As discussed in Chapter 1 perhaps the most important property of a pattern analysis algorithm is that it should identify statistically stable patterns. A stable relation is one that reflects some property of the source generating the data, and is therefore not a chance feature of the particular dataset. Proving that a given pattern is indeed significant is the concern of ‘learning theory’, a body of principles and methods that estimate the reliability of pattern functions under appropriate assumptions about the way in which the data was generated. The most common assumption is that the individual training examples are generated independently according to a fixed distribution, being the same distribution under which the expected value of the pattern function is small. Statistical analysis of the problem can therefore make use of the law of large numbers through the ‘concentration’ of certain random variables.

Concentration would be all that we need if we were only to consider one pattern function. Pattern analysis algorithms typically search for pattern functions over whole classes of functions, by choosing the function that best fits the particular training sample. We must therefore be able to prove stability not of a pre-defined pattern, but of one deliberately chosen for its fit to the data.

Clearly the more pattern functions at our disposal, the more likely that this choice could be a spurious pattern. The critical factor that controls how much our choice may have compromised the stability of the resulting pattern is the ‘capacity’ of the function class.

In the preface I think it is better if I abandon the formality of the text and address you the reader, directly.

As I hope you will have gathered from the title, this is a book that attempts to lay out the basis for the design of analog optical links. Let me give an example that should drive home this point. It is customary in books on lasers to start with an extensive presentation based on the rate equations (do not worry at this point if you do not know what these are). In this book we also discuss lasers, but the rate equations are relegated to an appendix. Why? Because in over 15 years of link design, I have never used the rate equations to design a link! So why all the emphasis on the rate equations in other texts? Probably because they are targeted more to, or at least written by, device designers. The view in this book is that you are a user of devices, who is interested in applying them to design of a link. Of course to use a device most effectively, or even to know which device to choose for a particular link design, requires some knowledge of the device, beyond its terminal behavior. To continue the laser example, it is important to know not only what the laser frequency response is, but also how it changes with bias.

Introduction

In this chapter we develop the small-signal relationships between the RF and optical parameters for the most common electro-optic devices used in intensity modulation, direct detection links. There are numerous device parameters we could use for this task; we concentrate here – as we will throughout this book – on those parameters that can be measured and selected by the link designer – as opposed to those parameters that can only be measured and controlled by the device designer.

To provide the basis for comparing these and future devices, we develop a figure of merit for optical modulators and detectors: the RF-to-optical incremental modulation efficiency for modulation devices and its converse the optical-to-RF incremental detection efficiency for photodetection devices. These efficiencies are useful in link design because they provide a single parameter for evaluating device performance in a link that represents the combined effects of a device's optical and electrical parameters. Further, by using the same parameter for both direct and external modulation devices, we begin the process – which will carry on through much of the book – of using a single set of tools for evaluating both types of links.

The most common electro-optic devices in use for links today are the in-plane diode laser, both Fabry–Perot and DFB, for direct modulation, the Mach–Zehnder modulator for external modulation and a photodiode for photodetection. Thus on a first reading, one may want to focus on these devices.

Introduction

The device slope efficiencies that we developed in Chapter 2, and that were cascaded to form links in Chapter 3, explicitly ignored any frequency dependence. In this chapter we remove that restriction. As we shall see, virtually all modulation and photodetection devices have an inherently broad bandwidth. Digital links require broad bandwidth, which is one of the reasons for the numerous applications of fiber optic links to digital systems. A few analog link applications also require the full device bandwidth. However, it is far more common for analog links to need only a portion of the devices' inherent bandwidth. Consequently most analog link designs include some form of RF pre- or post-filtering to reduce the bandwidth.

For completeness we address bandpass and broad bandwidth impedance matching for three electro-optic devices: PIN photodiode, diode laser and Mach–Zehnder modulator. We then combine the bandpass impedance matched cases to form both direct and external modulation links. However, the same analytical approach is used for both impedance matching methods and both modulation techniques. Therefore those readers desiring a less exhaustive treatment can obtain a complete introduction to the subject by studying only one of the impedance matching methods and one of the modulation techniques.

