Noise-figure limit of fiber-optical parametric amplifiers andwavelength converters: experimental investigation
Renyong Tang, Paul L. Voss, Jacob Lasri, Preetpaul Devgan, and Prem Kumar
Center for Photonic Communication and Computing, Department of Electrical and Computer Engineering, Northwestern University,2145 Sheridan Road, Evanston, Illinois 60208-3118
Fiber-optical parametric amplifiers (FOPAs) arecurrently the subject of much research for use inwavelength conversion1 and eff icient broadband am-plification.2 They are also candidates for performingall-optical network functions.3,4 Advances in themanufacture of microstructure and other highly non-linear fibers have led to improvements in the gainslope5,6 of FOPAs, and refinements in the pumpingtechniques have permitted improvements in the noisefigure (NF).1,7,8 To date, to our knowledge, the lowestpublished NF measurements in phase-insensitiveoperation of a x �3� amplif ier have been 3.7,9 3.8,1
and 4.2 dB.7 A FOPA may suffer from one or moretechnical impairments that add excess noise to thesignal being amplified. These impairments caninclude injection of amplified spontaneous emission(ASE) at the signal wavelength from the erbium-dopedfiber amplifier (EDFA) used to amplify the pump, andsaturation of the FOPA, which produces higher-orderfour-wave-mixing products. Gain modulation due topump f luctuations can also degrade the performanceof a FOPA.
Although the above impairments can be eliminatedthrough good design, fundamental quantum noisewill remain. Our recent theoretical work has shownthat the quantum-limited NF of a FOPA operatedphase insensitively, as is typically the case, or as awavelength converter (WC), exceeds the standard 3-dBlimit at high gains due to the Raman effect.10,11 Thedegree to which the NF exceeds the 3-dB limit in-creases with pump-signal detuning (up to the Ramangain peak), with an increasing fraction of the high-Raman-gain material in the f iber (such as germanium)and with temperature. Previously, we measured theNF of a quasi-cw parametric amplif ier at a f ixedpump-signal detuning by use of a technique calledoptical homodyne tomography.9 The measured NF of3.7 dB was in excellent agreement with the theoreticalprediction.10,11 In this Letter we present the f irstdetailed experimental evidence in support of thistheory through measurements of the NF spectra forparametric amplif ication and wavelength conversion
0146-9592/04/202372-03$15.00/0
in a cw FOPA made from 4.4 km of dispersion-shiftedfiber (DSF). The theory is also extended to includethe effect of distributed linear loss on the noise f ig-ure of such a long-length parametric amplifier andwavelength converter. Our measurements show goodagreement with predictions of the extended theory.
When a FOPA is operated in a phase-insensitiveconfiguration as an amplifier, a coherent-state inputsignal is injected on the Stokes (anti-Stokes) side whileno light is injected on the anti-Stokes (Stokes) side.The NF is then defined as NFPIA � SNRin,j�SNRout, j ,where j � s�a� if the signal frequency is on the Stokes(anti-Stokes) side and SNR is the signal-to-noiseratio. When the input-signal photon number in themeasurement bandwidth is much greater than theamplifier gain, one can obtain the following expressionfor the NF10,11:
NFj , PIA � 1 1jnj j
2 1 �1 1 2nth� jcj ,R j2 1 jcj ,vj2
jmj j2,
(1)
where nth � �exp�h̄V�kT � 2 1�21 is the mean numberof optical phonons at detuning V and temperatureT ; h̄ is Planck’s constant over 2p; k is Boltzmann’sconstant; V � va 2 vp � vp 2 vs; and vj for j �p, s, a is the angular frequency of the pump, Stokes,and anti-Stokes fields, respectively. In Eq. (1),jna�s�j
2, �1 1 2nth� jcj ,R j2, and jcj ,vj2 represent am-plified noise seeded by vacuum f luctuations of theStokes (anti-Stokes) mode, by thermally populatedoptical phonon modes coupled in by the Ramanprocess, and by vacuum modes coupled in by thedistributed loss, respectively. When the time-domain Raman response function h�t� is real, itsFourier transform satisfies H �V� � H �2V��.12 Thisassumption is usually valid for V up to severalterahertz in standard fibers.13 When the Ramaneffect10,11 and the linear loss are included, a seriessolution exists, and one obtains for a FOPA of length L
