Ultra-high capacity non-soliton optical transmission using optical phase conjugation

The present invention provides an apparatus and method for achieving bit rate distance products on the order of 200 Tbits/s-km in non-soliton optical communication using optical phase conjugation. The apparatus and method utilize phase conjugation and adjustments of in-line amplifier number, spacing, and/or output power in order to compensate for the interaction between first order dispersion and fiber nonlinearity dispersion effects in an optical fiber span. The present invention provides additional techniques for adjusting system parameters, such as dispersion-length products of first and second portions of the fiber span, in order to compensate for changes in first order dispersion resulting from non-zero second order dispersion. The method and apparatus also provide an improved multi-channel optical phase conjugation system design.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to improvements in optical 
communication systems. More particularly, the present invention relates to 
optical communication systems using optical phase conjugation to 
compensate for fiber dispersion. 
2. Description of the Prior Art 
Optical communication typically involves transmitting high bit rate digital 
data over silica glass fiber by modulating a laser or other optical 
source. Glass fibers have a very broad bandwidth, on the order of 40,000 
THz, and can therefore in theory support total data rates on the order of 
20,000 Tbits/sec. However, the practical fiber transmission capability is 
limited by system constraints, among the most important of which are the 
chromatic dispersion and nonlinearities of the optical fiber itself. 
Although optical fiber also attenuates the transmitted signal, at a rate 
of about 0.2 dB per km, the development of erbium-doped fiber amplifiers 
(EDFAs) has essentially eliminated fiber attenuation as an obstacle to 
achieving longer transmission distances. 
Chromatic dispersion, often simply called dispersion, refers to a 
phenomenon in which the speed of an optical signal through the fiber 
varies as a function of the optical signal frequency or wavelength in 
standard single-mode fibers. For wavelengths below about 1.3 .mu.m, longer 
wavelengths travel faster than shorter ones, and the resulting dispersion 
is commonly referred to as normal. Above 1.3 .mu.m, shorter wavelengths 
travel faster than longer ones, and the dispersion is referred to as 
anomalous. Dispersion is typically expressed in units of picoseconds per 
kilometer-nanometer (ps/km-nm), indicating the number of picoseconds a 
pulse with a bandwidth of 1 nanometer will spread in time by propagating 
over 1 kilometer of fiber. 
One important fiber nonlinearity which can limit transmission capability is 
the Kerr effect, in which the index of refraction increases with the 
intensity of the applied optical signal. Changes in the fiber index of 
refraction modulate the phase of a signal passing through the fiber, and 
thereby impose a frequency chirp which redistributes the signal frequency 
spectrum. This phenomenon is known as self-phase modulation in single 
channel systems in which the optical signal modulates itself. In 
multi-channel systems, in which one signal causes modulation of other 
signals, the phenomenon is referred to as either cross-phase modulation or 
four-photon mixing. Lower frequencies are shifted toward the leading edge 
of an optical signal pulse and higher frequencies are shifted toward the 
trailing edge. The resulting changes in frequency distribution are 
translated to amplitude modulation by the fiber dispersion. 
Chromatic dispersion and the Kerr effect therefore both lead to increasing 
optical signal distortion as a function of transmission distance. For long 
distance communication over optical fiber, therefore, dispersion and 
nonlinearities must be controlled, compensated or suppressed. A dispersion 
and nonlinearity control technique, currently used in terrestrial and 
transoceanic optical fiber transmission, is electronic regeneration. 
Repeaters are spaced at appropriate locations along the transmission path 
to electronically detect, regenerate and retransmit the optical signal 
before the signal distortion becomes excessive. Electronic regeneration, 
however, limits the maximum achievable data rate to that of the electronic 
hardware, rather than that of the wider bandwidth optical fiber. In 
addition, repeaters are expensive to build and maintain, do not permit 
flexible system upgradability, and must be spaced at relatively short 
intervals along the fiber to effectively control optical signal 
distortion. 
Repeaterless compensation techniques have also been developed. One such 
technique involves solitons, which are optical signal pulses having a 
well-defined amplitude, pulse width and peak power for a given anomalous 
dispersion value, such that self-phase modulation due to the Kerr 
nonlinearity and anomalous chromatic dispersion interact to stabilize the 
pulse shape. A soliton maintains its shape due to this interplay between 
dispersion and nonlinearity, and can therefore travel greater distances 
without regeneration. However, soliton systems also suffer from a number 
of significant drawbacks, including the need for mode-locked sources and a 
large number of distributed sliding frequency filters to overcome timing 
jitter at bit rate distance products on the order of about 100 Tbits/s-km, 
a need for a large number of distributed amplifiers due to high signal 
power requirements, a greater sensitivity to amplifier degradation or 
failure, and difficulty in tracing system failures to a particular portion 
of the span. These problems generally lead to higher costs for system 
implementation, maintenance and upgrade. However, soliton transmission 
provides the highest currently available optical transmission capacity. 
With sliding frequency filters, a bit rate-distance product of about 200 
Tbit/s-km has been demonstrated. This bit rate-distance product will 
allow, for example, single channel 10,000 km transoceanic transmission at 
a data rate of 20 Gbit/s. High capacity non-soliton transmission typically 
requires either non-dispersive fiber or complicated dispersion management, 
and is limited to a bit rate distance product of about 90 Tbits/s-km. 
