Introduction

This chapter is dedicated to the evaluation of optical interconnects between electronic processors in multiprocessor systems. Each processor is fully electronic except for the incorporation of a number of photodetectors and optical signal transmitters (e.g., laser diodes, light emitting diodes (LEDs) or optical modulators).

The motivation for this analysis stems from fundamental advantages of optics as well as those of electronics. While electrons are charged fermions, subject to strong mutual interactions and strong reactions to other charged particles, photons are neutral bosons, virtually unaffected by mutual interactions and Coulomb forces. Thus, unlike electrons, multiple beams of photons can cross paths without significant interference. This property allows holographic interconnects to achieve a 3-D (three-dimensional) connection density with only 2-D optical elements. Similarly, photons can propagate through transparent materials without appreciable attenuation or power dissipation. Thus, neglecting speed of light delays, the speed of an optical link is limited only by the switching speed and capacitance of the transmitters and detectors. (For a 10 cm connection length, and a 50° hologram deflection angle, the speed-of-light delay is 0.5 ns.) Hence, the speed and power requirements of an optical interconnect are independent of the connection length. Since electrical very large scale integration (VLSI) connections have a switching energy directly proportional to the line length and an RC delay that grows quadratically with line length, for long enough communication links, optical connections will dissipate less power and provide faster data rate communication.

Introduction

When a scientist or engineer is provided with a given processing problem and asked whether optical processing techniques can solve it, how does he answer the question and approach the problem? To address this, he first considers the basic operations possible. They are often not a direct match to a new problem. Hence new algorithms arise to allow new operations to be performed (often on a new optical architecture). The final system is thus the result of an interaction between optical components, operations, architectures, and algorithms. This chapter describes these issues for the case of image processing. By limiting attention to this general application area, specific examples can be provided and the role for optical processing in most levels of computer vision can be presented. (Other chapters address other specific optical processing applications.)

Section 1.2 presents some general and personal philosophical remarks. These provide guidelines to be used when faced with a given data processing problem and to determine if optical processing has a role in all or part of a viable solution. Section 1.3 describes optical feature extractors. These are the simplest optical systems. This provides the reader with an introduction and summary of some of the many different operations possible on optical systems and how they are of use in image processing. A major application for these simple systems, product inspection, is described to allow a comparison of these optical systems and electronic systems to be made.

Section 1.4 addresses the optical correlator architecture, since it is one of the most powerful and most researched architectures. The key issues in such a system used for pattern recognition are noted.

The design of optical hardware for signal and image processors and in computing systems can be expected to become an increasingly important activity as optics moves from the laboratory to actual usage. Over the past decades a variety of concepts have been developed to exploit the capabilities of optics for ultrahigh-bandwidth and massively-parallel processing such as for analog front-end operations, image-processing and neural-net applications, high-bandwidth interconnection of electronic systems such as computers and microwave subsystems, execution of logic and other nonlinear operations for routing of optical interconnects, as well as for general reduction of hardware size, weight and power consumption. Original concept investigations usually identify theoretical advantages of performing various tasks with optics, but one then needs to address whether the advantages can be maintained as one addresses various new issues involving usage in a real-world environment; e.g., can demonstrations of optical processing speed and parallelism, optical routing, and communication bandwidth be retained in full-scale application? Addressing these questions very often requires an optical approach that employs different algorithmic/architectural approaches than conventional alternatives; hence, new architectures are devised to utilize maximally the strengths of optics. Finally, the capabilities of optical technology may dictate specific optical hardware designs.

It is therefore difficult to predict whether a specific optical hardware configuration will still possess the originally identified advantages. Although full-scale demonstrations can provide a direct answer, careful design and analyses must be performed to ensure an effective demonstration. The design and analysis stage can involve fundamental issues that are quite removed from the original optical-processing concept.

Introduction

This chapter discusses the issues involved in the design of a free-space digital optical logic system. The first section is an introduction to this field with an overview of the justification of pursuing this exciting and challenging course. The second section is a discussion of the basic characteristics of the devices that must be used in a system of this type with specific examples of the behavior of three of the most popular devices. Section 6.3 is a discussion of the optical and mechanical constraints involved in the design process. The fourth section is a design example using logic gates made from symmetric self electro-optic effect devices (S-SEEDs). The final section summarizes the likely future directions.

