I M P A C T O F Nonlinearities

O N L I G H T W A V E S Y S T E M S The field of

nonlinear optics in silica fibers

is over 20 years old.1 However, until recently,

nonlinear effects in single-mode

silica fibers were laboratory

curiosities requiring

powerful lasers for their

observation. Recent advances

in optical amplifiers for the

1.5 μm Wavelength region have drastically altered the lightwave

communications landscape and elevated optical nonlinearities to

a primary systems

consideration.

In current long-haul, high-speed, digital l ightwave systems, about 1 m W of diode

laser power is required to transmit gigabit per second in format ion over about 40 k m of fiber (typical distance between regenerators). Typically, only one information channel is trans­mitted over each fiber. In principle many infor­mation channels, each at a separate wavelength, could be transmitted over a single fiber. This technique is k n o w n as wave leng th -d i v i s i on mult iplexing (WDM). However, at each regen­erator site the W D M channels must be demult i ­plexed, indiv idual ly regenerated, and then mu l ­tiplexed onto the next fiber. For a large number of channe ls th is is i m p r a c t i c a l . In present single-channel systems, even though the light is confined to the core of the fiber (9 μm diameter) over tens of kilometers, nonlinear effects are not observable and no system impairments occur.

The advent of erbium-doped fiber ampl i ­fiers,2 wh ich provide large, broadband optical gains in the wavelength region of m i n i m u m loss of si l ica fibers (1.55 μm), has altered the course of development of future l ightwave sys­tems. Optical amplifiers not only can replace a large fraction of the regenerators, but the dis­tance between ampl i f iers can be much larger than present regenerator spacings. More impor­tant ly, because the amp l i f i e r ga in is b road (about 35 nm) many W D M channels can be simultaneously ampl i f ied, thereby el iminat ing the need for demult ip lexing at each amplif ier. Ironically, these major benefits of optical ampl i ­fiers increase the effects of optical nonl ineari­ties. W D M increases the optical power propa­ga t i ng t h rough f i be rs , and r e p l a c i n g regenerators wi th amplif iers increases the dis­tances between signal regeneration. Increased optical powers and longer interaction lengths magnify the effects of nonlinearities.

In this paper I w i l l qual i tat ively describe the various optical nonlinearities that can occur in silica fibers and how they impact communi­cation systems. More detai led descript ions of

BY A . R . CHRAPLYVY

nonlinear fiber optics can be found in the refer-ences.3-56

There are a number of nonlinearities in si l i ­ca fibers that can impact ampl i f ied l ightwave systems. They fall into two general categories. St imulated scattering such as st imulated Br i l ­louin scattering and stimulated Raman scatter­ing are interactions between optical signals and acoustic or molecular v ibrat ions in the fiber. A l t h o u g h both processes exhibi t exponent ia l gain they are qual i tat ively very different and affect l ightwave systems in completely different ways . The second category of nonl inear i t ies arises from modulat ion of the refractive index of silica by intensity changes in the signal. This gives rise to nonlinearit ies such as self-phase modulation, whereby an optical signal alters its o w n phase; cross-phase modula t ion in W D M systems, where one opt ical s ignal affects the phases of al l other op t i ca l s igna ls and v ice versa; and four-photon mixing, whereby W D M signals interact to produce mixing sidebands (as in intermodulation distortion).

S T I M U L A T E D S C A T T E R I N G

Stimulated Brillouin Scattering Stimulated Bri l louin scattering (SBS) is an inter­ac t ion between l ight and acoustic waves. In op t i ca l f ibers SBS has the lowest th resho ld power of all the nonlinearities. 3 2 Light scatters from acoustic phonons and is downshi f ted in frequency. The magn i tude of the downsh i f t depends on the scattering angle. In single-mode silica fibers the only frequency-shifted scattered l i gh t that c o n t i n u e s to be g u i d e d is backward-propagating light. The Bri l louin shift in this case is 11 G H z . This backscattered light expe r i ences e x p o n e n t i a l g a i n d u e to forward-propagat ing signals. System impai r ­ment occurs when the backscattered light level becomes comparable to the signal power and begins to deplete the signal. For typical fibers the threshold power for this process is about 10 m W for single fiber spans and correspondingly