Several of the problems associated with soliton transmission are alleviated 
by another known repeaterless dispersion compensation technique, midsystem 
optical phase conjugation. Because the phase conjugate of an optical pulse 
is in effect a time reversal of the pulse, an optical phase conjugator 
placed at the midpoint of a fiber optic transmission path allows the first 
order chromatic distortion of the first half of the path to be eliminated 
by the identical first order distortion produced as the conjugated signal 
propagates along the second half. See A. Yariv, D. Fekete and D. Pepper, 
"Compensation for channel dispersion by nonlinear optical phase 
conjugation", optics Letters, vol. 4, pp. 52-54, 1979; K. Kikuchi and C. 
Lorattanasane, "Compensation for Pulse Waveform Distortion in Ultra-Long 
Distance Optical Communication Systems by Using Nonlinear Optical Phase 
Conjugation," 1993 Technical Digest Series Volume 14, Conference Jul. 4-6, 
1993, Yokohama, Japan. Midsystem optical phase conjugation has extended 
the bit rate distance product achievable in the anomalous dispersion 
region at 1.5 .mu.m wavelength of the conventional single-mode fiber which 
makes up much of the world's existing fiber communication channels. See A. 
Gnauck, R. Jopson and R. Derosier, "10 Gb/s 360 km Transmission over 
Dispersive Fiber Using Midsystem Spectral Inversion", IEEE Photonics 
Technology Letters, vol. 5, no. 6, June 1993. However, previously 
demonstrated phase conjugation techniques can achieve a maximum bit rate 
distance product of only about 3.6 Tbit/s-km, considerably less than that 
achievable with either soliton systems or non-soliton systems with 
dispersion management. Thus, the many advantages of optical phase 
conjugation over soliton or dispersion managed transmission may not 
presently be obtained for optical communication capacities greater than 
about 3.6 Tbit/s-km. 
Demonstrated optical phase conjugation compensation techniques generally 
ignore the effects of second order chromatic distortion and nonlinearities 
in the optical fiber. First order chromatic dispersion is typically 
approximated as a constant function of wavelength and second order 
dispersion, its derivative, is therefore taken to be zero. However, in 
practical systems, second order dispersion is typically on the order of 
0.05 to 0.09 ps/km-nm.sup.2. In a linear system, distortions resulting 
from second order dispersion cannot presently be compensated by optical 
phase conjugation. The presence of higher order dispersion thus acts as a 
limit on achievable transmission distance using optical phase conjugation. 
As is apparent from the above, a need exists for an improved non-soliton 
optical communication system which extends the achievable bit rate 
distance products for non-soliton systems. The improved system should 
compensate for linear second order chromatic dispersion, for the interplay 
between first order dispersion and fiber nonlinearities and also for the 
interplay between second order dispersion and nonlinearities. Furthermore, 
the improved system should provide bit rate distance products comparable 
to those presently achievable only with solitons, while avoiding the cost 
and complexity of soliton transmission. 
SUMMARY OF THE INVENTION 
The present invention provides a non-soliton optical communication system 
having a bit rate-distance product on the order of 200 Tbit/s-km for 
single channel transmission. The present invention includes a method of 
optical signal transmission which includes the steps of providing an 
optical fiber span made up of at least one segment, each segment divided 
into first and second portions; providing an optical signal transmitter at 
one end of the optical fiber span for supplying an optical signal to the 
fiber span; providing an optical signal receiver at the opposite end of 
the fiber span for receiving the optical signal from the fiber span; 
providing one or more in-line amplifiers within each of the portions of 
each segment; phase conjugating the optical signal in an optical phase 
conjugator located between the first and second portions of each segment 
to compensate for dispersion and nonlinearities within the fiber span; and 
adjusting a power level of the optical signal in at least one of the 
portions of a segment such that nonlinearities within the span are 
compensated. The method of the present invention obtains improvement over 
optical phase conjugation in accordance with the prior art in part by 
compensating for the interaction between first order dispersion and fiber 
nonlinearities. 
In accordance with one aspect of the present invention, the interplay 
between the first order dispersion and fiber nonlinearities on the first 
portion of a fiber span may be undone in the second portion by adjusting 
the optical signal power level within the first and/or second portions. 
The adjustment may be made by varying one or more system parameters, 
including amplifier number, spacing and output power within a given 
portion of the span. 
In accordance with another aspect of the present invention, the method may 
include the additional step of increasing the length of the second portion 
of at least one of the segments by an amount sufficient to compensate for 
second order dispersion within the fiber span. Improvements are thereby 
obtained over current techniques which ignore the effects of second order 
chromatic dispersion. 
In accordance with another aspect of the present invention, the step of 
increasing the length of the second portion of at least one segment may be 
accomplished by adding a single additional length of fiber to the second 
portion after the final in-line amplifier within the second portion of 
that segment, or by adding substantially equivalent additional lengths of 
fiber between each of the in-line amplifiers within the second portion of 
the segment. The amount of the increase is determined by an equation based 
upon the derivative of chromatic dispersion as a function of wavelength. 
