook (NetLibrary) eBook (NetLibrary) hardback To Carol and to the memory of Charles H. Cox, Jr. and John A. Hutcheson, whose combined influences on me defy measure or acknowledgement Contents Preface page xi 1 Introduction 1 1.1 Background 1 1.2 Applications overview 8 1.2.1 Transmit optical links 8 1.2.2 Distribution optical links 9 1.2.3 Receive optical links 11 1.3 Optical fibers 12 References 17 2 Link components and their small-signal electro-optic models 19 2.1 Introduction 19 2.1.1 Notation 20 2.2 Modulation devices 20 2.2.1 Direct modulation 20 2.2.2 External modulation 34 2.3 Photodetectors 49 Appendix 2.1 Steady state (dc) rate equation model for diode lasers 54 Appendix 2.2 Absorption coefficient of an electro-absorption modulator 63 References 63 3Low frequency, short length link models 69 3.1 Introduction 69 3.2 Small-signal intrinsic gain 70 3.2.1 Direct modulation 72 3.2.2 External modulation 74 3.3 Scaling of intrinsic gain 75 vii viii Contents 3.3.1 Optical power 75 3.3.2 Wavelength 79 3.3.3 Modulation slope efficiency and photodetector responsivity 81 3.4 Large signal intrinsic gain 82 Appendix 3.1 External modulation links and the Manley–Rowe equations 87 References 88 4 Frequency response of links 91 4.1 Introduction 91 4.2 Frequency response of modulation and photodetection devices 93 4.2.1 Diode lasers 93 4.2.2 External modulators 98 4.2.3 Photodetectors 105 4.3 Passive impedance matching to modulation and photodetection devices 110 4.3.1 PIN photodiode 112 4.3.2 Diode laser 117 4.3.3 Mach–Zehnder modulator 129 4.4 Bode–Fano limit 138 4.4.1 Lossy impedance matching 139 4.4.2 Lossless impedance matching 142 Appendix 4.1 Small signal modulation rate equation model for diode lasers 152 References 156 5 Noise in links 159 5.1 Introduction 159 5.2 Noise models and measures 160 5.2.1 Noise sources 160 5.2.2 Noise figure 167 5.3 Link model with noise sources 168 5.3.1 General link noise model 168 5.3.2 RIN-dominated link 169 5.3.3 Shot-noise-dominated link 173 5.4 Scaling of noise figure 178 5.4.1 Impedance matching 179 5.4.2 Device slope efficiency 180 5.4.3 Average optical power 182 5.5 Limits on noise figure 185 5.5.1 Lossless passive match limit 185 Contents ix 5.5.2 Passive attenuation limit 187 5.5.3 General passive match limit 189 Appendix 5.1 Minimum noise figure of active and passive networks 196 References 199 6 Distortion in links 201 6.1 Introduction 201 6.2 Distortion models and measures 202 6.2.1 Power series distortion model 202 6.2.2 Measures of distortion 205 6.3 Distortion of common electro-optic devices 217 6.3.1 Diode laser 217 6.3.2 Mach–Zehnder modulator 222 6.3.3 Directional coupler modulator 225 6.3.4 Electro-absorption modulator 227 6.3.5 Photodiode 228 6.4 Methods for reducing distortion 232 6.4.1 Primarily electronic methods 233 6.4.2 Primarily optical methods 240 Appendix 6.1 Non-linear distortion rate equation model for diode lasers 249 References 259 7 Link design tradeoffs 263 7.1 Introduction 263 7.2 Tradeoffs among intrinsic link parameters 263 7.2.1 Direct modulation 263 7.2.2 External modulation 268 7.2.3 SNR vs. noise limits and tradeoffs 273 7.3 Tradeoffs between intrinsic link and link with amplifiers 277 7.3.1 Amplifiers and link gain 277 7.3.2 Amplifiers and link frequency response 278 7.3.3 Amplifiers and link noise figure 278 7.3.4 Amplifiers and link IM-free dynamic range 279 References 284 Index 285 [...]... One important aspect of many receive links that does simplify the distortion problem is that broadband antennas are rare, and those that are broadband achieve a wide bandwidth at a severe tradeoff in sensitivity Consequently most receive links need only an octave (2:1) bandwidth or less, which means that wide-band distortion can be filtered out and that narrow-band distortion is the dominant factor... amplifiers per level of splitting may be needed Each optical amplifier emits broad bandwidth noise in addition to the amplified coherent (narrowband) light If this noise is not reduced through filtering, it is possible for subsequent stages of optical amplification to amplify and eventually be saturated by this broadband light 1.2.3 Receive optical links These links are designed to convey an RF signal detected... distribution, the bandwidth is sufficiently wide that both narrow-band and wide-band distortion – two terms that will be defined in Chapter 6 – must be taken into consideration in designing links for this application Typically, external modulation links are used in the primary ring and direct modulation is used in the secondary ring Distribution links by their very nature have a high optical loss that... However, all the known broadband linearization techniques – i.e those that reduce both the wide-band and narrow-band distortion – invariably increase the link noise In contrast, narrow-band-only linearization techniques, which invariably increase the wide-band distortion, do not suffer a significant noise penalty (Betts, 1994) There is a need for wide-band receive links, and they present one of the principal... links In this case, the comparison is not between an optical fiber and free space but between an optical fiber and an electrical cable Figure 1.1 shows typical cable and optical fiber losses vs length As can be seen, the highest loss for optical fiber is lower than even large coax for any usable frequency For the purposes of discussion in this book, an optical link will be defined as consisting of all the... device and fiber constraints is that there are three primary wavelength bands that are used in fiber optic links By far the dominant wavelengths in use at present are located in bands around 1.3 and 1.55 ␮m From Fig 1.8 it would appear that the best wavelength band would be the one around 1.55 ␮m Indeed, this is where the lowest loss is and hence this would be the best wavelength to use for long length links. .. direct-detection analog optical links, IEEE Trans Microwave Theory Tech., 45, 1375–83 Darcie, T E and Bodeep, G E 1990 Lightwave subcarrier CATV transmission systems, IEEE Trans Microwave Theory Tech., 38, 524–33 Desurvire, E 1994 Erbium-Doped Fiber Amplifiers, New York: Wiley Gowar, J 1983 Optical Communication Systems I, Englewood Cliffs, NJ: Prentice Hall, Section 16.2.1 Noguchi, K., Miyazawa, H and Mitomi,... Introduction 1.1 Background Optical communication links have probably been around for more than a millennium and have been under serious technical investigation for over a century, ever since Alexander Graham Bell experimented with them in the late 1800s However, within the last decade or so optical links have moved into the communications mainstream with the availability of low loss optical fibers There are... while the optical fiber link loss does not The zero length loss for the optical fiber link represents the combined effects of the RF /optical conversion inefficiencies of the modulation and photodetection devices For long length links this zero length conversion loss is less important because the sum of the conversion and fiber losses is still less than the coaxial loss But for shorter length links, where... fiber optic links into three functional categories that dominate the applications at present: transmit, distribution and receive links 1.2.1 Transmit optical links An optical link for transmit applications is aimed at conveying an RF signal from the signal source to an antenna, as shown in generic block diagram form in Fig 1.5 Applications include the up-link for cellular/PCS antenna remoting and the transmit . ANALOG OPTICAL LINKS Analog Optical Links presents the basis for the design of analog links. Following an introductory. Transmit optical links 8 1.2.2 Distribution optical links 9 1.2.3 Receive optical links 11 1.3 Optical fibers 12 References 17 2 Link components and their