All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification.
ABSTRACT All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification is described. Nearly ideal phase regeneration can be achieved in the undepleted-pump regime, and simultaneous amplitude and phase regeneration can be realized in the depleted-pump regime.
- [Show abstract] [Hide abstract]
ABSTRACT: Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit-the upper bound of regeneration efficiency-is derived.Nature Communications 05/2014; 5:3861. · 10.74 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: Future high capacity optical links will have to make use of frequent signal regeneration to enable long distance transmission. In this respect, the role of all-optical signal processing becomes increasingly important because of its potential to mitigate signal impairments at low cost and power consumption. More substantial benefits are expected if regeneration is achieved simultaneously on a multiple signal band. Until recently, this had been achieved only for on-off keying modulation formats. However, as in future transmission links the information will be encoded also in the phase for enhancing the spectral efficiency, novel subsystem concepts will be needed for multichannel processing of such advanced signal formats. In this paper we show that phase sensitive amplifiers can be an ideal technology platform for developing such regenerators and we discuss our recent demonstration of the first multi-channel regenerator for phase encoded signals.Transparent Optical Networks (ICTON), 2012 14th International Conference on; 01/2012
- [Show abstract] [Hide abstract]
ABSTRACT: We propose and demonstrate an all-optical phase noise reduction scheme that uses optical nonlinear mixing and tunable optical delays to suppress the low-speed phase noise induced by laser linewidth. By utilizing the phase conjugate copy of the original signal and two narrow-linewidth optical pumps, the phase noise induced by laser linewidth can be reduced by a factor of ∼5 for a laser with 500-MHz phase noise bandwidth. The error-vector-magnitude can be improved from ∼30% to ∼14% for the same laser linewidth for 40-Gbit/s quadrature phase shift keying signal.Optics Letters 05/2014; 39(10):2928-2931. · 3.39 Impact Factor
October 15, 2004 / Vol. 29, No. 20 / OPTICS LETTERS
All-optical regeneration of differential phase-shift keying
signals based on phase-sensitive amplification
Kevin Croussore, Cheolhwan Kim, and Guifang Li
Center for Research and Education in Optics and Lasers, University of Central Florida, 4000 Central Florida Boulevard,
Orlando, Florida 32816
Received May 18, 2004
All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification is de-
scribed. Nearly ideal phase regeneration can be achieved in the undepleted-pump regime, and simultaneous
amplitude and phase regeneration can be realized in the depleted-pump regime.
060.4370, 060.4510, 060.5060, 060.2330, 190.4380.
© 2004 Optical Society of
emerged as an alternative to on–off keying, especially
for long-haul transmission.
DPSK signals offers a 3-dB improvement in receiver
sensitivity over direct detection of on–off keying
DPSK signals also exhibit enhanced toler-
ance to fiber nonlinearity, particularly the effects of
interchannel cross-phase modulation3,4(XPM).
properties allow DPSK signals to be transmitted over
Excluding timing jitter, DPSK systems are limited
primarily by linear and nonlinear phase noise,5unlike
on–off keying systems that are limited primarily
by intensity noise.Linear phase noise (as well as
amplitude noise) is added by amplified spontaneous
emission from optical amplifiers.
noise arises when amplified spontaneous emission
amplitude noise and dispersion-induced pattern effects
are converted to phase noise by self-phase modulation
(SPM) in single-channel systems and from both SPM
and XPM in wavelength-division multiplexed systems.
Experiments have shown that when the nonlinear
contribution to phase noise becomes dominant the
advantages of using balanced DPSK detection are
managing fiber nonlinearity7,8and compensating for
nonlinear phase noise.9,10
multiplexed systems it is complicated to accurately
assess the linear and nonlinear contributions to
phase noise and to differentiate effects of SPM and
XPM because of the large number of possible XPM
interactions.Schemes for posttransmission nonlinear
phase-shift compensation that rely on pulse-relative
amplitudes to indicate the accumulated nonlinear
phase shift cannot accurately compensate for XPM
or linear phase noise.This limits the effectiveness
of these nonlinear phase-shift compensation tech-
niques, although recent simulated results show that
significant performance enhancement may still be
To date, limited emphasis has been
placed on removing amplitude noise of DPSK data,
although it is precisely this amplitude noise that leads
to the accumulation of nonlinear phase noise.
In this Letter we describe a method for re-
Balanced detection of
have been proposedfor
of degraded DPSK signals based on an optical
degenerate four-wave mixing (FWM) in a nonlinear
of the optical gain forces the signal (degraded data)
phase to a value of 0 or p relative to a strong pump at
the same frequency.Simultaneously, when the signal
power becomes comparable to the pump power the
gain saturates and limiting amplification is achieved.
PSAs were studied previously and show interesting
Here we explicitly show how a PSA can perform DPSK
A PSA can be configured as shown in Fig. 1.
pump Epand signal Es, which are at the same optical
frequency, are combined in the input coupler into a bal-
anced nonlinear Mach–Zehnder interferometer.
the absence of the signal (pump) field, the pump (sig-
nal) emerges completely from the pump (signal) port.