Background of digital optics

Two methods exist for communicating high bandwidth information: light and electricity. It is clear that the optimum choice for long distances (>1 km) is light; hence the adoption of fiber for telephony. It is equally clear that over short distances (<1 mm), the optimum choice is electricity hence its use for gate-to-gate interconnection in a chip. It has been shown that as the distance between the transmitter and receiver increases, the energy required by an electrical connection increases more rapidly than if optics is used (Miller, 1989). It is difficult to justify the use of optics over short distances and conversely, electrical connection is not ideal except over the shortest distances. The ultimate optimum choice for chip-to-chip and board-to-board interconnection is unclear.

Introduction

Optical linear algebra processors (OLAPs) perform numerical calculations such as matrix–vector multiplication by equating a particular property of light, normally its intensity level, to a number. Through various effects to be discussed in this section, uncertainty is introduced either through random fluctuations or the addition of a bias. The fluctuating intensity can now be considered a random variable for which a mean and standard deviation can be determined. After corrections for bias, the mean value can be taken as the correct level that relates to the expected numerical value while the nonzero standard deviation represents processor noise.

In the design of analog OLAPs such as matrix–vector and matrix–matrix processors, the effect of noise from both device and system sources has a major impact on the choice of system architecture and components. The ability of a particular system design to meet system performance specifications such as signal-to-noise ratio (SNR), dynamic range, and accuracy is directly connected to the noise properties of the system and its components. As an example, the choice of the spatial light modulator (SLM) has a significant impact (Casasent & Ghosh, 1985; Perle & Casasent, 1990; Taylor & Casasent, 1986; Batsell, Jong, Walkup & Krile, 1989a, 1990; Jong, Walkup & Krile, 1986). This chapter examines the effects of noise on these system specifications and their implications for OLAP design.

We begin with a theoretical analysis of a simple matrix–vector multiplier and then generalize the results for N cascaded matrix–vector multipliers.

Introduction

The theoretical studies of long-distance soliton transmission in optical fibres with periodic Raman gain were outlined in Chapter 2 ‘Solitons in Optical Fibres: An Experimental Account’ by L. F. Mollenauer. From this work, it was anticipated that the overall information rates made possible by the all-optical nature of the system were potentially orders of magnitude greater than in conventional communication systems. Rate–length products were predicted to be as high as approximately 30000 GHz · km for a single wavelength channel. In the following sections we will describe the first set of experiments designed to explore the fundamentals of such long-distance repeaterless soliton transmissions.

Experimental investigation of long-distance soliton transmission

In the following experiments, a train of soliton pulses was injected into a closed loop of fibre, the length of which corresponded to one amplification period in a real communication system. The pulses propagated around the loop many times until the net required fibre pathlength had been reached (Mollenauer and Smith, 1988). The experimental configuration is shown schematically in Figure 3.1. A 41.7 km length (L) of low-loss (0.22 dB/km at 1.6 μm) standard telecommunications single-mode fibre was closed on itself with a wavelength selective directional coupler (an all-fibre Mach–Zehnder (FMZ) interferometer). The interferometer allowed efficient coupling of the bidirectional pump waves at approximately 1.5 μm (provided by the 3 dB coupler at the pump input) into the loop. At the same time, the signals at approximately 1.6 μm (50 ps sech2 intensity profile pulses at a 100 MHz repetition rate from a synchronously mode-locked NaCl:OH– colour centre laser) were efficiently recirculated (<5% coupled out).

Introduction

In a communication system, it is desirable to launch the pulses close to each other so as to increase the information-carrying capacity of the fibre. But the overlap of the closely spaced solitons can lead to mutual interactions and therefore to serious performance degradation of the soliton transmission system. This has been pointed out independently by three groups (Chu and Desem, 1983a; Blow and Doran, 1983; Gordon, 1983).

Karpman and Solov'ev (1981) first considered the two-soliton interaction in their study of the non-linear Schrödinger equation (NLS) by means of single-soliton perturbation theory. Although they did not have optical fibre transmission in mind their results are applicable to fibres since the soliton propagation in optical fibres are described by the same equation. However, their method is restricted to large soliton separation only.