In accordance with yet another aspect of the present invention, the optical 
signal may be a multi-channel optical signal and the phase conjugator may 
be a multi-channel phase conjugator. The individual channel signals making 
up the multi-channel optical signal may be individually phase conjugated 
by passing the multi-channel signal through a channel router, passing each 
of the individual channel signals through a single channel phase 
conjugator, and recombining phase conjugated versions of the channel 
signals. Phase conjugation of the optical channel signals may be designed 
to minimize second order dispersive effects in such a multi-channel 
optical phase conjugation system. One such technique involves frequency 
shifting each channel signal by an equivalent frequency amount such that 
each channel signal experiences the same second order dispersion effect. 
This may accomplished by, for example, frequency shifting each channel 
such that it occupies the frequency position of its adjacent channel prior 
to phase conjugation. 
As a feature of the present invention, an improved non-soliton optical 
communication system is provided which can achieve substantially higher 
bit rate distance products than existing non-soliton systems. 
As another feature of the present invention, the improved system 
compensates for the interplay between first order dispersion and fiber 
nonlinearities by using a variety of techniques. One such technique is 
adjusting the number, spacing, and/or the output power levels of the 
in-line amplifiers. An alternative technique involves adjusting the types 
of fiber used in different portions of the span such that each of the 
portions have the same first order dispersion and nonlinearity 
interaction. Improvements are thereby obtained over existing techniques 
which generally use optical phase conjugation to compensate for linear 
first order dispersive effects only. 
As another feature of the present invention, the improved system 
compensates for changes in first order dispersion resulting from non-zero 
second order dispersion. A simple computation may be made to determine the 
amount of additional length required in the second portion of a given 
segment to substantially compensate for the effects of second order 
dispersion and thereby extend transmission distance for a given bit rate. 
As yet another feature of the present invention, an optical communication 
system is provided which is capable of achieving non-soliton transmission 
across 10,000 km at a single channel bit rate of 20 Gbit/s. The system can 
achieve this performance using a single optical phase conjugator located 
between a first and second portion of a single segment optical fiber span. 
Ultra-high capacity transoceanic transmission in an optical phase 
conjugation system is now made possible. 
As a further feature of the present invention, the improved system provides 
bit rate-distance products comparable to those presently achievable only 
with solitons, while avoiding the cost and complexity of soliton 
transmission. Optical phase conjugation systems are in principle simpler 
to implement, easier to maintain, troubleshoot and upgrade, and require 
lower optical signal power levels and therefore fewer distributed 
amplifiers. These advantages are provided by the present invention, but at 
significantly higher bit rate-distance products than previously possible. 
The above discussed features, as well as additional features and advantages 
of the present invention, will become apparent by reference to the 
following detailed description and accompanying drawings.

DETAILED DESCRIPTION 
The present invention extends the achievable bit rate-distance product of a 
non-soliton optical phase conjugation system by adjusting various system 
parameters, including the number, spacing and/or output power of the 
in-line amplifiers, and the length-dispersion products of portions of the 
span. The adjustments compensate for the interaction between first order 
dispersion and fiber nonlinearities, as well as for the effects of second 
order dispersion. Although the following detailed description illustrates 
the utility of the present invention primarily in terms of a fiber span 
incorporating a single phase conjugator, it should be understood that this 
is by way of example and not limitation. The present invention may also be 
used on a multiple segment fiber span incorporating optical phase 
conjugators within each segment. Furthermore, although the present 
invention is particularly well-suited to long-haul fiber spans, it may 
also be used to improve optical phase conjugation on shorter spans. 
The dispersion compensation effects of midsystem optical phase conjugation 
are illustrated qualitatively in FIG. 1. A typical power distribution as a 
function of distance along an optical fiber of length L/2 is shown in FIG. 
1(a). Due to the time reversal of phase, phase conjugating a distorted 
signal at position L/2 and propagating it back down the optical fiber as 
indicated by the arrows will cause dispersion effects to cancel out. As a 
result, an undistorted input signal is reproduced at position 0. Instead 
of utilizing backward propagation, the same effect can be produced using a 
virtual reversal of propagation direction by inverting the power 
distribution along the second half of the fiber span of length L with 
respect to the system midpoint L/2, as shown in FIG. 1(b). The power 
distribution along each half of the span is symmetric about the system 
midpoint, and thus the conditions required for dispersion cancellation by 
phase conjugation are satisfied. The symmetric power distribution shown 
may be produced in a repeaterless system by double-sided distributed 
amplification. 
Another approach is to incorporate a an appropriate quantity of 
erbium-doped fiber amplifiers (EDFAs) such that the power distribution 
along the fiber optic span is as shown in FIG. 1(c). The fiber amplifiers 
are spaced such that the fiber span power distribution approximates that 
of a lossless line. Since the distribution is approximately lossless, a 
substantial duplicate of the input signal is obtained at position L after 
phase conjugation at L/2, without an inversion of the power distribution 
about the system midpoint. The remaining description will assume that the 
latter approach, spacing EDFA amplifiers so as to approximate a lossless 
distribution, is used. It should be recognized, however, that the present 
invention may be practiced without such an approximate distribution as 
long as a symmetric distribution is provided. 
