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Recent Advances in Fiber-OpticParametric Amplifiers
Govind P. Agrawal
Institute of OpticsUniversity of RochesterRochester, NY 14627
c�2005 G. P. Agrawal
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Introduction• Industrial revolution of 19th century was followed by
Information revolution during the 1990s.
• Fiber-optic revolution is a natural consequence of theInternet growth.
c�2004 TRG, PriMetrica, Inc.
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Five Generations• 0.8-µm systems (1980); Graded-index fibers
• 1.3-µm systems (1985); Single-mode fibers
• 1.55-µm systems (1990); Single-mode lasers
• WDM systems (1996); Optical amplifiers
• L and S bands (2001); Raman amplification
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Parametric AmplifiersFiber-optic Parametric Amplifiers (FOPAs) exhibit
• Large signal amplification (>40 dB)
• Wide gain bandwidth (>50 nm)
• Nearly uniform gain spectrum (<1 dB variations)
• Relatively low noise (noise figure <4 dB)
FOPAs can be used for
• Optical amplification
• Wavelength conversion
• Phase conjugation
• Ultrafast signal processing
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Four-Wave Mixing (FWM)
• FWM is a nonlinear process that transfers energy of pumpsto signal and idler waves.
• FWM requires conservation of (notation: E = Re[Aexp(ib z�iwt)])
? Energy w1
+w2
= w3
+w4
? Momentum b1
+b2
= b3
+b4
• Degenerate FWM: Single pump (w1
= w2
).
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Single- and Dual-Pump FOPAs
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⇤
�
⇥
⌅
⇧
⌃
Four-Wave Mixing (FWM)Pump
IdlerSignal
�3 �1 �4
• Pump close to fiber’sZDWL
• Wide but nonuniform gainspectrum with a dip
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⇤
�
⇥
⌅
⇧
⌃
Four-Wave Mixing (FWM)
IdlerSignal
Pump 2Pump 1
�1 �3 �0 �4 �2
• Pumps at opposite ends
• Much more uniform gain
• Lower pump powers (⇠0.5 W)
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Dual-Pump FOPAs
• Typical output spectrum of dual-pump FOPAs.
• Multiple idlers generated when signal is launched with two pumps.
• Two pumps act togther to genrate an idler (nondegenerate FWM).
• Each pump also produces its own idler through degenerate FWM.
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Theory of FOPAs• Full problem quite complicated (4 coupled nonlinear equations)
• Undepleted-pump approximation =) two linear coupled equations:
dA
3
dz
=i
2
kA
3
+2igp
P
1
P
2
A
⇤4
dA
4
dz
=i
2
kA
4
+2igp
P
1
P
2
A
⇤3
• Phase mismatch: k = b3
+b4
�b1
�b2
+ g(P1
+P
2
).
• Nonlinear parameter: g = n
2
w0
/(ca
eff
)⇠ 2–20 W�1/km.
• Signal power P
3
and Idler power P
4
are much smaller thanpump powers P
1
and P
2
(Pn
= |An
|2).
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Simple Theory of FOPAs• Signal and idler powers obey the same equation (A
3
=p
P
3
e
if3)
dP
3
dz
=dP
4
dz
= 4gp
P
1
P
2
P
3
P
4
sinq
• Phase equation (q = f3
+f4
�f1
�f2
)
dqdz
= k +2g(P3
+P
4
)r
P
1
P
2
P
3
P
4
cosq
• In the case of perfect phase matching (k = 0), idler is generatedsuch that q = p/2, and q remains fixed.
• When no idler power is launched initially, q = p/2 even ifphase matching is not perfect (k 6= 0).
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Gain Spectrum• Signal amplification factor or FOPA gain G:
G(w) =P
3
(L,w)P
3
(0,w).
• Coupled signal and idler equations can be written in a matrix form:
∂∂ z
✓A
3
A
⇤4
◆=
i
2
✓k(w) 4g
pP
1
P
2
�4gp
P
1
P
2
�k(w)
◆✓A
3
A
⇤4
◆.
• This matrix equation is easily solved for a FOPA of length L toobtain
G(w) =
1+✓
1+k2(w)4g
2(w)
◆sinh
2[g(w)L]�.
• Parametric gain: g(w) =p
4g2
P
1
P
2
�k2(w)/4.
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Phase-Matching Condition• Total phase mismatch k = Db
L
+DbNL
• Linear phase mismatch: DbL
(w) < 0 is required.