Our numerical investigations (Chu and Desem, 1983a) show that soliton interaction can lead to a significant reduction in the transmission rate by as much as ten times. At about the same time, Blow and Doran (1983) showed that the inclusion of fibre loss also leads to dramatic increase of soliton interactions. Gordon (1983) derived the exact solution of two counter-propagating solitons (of nearly equal amplitudes and velocities) and analysed the interaction by obtaining the approximate equations of motion corroborating the results of Karpman and Solov'ev (1981).

A considerable amount of research effort has been spent on the reduction of soliton interactions.

Introduction

Although soliton phenomena arise in many distinct areas of physics, the single-mode optical fiber has been found to be an especially convenient medium for their study. As described in the previous chapters of this book, soliton propagation of bright optical pulses has been verified in a number of elegant experiments performed in the negative group velocity dispersion (GVD) region of the spectrum; most recently, transmission of 55-ps optical pulses through 4000 km of fiber was achieved, by use of a combination of non-linear soliton propagation to avoid pulse spreading and Raman amplification to avoid losses (Mollenauer and Smith, 1988). For positive dispersion (λ < 1.3 μm in standard single-mode fibers), bright pulses cannot propagate as solitons and the interaction of the non-linear index with GVD leads to spectral and temporal broadening of the propagating pulses. These effects form the basis for the fiber-and-grating pulse compressor (Nakatsuka et al., 1981; Grischkowsky and Balant, 1982; Tomlinson et al., 1984), which was utilised to produce the shortest optical pulses (6 fs) ever reported (Fork et al., 1987). For both signs of GVD, the experimental results are in quantitative agreement with the predictions of the non-linear Schrödinger equation (NLS).

Although bright solitons are allowed only for negative GVD, the NLS admits other soliton solutions for positive GVD (Hasegawa and Tappert, 1973; Zakharov and Shabat, 1973). These solutions are ‘dark pulse solitons’, consisting of a rapid dip in the intensity of a broad pulse of a c.w. background.

In this chapter, soliton amplification and transmission using erbium-doped fiber amplifiers are presented. First, the general features of the erbium-doped fiber amplifier are described. A new method called dynamic soliton communication is presented, in which optical solitons can be successfully amplified and transmitted over an ultralong dispersion-shifted fiber by using the dynamic range of N = 1–2 solitons. Multi-wavelength optical solitons at wavelengths of 1.535 and 1.552 μm have been amplified and transmitted simultaneously over 30 km with an erbium-doped fiber repeater. It is shown that there is saturation-induced cross talk between multi-channel solitons, and the cross talk (the gain decrease) is determined by the average input power in high bit-rate transmission systems.

The amplification of pico, subpico and femtosecond solitons and 6–24 GHz soliton pulse generation with erbium-doped fiber are also described, which indicates that erbium fibers are very advantageous for short pulse soliton communication. Some soliton amplification characteristics in an ultralong distributed erbium fiber amplifier are also presented. Finally, we describe 5–10 Gbit/s transmission over 400 km in a soliton communication system using the erbium amplifiers.

Introduction

Recent progress on erbium-doped fiber amplifiers (EDFA) has been very rapid since they show great potential for opening a new field in high-speed optical communication (Mears et al., 1985; Poole et al., 1985; Desurvire et al., 1987; Snitzer et al., 1988; Kimura et al., 1989; Suzuki et al., 1989; Nakazawa et al., 1989).

Introduction

In optical fibers, solitons are non-dispersive light pulses based on non-linearity of the fiber's refractive index. Such fiber solitons have already found exciting use in the precisely controlled generation of ultrashort pulses, and they promise to revolutionise telecommunications. In this chapter, I shall describe those developments, and the experimental studies they have stimulated or have helped to make possible. Thus, besides the first experimental observation of fiber solitons, I shall describe the invention of the soliton laser, the discovery of a steady down-shift in the optical frequency of the soliton, or the ‘soliton self-frequency shift’, and the experimental study of interaction forces between solitons.

