Fiber-Optic Parametric Amplifiers

156 Pages·2006·1.37 MB·English

Fiber-Optic Parametric Amplifiers:
Their Advantages and Limitations
by
Fatih Yaman
Submitted in Partial Fulfillment
of the
Requirements for the Degree
Doctor of Philosophy
Supervised by
Professor Govind P. Agrawal
The Institute of Optics
The College
School of Engineering and Applied Sciences
University of Rochester
Rochester, New York
2006
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Curriculum Vitae
The author was born in Diyarbakir, in 1978 and grew up in Aydin, Turkey. He grad-
uated first in his class with B.S. degrees in both Physics and Mathematics from Koc
University, Istanbul in 2000. He then began graduate studies at the Institute of Optics
same year. He has carried out his doctoral research in nonlinear fiber optics under the
directionofProfessorGovindP.Agrawal.
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Publications
Journal Articles
F.Yaman,Q.Lin,andG.P.Agrawal,“Anoveldesignforpolarization-independent
single-pumpfiber-opticparametricamplifiers,”submittedtoIEEEPhoton. Tech-
nol. Lett.
Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers
through four-wave mixing: role of Raman scattering and pump polarization,”
submittedtoPhys. Rev. A.
F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of polarization-mode
dispersion and polarization-dependent loss on fiber-optic parametric amplifiers,”
acceptedforpublicationinJ.LightwaveTechnol.
Q. Lin, F. Yaman, and G. P. Agrawal, “Raman-induced polarization-dependent
gain in parametric amplifiers pumped with orthogonally polarized lasers,” IEEE
Photon. Technol. Lett. 18,397(2006).
Q.Lin,F.Yaman,andG.P.Agrawal,“Photon-pairgenerationbyfour-wavemix-
inginsideopticalfibers,”Opt. Lett. 31,1286(2006).
A.Sennaroglu,U.Demirbas,S.Ozharar,andF.Yaman,“Accuratedetermination
of saturation parameters for Cr4+-doped solid-state saturable absorbers,” J. Opt.
Soc. Am. B23,241(2006).
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F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of pump-phase modula-
tion on dual-pump fiber-optic parametric amplifiers and wavelength convertors,”
IEEEPhoton. Technol. Lett. 17,2053(2005).
F.Yaman,Q.Lin,S.Radic,andG.P.Agrawal“Pumpnoisetransferindual-pump
fiber-opticparametricamplifiers: walk-offeffects,”Opt. Lett. 30,1048(2005).
F.Yaman,Q.Lin,S.Radic,andG.P.Agrawal,“Impactofdispersionfluctuations
on dual-pump fiber-optic parametric amplifiers,” IEEE Photonic Technol. Lett.
16,1292(2004).
F.Yaman,Q.Lin,andG.P.Agrawal,“Effectsofpolarizationmodedispersionin
dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16,
431(2004).
A. Levent, S. G. Rajeev, F. Yaman, and G. P. Agrawal, “Nonlinear theory of
polarization-mode dispersion for fiber solitons,” Phys. Rev. Lett. 90, 013902
(2003).
Book Chapters
F.Yaman,Q.Lin,andG.P.Agrawal,“Fiber-opticparametricamplifiersforlight-
wave systems,” Guided Wave Optical Components and Devices, B. P. Pal Ed.
(AcademicPress,SanDiego,CA,2005),Chap.7,pp. 101–117.
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Presentations
F.Yaman,Q.Lin,andG.P.Agrawal,“Anoveldesignforpolarization-independent
single-pump fiber-optic parametric amplifiers,” in Proc. Conf. on Lasers and
Electro-Optics(CLEO)2006,LongBeach,CA,PaperJWB59.
F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of pump-phase modu-
lation on fiber-optic parametric amplifiers and wavelength converters,” in Proc.
Conf. onLasersandElectro-Optics(CLEO)2005,Baltimore,MD,PaperCTuJ6.
Q. Lin, F. Yaman, S. Radic, and G. P. Agrawal, “Fundamental noise limits in
dual-pumpfiber-opticparametricamplifiersandwavelengthconverters,”inProc.
