Table Of ContentProgress in Optical Science and Photonics
Soloman Raju Thokala
Asymmetric
Dual Core
Waveguides
Dynamics of Self-Similar Waves
Progress in Optical Science and Photonics
Volume 22
SeriesEditors
JavidAtai,Sydney,NSW,Australia
RongguangLiang,CollegeofOpticalSciences,UniversityofArizona,Tucson,
AZ,USA
U.S.Dinish,InstituteofBioengineeringandBioimaging,A*STAR,Singapore,
Singapore
The purpose of the series Progress in Optical Science and Photonics is to provide
a forum to disseminate the latest research findings in various areas of Optics and
its applications. The intended audience are physicists, electrical and electronic
engineers, applied mathematicians, biomedical engineers, and advanced graduate
students.
Soloman Raju Thokala
Asymmetric Dual Core
Waveguides
Dynamics of Self-Similar Waves
SolomanRajuThokala
DepartmentofPhysics,FacultyofScience
andTechnology
ICFAIFoundationforHigherEducation
Dontanapally,Hyderabad,Telangana,India
ISSN 2363-5096 ISSN 2363-510X (electronic)
ProgressinOpticalScienceandPhotonics
ISBN 978-981-19-7117-4 ISBN 978-981-19-7118-1 (eBook)
https://doi.org/10.1007/978-981-19-7118-1
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TomyParents:Mrs.&Mr.Thokala
JayamaniandRatnaRaju
Preface
Eversincetheirdiscovery,opticalsolitonsareconsideredtobeoneofthehottesttech-
nologiesofthetwenty-firstcentury.Theyplayadecisiveroleinlong-haultelecom-
municationnetworks.Inprinciple,solitonsareshape-preservingwaves,andifthey
encounteranynonuniformityinthewaveguide,theyradiateenergyandhencethere
maybealossofinformation.Inordertoavertthissituation,scientistshavedevised
nonequilibrium waves such as similaritons. Similaritons are nothing but solitons
or solitary waves and they get modulated in their width and amplitude as a func-
tionofthelengthofthewaveguide.Themagnificentfeatureofthesewavesisthat
theyundergoself-compressionoramplificationasalsoself-breathingwhereverthey
encounternonuniformityinthewaveguide.Thisbookhasbeendealtwithdifferent
typesofsimilaritonsandtheirdynamicsinasymmetricdual-corewaveguides.Asitis
easytomanufacturethistypeofnonlinearcoupler,itishopedthatitwillbeexploited
inlong-haultelecommunicationnetworksfortransmittingsuchsimilaritons.
Themajorityofthematerialpresentedmainlydescribessolitarywavesolutions
or similaritons in (1 + 1)− dimensional systems and their dynamical behavior.
Novelfeaturessuchasself-compressionandself-breathingofsuchwaveshavebeen
exemplifiedingreatdetail.
In the seventh chapter, we describe light bullets which are higher dimensional
solitons and their dynamics. Numerical simulations carried out indicate that these
lightbulletsaresensitivetofiniteperturbations.
ManyoftheseideaswereconceivedwhileIwasworkinginUSAanddifferent
parts of India. There is only one person from whom I’ve drawn great inspiration
toconceivemanyoftheseideas—Mr.GilCohen,HebrewUniversityofJerusalem,
Israel.Iprofuselythankhim.IthankmythesisadvisorProf.P.K.Panigrahi,forhis
manyhelpfulsuggestions.
I’m indebted to my brothers—Mr. Thokala Mohan Rao and Mr. Thokala
JanardhanRao—andtheirfamiliesfortheirmoralsupport.
Lastbutnottheleast,IthankmywifeMrs.P.SwaroopaRaniandtwoteenagechil-
dren—Ms.ThokalaNancyGraceandMr.ThokalaSharonRaju—forunderstanding
whyIneededtospendweekendsonthebookinsteadofspendingtimewiththem.
vii
viii Preface
Above all, I extol the name of my Lord and Savior—Jesus Christ—for His
everlastingpromiserecordedinPhilippians1:6.