1047-6938/94/5/0016/06-$06.00 © Optical Society of America

Nonlinearities

lower for concatenated ampl i f ied spans. However , amplif iers usual ly have optical isolators (otherwise long ampl i f ied systems cou ld easi ly oscillate) that el iminate SBS light. Consequent ly the SBS impair ­ment in amplif ied systems occurs at the same power levels as in regenerated systems. Fortunately, SBS impairments are not exacerbated i n W D M systems, because each channe l interacts w i t h phonons of slightly different frequencies. Consequently, the non-linearities accumulate indiv idual ly for each channel.

Some systems require signal powers greater than 10 mW. For example, to overcome fiber attenuation in extremely long single-span systems, higher signal powers are used that may exceed the SBS threshold. Because the l i f e t ime of the acous t i c p h o n o n s involved in SBS is about 15 nsec (which corresponds to a l inewidth of about 20 M H z ) , there are a number of techniques to reduce SBS effects. By dithering the center frequency of the signal, the SBS gain can be reduced by the ratio of the magnitude of the dither to 20 M H z . It is easy to increase the SBS threshold by an order of magnitude s imply by di ther ing the diode laser frequency over a 200 M H z range. This corre­sponds to a dither current of about 0.2 m A on the diode laser. A l though SBS has the lowest threshold of al l the fiber nonlinearities, it is also the easiest nonl in­earity to counteract.

Stimulated Raman Scattering Stimulated Raman scattering (SRS) is an interaction between l ight and the v ibra t iona l modes of s i l ica molecules. There are a number of key differences between SRS and SBS. Unl ike SBS, SRS is an extreme­ly broadband effect. The Raman transitions i n sil ica glass are very broad and overlap into a continuous gain curve shown in Figure 1.47 Note that the peak SRS gain occurs at 15 T H z . Unl ike SBS, SRS can occur in both forward and backward directions. Isolators at amplifier sites w i l l not d iminish forward SRS.

In single-channel systems some of the sponta­neously scattered, Raman-shifted light w i l l be guided in the core of the fiber in the forward direction. This light w i l l be amplif ied by the co-propagating signal l ight. Because the peak SRS gain is m u c h smal ler than the peak SBS gain, 4 9 significantly higher optical powers are required for SRS impairment. The SRS threshold for single f iber spans is about 1 W, two orders of magnitude greater than SBS. In ampl i f ied systems one might expect that the threshold is 1 W div ided by the number of spans. However, recall that the amplifier bandwidth is roughly four times smal l­er than the SRS ga in pro f i le . Consequent ly , on ly Raman light generated wi th in the amplif ier gain pro­file w i l l propagate through the amplif ied chain. Since the SRS gain profi le is roughly triangular, the peak Raman gain at 35 n m is roughly 25% of the max i ­m u m gain. It fol lows that in the worst case, the SRS threshold for an ampl i f ied chain w i l l be about 4 W d i v i d e d by the n u m b e r e d of a m p l i f i e d spans

between regenerators. SRS can be easily suppressed in single-channel ampl i f ied systems by periodical ly insert ing opt ical bandpass fi lters that transmit the signal and reject the SRS spectrum.

It is i n W D M sys tems that the d i f f e rence between SRS and SBS is clearly seen. Because the SRS gain is so broadband, W D M channels w i l l be coupled to each other for channel spacings up to 20 T H z (150 nm). The short-wavelength channels w i l l act as Raman pumps for long-wavelength channels. The long-wavelength channels w i l l be ampl i f ied at the expense of the short-wavelength channels wh ich w i l l be attenuated. Impairments f rom such interac­tions w i l l occur at powers much lower than 1 W. For example, for two channels separated by 15 T H z (110 nm), unacceptable system degradations w i l l occur at 50 m W in a single fiber span. For mult iple channels and mult ip le spans the threshold powers for degra­dat ion w i l l be proport ionately smaller. Ult imately, SRS l imits the number W D M channels that can be t ransmi t t ed t h r o u g h s i n g l e - m o d e f ibers . In the absence of nonlinear effects, single-mode fibers have roughly 25 T H z of usable optical bandwidth. H o w ­ever , S R S c a n l i m i t the u s a b l e b a n d w i d t h i n transcontinental ampl i f ied systems to less than 100 G H z . 1 2

To date, no practical techniques to combat SRS have been demonstrated. The techniques for sup­pression of SBS exploit the narrow SBS gain band­w i d t h and consequently are not appl icable to SRS suppress ion. In the future it might be possible to implement some type of optical equalization at the amp l i f i e r sites to m i n i m i z e the dep le t i on of the short-wavelength channels.