• Nonlinear phase mismatch: DbNL
(P1
,P2
) = gP
1
P
2
> 0
1475 1500 1525 1550 1575 1600 16250
10
20
30
40
Gai
n (d
B)
Signal Wavelength (nm)
0
20
40
60
Phase M
ismatch
FOPA length = 0.5 kmP
1
= P
2
= 0.5 Wg = 10 W�1/kmb
3
= 0.1 ps3/kmb
4
= 10
�4 ps4/kmSingle pump (blue curves)Two pumps (red curves)
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Applications of FOPAs• Parametric amplification
• Optical Phase Conjugation
• Wavelength Conversion
• Optical Sampling
• Time-Domain Demultiplexing
• Packet and Bit-Level Switching
• All-Optical Regeneration
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Parametric amplificationPhaseModulation
EDFA
Amplification Filters
EDFA
• SBS problem =) Modulate pump phases at bit rates ⇠5 Gb/s.
• Amplifier noise =) Use narrowband optical filters.
• Highly nonlinear fiber: Narrow core enhances g and G.
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Comparison with Theory
1520 1540 1560 1580 1600 1620 16400
10
20
30
40
ZDWL
Pump 2Pump 1
Gai
n (d
B)
Signal Wavelength (nm)
Figure 3
• Experiment by Radic et al., Electron. Lett. 39, 838 (2003).
• FWM theory predicts bandwidths > 50 nm under ideal conditions.
• Maximum bandwidth realized experimentally is around 40 nm.
• Fit to data requires inclusion of the Raman e↵ects.
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Optical Phase Conjugation
• FWM generates an idler wave during parametric amplification.
• Its phase is complex conjugate of the signal field (A4
µ A
⇤3
).
• Phase conjugation can be used for dispersion compensation byplacing a parametric amplifier midway.
• Basic idea patented in 1979; first demonstration in 1993.
• Phase conjugation can also reduce timing jitter in lightwave systems.
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Experimental Results
• Jopson et al., Photon. Technol. Lett. 5, 663 (1993).
• Pump wavelength coincided with the zero-dispersion wavelength.
• 10-Gb/s signal could be transmitted over 360 km of standard fiber.
• Distance limited to 32 km without phase conjugation.
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Wavelength Conversion
• FOPAs can transfer data to a di↵erent wavelength.
• A CW pump beam is launched into the fiber togetherwith the signal channel.
• Pump wavelength is chosen half way from the desired shift.
• FWM transfers the data from signal to the idler waveat the new wavelength.
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Multichannel Wavelength Conversion
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 8, NO. 3, MAY/JUNE 2002 527
Fiber Parametric Amplifiers forWavelength Band ConversionMohammed N. Islam and Özdal Boyraz, Student Member, IEEE
Invited Paper
Abstract—By using a loop configuration formed by a polariza-tion beam splitter, we experimentally demonstrate that the existingwavelength-division multiplexing (WDM) sources in -band canbe wavelength converted to the -band with low polarization sen-sitivity and low crosstalk. Using a fiber parametric amplifier as aband converter, we achieve experimentally 0.65-dB polarizationsensitivity and 4.7-dB conversion efficiency over 30-nm conver-sion bandwidth in 315 m of fiber. Compared to the conventionalstraight fiber wavelength conversion scheme, a more than 2-dB im-provement in polarization sensitivity is measured. In addition tothe polarization insensitivity, channel crosstalk is measured to be
27 dB in 315 m of high nonlinearity fiber. In a detailed exper-imental study, the pattern of crosstalk in longer fiber lengths andthe coupling between the polarization sensitivity and crosstalk aremeasured. For example, with a 430-m fiber length, we measure thedegradation in polarization sensitivity to be 4 dB for 12-dB in-creased signal power. The experimental results are also confirmedby theoretical calculations.Moreover, in a 32 channels systems sim-ulation, the signal-to-noise ratio (SNR) of the converted signalsafter 800-km propagation is calculated to be only 0.8-dB degradedcompared to using laser diodes with the same initial SNR values.Furthermore, we calculate the effect of pump noise and show thatthe relative intensity noise of the pump is transferred to the con-verted signals with an additional 8-dB/Hz degradation.Index Terms—Broad-band amplifiers, crosstalk, nonlinear
optics, optical fiber amplifiers, optical parametric amplifiers,optical fiber communication, optical fiber polarization, opticalpropagation in nonlinear media, optical transmitters, parametricamplifiers, polarization sensitivity, wavelength-division multi-plexing, wavelength conversion.