Conf. onLasersandElectro-Optics(CLEO)2005,Baltimore,MD,PaperCTuT4.
F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of pump-phase modula-
tionontheperformanceofdual-pumpfiber-opticparametricamplifiers,”inProc.
Conf. OpticalFiberCommunications(OFC)2005,Anaheim,CA,PaperOWN3.
F.Yaman,Q.Lin,andG.P.Agrawal,“Impactofpolarizationmodedispersionon
dual-pump fiber optic parametric amplifiers,” in Proc. Conf. Nonlinear Guided
Waves(NLGW)2004,Toronto,PaperMC31.
Q. Lin, F. Yaman, and G. P. Agrawal, “Impact of randomly varying fiber disper-
sion on dual-pump fiber optic parametric amplifiers,” in Proc. Conf. Nonlinear
GuidedWaves(NLGW)2004,Toronto,MC36.
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Acknowledgements
I would like to express my gratitude to all those who gave me the opportunity to com-
pletethisthesis. Firstandforemost,Iwouldliketothankmyadvisor,ProfessorGovind
P.Agrawal. Henotonlytaughtmehowtodoscientificresearch,healsotaughtmehow
to think coherently and write coherently. I am also grateful to him for leading me into
theexcitingfieldofnonlinearfiberoptics.
IamgratefultoProfessorStojanRadicforhisvaluablediscussionsandsuggestions,
as well as providing the point of view of an experimentalist. I would like to thank
Professor Sarada G. Rajeev for helping me see the concept of soliton propagation in
fibers from a whole new perspective. I am grateful to Professor John C. Howell for
lettingmeusehislaboratoryequipment.
Amongmycolleagues,IamparticularlygratefultoQiangLinforhisconstantcon-
tributions to my work, through passionate and fruitful discussions. He not only helped
me develop a sound physical intuition about nonlinear processes in fibers but he also
helpedmefindmywaythroughthecomplicatedmathematicsofpolarization-modedis-
persionandstochasticprocesses. IwouldliketothankNickUsechakforthestimulating
discussions about mode-locked lasers and pulse characterization. I am grateful to him
for answering my questions about laboratory equipment. I thank Dr. Ekaterina Pout-
rina and Dr. Jayanthi Santhanam for helping me have a better understanding of fiber
communication systems. I am grateful to Dr. Levent Akant for introducing to me the
exciting mathematical tools that were so helpful in understanding soliton propagation
infibers. IthankIrfanAliKhanforhelpingmeinProfessorHowell’slaboratory.
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Abstract
Fiber-opticparametricamplifiers(FOPAs)canbeusedinlightwavesystemsforseveral
signal-processing applications including optical amplification, phase conjugation, and
wavelengthconversion. Inprinciple,FOPAscanprovidehighgainuniformoverawide
wavelength range (>100 nm). What is more, FOPAs add little noise to the amplified
signal. FOPAscanhavenoisefigureaslowas0dBwhenoperatedinthephase-sensitive
mode and 3 dB in the phase insensitive mode. However, in practice, these advantages
of FOPAs are compromised. In this work, I investigate several factors that limit the
performanceofFOPAs,andproposepracticalschemestominimizethoselimitations.
FOPAs can provide a relatively large gain bandwidth because the gain spectrum of
FOPAs is not determined by material resonances but by the phase-matching condition.
For the same reason, FOPAs are very sensitive to perturbations stemming from fiber
irregularities. One such irregularity is that fiber dispersion varies randomly along the
fiber length. My numerical modeling showed that, because of such variations, FOPA
gainspectrumcannotmaintainitsflatnessandalsothatFOPAgainprofilechangesfrom
one fiber to the other. Using stochastic methods, an analytic theory is developed that
can predict an “average gain spectrum.” This analytic theory can be used to show that
flatnessofFOPAgainisrecoveredattheexpenseofreducingthegainbandwidth.