One may be tempted to ask: why bother with bandwidth reduction, since this adds components and complicates the design? There are at least two key reasons for implementing bandwidth reduction.

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 of course many reasons for this, but from a link design point of view, the reason for fiber's popularity is that it provides a highly efficient and flexible means for coupling the optical source to a usually distant optical detector. For example, the optical loss of a typical terrestrial 10-km free-space optical link would be at least 41 dB (Gowar, 1983), whereas the loss of 10 km of optical fiber is about 3 dB at wavelengths of ~1.55 μm. To put the incredible clarity of optical fibers in perspective, if we take 0.3 dB/km as a representative loss for present optical fibers, we see that they are more transparent than clear air, which at this wavelength has an attenuation of 0.4 to 1 dB/km (Taylor and Yates, 1957).

Today the vast majority of fiber optic links are digital, for telecommunications and data networks. However, there is a growing, some might say exploding, number of applications for analog fiber optic links. In this case, the comparison is not between an optical fiber and free space but between an optical fiber and an electrical cable.

Introduction

In Chapter 5 we explored one type of extraneous signals in links – noise – that because of its random nature is characterized byits statistical properties. In this chapter we investigate the other type of extraneous signals in links– distortion. Unlike noise however, distortion signals are deterministic. A further distinctionbetween noise and distortion is the fact that while noise is always present, independent ofwhether there are any signals present, distortion is only present when at least one signal is present. We continue in this chapter a theme of this book by using one model to describe the distortionof both direct and external modulation, although the detailed nature of the distortion will dependon the particular modulation method that is used.

The discussion that begins this chapter is general in that the results apply to all devices with some non-linearity. The general results include the frequencies at which distortionproducts occur, the measures of distortion and the conversions among them. We then apply thesetools to the characterization of the distortion produced by the modulation and photodetection devicesthat we have been studying throughout this book. For some applications the distortion levels areunacceptably high. This has led to the development of a variety of linearization techniques. The chapterconcludes with an examination of two linearization techniques.

An optical link as defined in this book consists of linear passive electrical andoptical components as well as modulation and photodetection devices.

Introduction

In Chapters 2 through 4 we have shown how a single formalism can be used to describe the gain and frequency response of both direct and external modulation links. We continue with that same approach in this chapter. However, we will see that because different noise sources dominate in each type of link, the specific form of the link noise model depends on the type of link.

Up to this point all the signal sources we have dealt with were deterministic, in the sense that we could express their output voltage at any instant of time in terms of a known function of time, say v(t). In the case of the noise sources discussed here, there are – at present – no known expressions for any of the noise sources that give the noise source output as a deterministic function of time. Consequently we are forced to use the next best description, which is to describe the noise source output in terms of its statistical properties.

There are many statistical descriptors that could be used; by far the most common one for describing noise sources in electrical and optical applications is the mean-square value. There are primarily two bases for the popularity of the mean-square value. One is that it can be derived from the statistical distribution for the noise source, without ever knowing the underlying deterministic function. The other reason is that the mean-square value corresponds to the heating effect generated by the noise source.

Introduction

Up to this point we have discussed each of the primary measures of link performance – gain, bandwidth, noise figure and dynamic range – in as complete isolation from the other parameters as possible. While such an approach permitted us to focus on the various aspects of each parameter, it did miss the effects of interactions among the parameters to a large extent. Clearly when designing a link, one needs to take into account such interactions; in fact one might argue that maturity in link design is gauged by the link designer's ability to balance often conflicting requirements to meet a given combination of link parameters.

As one might expect, there are myriad potential interactions among link parameters. Therefore in this chapter we can only offer a sampling of these interactions. We begin by exploring interactions among the primary parameters of the intrinsic link. In general the best link designs usually result from attaining the required performance via optimization of the intrinsic link.