R E F R A C T I V E I N D E X N O N L I N E A R I T I E S

The refractive indices of many optical materials are weakly intensity dependent (n = n 0+n 2I). The inten­si ty-dependent refractive index, n 2 , of s i l ica has a value of 3X10 - 1 6 cm 2 . A l though this is a very smal l n 2 , i n long ampl i f ied systems or i n certain W D M sys­tems the effects of the nonlinear refractive index can be quite prominent.

F I G U R E 1

FIGURE 1: The relative gain cross-section

for (used silica fibers at 1.5 µm.

OPTICS & PHOTONICS N E W S / M A Y 1994 17

Nonlinearities

F I G U R E 2

Figure 2 schematic description of spectral broadening due to self-phase modulation

Figure 3. Spectral broadening and narrowing due to cross-phase modulation during pulse collision. F I G U R E 3

Self-Phase Modulation Self-phase modulat ion (SPM) describes the effect of a pulse on its own phase. The edge of an optical pulse represents a t ime-varying intensity. A t ime-varying intensity i n a med ium w i th an intensity-dependent refractive index w i l l produce a t ime-varying refrac­tive index, wh i ch i n turn produces a t ime-vary ing phase wh ich corresponds to a spectral broadening (Fig. 2).5 2 Therefore, one of the consequences of the nonlinear refractive index of sil ica is that the spectral w id th of signal pulses w i l l gradually increase as they propagate in a fiber. This effect is quite smal l . For example, a 1 m W pulse exhibits observable broaden­ing (factor of 2) after propagating several thousand ki lometers in an ampl i f ied system. However , a 10 m W pulse experiences the same spectral broadening but in a length 10 times shorter than a 1 m W pulse.

Spectral broadening of l ightwave signals does not always lead to system impairments. Depending on composi t ion, different s ingle-mode fibers have different values of chromatic dispersion. In a fiber that has zero chromatic dispersion, spectral broaden­ing of the s ignal w i l l not degrade system perfor­mance. Systems installed wi th fibers having non-zero chromatic dispersion might suffer degradations due to S P M . Systems that, i n the absence of nonl inear i­ties, a l ready are l im i ted by chromat ic d ispers ion effects cannot tolerate addit ional spectral broadening due to S P M . Pulses spectrally broadened by S P M w i l l be temporal ly broadened by chromatic d ispers ion and interfere wi th adjacent signal pulses.

In densely-spaced W D M systems that are not already limited by chromatic dispersion, impairments w i l l arise if the spectral broadening is large enough to cause spectra in adjacent channels to overlap.

C R O S S - P H A S E MODULATION

In W D M systems, the intensity variations i n any sig­nal channel w i l l affect the phases of al l the other sig­na ls . The o r i g i n of this c ross-phase m o d u l a t i o n (CPM) is the same nonl inear refractive index that gives rise to S P M . If the fiber chromatic dispersion is zero for a l l channe l s (a l l p u l s e s p r o p a g a t e i n lock-step), the effects of C P M due to each interfering

channel are exactly twice as strong as the S P M effect. Howeve r , there are no prac t ica l "d ispers ion- f la t ­tened" fibers. Consequently, the group velocities of various channels i n a W D M system are different and pulses i n different channels w i l l pass through each other wh i le propagat ing i n the fiber. Unde r some condit ions these pulse coll isions vir tual ly eliminate spectral broadening due to C P M . Figure 3 depicts pulses from two different channels passing through each other. Note that dur ing the first half of the col l i ­sion the interfering pulse produces a red shift in the signal pulse. In the second half of the col l is ion, the trailing edge of the interfering pulse produces a blue shift in the signal pulse. The blue shift exactly reverses the effects of the red shift if the intensities of the pulses have not significantly changed during the collision.