FIG. 2 shows an exemplary optical communication system incorporating 
optical phase conjugation for dispersion compensation. The optical 
communication system shown includes an optical fiber span 9 and an optical 
signal transmitter 10 at one end of the fiber span. A booster amplifier 11 
follows the transmitter 10 to amplify the optical signal output of the 
transmitter 10 to a power level of sufficient to satisfy system 
performance specifications. The booster amplifier 11 is not considered 
part of the optical fiber span and may be contained within transmitter 10. 
An optical signal receiver 12 is located at the opposite end of the 
optical fiber span 9. The optical fiber span 9 thus provides a 
communication path between the transmitter 10 and the receiver 12. A 
preamplifier 13 amplifies the optical signal before it arrives at the 
receiver 12. The preamplifier 13 is not considered part of the optical 
fiber span 9 and may be contained within receiver 12. The exemplary 
optical fiber span 9 of FIG. 2 may be considered to comprise a single 
segment having a first portion 14 of length L1 and a second portion 15 of 
length L2. The fiber span 9 is of length L, where L=L1+L2. Each single 
segment span 14 and 15 includes a number of in-line erbium-doped fiber 
amplifiers (EDFAs) 16 connected by a number of individual fiber loops 17. 
The fiber loops 17 represent lengths of fiber within the fiber span 9. The 
EDFAs 16 compensate for the attenuation of the optical fiber and are 
spaced in a manner to approximate a lossless power distribution, as 
discussed above. A single optical phase conjugator 20 is located between 
first portion 14 and second portion 15 of the fiber span. 
The segment terminology used above in describing the optical fiber span is 
related to the number of optical phase conjugators within the span. In the 
embodiment shown in FIG. 2, the span includes only a single optical phase 
conjugator placed between a first and second portion of the span. Thus, in 
the single phase conjugator case, the span and segment are one and the 
same. However, in other cases, to be discussed in greater detail below, it 
may be desirable to divide the span into several segments, each of which 
includes a phase conjugator between a first and a second portion of its 
respective segment. 
In the prior art systems, the phase conjugator 20 is typically placed at 
the system midpoint, or as shown in FIG. 1, the point L/2 for a fiber span 
of length L. This arrangement in the prior art systems is used to 
compensate for the effects of first order linear dispersion. In these 
linear systems, the power distribution is in principle arbitrary and 
equi-distant amplifier spacing is often used for convenience. The known 
midspan placement generally does not compensate for second order 
dispersion nor for the interaction between first order dispersion and 
fiber nonlinearities. 
The interaction between first order dispersion and fiber nonlinearities may 
be compensated by adjusting the power level of an optical signal at 
various points in the fiber span. The adjustment in optical signal power 
may be made by changing the number of in-line amplifiers, the relative 
positions or spacing between the amplifiers, and/or the output power of 
one or more of the amplifiers. By performing power adjustments in this 
manner, the interplay or interaction between the first order dispersion 
and fiber nonlinearity on a first position of the span or segment of the 
span may be undone by, for example, providing the same interaction in the 
second portion. The same interaction may be provided by the power level 
adjustments described above. Alternatively, the fiber characteristics on 
the first and second portion may be adjusted such that effects of the 
interaction are undone after phase conjugation. 
In known optical phase conjugation techniques, in which second order 
dispersion is not taken into account and usually considered to be zero, 
the number, position and output power of the in-line amplifiers is in 
principle arbitrary, and generally the same on both portions of a span on 
either side of a phase conjugator. In practical systems, however, in which 
second order dispersion is non-zero, the length of a portion of the span 
may be adjusted in accordance with the present invention, which results in 
a change in the power distribution on that portion. Therefore, in order to 
achieve the same scaled nonlinearity effects on both spans the present 
invention adjusts the in-line amplifier number, spacing and/or output 
power as will be described below. It should be understood that the term 
"adjusting" as used herein may be taken to refer to actual physical 
variation of system parameters, or determination of appropriate system 
parameters by solution of well-known equations governing signal 
propagation in optical fiber, as well as other adjustment techniques. 
The appropriate amplifier number, spacing and power may be determined in 
accordance with the following equation for nonlinear bit rate distance 
product. 
##EQU1## 
In this equation, G is the amplifier gain, equivalent to 
exp(.alpha..DELTA.L), where .alpha. is the fiber attenuation and .DELTA.L 
is the amplifier spacing; B is the system bit rate; L is the length of a 
fiber span or a portion thereof; the quantity .gamma. is the nonlinear 
coefficient, which is a function of fiber parameters; P.sub.ave is the 
average power supplied to the span from a transmitter or amplifier; 
.beta..sub.2 is the first order dispersion; and .xi..sub.n is a constant 
characterizing the particular modulation/demodulation scheme used. 
In order to equalize nonlinearity in span portions on either side of a 
phase conjugator, the bit rate distance product BL for each portion may be 
solved for B. If B.sub.1 is the bit rate for a first portion of a span and 
B.sub.2 the bit rate for a second portion, the nonlinearity in each 
portion will be equivalent if B.sub.1 =B.sub.2. Since the length of the 
two portions L.sub.1, L.sub.2 will typically be different in accordance 
with the present invention, either the power level .gamma.P.sub.ave, or 
the amplifier spacing .DELTA.L on the first or second portion of the span, 
should be adjusted to achieve the desired condition of B.sub.1 =B.sub.2. 