Ip�0�Leff 2 iDkL�2 2 aaL�4 2 asL�4, and whereDk � b2V2 is the phase mismatch with b2 as thegroup-velocity-dispersion coeff icient at the pumpwavelength; aj is the attenuation coeff icient forj � p, a, s at the pump, anti-Stokes, and Stokeswavelengths, respectively; Ip�0� � jAp�0�j2 is the inputpump power in watts; and the effective f iber length isdefined as Leff � �1 2 exp�2apL���ap. The functionna is the same series as ma except that the initialcondition is �a0 � 0, s�
0 � 1�. The function ns is thesame series as ms except that the initial conditionis �a0 � 1, s�
0 � 0�. The coefficients an and s�n are
calculated through the recursion relations
an �Gan21 1 j1s
�n21 1 L
Pn21j�0 a
jpan212j
n, (4)
s�n �
2Gs�n21 1 j2an21 2 L
Pn21j�0 a
jps�
n212j
n, (5)
where G � i�H �V� 1 H �2V���Ip�0��2, L ��as�2 2 aa�2 1 iDk��2, j1 � iH �V�Ip�0�, andj2 �2iH �2V��Ip�0�. Finally, we calculate jcj ,R j2 andjcj ,vj2 to be
jcj ,R j2 �Z L
02 Im�H �V��Ip�0�exp�2apz�
3 jmj �L 2 z� 2 nj �L 2 z�j2dz , (6)
jca�s�,vj2 �
Z L
0�a�a�sjma�s��L 2 z�j2
1 as�a�jna�s��L 2 z�j2�dz . (7)
The power gain seen by the signal exiting the amplif ieris Gj � jmj j
2.We define the NF of wavelength conversion as
NFa�s�,WC � SNRs�a�, in�SNRa�s�, out, where a signal ina coherent state on the Stokes (anti-Stokes) side isinserted into the amplif ier and the SNR of the gener-ated wave on the anti-Stokes (Stokes) side is measuredat the output. Once again under the condition thatthe number of input photons over the measurementbandwidth is much greater than the FOPA gain, theNF of a WC is11
NFj ,WC � 1 1jmj j
2 1 �1 1 2nth� jcj ,R j2 1 jcj ,vj2
jnj j2(8)
for j [ �a, s�.Our setup for NF measurements is shown in
Fig. 1(a). The parametric amplif ier consists of a4.4-km-long piece of DSF. The nonlinear coefficientH �0� is 2.0 W21 km21, which was measured as in
Boskovic et al.14 By fitting the experimentally mea-sured gain spectra to our theory, we found the fiber’szero-dispersion wavelength �l0� to be 1551.16 nmand the dispersion slope �S0� to be 0.057 ps�nm2 km,which turn out to be within 4% of the manufacturer’sspecifications. The measured linear loss of the fiberis 0.41 dB�km at all wavelengths of interest. Toobtain H �V�, we assume that Re�H �V�� � H �0� (i.e.,we neglect the small variation of the real part ofthe nonlinear coefficient with detuning frequency V)and use Raman-gain coefficient gr�V��Aeff measuredwith an optical spectrum analyzer (OSA) to obtainIm�H �V�� � gr�V���2Aeff�. For measurement of theRaman-gain coefficient the pump wavelength wasplaced at 1536 nm so that the four-wave-mixingprocess did not phase match eff iciently.
For the parametric gain experiments, cw pump lightat a 1551.5-nm wavelength is phase modulated tosuppress stimulated Brillouin scattering and then am-plified to 300 mW of power. The phase modulator isdriven with three rf tones of approximately 100 MHz,300 MHz, and 2.7 GHz, each having 19 dBm of power.A 1-nm optical bandpass f ilter is used to remove theASE light at the Stokes and anti-Stokes wavelengthsthat would otherwise enter the amplif ier. The rela-tive intensity noise of the amplified and filtered pumpwas too small to affect the measurements reportedin this Letter. The signal source used to measurethe FOPA gain is a wavelength-tunable external-cavity distributed-feedback laser. The pump andsignal are coupled into the DSF with a 90�10 coupler.The gain is measured with the OSA by comparing thecw signal power levels with and without the pumpat an optical resolution bandwidth of 0.2 nm. Indetermining the amplif ier gain, the 1.8-dB insertionloss of the fiber was subtracted. The calibrated OSAis also used to measure parametric f luorescence powerPPF after the amplifier. The measurements are cor-rected for the combined insertion loss of an attenuatorand a polarizer (20.5 dB) inserted between the DSFand the OSA. In Fig. 1(b) we show the parametricf luorescence spectrum with the polarizer (solid curve),corrected for insertion loss, and the spectrum withoutthe polarizer (dashed curve). The two remain equaluntil approximately 1.3 THz of pump-signal detuning.Thus the use of our scalar theory is justified to this
Fig. 1. (a) Schematic of the experimental setup.PM, phase modulator; OBPF, optical bandpass filter;FPC1–FPC3, f iber polarization controllers. (b) Paramet-ric f luorescence spectra with a f iber polarizer placed beforethe spectrum analyzer (solid curve) and compensated forits 0.9-dB insertion loss and without f iber polarizer(dashed curve).
