Publisher Summary

This chapter provides an overview of optical bistability. Optical bistability is a rapidly expanding field of research because of its potential application to all-optical logic and because of the interesting phenomena it encompasses. Many bistable devices consist of a nonlinear medium within an optical resonator, just as lasers do; however, passive bistable devices are excited only by the incident coherent light. The counterparts of many phenomena studied in lasers, such as fluctuations, regenerative pulsations, and optical turbulence, can be observed in passive bistable systems, often under better controlled conditions. A system is said to be optically bistable if it has two output states for the same value of the input over some range of input values. There are two reasons for making a strong distinction between optical bistability in passive systems and optical bistability in lasers. First is the guess that passive systems are more likely to become practical because they are simpler and hence are likely to be smaller and require less power. Second, the two fields have evolved independently.

1.1 DEFINITION AND TYPES OF OPTICAL BISTABILITY

A system is said to be optically bistable if it has two output states IT for the same value of the input II over some range of input values. Thus a system having the transmission curve of Fig. 1.1-1 is said to be bistable between I↓ and I↑. Such a system is clearly nonlinear, i.e., IT is not just a multiplicative constant times II. In fact, if II is between I↓ and I↑, knowing II does not reveal IT. Nonlinearity alone is insufficient to assure bistability. It is feedback that permits the nonlinear transmission to be multivalued, i.e., bistable. It is this restricted definition of optical bistability defined by Fig. 1.1-1, with the nonlinear medium unexcited, that is adopted here. This definition implies that the bistable system can be cycled completely and repeatedly by varying the input intensity. Systems that exhibit hysteresis as a function of some other parameter but not light intensity are not of interest here. This restricted definition rules out “bistable” optical systems that cannot be reset merely by reducing the input intensity, such as a burglar alarm or a card in a laser beam powerful enough to burn through the card. Even an optical damage device that can be restored by irradiation with light of a different wavelength is not in the spirit here of an all-optical completely recyclable passive system.

An example of a system exhibiting optical bistability is a Fabry-Perot interferometer containing a saturable absorber; see Fig. 1.1-2. A simple analysis of such a nonlinear etalon reveals the possibility of bistability. For weak input intensity, II, the intracavity absorption spoils the finesse of the cavity even though the laser frequency ν and cavity frequency νFP of peak transmission are coincident. Therefore the intracavity intensity IC at z = 0 is simply II times the input mirror transmission T. At the cell exit

(1.1-1)

and the transmitted intensity is

(1.1-2)

Equation (1.1-2) holds as long as the saturation intensity Is of the medium is large compared with the intracavity intensity, i.e., if

(1.1-3)

is satisfied sufficiently. Figure 1.1-3 depicts the case of strong input intensity in which the medium is bleached, the finesse is high, and the etalon transmits perfectly; i.e., IT II and IC IT/T. This clearly holds for IC Is, i.e., if

(1.1-4)

is satisfied sufficiently. The possibility of bistability is suggested by noting that both Eqs. (1.1-3,4) can be satisfied by the same input intensity. For example, take II = Is, then both inequalities require that T be less than 1 as it always is. This physical argument is substantiated by the more rigorous derivation in Section 2.1.

There are two useful classifications of bistable systems. A system may be absorptive or dispersive, and it may be intrinsic or hybrid. For example, the nonlinear Fabry-Perot interferometer just discussed is an absorptive intrinsic system. A system is absorptive or dispersive depending on whether the feedback occurs by way of an intensity-dependent absorption or refractive index. Clearly this distinction is not sharp, since both absorptive and refractive mechanisms may be significant simultaneously. The distinction between intrinsic (all-optical) and hybrid (mixed optics and electronics) is sharp. In an intrinsic system the intensity dependence arises from a direct interaction of the light with matter. In a hybrid system the intensity dependence arises from an electrical signal from a detector monitoring the transmitted intensity, usually applied to an intracavity phase shifter. Experimental embodiments of intrinsic and hybrid systems are described in Chapters 3 and 4, respectively.

For further reading: a simple introduction to optical bistability is Gibbs, McCall, and Venkatesan (1979) and recent collections of papers are: Bowden, Ciftan, and Robl (1981); Bowden, Gibbs, and McCall (1984); and A. Miller, Smith, and Wherrett (1984). Apart from this book, the most extensive review of optical bistability, both theory and experiment, is Abraham and Smith (1982a). Lugiato (1984) gives a more recent and thorough review of the theory of optical bistability. Goldstone (1984) is a good introduction, especially for dynamic effects.

1.2 OPTICAL LOGIC WITH BISTABLE DEVICES

The transmission of information as signals impressed on light beams traveling through optical fibers is replacing electrical transmission over wires. The low cost and inertness of the basic materials of fibers and the small size and low loss of the finished fibers are important factors in this evolution. Furthermore, for the very fast transmission systems, for example, for transmitting a multiplexed composite of many slow signals, optical pulses are best. This is because it is far easier to generate (Hochstrasser, Kaiser, and Shank, 1980; Shank, Ippen, and Shapiro, 1978) and propagate (Bloom, Mollenauer, Lin, Taylor, and DelGaudio, 1979) picosecond optical pulses than electrical pulses. With optical pulses and optical transmission a reality, the missing component of an all-optical signal processing system is an optical logic element in which one light beam or pulse controls another. The optical bistable systems described in this book have many desirable properties of an all-optical logic element. Hopefully they are the forerunners of tiny, low-energy, subpicosecond, room-temperature devices. The high frequencies of optical electromagnetic radiation give optical devices a potential for subpicosecond switching and room-temperature operation unavailable to Josephson junctions or electronics. The fact that electrical charges are not used or are used only in tiny beam-interacting regions makes an all-optical system much more immune to electromagnetic interference from electrically noisy industrial environments or the electromagnetic pulses from a nuclear explosion. If this book aids and accelerates the understanding and development of such all-optical systems, it will have served its purpose.

Bistable devices have already performed a host of logic functions. Both two-state (Fig. 1.2-1) and many-state (Fig. 1.2-2) optical memories have been demonstrated. The amount of transmitted light reveals the past history of the input light; i.e., the system “remembers” whether or not the input ever...