Hyderabad,India SolomanRajuThokala
August2022
Contents
1 NonlinearCompressionofSelf-SimilarWavesinAsymmetric
Dual-CoreWaveguides ........................................... 1
1.1 Introduction ................................................ 1
1.2 AsymmtericDual-CoreWaveguides ............................ 2
1.3 CompressionProblem ........................................ 8
1.4 Conclusion ................................................. 9
References ...................................................... 10
2 ChirpedSelf-SimilarWavesinAsymmetricTwin-CoreFibers
withNonlinearGain ............................................. 11
2.1 Introduction ................................................ 11
2.2 Self-SimilarPropagationinAsymmetricTCF ................... 13
2.3 ExactSelf-SimilarSolutions .................................. 18
2.3.1 TrigonometricSolution ................................ 19
2.3.2 PureEllipticSolution .................................. 19
2.3.3 DarkSolitaryWave ................................... 19
2.4 NonlinearChirping .......................................... 20
2.5 NonlinearCompression ...................................... 22
2.6 The Nonlinear Coherent Asymmetric Twin-Core Photonic
CrystalFiberCoupler ........................................ 23
2.7 Conclusion ................................................. 24
References ...................................................... 25
3 ControllingOpticalSimilaritonsinGraded-Index Nonlinear
WaveguidewithanExternalSource ............................... 27
3.1 Introduction ................................................ 27
3.2 OurModel ................................................. 28
3.3 ExplicitSelf-SimilarSolutions ................................ 30
3.3.1 Self-FocusingNonlinearityσ =1 ....................... 31
3.3.2 Self-FocusingNonlinearityσ =−1 ..................... 33
3.4 Conclusion ................................................. 35
References ...................................................... 35
ix
x Contents
4 Dynamical Behavior of Optical Similaritons in a Tapered
Graded-IndexNonlinearFiberAmplifierwithanExternalSource ... 37
4.1 Introduction ................................................ 37
4.2 AsymmetricTCFandSimilaritonPropagation ................... 38
4.3 ExactSelf-SimilarSolutions .................................. 40
4.3.1 Self-FocusingNonlinearity,σ =1 ....................... 41
4.3.2 StabilityoftheExactSimilaritons ....................... 45
4.3.3 Self-DefocusingNonlinearity,σ =−1 ................... 46
4.4 Conclusion ................................................. 49
References ...................................................... 50
5 Controllable Approximate and Asymptotic Similaritons
inAsymmetricDual-CoreWaveguide ............................. 51
5.1 Introduction ................................................ 51
5.2 SimilaritonPropagationinTCF ............................... 52
5.3 ControllableBehaviorofSimilaritons .......................... 54
5.3.1 DispersiveSimilaritons ................................ 54
5.3.2 RectangularSimilaritons ............................... 56
5.4 StabilityoftheSimilaritons ................................... 58
5.5 Self-SimilarEvolutionsofTrigonometricandHermite–Gaussian
OpticalPulsesinAsymmetricTwin-CoreFibers ................. 59
5.6 OurModel ................................................. 60
5.7 AsymptoticNovelSimilaritons ................................ 60
5.7.1 TrigonometricSimilariton .............................. 61
5.7.2 Hermite–Gausssimilariton ............................. 62
5.8 Conclusion ................................................. 62
References ...................................................... 63
6 Airy–Bessel Modulated Self-Similar Waves in Asymmetric
Twin-CoreFiberAmplifiers ...................................... 65
6.1 Introduction ................................................ 65
6.2 ModelEquation ............................................. 66
6.3 Self-SimilarWavePacketsinAsymmetricTwin-CoreFibers ....... 67
6.3.1 Möbius Transform Wave Packet Similaritons
forSelf-FocusingNonlinearity,σ =1 .................... 70
6.3.2 MöbiusTransformSimilaritonsforSelf-Defocusing
Nonlinearity,σ =−1 .................................. 71
6.4 ComputerSimulations ....................................... 72
6.5 Conclusion ................................................. 74
References ...................................................... 75
7 ControllingSpatiotemporalWavesinAsymmetricDual-Core
Waveguides ..................................................... 77
7.1 Introduction ................................................ 77
7.2 Self-SimilarPropagationThroughAsymmetricDWG ............. 78
7.3 AsymptoticExactSelf-SimilarSolutions ........................ 80