However, there are situations where despite a link designer's best efforts, the intrinsic link performance falls below the requirements. In some of these cases electronic pre- and/or post-amplification may be used to improve performance. Consequently we expand our interaction space to include a sampling of tradeoffs between amplifier and link parameters.

Tradeoffs among intrinsic link parameters

Direct modulation

Diode laser bias current

In Fig. 2.2 we saw that the slope efficiency of a directly modulated link is highest just above threshold and decreases as the bias current is increased above threshold – slowly at first and then more rapidly as the bias current is increased further.

Introduction

The devices discussed in Chapter 2 are rarely used individually. More commonly a modulation device – either a diode laser or an external modulator – is combined with a photodetection device to form a link. In this chapter we begin to examine the performance of complete links by developing expressions for the gain of a link in terms of the modulation and photodetection device parameters. In subsequent chapters we develop analogous expressions for link frequency response, noise figure and dynamic range.

Recall from Chapter 1 that we defined a link as comprising all the components necessary to convey an electrical signal over an optical carrier. Since the definition of available power requires an impedance match, we expand the link definition slightly to include those passive electrical components needed to impedance match the modulation and photodetection devices to the electrical signal source and load, respectively. The impedance matching function is also required by the definitions of some of the link parameters we will be discussing. A more detailed version of the link block diagram is shown in Fig. 3.1.

Although the models we develop have applicability at any frequency, we choose to focus on relatively low frequencies here where lumped-element RLC passive elements are appropriate. This permits us to get the important concepts across without their being obscured by the myriad detailed effects that microwave models require.

INTRODUCTION

Semiconductors form the basis of most modern information processing devices. Electronic devices such as diodes, bipolar junction transistors, and field effect transistors drive modern electronic technology. Optoelectronic devices such as laser diodes, modulators, and detectors drive the optical networks. In addition to devices, semiconductor structures have provided the stages for exploring questions of fundamental physics. Quantum Hall effect and other phenomena associated with many-body effects and low dimensions have been studied in semiconductor structures.

It is important to recognize that the ability to examine fundamental physics issues and to use semiconductors in state of the art device technologies depends critically on the purity and perfection of the semiconductor crystal. Semiconductors are often associated with clean rooms and workers clad in “bunny suits” lest the tiniest stray particle get loose and latch onto the wafer being processed. Indeed, semiconductor structures can operate at their potential only if they can be grown with a high degree of crystallinity and if impurities and defects can be controlled. For high structural quality it is essential that a high quality substrate be available. This requires growth of bulk crystals which are then sliced and polished to allow epitaxial growth of thin semiconductor regions including heterostructures.

In this chapter we start with a brief discussion of the important bulk and epitaxial crystal growth techniques. We then discuss the important semiconductor crystal structures. We also discuss strained lattice structures and the strain tensor for such crystals.

Semiconductor-based technologies continue to evolve and astound us. New materials, new structures, and new manufacturing tools have allowed novel high performance electronic and optoelectronic devices. To understand modern semiconductor devices and to design future devices, it is important that one know the underlying physical phenomena that are exploited for devices. This includes the properties of electrons in semiconductors and their heterostructures and how these electrons respond to the outside world. This book is written for a reader who is interested in not only the physics of semiconductors, but also in how this physics can be exploited for devices.

The text addresses the following areas of semiconductor physics: i) electronic properties of semiconductors including bandstructures, effective mass concept, donors, acceptors, excitons, etc.; ii) techniques that allow modifications of electronic properties; use of alloys, quantum wells, strain and polar charge are discussed; iii) electron (hole) transport and optical properties of semiconductors and their heterostructures; and iv) behavior of electrons in small and disordered structures. As much as possible I have attempted to relate semiconductor physics to modern device developments.

There are a number of books on solid state and semiconductor physics that can be used as textbooks. There are also a number of good monographs that discuss special topics, such as mesoscopic transport, Coulomb blockade, resonant tunneling effects, etc. However, there are few single-source texts containing “old” and “new” semiconductor physics topics.