Using the above equation, optimal values for P.sub.ave may be calculated 
for a given amplifier spacing and given lengths of first and second 
portions of the span. The actual amplifier output power along the span 
would then be adjusted to achieve this power distribution. Alternatively, 
both spacing and average power could be varied to determine a variety of 
configurations which would satisfy the B.sub.1 =B.sub.2 condition. The 
number of in-line amplifiers used could also be varied to achieve a 
similar effect. 
As previously mentioned, the placement of the optical phase conjugator in 
accordance with the present invention may not be at the precise system 
midpoint. An alternative placement may be chosen in order to compensate 
for the effects of second order dispersion. The second order dispersion 
may be compensated by, for example, adjusting a length-dispersion product 
of first and second portions of the span or segment of the span in a 
manner to be discussed more fully below. As mentioned above, the first 
portion 14 of the single segment span shown has a length L1, while the 
second portion 15 of the span has a length L2. The present invention 
provides for improved optical communication using optical phase 
conjugation in part by this compensation for the effects of non-zero 
second order dispersion. 
An exemplary plot of fiber dispersion D as a function of wavelength 
.lambda. is shown in FIG. 3. In the plot, the dispersion D is plotted on 
the vertical axis as a function of the wavelength .lambda. on the 
horizontal axis. First order dispersion, also referred to as B.sub.2, is 
represented as an exemplary linear function F1. Second order dispersion, 
also referred to as B.sub.3, is represented by the slope of the exemplary 
function F1 in FIG. 3 and is constant for a linear function F1. In order 
to have optimal dispersion compensation using phase conjugation, the 
dispersion-length product of the first and the second portion of the span 
or segment should be equivalent. In other words, the dispersion-length 
product D1L1 should be substantially equivalent to the dispersion-length 
D2L2. Second order dispersion gives rise to unequal dispersion-length 
products in systems incorporating midsystem phase conjugation, as a result 
of the frequency shift of the phase conjugated signal coupled with the 
slope of the first order dispersion curve as a function of frequency. 
An exemplary frequency spectrum is also shown along the horizontal axis in 
FIG. 3. In optical phase conjugation, to be discussed in greater detail 
below, an optical signal of frequency fs is four-photon mixed with a pump 
signal of frequency fp to produce a phase conjugate of frequency fs*. The 
optical input signal of frequency fs has a first order dispersion value of 
D1 for fiber having the dispersion function F1. The phase conjugate fs*, 
however, has a first order dispersion value of D2 in the same fiber, since 
its frequency has been shifted by an amount fs*-fs. The difference in 
dispersion D2-D1 between the original optical input signal of frequency fs 
and its conjugate of fs* will, in the considered case, result in less than 
total cancellation of dispersion as the phase conjugate propagates down 
the second portion of the fiber. The difference is due to the slope of the 
dispersion function, and the effect of this slope is not compensated for 
in existing systems. Instead, as previously mentioned, existing system 
designs assume the second order dispersion is zero, and therefore that the 
equivalent dispersion-length product condition L1D1=L2D2 required for 
perfect dispersion cancellation is met for L1= L2. 
The method of the present invention compensates for the slope of the fiber 
dispersion curve, or second order dispersion, by determining the optimal 
placement of the optical phase conjugator within a fiber span. An equation 
relating the length L2 of the second portion of a single segment span is: 
##EQU2## 
In the above equation, .DELTA.fp represents the frequency spacing between 
the optical signal and the pump signal, and dD/d.lambda. is the second 
order dispersion. The above equation relates L2 to L1 as a function of 
second order dispersion. This equation may be used to calculate a value 
for L2 given a length L1, or vice versa. As previously indicated, the 
optical phase conjugator is placed between the first and second portions, 
having length L1 and L2 respectively, of the single segment span. The 
determination of the lengths L1 and L2 establishes the desired placement 
of the optical phase conjugator for compensating second order dispersion 
in accordance with the present invention. In a system incorporating a 
single phase conjugator, performance may be improved either by increasing 
the length of the second portion of the span, or decreasing the length of 
the first portion of the span, for phase conjugation as depicted in FIG. 
3. 
An alternative to increasing or decreasing the length of the second portion 
of the span is to use fiber with a different dispersion function in the 
second portion of the span. Referring again to FIG. 3, fiber with a 
dispersion function F2 may be used in the second span to compensate for 
the slope of the dispersion function F1 in the first portion of the span. 
Since the phase conjugation process produces a signal component at 
frequency fs*, the fiber in the second span could be chosen such that D1 
at fs is the same as D2 at fs*, or F1(fs)=F2(fs*). Since the two 
dispersion values D1 and D2 are equivalent, equal lengths L1 and L2 would 
satisfy the condition L1D1=L2D2 desired for optimal dispersion 
compensation using phase conjugation. The fiber dispersion function of the 
first portion could be adjusted in a similar manner to produce a 
dispersion value D1 that will be compensated by the dispersion D2 in the 
second portion. Thus, as in the case of length changes, either the 
dispersion function of the first or the second portion may be altered to 
compensate for the difference in first order dispersion D1-D2 resulting 
from non-zero second order dispersion. 