When both the pump and the signal are present, the
total fields in the two arms are E2,1? ?Ep6 Es??p2,
respectively. The fields experience different non-
linear phase shifts, and the interferometer becomes
unbalanced.As a result, energy from the pump is
transferred to the signal port and vice versa.
output at the signal port is given by15
where f02 g?L?2??jEp0j21 jEs0j2?; L is the amplifier
length; fp0 and fs0 are the injected pump and sig-
nal phases, respectively; g is the fiber nonlinear co-
efficient; and fnl? gLjEp0jjEs0j cos?fp02 fs0? is the
plers and highly nonlinear optical fiber (HNLF) make up a
nonlinear Mach-Zehnder interferometer.
Schematic of the PSA.Two 50:50 directional cou-
0146-9592/04/202357-03$15.00/0© 2004 Optical Society of America
OPTICS LETTERS / Vol. 29, No. 20 / October 15, 2004
nonlinear phase shift.
output signal peak power Psis given by
From Eq. (1) it follows that the
Ps? Ps0cos2?fnl? 1 Pp0sin2?fnl?
where Ps0? jEs0j2and Pp0? jEp0j2are the input pump
and signal powers, respectively.
(2) it is straightforward to verify that the coupling
between the pump and the signal is phase sensitive.
When fp02 fs0? 0 or p, the nonlinear phase shift
reaches the maximum value.
fp02 fs0? p?2, or 3p?2, the nonlinear phase shift
vanishes and there will be no coupling between the
pump and signal.The signal gain, determined by the
nonlinear phase shift, is affected by the choice of ampli-
fier length and input powers as well as the input phase
difference.When the nonlinear phase shift reaches a
value of p?2, the signal output power is equal to the
input pump power.
In Fig. 2(a) the output power at the signal port
for the case of fp0? fs0is plotted as a function of
amplifier length for different values of input signal
power. The pump power is 20 mW.
culations we use g ? 27 W21km21.
phase-sensitive amplification can be observed.
the case of low input signal power, fNL, , 1 and the
output signal power remains small compared with
the pump power (undepleted pump).
signal power the output signal power reaches the
level of the input pump power (depleted pump) and
oscillates with distance. The FWM length, defined as
the fiber length at which the signal power reaches its
maximum value, decreases as the input signal power
phase-sensitive amplification can be employed to per-
form DPSK regeneration.
an undepleted-pump PSA leads to nearly perfect phase
regeneration while a depleted-pump PSA can achieve
simultaneous phase and amplitude regeneration.
First we consider regeneration of DPSK signals in
the undepleted-pump regime.
the normalized field gain, defined as jEs,outj?jEs,inj, as
a function of the relative pump–signal phase.
pump and signal input powers are 20 mW and 175 mW,
respectively.The amplifier length is 6 km, compared
with a FWM length of nearly 35 km.
the gain curve occur at multiples of p, signifying that
field components either in phase or out of phase by p
with the pump are amplified strongly, while those that
are out of phase by p?2 are not amplified.
dependent gain forces the output phase of the DPSK
signal pulses to be nearly 0 or p, depending on the
initial quadrant in which the pulse phase lies.
output signal phase versus input signal phase relative
to that of the pump for the undepleted-pump PSA is
also shown in Fig. 2(b). As seen in the figure, the
output phase of the signal is forced to a nearly con-
stant value for large variations of input signal phase.
The difference between the two output phase states
is verified to be exactly p, indicating that all regen-
erated signal pulses have a differential phase shift of
From Eqs. (1) and
On the other hand, if
In all our cal-
Two regimes of
For high input
As we show subsequently,
In Fig. 2(b) we show
The peaks in
either 0 or p.
simulated regeneration of a 40-Gbit?s DPSK signal af-
ter transmission in fiber. Figure 3(a) shows degraded
DPSK data after transmission through five spans of
a dispersion-compensated system in which each span
consists of 80 km of standard single-mode fiber [D ?
16 ps??nm km?, a ? 0.2 dB?km], followed by 16 km of
dispersion-compensating fiber [D ? 280 ps??nm km?,
a ? 0.5 dB?km], and a single erbium-doped fiber am-
plifier with a noise figure of 6.
gram each point represents the amplitude and phase
of a DPSK bit sampling at the center of the bit pe-
riod.The degree of amplitude noise is greater than
3 dB, and the total phase variation is nearly 60±.
ure 3(b) shows the same data after phase regenera-
tion, with the parameters of Fig. 2(b).
noise is not affected, but the output phase states have a
difference of p, thus achieving near-ideal phase regen-
eration.Figure 3(c) showsthe dataafter phase regen-
eration for an amplifier length of 10 km.
is reduced even further; however, in this case the pump
is approximately 25% depleted.
To further illustrate these results we
On the phasor dia-
four input powers (labeled) and pump power of 20 mW.