Another fiber irregularity that affects FOPA gain spectrum is the residual birefrin-
gence. Duringthefiber-drawingprocess,thecrosssectionoffibercoreinevitablydevi-
atesfromperfectcircularsymmetry. Asaresult,allnon-polarizationmaintainingfibers
exhibitresidualbirefringence. Boththemagnitudeofbirefringenceandthedirectionof
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itsprincipalaxisvaryalongthefiberlengthaswellasintime. Becauseofresidualbire-
fringence, state of polarizations of the propagating fields change randomly also. Since
the underlying four-wave mixing (FWM) process depends on the state of polarizations
of the interacting fields, FOPA gain profile cannot maintain its flatness, and changes
in time. The impact of residual birefringence on dual-pump FOPAs are investigated
by means of numerical simulations. It is shown that residual birefringence also causes
a trade off between flatness of FOPA gain spectrum and FOPA gain bandwidth. The
FOPAgainbandwidthrequiredtomaintainaflatgainprofileisdetermined.
FOPAs canbe used for all-opticalsignal processing applications sincethe underly-
ing FWM process responds almost instantaneously. However, the ultrashort response
time of FWM makes FOPAs susceptible to pump noise. This becomes a limitation on
thenoisepropertiesofFOPAs. Iinvestigatedtheimpactofpumpnoiseontheamplified
signal in the context of intensity noise transfer. It is shown that the group-velocity dif-
ference between the signal and pumps play an important role and reduces the transfer
ofintensitynoisefromthepumptothesignal.
Another limitation of FOPAs is that, since the efficiency of FWM process depends
onpolarizationstatesoftheinteractingfields,FOPAgainbecomessensitivetoinputpo-
larizationofthesignal. Thereareseveralschemesthathavebeenproposedtoeliminate
polarization dependence of FOPA gain. However, in the case of single-pump FOPAs
theexistingmethodsarecumbersometoimplement. Inthiswork,Iproposearelatively
simplewaytoachievepolarization-insensitivegainbyusingahighlybirefringentfiber.
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Table of Contents
CurriculumVitae ii
Publications iii
Acknowledgements vi
Abstract vii
ListofTables xii
ListofFigures xiii
1 Introduction 1
1.1 HistoricalReviewofPreviousWork . . . . . . . . . . . . . . . . . . . 1
1.2 ThesisObjective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 ThesisOrganization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 TheoreticalFramework 5
2.1 BasicPropertiesofFWM . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Maxwell’sandHelmholtz’sEquations . . . . . . . . . . . . . . . . . . 7
2.3 ModesofOpticalFibers . . . . . . . . . . . . . . . . . . . . . . . . . 10
x
2.4 Third-orderNonlinearResponse . . . . . . . . . . . . . . . . . . . . . 13
2.5 VectorialNLSEquation . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 VectorialFWMEquations . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 ScalarFWMEquations . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 ParametricAmplifiers 27
3.1 Single-PumpParametricAmplifiers . . . . . . . . . . . . . . . . . . . 28
3.2 Dual-PumpParametricAmplifiers . . . . . . . . . . . . . . . . . . . . 36
3.3 PolarizationDependenceofFOPAGain . . . . . . . . . . . . . . . . . 41
3.3.1 TheoreticalModel . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.2 FWMinShortFibers . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.3 FWMinLongFibers . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 ApplicationsandLimitations . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.1 WavelengthConversionandOtherApplications . . . . . . . . . 52
3.4.2 PracticalLimitations . . . . . . . . . . . . . . . . . . . . . . . 55
4 ImpactofFiberImperfections 57
4.1 FluctuationsofZero-DispersionWavelength . . . . . . . . . . . . . . . 57
4.1.1 NumericalSimulations . . . . . . . . . . . . . . . . . . . . . . 58
4.1.2 NumericalResults . . . . . . . . . . . . . . . . . . . . . . . . 60
4.1.3 MitigationofZDWLFluctuations . . . . . . . . . . . . . . . . 62
4.1.4 AnalyticalModel . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 EffectofResidualFiberBirefringence . . . . . . . . . . . . . . . . . . 70
4.2.1 TheoreticalModel . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.2 NumericalModel . . . . . . . . . . . . . . . . . . . . . . . . . 72