Another alternative to increasing or decreasing the length of the second 
portion of the span is to use fiber in the second portion which has an 
equal but opposite second order dispersion value to that in the fiber of 
the first portion. The phase conjugation reverses the phase of an optical 
signal with respect to time but does not reverse the effects of second 
order dispersion. Second order dispersion is therefore not undone as the 
conjugate of the optical signal propagates along the second portion of the 
span or segment of the span. However, by reversing the sign of the second 
order dispersion in the fiber making up the second portion, the second 
order dispersion effects on each portion can be made to cancel each other 
out. If the length of the first and second portions are unequal, an 
appropriate adjustment to the value as well as the sign of the second 
order dispersion could be made to ensure cancellation. One technique for 
achieving this sign change in second order dispersion is by designing a 
multi-cladding fiber, in which a different core area may lead to a 
difference in .gamma.. The difference in .gamma.can then be adjusted, for 
example, by varying P.sub.ave, amplifier number and/or amplifier spacing. 
The above techniques may be extended to systems utilizing more than one 
phase conjugator. In such a system, a fiber span of length L is divided 
into a number of segments, each of the segments having a first and a 
second portion. An optical phase conjugator is placed between the first 
and second portions of each segment, in order to cancel the dispersion 
effects within that segment. Dispersion effects resulting from propagation 
along the first portion of each segment are eliminated during propagation 
along the properly matched lengths of the second portions. Dispersion 
compensated reproductions of the transmitter output signal occur at the 
endpoints of the second portion of each segment. For a fiber span of 
length L, divided into n segments, each of approximately L/n length, n 
optical phase conjugators are required. The length of the first and second 
portion of each of the segments, and thereby the placement of the optical 
phase conjugator within each segment, will be determined in the same 
manner as in the single segment case described above. Using additional 
phase conjugators in effect breaks the fiber span into separately 
compensated segments of shorter length, and therefore may improve 
dispersion cancellation, since the amount of compensation necessary in 
each segment is reduced. It should be noted that the segments need not be 
of equal or approximately equal length. For example, a fiber span of 
length L could be divided into two segments, one of length 1/3 L and the 
other of length 2/3 L. Dispersion cancellation within each segment could 
then be accomplished by placing a phase conjugator between a first and 
second portion of each segment with the relative lengths of each portion 
determined in accordance with the invention. 
The length of a first or a second portion of a given segment may be 
adjusted in a number of ways, including either distributing any additional 
length increase or decrease across the loops 17 between the in-line 
amplifiers 16, or adding or deleting a single piece of length after the 
final in-line amplifier in the second portion. Other length adjusting 
techniques could also be used. In distributing the additional length 
across the second portion of a segment, substantially equivalent lengths 
of fiber are added between the in-line amplifiers such that the amplifier 
spacing is increased by the amount of additional length L2-L1 divided by 
one less than the number of in-line amplifiers in that portion. A 
substantially equivalent distribution across in-line amplifiers is 
desirable in order to maintain an approximately lossless distribution 
across the fiber span or segment. 
It may be necessary, when adjusting the length of the first or second 
portion of a span or segment as described above, to adjust in-line 
amplifier output power as well. In order to perform optimal dispersion 
compensation using phase conjugation, the same average power should be 
maintained throughout the first and second portions of a given segment. 
The rationale for equivalent power distribution was discussed above in 
conjunction with FIG. 1. When the length of a first or second segment 
portion is increased or decreased to compensate for second order 
dispersion, the average power along that portion will also change. A 
significant change in output power will prevent optimal dispersion 
cancellation. An adjustment to amplifier output power can maintain the 
desired equivalence between average power on the first and second 
portions. For example, the output power of the amplifiers in a lengthened 
second portion of a given segment may be increased to compensate for the 
change in average power resulting from the increased length. The power 
adjustment will differ depending upon whether the length increase is 
distributed across the second portion of the segment or added as a single 
additional length following the final in-line amplifier. In the case of a 
distributed length, a small adjustment to the output power of each in-line 
amplifier may be necessary. For a single additional length, an adjustment 
to the output power of the final in-line amplifier in the portion could be 
made. 
The process of phase conjugation will now be described in greater detail. 
Phase conjugation of optical signals is typically performed using 
four-photon mixing, also known as four-wave mixing. Four-photon mixing is 
a nonlinear process which generates mixing products by mixing an input 
optical communication signal with one or more higher power optical 
signals, or pumps, in a nonlinear mixing medium. The nonlinear mixing 
medium may comprise a semiconductor laser amplifier, a semiconductor laser 
amplifier or a length of dispersion-shifted fiber. The efficiency of the 
four-photon mixing process depends upon the relative polarizations of the 
optical signal and the pump. Although optical signal polarization usually 
varies randomly with time, one can maintain optimal efficiency in the 
four-photon mixing process by, for example, detecting the input signal 
polarization and adjusting the pump. However, this detection and 
adjustment hardware complicates the phase conjugator, and may depolarize 
the optical signal such that each component of the signal has its own 
polarization, and the optical signal itself has no macroscopic 
polarization. Other techniques for controlling and/or adjusting the 
relative polarization of the optical signal and the pump are well known in 
the art and will not be further discussed herein. Failure to maintain 
proper polarization alignment between the signal and the pump will 
generally result in a decrease in signal power at the output mixing 
product frequency. In the case of four-photon mixing to obtain a phase 
conjugate, the advantages of optical phase conjugation could be offset by 
such a reduction in conjugated signal power. 