Fig. 2. (a) Signal gain spectrum of the FOPA. (b) Wave-length conversion gain spectrum of the FOPA. Solid curve,theory with inclusion of the Raman effect and linear loss;circles, experimental data.
Fig. 3. (a) Noise figure of the FOPA. (b) Noise figure ofthe WC. Dashed curve, theory without the Raman effector distributed loss; dashed–dotted curve, theory with theRaman effect but neglecting distributed loss; solid curve,theory with the Raman effect and distributed linear loss;circles, experimental data. The size of the circles is ofthe order of the measurement error. Measurements nearthe pump wavelength are contaminated by excessive ASEleakage through the OBPF.
detuning and would be valid to greater detunings for ashorter-length FOPA made from the same DSF. Thefollowing equation is then used to obtain the NFspectra for the FOPA and WC:
NF �1G
1 2PPF
h̄vBoG, (9)
where G is the FOPA or WC gain, Bo is the opticalresolution bandwidth of the measurement, and PPFis the parametric f luorescence power that is copo-larized with the signal at the output of the FOPAat the measurement wavelength. We note that thesecond term in Eq. (9) differs by a factor of 2 from theusual formula used for measurements on conventionalEDFAs. When spontaneous emission is presentequally in both polarization modes, as in an EDFA, andboth are detected, the measured ASE power is twice asmuch as what would beat with the signal. The factorof 2 in Eq. (9) arises because parametric f luorescenceis produced predominantly in only one polarization
mode in a single-pump FOPA; see Fig. 1(b). The two-polarization-mode NF formula, i.e., Eq. (9) withoutthe factor of 2, has been incorrectly cited in previousworks.1,7
As can be seen in Fig. 2(a), which shows thegain spectrum for parametric amplif ication, and inFig. 2(b), which shows the gain spectrum for wave-length conversion, the experimental data agree wellwith the theory. In Figs. 3(a) and 3(b) we show theNF results for the FOPA and the WC, respectively.The solid curves are plots of Eq. (1) and Eq. (8), respec-tively, that include the effects of the Raman processand distributed linear losses. No additional fittingparameters are used except l0 and S0 obtained fromthe fits in Fig. 2. The dashed–dotted curves are ob-tained by setting distributed losses to 0. The dashedcurves are obtained by also removing the Ramaneffect in theory by setting Im�H�V�� � 0. The datain Fig. 3 show good agreement with the theory. Thedifferences, we believe, are due to the asymmetryobserved in the measured Raman gain spectrum,which is assumed symmetric in the theory, and topolarization-mode dispersion in the large pump-signaldetuning regime.
In conclusion, we have measured the NF spectra forphase-insensitive parametric amplif ication and wave-length conversion in a cw FOPA. We have shown thatthe inclusion of the Raman effect is necessary to prop-erly model the quantum-limited performance of fiberparametric amplif iers and wavelength converters.
This work was supported by the National Sci-ence Foundation under grants ANI-0123495 andECS-0000241 and by the U.S. Army Research Off iceunder Multidisciplinary University Research Initia-tive grant DAAD19-00-1-0177.
References
1. K. K. Y. Wong, K. Shimizu, M. E. Marhic, K. Uesaka,G. Kalogerakis, and L. G. Kazovsky, Opt. Lett. 28, 692(2003).
2. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, andP. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8,506 (2002).
3. L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J.Quantum Electron. 38, 614 (2002).
4. Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron.Lett. 36, 1103 (2000).
5. R. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P.Kumar, Electron. Lett. 39, 195 (2003).
6. S. Radic, C. J. McKinstrie, R. M. Jopson, J. Centanni,Q. Lin, and G. Agrawal, Electron. Lett. 39, 838 (2003).
7. J. L. Blows and S. E. French, Opt. Lett. 27, 491 (2002).8. K. Inoue and T. Mukai, IEEE J. Lightwave Technol.
20, 969 (2002).9. P. L. Voss, R. Y. Tang, and P. Kumar, Opt. Lett. 28,
549 (2003).10. P. L. Voss and P. Kumar, Opt. Lett. 29, 445 (2004).11. P. L. Voss and P. Kumar, J. Opt. B 6, S762 (2004).12. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A.
Haus, J. Opt. Soc. Am. B 6, 1159 (1989).13. N. R. Newbury, Opt. Lett. 27, 1232 (2002).14. A. Boskovic, S. V. Chernikov, J. R. Taylor, L.
Gruner-Nielsen, and O. A. Levring, Opt. Lett. 21,1966 (1996).