I. INTRODUCTION
F IBER PARAMETRIC amplifiers can be used to convertsimultaneously a set of wavelengths to a new set of
wavelengths, which are a mirror image of the original. Aband converter of this sort can fulfill a number of uniquefunctions in telecommunications networks. For example, in aprotection switching or restoration mode, the band convertercan take an existing band of wavelengths on a damaged linkand transfer it to a new band of wavelengths on an already usedfiber. Alternately, to reduce capital expenses and operational
Manuscript received January 31, 2002; revised April 2, 2002. This work wassupported by DARPA at the University of Michigan.M.N. Islam iswith Xtera Communications, Inc., Allen, TX 75013USA.He is
on leave-of-absence from the EECS Department, University of Michigan, AnnArbor, MI 48109 USA.Ö. Boyraz is with Xtera Communications, Inc., Allen, TX 75013 USA.Publisher Item Identifier S 1077-260X(02)05900-2.
Fig. 1. Illustration of -band source generation by wavelength conversion. Byusing a single pump laser to utilize modulation instability, the existing sourcesin -band can be converted to -band. The mirror image of the sources in the-band is generated in the -band.
expenses through fewer part numbers, it may be desirable toonly stock a fixed number of WDM transmitters, such as onlyin the conventional -band. Then, new transmitters in thesurrounding bands—such as the short-wavelength -band orlong-wavelength -band—can be made by using the existingtransmitters and band shifting them to either the - or -band.However, a band converter for any of these telecommunicationsapplications must be polarization insensitive with low crosstalkbetween WDM channels.An attractive method of implementing the band conversion
process is based on the modulation instability (MI) effect in thefiber. MI is a four-photon process, where two photons from thepump laser and one photon from the signal interact and generateone photon in signal wavelength and one in conjugate, which isthe image of the signal. Fig. 1 shows the basic idea behind theprocess. Starting with high-power pump laser near low powersignal channels stimulates the third-order nonlinear effectsin fiber. The MI process is the special case of third-order non-linear effect when the pump and signal wavelengths are nearzero dispersion wavelength of the fiber and both at anomalous
1077-260X/02$17.00 © 2002 IEEE
• Islam et al., IEEE JSTQE 8, 527 (2002).
• 860-mW peak power pump at 1532 nm; 315-m-long fiber.
• 32 channels converted into S band with 4.7 dB conversion e�ciency.
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Optical SamplingLI et al.: 300-Gb/s EYE-DIAGRAM MEASUREMENT BY OPTICAL SAMPLING 989
Fig. 5. Eye diagrams of 160-, 200-, and 300-Gb/s optical signals.
SNR is thermal noise limited while signal-de-pendent noise dominates above it . This clas-sical feature of a p-i-n photodiode indicates that the power ofthe sampled signal is indeed linearly dependent on the power ofthe input data signal of the sampling system. 20-dB SNR wasachieved at a signal peak power of 10 mW. 10-Gb/s data signalwas used to estimate the possible maximum input signal peakpower. The sampled signal became distorted due to self-phasemodulation (SPM)when the input signal peak power was ampli-fied above 500 mW. The dynamic range of the optical samplingsystem is thus 10–500 mW or 17 dB for a SNR 20 dB withnegligible distortion of the signal.The inset of Fig. 3 shows themeasured eye diagram at 10Gb/s
with the data signal set at 1541 nm. The RMS timing jitter esti-mated from the measured eye is 0.3 ps. The ”bulge” at the zerolevel of the eye is due to ringing generated by the limited band-
width of the 125-MHz detector with the ultrashort idler pulses atits input. The full-width at half-maximum (FWHM) pulsewidthmeasured from the sampled eye is 2.6 ps. The width of the datasignal pulse measured with an autocorrelator is 2 ps. This re-sults in an estimated resolution of 1.6 ps, which is equal to,and therefore solely determined by the width of the samplingpulse after amplification in the EDFA. Obviously, the wave-form changes of the sampling pulse inside the HNLF, due toSPM and chromatic dispersion, have little influence on the tem-poral resolution. Furthermore, the walkoff between signal andsampling pulses does not decrease the temporal resolution ei-ther, although they are separated by 19 nm. This is verified inFig. 4, which shows the calculated walkoff between signal andsampling pulses versus wavelength seperation for three HNLFlengths. With 50-m HNLF, the group delay is only 0.5 ps evenfor a wavelength separation of 30 nm and less than 0.2 ps witha 19-nm separation that was used in the eye-diagram measure-ment.Fig. 5 shows the eye diagrams of quasi-160-, 200-, and
300-Gb/s signals. The -value should be possible to estimatefrom the measured eye diagrams. For an increased bit rate, theeye diagram becomes somewhat noiser due to the nonidealPM extinction and overlapping of signal pulse tails in themultiplexer. However, at 300 Gb/s, the eyes are still clearlyopen.
