# Light amplifiers and solitons.

It is always good to look into your neighbor's backyard and see what is going on. At present, our colleagues in the telecommunications industry are excited about the possibility of building long-distance submarine cables with amplifiers instead of repeaters. The light amplifier is one of the most remarkable inventions of recent years. When you know how to make one, and have the right materials available, the concept is very simple. In a light amplifier, the amplification depends on laser action, the word laser, it will be recalled, being an acronym for light amplification by stimulated emission of radiation.Surprisingly, special fiber is not essential. Regular fiber can provide the laser action. All that is necessary is to inject, at a point where the signal is weak, a strong input known as the pump. Its effect is to raise some of the atoms of the glass of which the fiber is composed to an excited (metastable) state known as a Raman state. The wavelength on which the pump operates--slightly different from that of the signal--is chosen to be efficient for this purpose. The atoms would eventually decay spontaneously but, since they are in a metastable state, this would take some time. In practice, the great majority of the excited atoms are acted on by the signal and stimulated to decay. In doing so, they emit radiation which is coherent with the signal, and serves to augment it. As the signal and pump progress along the fiber, energy is progressively transferred from the pump to the signal.

Raman amplification needs a powerful pump and it is better to use fiber doped with a minute amount of erbium. A few meters of this cable is sufficient and much less pump is needed. It is then possible to make a lumped amplifier, consisting of a tiny semiconductor laser and a small coil of fiber. Such an amplifier can be inserted into the cable wherever gain is required.

Light amplifiers may be expected to find wide application. For example, they will greatly facilitate the use of optical fiber for cable television since, given the availability of an amplifier, the amount of energy necessary to bleed off for each subscriber or group of subscribers is very small.

Submarine Cables

In telecommunications it is now possible to contemplate the design of submarine cables using amplifiers instead of repeaters. The advantages of doing this are threefold: (1) Amplifiers are much simpler than repeaters. In the latest transatlantic cable to be laid, the repeaters comprise as many as nine custom bipolar ICs, along with associated supervisory circuits of comparable complexity. (2) If wavelength multiplexing is used, a separate repeater must be provided for each channel, whereas an amplifier has sufficient bandwidth to cover all the channels. (3) Since the design of the amplifiers does not depend on the modulation method used, upgrading the cable to use a more efficient form of modulation can be done by making changes in the terminal equipment only.

On the other hand, digital repeaters have the advantage of removing all noise and jitter; the pulses emerging after 6,000 km are as clean as those that went in. Design problems might be encountered if the cable stretched as far as the moon, but for terrestrial distances there are no problems. With amplifiers, however, noise builds up. This is not a serious problem over distances of about 1,000 km. Unfortunately some of the noise is due to spontaneous decay of atoms from a metastable state and affects phase as well as amplitude. This has a serious effect in the case of very long distance cables, such as those necessary to cross the Atlantic and the Pacific.

A less expected problem is that, over very long distances, nonlinearity in the fiber makes itself felt. It has long been known that pronounced nonlinear effects are observed if fibers are operated at very high power levels and, as we will see later, work is proceeding with a view to turning these effects to practical advantage. The mild nonlinearity observed at low power levels has various effects, one being cross modulation between the Fourier components of the transmitted pulse. It is surprising that nonlinearity should become important with a power input of only about a milliwatt. The source of the nonlinerity is the Kerr effect. This has long been known and exploited, for example, in the Kerr cell used in light switches in television and similar applications.

The combined result of nonlinearity and amplifier noise is that the spectrum of the emerging pulse is much distorted. It appears that, in the case of very long submarine cables, this distortion may be sufficiently severe to render wavelength multiplexing impracticable. Similarly, it rules out signaling methods, such as phase modulation or coherent detection, that assume preservation of phase.