As early as 1973, Hasegawa and Tappert (1973) pointed out that ‘single-mode’ fibers – fibers admitting only one transverse variation in the light fields – should be able to support stable solitons. Such fibers eliminate the problems of transverse instability and multiple group velocities from the outset, and their non-linear and dispersive characteristics are stable and well-defined. The first experiments (Mollenauer et al., 1980), however, had to wait a while, for two key developments of the late 1970s. The first was fibers having low loss in the wavelength region where solitons are possible, and the second was a suitable source of picosecond pulses, the mode-locked color center laser.

But the first experiments led almost immediately to further developments.

Introduction

The earliest experimental schemes for generating optical solitons, see for example the chapter by Mollenauer in this book or the original paper by Mollenauer et al. (1980), relied on launching pulses with power and transform limited spectral characteristics which matched the soliton requirements for the particular optical fibre used. However, it was shown by Hasegawa and Kodama (1981), that a pulse with any reasonable shape could evolve into a soliton. In such a case, the energy not required to establish the soliton appears as a dispersive wave in the system.

An alternative mechanism for soliton generation was proposed by Vysloukh and Serkin (1983), based on stimulated Raman scattering in fibres, which was later verified by Dianov et al. (1985), through compression in multisoliton Raman generation from a pulsed laser source. Since then, there has been a considerable number of experimental reports of soliton generation through stimulated Raman scattering in various configurations and using several different pump sources, Islam et al. (1986), Zysset et al. (1986), Kafka and Baer, (1987), Gouveia-Neto et al. (1987), Vodopyanov et al. (1987), Nakazawa et al. (1988) and Islam et al. (1989). More generally, it has been shown theoretically by Blow et al. (1988a), that soliton formation is possible in the case where there is coupling between waves leading to energy transfer, specifically via a gain term in the non-linear Schrödinger (NLS) equation description of the system.

Introduction

The study of non-linear waves has always been associated with numerical analysis since the discovery of recurrence in non-linear systems (Fermi et al., 1955) and elastic soliton–soliton scattering (Zabusky and Kruskal, 1965). Since then the mathematics of non-linear wave equations has grown into the industry of inverse scattering and numerical analysis has developed a number of techniques for studying non-linear systems. Inverse scattering theory has given us much insight into integrable non-linear systems and has supplied many useful exact solutions of non-linear partial differential equations. Numerical analysis has mostly been used in the complementary field of non-integrable systems. Since most non-integrable systems of interest, in physics, are ‘close’ to integrable ones the combination of perturbation theory and numerical analysis provides a powerful tool for investigating such systems. In this chapter we will show through illustrative examples how simple concepts and enhanced understanding can be derived for complex non-linear problems through insight gained from numerical simulation. A good example of this is described in Section 4.6 where the concept of a ‘soliton phase’ emerges from numerical simulation; this is a particularly simple and useful concept enabling the design of a number of soliton switching systems.

Before we begin let us clarify the use of the term soliton. When used by mathematicians the term soliton has a precise meaning in the context of inverse scattering theory and carries with it the associated properties of a localised non-linear wave, elastic scattering amongst solitons, stability and being part of an integrable system.

Although the concept of solitons has been around since Scott Russell's various reports on solitary waves between 1838 and 1844, it was not until 1964 that the word ‘soliton’ was first coined by Zabusky and Kruskal to describe the particle-like behaviour of the solitary wave solutions of the numerically treated Korteweg–deVries equation. At present, more than one hundred different non-linear partial differential equations exhibit soliton-like solutions.

However, the subject of this book is the optical soliton, which belongs to the class of envelope solitons and can be described by the non-linear Schrödinger (NLS) equation. In particular, only temporal optical solitons in fibres are considered, omitting the closely related work on spatial optical solitons.

Hasegawa and Tappert in 1973 were the first to show theoretically that, in an optical fibre, solitary waves were readily generated and that the NLS equation description of the combined effects of dispersion and the non-linearity self-phase modulation, gave rise to envelope solitons. It was seven years later, in 1980 before Mollenauer and co-workers first described the experimental realisation of the optical soliton, the delay primarily being due to the time required for technology to permit the development of low loss single-mode fibres.

Over the past ten years, there has been rapid developments in theoretical and experimental research on optical soliton properties, which hopefully is reflected by the contents of this book.