III. CONCLUSION
Up to 300-Gb/s eye diagrams are visualized through opticalsampling based on parametric amplification in an opticalfiber. The key to achieve these results are a short 50-m highlynonlinear fiber and a pulse source providing short opticalsampling pulses with low timing jitter. The system has anoperating wavelength range of at least 30 nm and a data signaldynamic range between 10–500 mW (17 dB). Furthermore,the sampling process is instantaneous. We believe our resultsshow that fiber-based optical sampling systems have theperformance necessary for direct monitoring and evaluation offuture ultrahigh bit-rate optical communication systems.
REFERENCES[1] H. Ohta, S. Nogiwa, Y. Kawaguchi, and Y. Endo, “Measurement of
200-Gb/s optical eye diagram by optical sampling with gain switchedoptical pulse,” Electron. Lett., vol. 36, pp. 737–739, 2000.
[2] H. Takara, S. Kawanishi, A. Yokoo, S. Tomaru, T. Kitoh, and M.Saruwatari, “100-Gb/s optical signal eye-diagram measurement withoptical sampling using organic nonlinear optical crystal,” Electron.Lett., vol. 32, pp. 2256–2258, 1996.
[3] S. Diez, R. Ludwig, C. Schmidt, U. Feiste, and H. G. Weber, “160-Gb/soptical sampling by gain-transparent four-wave mixing in a semicon-ductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 11, pp.1402–1404, Nov. 1999.
[4] B. P. Nelson and N. J. Doran, “Optical sampling oscilloscope using non-linear fiber loop mirror,” Electron. Lett., vol. 27, pp. 204–205, 1991.
[5] P. A. Andrekson, “Picosecond optical sampling using four-wave mixingin fiber,” Electron. Lett., vol. 27, pp. 1440–1441, 1991.
[6] J. Li, P. A. Andrekson, and B. Bakhshi, “Direct generation of subpi-cosecond chirp-free pulses at 10 GHz from a nonpolarization main-taining actively mode-locked fiber-ring laser,” IEEE Photon. Technol.Lett., vol. 12, pp. 1150–1152, Sept. 2000.
[7] B. Bakhshi, P. A. Andrekson, and X. Zhang, “A polarization-main-taining and dispersion-managed 10-GHzmode-locked erbium fiber-ringlaser providing both - and Gaussian-shaped pulses,” Opt. FiberTechnol., vol. 4, pp. 293–303, 1998.
• Short samplings pulses (⇠1 ps) actas the pump.
• Idler pulse width comparable to pump pulses.
• Eye diagrams produced up to 300 Gb/s.
• Temporal resolution of 1.6 ps possible;Li et al., PTL 13, 987 (2001).
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Time-Domain Demultiplexing
• FOPAs can be used to demultiplex OTDM channels.
• Pump is an optical clock at a di↵erent wavelength.
• Only signal pulses overlapping with clock pulsescan generate an idler pulse.
• An optical filter blocks the pump and other channels.
• This method can work at bit rates of 500 Gb/s or more;Morioka et al., Electron. Lett. 32, 832 (1996).
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Packet Switching of 40-Gb/s Signal
• Experiment by Lin,Radic, and Agrawal(2005).
• L-band pump mod-ulated to producepulses of packet size.
• FWM occurs only overthe packet duration
!"##$!%&' ())%*+,-./!0)#$)%&'
())%*+,-./
123 143
153 1-3
163 173
! (
!""8$)%&' ())%*+,-./
!""8$)%&' ())%*+,-./ !"9#$!%&' ())%*+,-./
:%42&-%*;'*%!"8#$)%&'
())%*+
• Both signal and idler contain bits belonging to one packet.
• This technique can be adopted to any packet size.
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Bit-Level Switching at 40 Gb/s
• Experiment by Lin,Radic, and Agrawal(2005).
• L-band pump contains1-bit-wide pulses.
• FWM occurs only overthe bit duration
!"# !$#
%&&'()*+,
&)*-./012
%&33(%*+,
&)*-./012
%
4%&&'()*+, &)*-./012
%5)3()*+, &)*-./012
%&63(%*+,
&)*-./012
7*89+0*-:,-
%&'3()*+,
&)*-./012
!9# !8#
• A single signal bit can be switched with this technique.