However, in spite of these problems, the use of amplifiers instead of repeaters remains an attractive proposition. At present there are two transatlantic cables that use digital transmission, TAT-8 laid in 1988 and TAT-9 laid in 1992. These both use repeaters. Two more cables using repeaters are planned, after which it is expected that a change to amplifiers will be made. Similar plans exist for cables across the Pacific. A traffic capacity of 2.5Gb is confidently expected, with the possibility of a subsequent increase to 5Gb brought about by changing the terminal equipment only.

Nonlinearity as an Ally

For the more distant future there is the interesting possibility of being able to treat nonlinearity as an ally rather than as an enemy. If the pulse shape and amplitude are correctly chosen, the effect of nonlinearity can be to cancel that of dispersion. Very high input powers are required--watts, as compared with about a milliwatt used in conventional cables. Since, a monomode fiber is only some four or five wavelengths in diameter, an optical input of a few watts can amount to megawatts per square centimeter.

That nonlinearity can cancel dispersion has long been known in the case of waves in a canal containing water. In 1834 Scott Russell was watching a barge being drawn along the Edinburgh to Glasgow canal by a pair of horses. Suddenly the barge was stopped. The water was thrown into some agitation. After a short time a solitary wave of simple form emerged and began to move steadily along the canal. Russell described it as a heap of water. He was able to follow it on horseback at a trot (about 8 mph) for one or two miles before he lost it in the windings of the canal.

Russell realized that if an attempt were made to launch a solitary wave of small enough amplitude for the motion to be linear, dispersion would soon cause the wave to lose its form, and that the stability of the wave he had observed depended on nonlinearity. A number of physicists, including Rayleigh, turned their attention to the theory of nonlinear waves and it fell to two Dutch researchers to give a definitive formulation of the equation governing the propagation of such waves in a shallow canal. This equation is known after them as the Kortweg-de Vries or KdV equation. A general solution of this equation could not at that time be hoped for, but a special solution corresponding to a single solitary wave was obtained. No discussion of the stability of this wave was possible.

Solitary waves in a canal can be of any amplitude. The larger the amplitude, the smaller the width of the wave and the higher its speed. Suppose two solitary waves, a large one and a small one, start out so far apart that they are essentially independent of one another. If the large one is behind, it will eventually catch up and collide with the smaller. In Russell's time no one seemed to have asked what would happen in these circumstances. Certainly no experiments were done. It was probably assumed that the two waves would destroy each other.

It was not until 1964 that numerical calculations revealed the astonishing fact that the large solitary wave passes through the small one almost as though no nonlinearity were present. The only difference is that the large wave emerges slightly ahead of where it would be expected to be, and the small wave lags slightly behind. Waves that behave in this way are called solitons. Here was perhaps the first indication that a nonlinear world is not necessarily a completely mad world. Solitons are like the people one meets in mental institutions--peculiar some ways, but normal a lot of the time.

In 1967 an analytical solution to the nonlinear KdV equation was obtained. This was a major mathematical breakthrough and had the effect of putting the subject on a firm theoritical basis. It confirmed the results obtained by numerical experiment and opened the way to theoretical discussion of stability.

Solitons in Optical Fibers

Had the method been applicable only to the KdV equation, it would have been greeted as a remarkable mathematical success, but an isolated one. In fact, the method is of more general application, and has made a welcome addition to the mathematical physicist's armory of methods for dealing with nonlinear differential equations. In particular, the method may be applied to the more difficult equation governing waves propagated in an optical fiber. These waves are modulated into an infrared carrier, whereas the waves in the canal are base band. In spite of this difference, very similar phenomena occur. In particular, if the size and shape of the pulse are correctly related and if there is negligible attenuation, the effect of nonlinearity is to cancel that of dispersion and make the propagation of solitons possible. It was 10 years before fiber was available with low enough attenuation for this theoretical prediction to be tested experimentally.

In 1980 L.F. Mollenaur and K. Smith, of AT&T Bell Laboratories, announced the results of a landmark experiment using a length of fiber sufficiently short for attenuation to be negligible. They were able to generate pulses of the shape required by the theory. They found that a low power input pulse of this shape gave rise to an output pulse showing dispersive broadening. As the power was increased, the broadening became less and at a critical power the output pulse was of the same shape and size as the input pulse. In other words, the pulse was a soliton. The observed critical power was in good agreement with that predicted by the theory.