An exemplary prior art optical phase conjugator is shown in FIG. 4. The 
phase conjugator 30 has a pump source 31, an optical signal input 32, and 
a phase conjugated optical signal output 34. The pump source 31 produces a 
pump signal, often simply referred to as a pump, which is combined with an 
input optical signal on line 32 in beam combiner 36. The combined signal 
drives a semiconductor laser amplifier 40 which serves as a nonlinear 
mixing medium. A first filter 42 separates the desired mixing product, the 
phase conjugate of the input signal, from the original signal, the pump 
and any undesired mixing products. The desired mixing product is then 
amplified in an optical amplifier 44 and finally filtered again in a 
second filter 46 to remove the amplified spontaneous emission (ASE) noise 
from the desired signal output on line 34. The phase conjugate of the 
input optical signal is available on line 34. It should be understood that 
the use of this exemplary phase conjugator requires polarization control 
as previously discussed in order to maintain the desired equivalent 
polarity between optical signal and pump. 
The four-photon mixing process itself may be either non-degenerate or 
degenerate. In non-degenerate four-photon mixing, two distinct pumps mix 
with the incoming optical signal to produce the fourth signal. For an 
optical signal of frequency fs, a first pump of frequency fp1, and a 
second pump of frequency fp2, the non-degenerate mixing process produces a 
phase conjugate of the optical signal at a frequency fp1+fp2-fs* as well 
as at other frequencies including 2fs-fp1 and 2fs-fp2. In degenerate 
four-photon mixing, two of the mixing signals are supplied by a single 
pump. Thus, for an optical signal of frequency fs and a pump at frequency 
fp, degenerate four-photon mixing produces phase conjugates of the optical 
signal at f1=2fp-fs and f2=2fs-fp. Either of the components f1 and f2 may 
be used as phase conjugates of fs in order to cancel the dispersive 
effects in a given length of fiber. 
The present invention may be applied to multi-channel optical signals by 
replacing the above described optical phase conjugator with a 
multi-channel optical phase conjugator. To perform optical phase 
conjugation on a multi-channel system, the phase conjugate of the 
multi-channel signal must be obtained. An exemplary multi-channel optical 
phase conjugator is shown in FIG. 5. The multi-channel optical phase 
conjugator 50 includes a first channel router 56 which receives a 
multi-channel optical signal on line 52 and separates it into its channel 
signals according to channel wavelength or carrier frequency. The 
multi-channel signal typically consists of a number of discrete channel 
signals at different frequencies, each of which serves as a carrier for 
digital data. The multi-channel optical phase conjugator also includes a 
plurality of single channel phase conjugators 60, each of which phase 
conjugates one of the channel signals via four-photon mixing as described 
in the above discussion of FIG. 4. After the mixing produces the desired 
phase conjugated output for a given input channel signal, the individual 
phase conjugated channel signals are recombined in a second channel router 
62 such that the desired phase conjugate of the entire multi-channel 
signal is obtained on line output 64. 
In applying the present invention to multi-channel optical signals, the 
frequency shift of each channel signal resulting from optical phase 
conjugation should be such that optimal compensation of second order 
dispersion effects is possible for each channel signal. One technique is 
to perform the phase conjugation process in such a way as to ensure that 
each phase conjugated channel signal experiences the same minimum amount 
of dispersion. This may be accomplished by phase conjugating each channel 
signal such that its frequency after phase conjugation is that of its 
adjacent channel before phase conjugation. Since the frequency shift is 
minimized, it can be seen by reference to the exemplary dispersion 
function of FIG. 3 that the second order dispersion effect will also be 
minimized. Furthermore, if the channel signals are spaced equally apart in 
frequency, the resulting second order dispersion will be the same for each 
of the channel signals, and therefore all of the second order dispersion 
effects on the signals of the individual channels may be canceled by, for 
example, an increase in L2 for the second portion of the span, as 
described above. Since it may be desirable to perform a global conversion 
of channel signal frequencies to offset the effects of stimulated Raman 
scattering (SRS), the adjacent channel frequency shift could be performed 
for subsets of the channel frequencies rather than all of the channel 
frequencies, in order to obtain some compensation for SRS while still 
minimizing second order dispersion on each channel signal. 
The need to control the optical signal and pump polarity during phase 
conjugation may be avoided by using a polarization insensitive optical 
phase conjugator. FIG. 6 shows an exemplary embodiment of a polarization 
insensitive optical four-photon mixer suitable for use with the present 
invention. Further detail regarding this embodiment may be found in U.S. 
patent application Ser. No. 08/120,013, entitled "Polarization-Insensitive 
Optical Four-Photon Mixer" filed on Sep. 10, 1993 and assigned to the 
present assignees. In the embodiment of FIG. 6, the optical phase 
conjugator 70 includes an optical signal input 72 and a polarization 
splitter 74. A single channel optical communication signal is applied to 
an optical signal input 72. The optical signal may be characterized as 
having both a TE and a TM polarization. For purposes of clarity, the TE 
polarization will be referred to herein as parallel and the TM as 
perpendicular. Polarization splitter 74 divides a single channel optical 
signal into parallel and perpendicular polarization components. The 
parallel polarization component of the input optical signal is supplied 
via polarization splitter 74 to a first mixing path 75, while the 
perpendicular polarization component is supplied to a second mixing path 
76. Mixing paths 75, 76 have pump sources 77, 78 respectively. The 
mutually orthogonal pump signals produced in the first and second mixing 
paths 75, 76 are combined with their respective communication signal 
polarization components in beam combiners 79, 80 within paths 75, 76, 
respectively. The first and second beam combiners 79, 80 each couple a 
polarized pump and signal component together onto a single line which is 
fed into the first and second nonlinear mixing devices 81, 82 which may be 
semiconductor laser amplifiers. Within the first and second mixing devices 
81, 82, the parallel and perpendicular signal components, respectively, 
are four-photon mixed with their respective substantially equivalently 
polarized pump signals. 