• Idler wave contains only switched bits in time slots selected by thepump.
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Optical RegenerationRADIC et al.: ALL-OPTICAL REGENERATION IN ONE- AND TWO-PUMP PAs USING HIGHLY NONLINEAR OPTICAL FIBER 959
Fig. 5. Transfer characteristics of higher order light generated using atwo-pump HNLF regenerator.
Fig. 6. Spectral broadening of higher order tones generated in two-pumpparametric regenerator as measured with a resolution of 1.5 GHz.
can be seeded by the degenerate processand the nondegenerate process . Itssubsequent growth can be augmented by the nondegenerate pro-cesses , ,where corresponds to an outer-band (1620.1 nm) photonand . The new frequency
is common to all these processes. Forcounterphased pumps, is constant. Since has anunbalanced , the newwave exhibits excessive pump-inducedbroadening, indicated by the heavy dashed curve. Similarly,wave (1578.5 nm) is generated by cascaded processes that sat-isfy the following energy relation .Since pump photons are balanced in all processes contributingto , this wave is not broadened by pump-phase modulation,in agreement with the thin solid curve in Fig. 6. Finally, thewave (1575.6 nm) is produced by cascaded processes satisfyingenergy relation . A similaranalysis can be used to analyze a cophased two-pump PA con-figuration [5].Processing a noisy input signal tests the performance of the
two-pump regenerator. A 10-Gb/s IM-NRZ signal is combinedwith amplified spontaneous emission in order to reduce the op-tical signal-to-noise ratio [(OSNR) measured within 0.1 nm]at the PA input to 17.6 dB, as shown in Fig. 7(a). The inputsignal power of 5.0 dBm allows for the mark fluctuations ofthe amplified signal to be efficiently suppressed, as illustrated
Fig. 7. (a) Input signal at 17.6-dB OSNR, (b) amplified signal at 1582.9 nmfor dBm, (c) term at 1571.3 nm for dBm, and(d) term at 1575.6 nm for dBm with output OSNR of 37 dB.The signal and idler are filtered out using a 0.25-nm filter, while isextracted using a 0.6-nm filter.
in Fig. 7(b). The poor ERs associated with both the signal andprimary idler result in the retention of considerable noise at thelow (space) signal levels. This noise can be suppressed by using
order, as shown in Fig. 7(c). The input power is held belowthe saturation level to avoid the pulse distortion present inFig. 7(b). By selecting and a wider optical filter, it is pos-sible to suppress both space and mark fluctuations, as shown inFig. 7(d). The result, however, comes at the price of significantpulse-shape distortion.
IV. CONCLUSIONThe regenerative performance of a two-pump PA was studied
and compared with that of the one-pump parametric device.The generation of higher order parametric waves is examinedand shown to have a varied spectral width in two-pump PAdriven by counterphased optical pumps. The steepness of 2Rtransfer function is shown to increase with the order of thegenerated light, thus retaining the high figure of merit foundin single-pump 2R devices. Excessive spectral broadeningdue to pump-phase modulation is observed in higher ordertones created by FWM between the pump and any other tone(signal–idler) within the two-pump PA band. While the spectralwidth of the higher order term generated by signal–idlernondegenerate process is greater than that of the signal, it isnot influenced by either pump modulation scheme. We notethat ultrafast material response guarantees rate transparency forboth one- and two-pump PA regeneration methods.
REFERENCES[1] E. Ciaramella and S. Trillo, “All-optical signal reshaping via four-wave
mixing in optical fibers,” IEEE Photon. Technol. Lett., vol. 12, pp.849–851, 2000.
[2] K. Inoue, “Suppression of level fluctuation without extinction ratiodegradation based on output saturation in higher order optical para-metric interaction in fiber,” IEEE Photon. Technol. Lett., vol. 13, pp.338–340, Apr. 2001.
[3] J. Hansryd and P. Andrekson, “Broad-band continous-wave-pumpedfiber optical parametric amplifier with 49-dB gain and wavelengthconversion efficiency,” IEEE Photon. Technol. Lett., vol. 13, pp.194–196, Mar. 2001.
[4] R. M. Jopson, U.S. Patent 5 386 314, 1994.[5] S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R.
Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selectivesuppression of idler spectral broadening in two-pump parametricarchitectures,” IEEE Photon. Technol. Lett, vol. 15, pp. 673–675, May2003.