The lengths of fiber used by Mollenaur and Smith were short enough for attenuation to be unimportant. To cause a soliton to be propagated without change of form for any useful distance, it would be necessary to provide continuous amplification along the length of the fiber, the gain just canceling the loss. This is not practicable, and there is no alternative to the use of lumped amplifiers. Fortunately solitons are remarkably stable and able to stand ill treatment. If the amplifiers are no more than about 30 km apart--corresponding to a 10db loss--the solitons emerging from each amplifier are restored to their original form. It is necessary that the soliton period, as defined in the next section, should be large compared with the amplifier separation.

Higher Order Solitons

Mollenaur and Smith tried increasing the input power above the critical value. They found that the total energy was still concentrated in the same time span, but that most of it was accounted for by a narrow centrally placed peak. Further increases in power resulted in more than one peak developing, the total energy remaining confined as before.

For an input pulse of the critical power, the output is of the same form whatever the length of the fiber, provided it is short enough for attenuation to be negligible. For higher powers, the exact shape and number of peaks depends on the length of the fiber. For input amplitudes that are integral multiples of the critical amplitude, the pulse comes back to its original form after traversing a certain distance along the fiber. It is then known as a higher order soliton. These results are in qualitative and quantitative agreement with predictions of the theory.

The distance for the pulse to come back to its original form is known as a soliton period, and is a fundamental distance as far as a particular fiber and a particular soliton width are concerned. The soliton period is proportional to the width of the soliton and inversely proportional to the dispersion coefficient, a property which can be controlled during manufacture of the fiber. By adjusting the dispersion coefficient, the soliton period can be varied from a number of meters to many kilometers.

It is a fortunate fact that optical solitons on the same carrier do not overtake one another in the way that solitons in a canal do. However, if several different wavelengths are used for multiplexing, solitons on different channels will travel at different speeds, since speed depends on carrier wavelength. It is found that they pass each other quite happily without mutual interference provided that they do not overlap when they are launched.

A soliton is sometimes defined as an isolated wave that travels without change of form. However, this is a poor definition since it depends on a property that no real soliton can possess, since significant attenuation must always be present in any real fiber. Moreover, higher order solitons do suffer a change of form although they periodically recover their original form. The important property of solitons is their stability, and the way they can interact with each other without losing their identity. In these respects, solitons behave more like particles than waves.

The Practical Outlook for Solitons

The use of solitons does not get over the problem of accumulated amplifier noise. Unfortunately, noise due to spontaneous emission can take the form of a small shift in the wavelength of the carrier of a soliton and hence in the speed at which it travels. This causes the soliton to wander in time as it passes through succeeding amplifiers. The resulting jitter--known as Gordon-Haus jitter--builds up in random walk fashion. It has been found, by numerical solution of the propagation equation, that this wandering of the solitons can be controlled to useful extent by inserting a bandpass filter after each amplifier. It is one more striking illustration of their particlelike stability that solitons should submit to being disciplined in this way.

A consequence of the jitter is that, over transatlantic distances, a soliton requires a time slot that is up to five times its width. This effectively limits the data rate that can be obtained with solitons to much the same as can be obtained with a conventional system. However, the pulse spectrum of a soliton, as well as its shape, changes little over great distances. Solitons may, therefore, lend themselves better than conventional pulses to wavelength division multiplexing, and this could give them an advantage of as much as five in data throughput.

It is possible that towards the end of the present decade firm plans will be put in place for laying a cable based on solitons. By then the problems of designing a conventional cable with amplifiers will have become clarified and more will have been learned about solitons and their behavior.

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Title Annotation: | a new method of communicating through cables |
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Author: | Wilkes, Maurice V. |

Publication: | Communications of the ACM |

Date: | Feb 1, 1993 |

Words: | 2548 |

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