Four-Photon Mixing A th i rd mani festat ion of the non l inear refract ive index in W D M systems is four-photon mix ing (FPM). In the case of two s ignals (F ig. 4) there exists an intensity modulat ion at the beat frequency that mod­ulates the refractive index, producing a phase modu­lation at the difference frequency. This phase modu­lat ion creates two side bands (in the l imi t of smal l modulat ion). These side bands are cal led two-tone products because they were produced by the mix ing of two signal waves. For three channels (Fig. 5), i n addi t ion to the two-tone products created by each pair of signals, there are 3 three-tone products gener­ated by al l three waves. Since there are two different ways of generating each three-tone electric f ield, the three-tone products are generated "with four times the optical power of the two-tone products. For N chan­nels there w i l l be N 2 (N—1)/2 mix ing products gener­ated. For example, i n an 8-channel W D M system, 224 mix ing products are generated!

Two different impairments are caused by F P M .

18 O P T I C S & P H O T O N I C S N E W S / M A Y 1994

Nonliearities

FIGURE 4 . Side band generation

due to four-photon

mixing of two signals.

FIGURE 5. Side band generation

due to four-photon

mixing of three signals FIGURE 4 F IGURE 5

The obvious degradation is depletion of signal power in creating the mixing products,especially in W D M systems with many channels. An even more serious degradation occurs if the signal channels are equally spaced. In this case many of the mixing products occur at the same optical frequencies as the signals. These mixing products can now interfere either con­structively or destructively depending on the (time-dependent) relative phases of the signals. Because the electric fields interfere, small mixing products can produce severe degradations. For example, a mixing product with 1% of the power of one of the signals can produce 20% depletion in the signal channel if it destructively interferes with the signal. Recently a frequency-allocation scheme has been devised that ensures that no mixing product wi l l have the same frequency as any signal.1 6 This eliminates interference impairments and leaves only the less-severe depletion effects with which to con­tend. The frequency control required by this tech­nique is quite rigorous (= 10 GHz) and it remains to be seen whether this method wil l be practical.

F P M depends strongly on chromatic disper­sion.44 In general, the intensity modulation generated by the beating between two or three signals propa­gates at a different speed than the signals themselves (FPM is a phase-matched process). If the difference in propagation velocities is large (high chromatic dis­persion), the F P M generation efficiency becomes small (poor phase matching) and system degrada­tions are inconsequential. In fibers with zero chro­matic dispersion near the signal wavelengths, FPM is a very efficient nonlinear process and dramatic sys­tem degradations can occur in short (= 20 km) lengths of fiber. If chromatic dispersion is used as a weapon against nonlinearities, the FPM requirements are exactly opposite to those of SPM.

It should be mentioned that there are ways of combating the effects of the nonlinear refractive index and, in fact, exploiting properties of silica fibers to construct systems immune to nonlinearities and chromatic dispersions. Optical solitons are puls­es that possess such properties. Presently there are no commercial soliton-based systems. However there are many research efforts in this area and experts pre­dict that such systems wil l be available by the end of

the millennium. In conclusion, silica optical fibers possess a rich

variety of optical nonlinearities which have become important with the advent of practical optical ampli­fiers. These nonlinearities can impose restrictions on system design (fiber dispersion, channel spacing in W D M systems, information capacity, and so on.). The most tangible effect of optical nonlinearities is to pro­vide employment for systems engineers trying to exploit the ultimate information-carrying capacity of optical fibers by counteracting nonlinear effects.

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20 OPTICS & PHOTONICS N E W S / M A Y 1994

Nonlinearities

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OPTICS & PHOTONICS N E W S / M A Y 1994 21

Nonlinearities

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A. R. CHRAPLYVY is Distinguished Member of Techni­cal Staff, AT&T Bell Laboratories, Holmdel, N.J.

22 OPTICS & PHOTONICS NEWS/MAY 1994