[6] S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Cen-tanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave para-metric gain synthesis using nondegenerate pump four-wave mixing,”IEEE Photon. Technol. Lett., vol. 14, pp. 1406–1408, Oct. 2002.
RADIC et al.: ALL-OPTICAL REGENERATION IN ONE- AND TWO-PUMP PAs USING HIGHLY NONLINEAR OPTICAL FIBER 959
Fig. 5. Transfer characteristics of higher order light generated using atwo-pump HNLF regenerator.
Fig. 6. Spectral broadening of higher order tones generated in two-pumpparametric regenerator as measured with a resolution of 1.5 GHz.
can be seeded by the degenerate processand the nondegenerate process . Itssubsequent growth can be augmented by the nondegenerate pro-cesses , ,where corresponds to an outer-band (1620.1 nm) photonand . The new frequency
is common to all these processes. Forcounterphased pumps, is constant. Since has anunbalanced , the newwave exhibits excessive pump-inducedbroadening, indicated by the heavy dashed curve. Similarly,wave (1578.5 nm) is generated by cascaded processes that sat-isfy the following energy relation .Since pump photons are balanced in all processes contributingto , this wave is not broadened by pump-phase modulation,in agreement with the thin solid curve in Fig. 6. Finally, thewave (1575.6 nm) is produced by cascaded processes satisfyingenergy relation . A similaranalysis can be used to analyze a cophased two-pump PA con-figuration [5].Processing a noisy input signal tests the performance of the
two-pump regenerator. A 10-Gb/s IM-NRZ signal is combinedwith amplified spontaneous emission in order to reduce the op-tical signal-to-noise ratio [(OSNR) measured within 0.1 nm]at the PA input to 17.6 dB, as shown in Fig. 7(a). The inputsignal power of 5.0 dBm allows for the mark fluctuations ofthe amplified signal to be efficiently suppressed, as illustrated
Fig. 7. (a) Input signal at 17.6-dB OSNR, (b) amplified signal at 1582.9 nmfor dBm, (c) term at 1571.3 nm for dBm, and(d) term at 1575.6 nm for dBm with output OSNR of 37 dB.The signal and idler are filtered out using a 0.25-nm filter, while isextracted using a 0.6-nm filter.
in Fig. 7(b). The poor ERs associated with both the signal andprimary idler result in the retention of considerable noise at thelow (space) signal levels. This noise can be suppressed by using
order, as shown in Fig. 7(c). The input power is held belowthe saturation level to avoid the pulse distortion present inFig. 7(b). By selecting and a wider optical filter, it is pos-sible to suppress both space and mark fluctuations, as shown inFig. 7(d). The result, however, comes at the price of significantpulse-shape distortion.
IV. CONCLUSIONThe regenerative performance of a two-pump PA was studied
and compared with that of the one-pump parametric device.The generation of higher order parametric waves is examinedand shown to have a varied spectral width in two-pump PAdriven by counterphased optical pumps. The steepness of 2Rtransfer function is shown to increase with the order of thegenerated light, thus retaining the high figure of merit foundin single-pump 2R devices. Excessive spectral broadeningdue to pump-phase modulation is observed in higher ordertones created by FWM between the pump and any other tone(signal–idler) within the two-pump PA band. While the spectralwidth of the higher order term generated by signal–idlernondegenerate process is greater than that of the signal, it isnot influenced by either pump modulation scheme. We notethat ultrafast material response guarantees rate transparency forboth one- and two-pump PA regeneration methods.
REFERENCES[1] E. Ciaramella and S. Trillo, “All-optical signal reshaping via four-wave
mixing in optical fibers,” IEEE Photon. Technol. Lett., vol. 12, pp.849–851, 2000.
[2] K. Inoue, “Suppression of level fluctuation without extinction ratiodegradation based on output saturation in higher order optical para-metric interaction in fiber,” IEEE Photon. Technol. Lett., vol. 13, pp.338–340, Apr. 2001.
[3] J. Hansryd and P. Andrekson, “Broad-band continous-wave-pumpedfiber optical parametric amplifier with 49-dB gain and wavelengthconversion efficiency,” IEEE Photon. Technol. Lett., vol. 13, pp.194–196, Mar. 2001.
[4] R. M. Jopson, U.S. Patent 5 386 314, 1994.[5] S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R.
Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selectivesuppression of idler spectral broadening in two-pump parametricarchitectures,” IEEE Photon. Technol. Lett, vol. 15, pp. 673–675, May2003.
