Forward Brillouin Scattering in Standard Optical Fibers: Single-Mode, Polarization-Maintaining, and Multi-Core

213 Pages·2022·6.215 MB·English

by  Avi Zadok, Hilel Hagai Diamandi, Yosef London, Gil Bashan

Springer Series in Optical Sciences 240
Avi Zadok
Hilel Hagai Diamandi
Yosef London
Gil Bashan
Forward Brillouin
Scattering in
Standard Optical
Fibers
Single-Mode, Polarization-Maintaining,
and Multi-Core
Springer Series in Optical Sciences
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Avi Zadok Hilel Hagai Diamandi
(cid:129)
Yosef London Gil Bashan
Forward Brillouin Scattering
in Standard Optical Fibers
Single-Mode, Polarization-Maintaining,
and Multi-Core
AviZadok HilelHagaiDiamandi
FacultyofEngineering FacultyofEngineering
Bar-IlanUniversity Bar-IlanUniversity
Ramat-Gan,TelAviv,Israel Ramat-Gan,TelAviv,Israel
YosefLondon GilBashan
FacultyofEngineering FacultyofEngineering
Bar-IlanUniversity Bar-IlanUniversity
Ramat-Gan,TelAviv,Israel Ramat-Gan,TelAviv,Israel
ISSN0342-4111 ISSN1556-1534 (electronic)
SpringerSeriesinOpticalSciences
ISBN978-3-031-13598-9 ISBN978-3-031-13599-6 (eBook)
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Preface
ThetermforwardBrillouinscatteringreferstotheinteractionsbetweenopticaland
acousticwavesthatco-propagateinanopticalmedium.ForwardBrillouinscattering
hasbeenanalyzedanddemonstratedinstandardsingle-modefibers(SMFs)forthe
first time by Shelby, Levenson, and Bayer in 1985 (Shelby, 1985). Since that first
report, the mechanism has been successfully carried over to specialty photonic-
crystal and nano-structured fibers (Kang, 2010) and silicon photonic-integrated
circuits (Kittlaus, 2016), and it has been studied extensively over those platforms.
On the other hand, interest in forward Brillouin scattering over the more standard
fiber platforms gradually reduced over time. Many properties of the effect were
alreadywelldescribedandunderstoodintheearlypapersonthetopic(Shelby,1985;
Biryukov,2002),andforwardBrillouinscatteringinthestandardfiberplatformswas
largelyconsideredastooweaktoserveforsignalprocessingorsensingapplications.
However,thispointofviewischangingoverthelastfewyears,asforwardBrillouin
scattering was shown to support new sensing concepts over standard fibers which
couldnotberealizedthroughothermechanisms(Antman,2016).
Theserecentadvancesraisetheneedforthecomprehensivetreatmentofforward
Brillouin scattering over standard fibers. This book is written in attempt to bridge
thisgap.Itisintendedtointroducethesubjecttonewgraduatestudentsintheareas
of fiber-optics, nonlinear optics, and opto-mechanics, and also help professionals
become acquainted with the latest development in the field. Emphasis is given to
SMFs, polarization maintaining (PM) fibers, and multi-core fibers (MCFs). While
the latter two are not nearly as popular and widely employed as SMFs, they are
nonetheless readily available off-the-shelf and used in large volumes, and they
provide additional degrees of freedom beyond those of SMF. There are several
downsides to the use of standard fibers: Like most nonlinear optical phenomena,
forwardBrillouinscatteringisordersofmagnitudeweakerthaninspecialtyfibersor
photonicintegratedcircuits.Inaddition,thedesignspaceofstandardfibersismuch
more restricted. However, these drawbacks are offset by long interaction lengths
overstandardfibers,reachingmanykilometers,andbysimpleavailabilitytoawider
v
vi Preface
community of researchers. References to landmark demonstrations of forward
Brillouinscatteringinotherplatformsaregiventhroughoutthetext.
Thisbookisorganizedasfollows.Afirstchapterisdedicatedtotheintroduction
of forward Brillouin scattering within the broader scope of opto-mechanical inter-
actions and fiber-optics. Chapters 2, 3, and 4 describe the acoustic modes that are
guidedbyopticalfibers,theirstimulationbyforcesassociatedwiththepropagation
of light in the fiber, and the counter-effect of photoelastic scattering of light. The
spontaneousandstimulatedregimesofforwardBrillouinscatteringarepresentedin
Chaps.5and6,respectively.Chapters7,8,and9arededicatedtotheextensionof
forward Brillouin scattering to fibers with coating layers, MCFs, and PM fibers.
ExperimentaltechniquesforthecharacterizationofforwardBrillouinscatteringare
described in Chap. 10, and measurement results are reported in detail in Chap. 11.
That chapter also highlights the application of forward Brillouin scattering to the
sensingofmediaoutsidethefibercladdingboundaries,whereguidedlightdoesnot
reach.Finally,asummaryandconcludingperspectivesaregiveninChap.12.
WewouldliketothanktheEuropeanResearchCouncil(ERC),theIsraelScience
Foundation, and the Israel Ministry of Science, Technology and Innovation, for
supportingpartsoftheresearchpresentedinthisbook.SpecialthanksgotoDr.Yair
Antman, formerly with Bar-Ilan University, Israel, and presently at Columbia
University, New York, NY, for initiating the study of forward Brillouin scattering
at the Zadok research group, Bar-Ilan University. We would also like to thank
present and former members of the Zadok group, who took part in the study of
this topic: Dr. ArikBergman, Alon Bernstein,Alex Clain, Dr. Mirit Hen, Dr. Eyal
Preter,Dr.KavitaSharma,KerenShemer,andEladZehavi.HilelHagaiDiamandiis
gratefultotheAzrieliFoundationfortheawardofanAzrieliFellowship.GilBashan
acknowledgesthesupportoftheAdamsFellowshipsProgramoftheIsraelNational