In each of the paths 75, 76, a first filter 83, 84 receives a signal from 
mixing device 81, 82 which includes the pump, optical signal, and mixing 
product frequencies. The mixing product 2fp-fs is usually used as a phase 
conjugate product of degenerated mixing. The other signal frequencies are 
therefore eliminated by filtering in first filters 83, 84. The first 
filter 83, 84 in each path 75, 76 is then followed by an erbium-doped 
fiber amplifier 85, 86 which amplifies the phase conjugate. The output of 
amplifiers 85, 86 is then preferably filtered by a second filter 87, 88 in 
order to limit ASE noise resulting from the amplification, as well as to 
further eliminate the input signal, pump and undesired mixing products. A 
polarization combiner 89 combines the orthogonally polarized parallel and 
perpendicular mixing products. The output of the combiner 89 on output 
line 90 is the desired phase conjugated version of the input optical 
signal. Use of this polarization insensitive embodiment avoids the need 
for polarization control based upon the time-varying input signal 
polarization. This polarization insensitive phase conjugator may be used 
in the multichannel phase conjugator of FIG. 5 by replacing each of the 
single channel phase conjugators 60 with the polarization insensitive 
phase conjugator 70 of FIG. 6. 
Other optical mixers may also be used as phase conjugators in the present 
invention. Another polarization insensitive four-photon mixer is disclosed 
in U.S. patent application Ser. No. 08/120,118, entitled 
"Polarization-Insensitive Optical Four-photon Mixer With 
Orthogonally-Polarized Pump Signals", filed on Sep. 10, 1993 and assigned 
to the present assignees. A dispersion-shifted fiber four-wave mixer 
suitable for use as a phase conjugator in the present invention is 
disclosed in T. Hasegawa et al., "Multi-Channel Frequency Conversion Over 
1 THz Using Fiber Four-Wave Mixing", Post Deadline Digest of the Optical 
Amplifiers and their Applications Conference, paper PD-7, Jul. 4-6, 1993, 
Yokohama, Japan. 
FIG. 7 illustrates simulation data obtained applying the techniques of the 
present invention to 100 Gbit/s single channel optical communication over 
a 1,062 km span. A single optical phase conjugator was used, and thus the 
span included only a single segment. The amplifier spacing was determined 
in accordance with the present invention to be 25 km on the first. portion 
of the span and 28.1 km on the second portion, corresponding to a length 
L1 of 500 km and a length L2 of 562 km. The input peak power was 20 mW and 
the fiber first and second order dispersion were -2 ps/km-nm and 0.08 
ps/km-nm.sup.2, respectively. A single optical phase conjugation carried 
out at a length L1 of 500 km produced a signal at the end of the 1062 km 
fiber span having the eye diagram shown. The eye diagram provides a 
measure of system performance by showing the variations in received signal 
logic levels for a given bit position over all possible bits of a 
pseudorandom test data stream. A clear opening is observed, corresponding 
theoretically to a zero bit error rate. 
FIG. 8 shows simulation data obtained by applying the techniques of the 
present invention to 20 Gbit/s optical communication over a 10,000 km 
span. The other system parameters were the same as the case shown in FIG. 
7. In FIG. 8(a) an eye diagram is shown for the case of noiseless 
amplifiers and perfectly homogeneous dispersion. Although the bit 
rate-distance product has been increased to 200 Tbit/s-km, an even more 
open eye is obtained. FIG. 8(b) shows the effect of adding an amplifier 
noise figure of 6 dB to the simulation on the results of FIG. 8(a). FIG. 
8(c) shows the effect of combined 6 dB amplifier noise figure and 5% 
dispersion fluctuations on the results of FIG. 8(a). Although some 
reduction in phase margin is apparent, these results indicate that the 
improvements of the present invention are relatively insensitive to 
amplifier noise, amplifier degradation, and fluctuation in fiber 
dispersion. 
It should again be emphasized that the foregoing embodiments are exemplary 
only. To compensate for second order dispersion and fiber nonlinearities 
in accordance with the present invention, many different variations may be 
made in the number and spacing of in-line amplifiers, the amplifier output 
power, the fiber span power distribution, the relative lengths and 
dispersion functions of the first and second portions of various segments 
of the fiber span, the number of segments and optical phase conjugators in 
each span, as well in other system parameters. Furthermore, the 
compensation techniques of the present invention may be utilized to 
improve performance in many different systems having a wide range of data 
rates and transmission distances. These and other alternatives and 
variations in the arrangements shown will be readily apparent to those 
skilled in the art.