[6] S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Cen-tanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave para-metric gain synthesis using nondegenerate pump four-wave mixing,”IEEE Photon. Technol. Lett., vol. 14, pp. 1406–1408, Oct. 2002.
• Radic et al., Photon. Technol. Lett. 15, 957 (2003).
• All-optical regeneration demonstrated with dual pump FOPAs.
• Up to 20 dB improvement in signal-to-noise ratio (SNR).
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Performance Limiting FactorsSeveral factors a↵ect FOPA performance:
• SNR degradation due to pump-phase modulation;PM-to-AM conversion through fiber dispersion.
• Noise added to pumps during their amplificationdegrades SNR of both signal and idler.
• Dispersion fluctuations in optical fibers.
• Polarization sensitivity of the FWM process.
• Birefringence of single-mode fibers (PMD).
• Raman-induced noise and power transfer.
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PM-to-AM Conversion of Pumps• Pump phases modulated to suppress stimulated Brillouin scattering.
• Phase modulation converted to amplitude modulation by dispersion.
• Signal gain sensitive to changes in pump power:
G⇡ 1
4
exp(gL) g = 2gp
P
1
P
2
.
• Signal and Idler SNR degraded considerably because ofpump power variations.
• Walk-o↵ e↵ects reduce the impact of pump-phase modulation.
• E↵ective parametric gain: (d = walk-o↵ parameter)
g =1
L
ZL
0
2g[P1
(z,t� zd )P
2
(z,t� zd )]1/2
dz.
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PM-to-AM Conversion
Length = 1 kmg = 4.2 W�1/kmP
1
= P
2
= 0.5 Wb
3
= 0.1 ps3/kmb
4
= 8 ⇥10
�5 ps4/kmT
r
= 33 ps (blue)T
r
= 14 ps (red)
• Signal power variation larger for shorter rise times.
• Group-velocity mismatch reduces the e↵ect considerably.
.
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Signal SNR
2.0 2.5 3.0 3.5 4.0 4.5 5.012
16
20
24
28
32
With walk off No walk off
Rise Time = 60 ps
Rise Time = 15 ps
Sig
nal-t
o-N
oise
Rat
io (d
B)
Bit Rate (Gb/s)
• SNR degrades with higher modulation rates and shorter rise times
• Walk-o↵ e↵ects improve the SNR at high bit rates.
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Pump Power FluctuationsPhaseModulation
EDFA
Amplification Filters
EDFA
• Erbium-doped fiber amplifiers add noise to pump.
• Noise is quantified through relative intensity noise (RIN)
• How does pump RIN a↵ect the amplified signal and idler?
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Dual-Pump FOPA Equations
∂A
1
∂ z
= ib0
(w1
)A1
� 1
v
g1
∂A
1
∂ t
+ ig(|A1
|2 +2|A2
|2)A1
∂A
2
∂ z
= ib0
(w2
)A2
� 1
v
g2
∂A
2
∂ t
+ ig(|A2
|2 +2|A1
|2)A2
∂A
3
∂ z
= ib0
(w3
)A3
� 1
v
g3
∂A
3
∂ t
+2ig(|A1
|2 + |A2
|2)A3
+2igA
1
A
2
A
⇤4
∂A
4
∂ z
= ib0
(w4
)A4
� 1
v
g4
∂A
4
∂ t
+2ig(|A1
|2 + |A2
|2)A4
+2igA
1
A
2
A
⇤3
This set of equations is solved numerically to calculate:
• RINp
(w,0) = 1
hP1
i2R •�•hdP
1
(t)dP
1
(t + t)iexp(�iwt)dt
• RINs
(w,L) = 1
hP3
i2R •�•hdP
3
(t)dP
3
(t + t)iexp(�iwt)dt
• RIN Enhancement factor: F
r
(w) = RIN
s
(w,L)/RIN
p
(w,0).
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RIN Spectra
0.00 0.15 0.30 0.45 0.60
-180
-170
-160
-150
-140Signal
Pumps
RIN
(dB
/Hz)
Frequency (THz)
Pumps: 1525, 1575 nmSignal Wavelengths:
1530 nm 1536 nm 1550 nm
• At low frequencies, signal RIN is enhanced by 15 dB.
• At high frequencies, RIN is reduced because of walk-o↵ e↵ects.
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Optical SNR
1530 1540 1550 1560 157012.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
3 nm
Filter Bandwidth = 1 nm
Opt
ical
Sig
nal-t
o-N
oise
Rat
io (d
B)
Signal Wavelength (nm)
• Signal SNR is degraded considerably because of pump RIN.