AcademyofScienceandHumanities.Last,Dr.Zadokwishestothankhisgraduate
studies advisors, Prof. Avishay Eyal and Prof. Moshe Tur of Tel-Aviv University,
Israel,fortheirlifelongmentoring.
We hope the readers would find this book useful, and that it would help draw
moreresearchersandstudentstoextendtheknowledgeinthefield.
Ramat-Gan,TelAviv,Israel AviZadok
HilelHagaiDiamandi
YosefLondon
GilBashan
References
1. Antman,Y.,A.Clain,Y.London,andA.Zadok,“Optomechanicalsensingofliquidsoutside
standardfibresusingforwardstimulatedBrillouinscattering,”Optica3,510–516(2016).
2. Biryukov, A. S., M. E. Sukharev, and E. M. Dianov, “Excitation of sound waves upon
propagationoflaserpulsesinopticalfibres,”J.Quant.Elect.32,765–775(2002).
Preface vii
3. Kang, M. S., A. Brenn, and P. St. J. Russell, “All-optical control of gigahertz acoustic
resonances by forward stimulated interpolarization scattering in a photonic crystal fibre,”
Phys.Rev.Lett.105,153901(2010).
4. Kittlaus, E.A., H.Shin,andP. T.Rakich.“LargeBrillouin amplification in silicon,”Nature
Photonics10,463–467(2016).
5. Shelby,R.M.,M.D.Levenson,andP.W.Bayer,“Guidedacoustic-waveBrillouinscattering,”
Phys.Rev.B31,5244–5252(1985).
Contents
1 Introduction:InteractionsBetweenGuidedOptical
andAcousticWaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ScatteringEffectsinOpticalFibers. . . . . . . . . . . . . . . . . . . . . 2
1.1.1 RayleighScattering. . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 RamanScattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 TheOpticalKerrEffect. . . . . . . . . . . . . . . . . . . . . . . 6
1.1.4 Short-PeriodFiberGratings. . . . . . . . . . . . . . . . . . . . 8
1.1.5 Long-PeriodFiberGratings. . . . . . . . . . . . . . . . . .. . . 9
1.1.6 BrillouinScattering. . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 PhysicalPrinciplesofOpto-MechanicalInteractions. . . . . . . . . 16
1.2.1 ElectrostrictiveForcesintheBulk. . . . . . . . . . . . . . . . 16
1.2.2 OpticallyInducedPressureatRefractiveIndex
Discontinuities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.3 PhotoelasticScatteringintheBulk. . . . . . . . . . . . . . . 18
1.2.4 MovingBoundaries. . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.5 ElectrostrictiveForcesinStandardSingle-Mode
Fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.6 PhotoelasticScatteringinStandardSingle-Mode
Fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 BrillouinScatteringoverDifferentFiberandWaveguide
Platforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.1 Polarization-Maintaining(PM)Fibers. . . . . . . . . . . . . 26
1.3.2 Multi-CoreFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.3 PhotonicCrystal,Nanostructured,
andTaperedFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.3.4 Micro-Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.3.5 PlanarPhotonic-IntegratedWaveguides. . . . . . . . . . . . 31
ix
x Contents
1.4 ApplicationsofBrillouinScatteringinFibers. . . . . . . . . . . . . . 32
1.4.1 BrillouinLasersandMicrowaveOscillators. . . . . . . . . 32
1.4.2 Microwave-PhotonicandAll-OpticalSignal
Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4.3 DistributedBrillouinFiberSensors. . . . . . . . . . . . . . . 34
1.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 GuidedAcousticWavesinStandardSingle-ModeFibers. . . . . . .. 45
2.1 SolutiontotheElasticWaveEquationinCylindricalRods. . . . 45
2.2 BoundaryConditionsattheOuterEdgeoftheCladding. . . . . . 49
2.3 TransverseGuidedAcousticModes. . . . . . . . . . . . . . . . . . . . . 51
2.3.1 RadialGuidedAcousticModes. . . . . . . . . . . . . . . . . . 53
2.3.2 Torsional-RadialGuidedAcousticModes
ofTwofoldAzimuthalSymmetry. . . . . . . . . . . . . . . . 55
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 ElectrostrictiveStimulationofGuidedAcousticModes
inStandardSingle-ModeFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 OpticalTonesofAlignedLinearPolarizations. . . . . . . . . . . . . 57
3.2 ModulatedOpticalCarrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 OpticalTonesofLinearandOrthogonalPolarizations. . . . . . . . 66
3.4 OpticalTonesofCircularPolarizations. . . . . . . . . . . . . . . . . . . 66
3.5 AcousticDissipationandMediaOutsidetheCladding. . . . . . . . 68
3.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 PhotoelasticPerturbationstotheDielectricTensorDue
toGuidedAcousticModes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 RadialAcousticModes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Torsional-RadialModesofTwofoldAzimuthalSymmetry. . . . . 77
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 SpontaneousForwardBrillouinScatteringinStandard
Single-ModeFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 PhotoelasticScatteringofProbeWavesbyRadial
AcousticModes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 PhotoelasticScatteringofProbeWavesbyTorsional
RadialAcousticModes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6 StimulatedForwardBrillouinScatteringinStandard
Single-ModeFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.1 ForwardBrillouinCouplingofPowerBetweenTwo
Co-PropagatingContinuousWaves. . . . . . . . . . . . . . . . . . . . . 95
6.2 CascadedStimulationofMultipleSidebands. . . . . . . . . . . . . . . 99
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103