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.

I am very pleased to have completed this Second Edition of Laser Fundamentals. The encouragement I have received over the past few years from readers as well as from my editors was sufficient to provide me with the enthusiasm to take on this new task. Writing the first edition was essentially a ten-year endeavor from first thoughts to the completed book. I thought I had a better way to explain to senior-level and first-year graduate students how lasers work. Apparently there were others who agreed with me, judging from comments I have received. Writing the second edition was an attempt to fill in some of the gaps, so to speak; not surprisingly, it took much more time than I had anticipated. Some of the areas of the First Edition were not as complete as I would have liked. There were also errors that had to be corrected. In addition, there have been advances– primarily in the areas of solid-state and semiconductor lasers– that needed to be included. I think the new edition addresses those issues pretty well. I suppose it's up to the readers to make that judgment.

Naturally one canyt take on a task like this without gleaning information from experts in the various fields of lasers. I offer special thanks to my colleagues at the School of Optics/CREOL at the University of Central Florida: Michael Bass, Glenn Boreman, Peter Delfyett, Dave Hagan, Hans Jenssen, Patrick Li Kam Wa, Alexandra Rapaport, Kathleen Richardson, Martin Richardson, Craig Siders, Eric Van Stryland, Nikolai Vorobiev, and Boris Zeldovich.