• A narrowband optical filter helps but problem persists.
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Dispersion Fluctuations• Fiber-core diameter is not uniform along fiber length.
• Zero-dispersion wavelength (ZDWL) fluctuates along z.
• Even 1% variations in core diameter cause 4–6 nm change in ZDWL.
• Length scale of ZDWL fluctuations is typically ⇠10 m.
• Phase mismatch k depends on the ZDWL; it also varies randomly
along the FOPA length.
• Output signal power can vary considerably because of ZDWL
fluctuations for otherwise identical FOPAs.
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Signal Gain Fluctuations
L = 1 kmg = 4.2 W�1km�1
P
1
= P
2
= 0.5 Wb
3
= 0.1 ps3/kmb
4
= 8⇥10
�5 ps4/km
• Pumps separated by 100 nm in numerical simulations.
• Each curve corresponds to a fiber with a di↵erent ZDWL distributionbut the same average value.
• Central portion of the gain spectrum is a↵ected most.
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Compromise: Trade Bandwidth for Flatness
• Pumps separated by 50 nm; other parameters unchanged.
• Gain is nearly uniform in spite of dispersion fluctuations.
• FOPA bandwidth is reduced to below 45 nm.
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Polarization Effects• FWM process in optical fibers is polarization sensitive.
• Vector theory of FWM has been developed:Lin & Agrawal, J. Opt. Soc. Am. B 21, 1216 (2004).
• It makes use of Jones matrices and rotation of Stokes vectorson the Poincare sphere.
• Parametric gain depends on the relative polarization of two pumps.
• FOPA gain becomes independent of signal polarization fororthogonally polarized pumps (in the absence of PMD).
• Linearly but orthogonally polarized pumps used in practice.
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Linear versus Circular Polarization
• Parametric gain varies with the ellipticity of pumps.
• Linearly polarized pumps provide only 50% gain even for perfectphase matching.
• Circularly polarized pumps provide the best performance.
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Polarization-Mode Dispersion• A single-mode fiber supports two orthogonally polarized modes.
• Two modes degenerate for a perfect fiber (nx
= n
y
).
• In practice, |nx
�n
y
| ⇠ 10
�7 on average, but it changes along thefiber in a random fashion.
• State of polarization of light evolves randomly at a rate that dependson its frequency (PMD).
Evolution of polarizations of the four interacting fields along fiber.Input Polarizations
1 2 3 4
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PMD-Induced Gain Fluctuations
• Gain fluctuates by a large amount from fiber to fiber.
• For a given fiber, gain can also fluctuate with time.
• Gain uniformity is degraded in both cases.
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Average Gain Spectra
1500� 1520� 1540� 1560� 1580� 1600�0�
10�
20�
30�
40�
�
�
D�p�=0.15�
D�p�=0.1�
D�p�=0.05�
Isotropic Fiber�
Ave
rage
Gai
n (d
B)�
Signal Wavelength (nm)�
D
p
characterizes strengthof PMD e↵ects.
Typically, D
p
= 0.1 ps/km1/2
for modern fibers.
• Average gain is reduced because of birefringence fluctuations.
• Gain uniformity is degraded for large PMD.
• Uniformity can be improved by reducing pump separation (resultingin a lower gain bandwidth).
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Polarization-Dependent Gain (PDG)
1500� 1520� 1540� 1560� 1580� 1600�0�
5�
10�
15�
20�
25�
D�p�=0.1�
Isotropic Fiber�
45�0�
90�0�0�0�
� �
�
�
Ave
rage
Gai
n (d
B)�
Signal Wavelength (nm)�
• Gain is sensitive to input SOP of signal polarization even iforthogonally polarized pumps are used
• Theory agrees well with experimental measurementsS. Radic and C. J. McKinstrie, Opt. Fiber. Technol. 9, 7 (2003).
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Conclusions• FOPA is a new kind of fiber-based parametric device.
• It can act as an optical amplifier and provide >30 dB gain overa bandwidth of >40 nm.
• It can also be used for wavelength conversion, phase conjugation,and many other signal-processing applications.
• Dual-pump FOPAs require two pumps with ⇠0.5 W power.
• Power and phase fluctuations of pumps a↵ect the signal SNR andshould be minimized.
• PMD and dispersion fluctuations also a↵ect FOPA performance.
• FOPAs constitute an active topic of current research.