(b) Normalized field gain (solid curve) and output signal
phase (dotted curve) versus relative input phase for
Pp0? 20 mW, L ? 6 km, and Ps0? 175 mW.
(a) Signal power versus amplifier length for
transmission, (b) after phase-only regeneration, L ? 6 km,
(c) after phase-only regeneration, L ? 10 km, (d) after si-
multaneous phase and amplitude regeneration.
Phasor diagrams of DPSK data (a) after 500-km
October 15, 2004 / Vol. 29, No. 20 / OPTICS LETTERS
for different values of input pump–signal phase differ-
ence. Inset, output versus input power for a range of
5–15 mW.(b) Signal output versus input phase for input
powers of 5 and 15 mW.Inset, output versus input phase
near 0 or p points, 60.2p.
(a) Signal output power versus input power
When the amplifier length is chosen to be near the
FWM length, limiting amplification can be obtained,
as shown in Fig. 2(a). At an amplifier length of
?4 km (see the arrow), the signal output power is
almost independent of the input power (5–15 mW)
when we choose fp0 ? fs0. If the pump–signal
phase difference is nonzero, both the FWM length and
the maximum signal power will change.
signal suffering both amplitude and phase noise, the
amplitude regeneration property of the PSA (for a
fixed amplifier length of 4 km) needs to be verified.
In Fig. 4(a) we plot signal output power versus signal
input power for different values of pump–signal
phase mismatch. Limiting amplification is clearly
observed for signal powers greater than ?5 mW.
inset shows that for an input signal power range of
4.75 dB (5–15 mW) the output power will vary by
less than 2.5 dB and by much less than 1 dB when
the pump–signal phase mismatch is less than 15±.
To verify simultaneous phase regeneration for the
depleted pump case, in Fig. 4(b) we plot output phase
versus input relative phase for signal powers of 5
and 15 mW.The phase regeneration properties of
the depleted pump PSA are no longer ideal as for
the undepleted pump case.
input phase variations to 60.2p around the reference
(pump) phase [inset to Fig. 4(b)], we can see that
the output phase varies by less than 0.1p overall,
indicating a significant reduction of phase noise.
Finally, Fig. 3(d) shows the degraded data of Fig. 3(a)
after simultaneous phase and amplitude regeneration.
Amplitude noise is reduced to approximately 1 dB, and
the phase varies by only ?12±overall, in comparison
with the initial 60±overall variation.
In summary, we have demonstrated DPSK regen-
eration based on phase-sensitive amplification.
For a DPSK
However, if we restrict
the case of an undepleted-pump PSA the output phase
will in fact be forced to a constant value across the bit
period, except for phase jumps of p in regions where
optical intensity is negligible, e.g., for return-to-zero
data, resulting in differential phase shifts of only 0
or p in the regenerated pulses.
depleted-pump PSA, the amplifier can be configured
to achieve both amplitude and phase regeneration.
The proposed scheme will remove both linear and non-
linear contributions to phase noise.
phase-only regeneration will be better suited for pre-
processing before balanced detection at the receiver,
while simultaneous phase and amplitude regeneration
will be better suited for inline processing to reduce
amplitude-noise to phase-noise conversion resulting
from nonlinear propagation.
For the case of a
We envisage that
G. Li’s e-mail address is email@example.com.
1. W. A. Atia and R. S. Bondurant, in Proceedings of
the LEOS 12th Annual Meeting, Vol. 1 (Lasers and
2. A. H. Gnauck, S. Chandrasekhar, J. Leuthold, and
L. Stulz, IEEE Photon. Technol. Lett. 15, 99 (2003).
3. J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese,
IEEE Photon. Technol. Lett. 12, 1627 (2000).
4. O. Vassilieva, T. Hoshida, S. Choudhary, G. Castanon,
H. Kuwahara, T. Terahara, and H. Onaka, in Proceed-
ings of the LEOS 14th Annual Meeting, Vol. 2 (Lasers
and Electro-Optics Society, Piscataway, N.J., 2001),
5. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15, 1351
6. H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett.
15, 320 (2003).
7. C. Pare, A. Villeneuve, P. A. Belanger, and N. J. Doran,
Opt. Lett. 21, 459 (1996).
8. I. R. Gabitov and P. M. Lushnikov, Opt. Lett. 27, 113
9. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie,
Opt. Lett. 27, 1616 (2002).
10. C. Xu and X. Liu, Opt. Lett. 27, 1619 (2002).
11. K. Croussore, C. Kim, and G. Li, paper presented at the
Nonlinear Optics Topical Meeting, Waikoloa, Hawaii,
August 2–6, 2004.
12. W. Imajuku, A. Takada, and Y. Yamabayashi, Electron.
Lett. 36, 63 (2000).
13. R. D. Li, P. Kumar, and W. L. Kath, J. Lightwave
Technol. 12, 541 (1994).
14. A. Takada and W. Imajuku, Electron. Lett. 32, 677
15. M. E. Marhic and C. H. Hsia, Quantum Opt. 3, 341