Guided Wave Photonics : Fundamentals and Applications with MATLAB®

786 Pages·2012·19.92 MB·English

by  Binh, Le Nguyen

ELECTRICAL ENGINEERING
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hotonics
hotonics
Fundamentals and Applications with MATLAB®
A comprehensive presentation of the theory and simulation of optical waveguides
and wave propagations in a guided environment, Guided Wave Photonics: Fundamentals
and Applications with MATLAB® supplies basic and advanced understanding of Fundamentals
integrated optical devices that are currently employed in modern optical fiber
communications systems and photonic signal processing systems. While there are
many texts available in this area, none provide the breadth and depth of coverage and and Applications
computational rigor found in this one.
The author has distilled the information into a very practical, usable format. In a logical with MATLAB®
progression of theory and application, he starts with Maxwell’s equations and progresses
directly to optical waveguides (integrated optic and fiber optic), couplers, modulators,
nonlinear effects and interactions, and system applications. With up-to-date coverage
of applicable algorithms, design guides, material systems, and the latest device and
system applications, the book addresses:
• Fundamentals of guiding optical waves, including theoretical and
simplified techniques
• Linear and nonlinear aspects of optical waveguiding
• Manipulating lightwaves by coupling and splitting
• Interactions of lightwaves and ultra-fast electrical travelling waves in
modern optical modulators
• Applications of guided wave devices in optical communication systems
and optical signal processing
Providing fundamental understanding of lightwave guiding and manipulating techniques,
the text covers the field of integrated photonics by giving the principles, theoretical and
applications. It explains how to solve the optical modes and their coupling as well as how
to manipulate lightwaves for applications in communications and signal processing.
Le Nguyen Binh
K11400
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hotonics
Fundamentals
and Applications
with MATLAB®
Optics and Photonics
Series Editor
Le Nguyen Binh
Monash University, Clayton, Victoria, Australia
1. Digital Optical Communications, Le Nguyen Binh
2. Optical Fiber Communications Systems: Theory and Practice with MATLAB® and
Simulink® Models, Le Nguyen Binh
3. Ultra-Fast Fiber Lasers: Principles and Applications with MATLAB® Models,
Le Nguyen Binh and Nam Quoc Ngo
4. Thin-Film Organic Photonics: Molecular Layer Deposition and Applications,
Tetsuzo Yoshimura
5. Guided Wave Photonics: Fundamentals and Applications with MATLAB®,
Le Nguyen Binh
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uided ave
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hotonics
Fundamentals
and Applications
with MATLAB®
Le Nguyen Binh
Boca Raton London New York
CRC Press is an imprint of the
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MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy
of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not consti-
tute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB®
software.
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Version Date: 2011928
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To the memory of my father
To my mother
To Phuong and Lam

Contents
Preface............................................................................................................................................xix
Author............................................................................................................................................xxi
List.of.Abbreviations.and.Notations.......................................................................................xxiii
1. Introduction..............................................................................................................................1
1.1. Historical.Overview.of.Integrated.Optics.and.Photonics........................................1
1.2. Why.Analysis.of.Optical.Guided.Wave.Devices?.....................................................4
1.3. Principal.Objectives.......................................................................................................5
1.4. Chapters.Overview........................................................................................................6
References..................................................................................................................................8
2. Single-Mode Planar Optical Waveguides........................................................................11
2.1. Introduction..................................................................................................................11
2.2. Formation.of.Planar.Single-Mode.Waveguide.Problems.......................................13
2.2.1. Transverse.Electric/Transverse.Magnetic.Wave.Equation.......................13
2.2.1.1. Continuity.Requirements.and.Boundary.Conditions...............14
2.2.1.2. Index.Profile.Construction.............................................................14
2.2.1.3. Normalization.and.Simplification................................................15
2.2.1.4. Modal.Parameters.of.Planar.Optical.Waveguides.....................16
2.3. Approximate.Analytical.Methods.of.Solution.........................................................19
2.3.1. Asymmetrical.Waveguides...........................................................................19
2.3.1.1. Variational.Techniques...................................................................19
2.3.1.2. Wentzel–Kramers–Brilluoin.Method...........................................25
2.3.2. Symmetrical.Waveguides..............................................................................31
2.3.2.1. Wentzel–Kramers–Brilluoin.Eigenvalue.Equation.....................32
2.3.2.2. Two-Parameter.Profile-Moment.Method.....................................33
2.3.2.3. New.Equivalence.Relation.for.Planar.Optical.Waveguides......40
2.3.3. Concluding.Remarks......................................................................................49
2.4. Appendix.A:.Maxwell.Equations.in.Dielectric.Media...........................................49
2.4.1. Maxwell.Equations.........................................................................................49
2.4.2. Wave.Equation.................................................................................................50
2.4.3. Boundary.Conditions.....................................................................................50
2.4.4. Reciprocity.Theorems....................................................................................51
2.4.4.1. General.Reciprocity.Theorem........................................................51
2.4.4.2. Conjugate.Reciprocity.Theorem....................................................51
2.5. Appendix.B:.Exact.Analysis.of.Clad-Linear.Optical.Waveguides........................51
2.5.1. Asymmetrical.Clad-Linear.Profile...............................................................52
2.5.1.1. Eigenvalue.Equation.......................................................................52
2.5.1.2. Mode.Cutoff.....................................................................................53
2.5.2. Symmetrical.Waveguide................................................................................53
2.5.2.1. Eigenvalue.Equation.......................................................................53
2.5.2.2. Mode.Cutoff.....................................................................................53
vii
viii Contents
2.6. Appendix.C:.Wentzel–Kramers–Brilluoin.Method,.Turning.Points.and.
Connection.Formulae..................................................................................................54
2.6.1. Introduction.....................................................................................................54
2.6.2. Derivation.of.the.Wentzel–Kramers–Brilluoin.Approximate.
Solutions.........................................................................................................54
2.6.3. Turning.Point.Corrections.............................................................................57
2.6.3.1. Langer’s.Approximate.Solution.Valid.at.Turning.Point............57
2.6.3.2. Behavior.of.Turning.Point..............................................................59
2.6.3.3. Error.Bound.for.ϕ.Turning.Point...................................................60
2.6.4. Correction.Formulae......................................................................................62
2.6.5. Application.of.Correction.Formulae............................................................64
2.6.5.1. Ordinary.Turning.Point.Problem.................................................64
2.6.5.2. Effect.of.an.Index.Discontinuity.at.a.Turning.Point..................66
2.6.5.3. Buried.Modes.near.an.Index.Discontinuity.at.a.Turning.
Point..................................................................................................66
2.7. Appendix.D:.Design.and.Simulation.of.Planar.Optical.Waveguides..................67
2.7.1. Introduction.....................................................................................................67
2.7.2. Theoretical.Background.................................................................................67
2.7.2.1. Structures.and.Index.Profiles........................................................67
2.7.2.2. Optical.Fields.of.the.Guided.Transverse.Electronic.Modes......68
2.7.2.3. Design.of.Optical.Waveguide.Parameters:.Preliminary.Work.70
2.7.3. Simulation.of.Optical.Fields.and.Propagation.in.Slab.Optical.
Waveguide.Structures....................................................................................70
2.7.3.1. Lightwaves.Propagation.in.Guided.Straight.Structures...........71
2.7.3.2. Lightwaves.Propagation.in.Guided.Bent.Structures.................73
2.7.3.3. Lightwaves.Propagation.in.Y-Junction.(Splitter).and.
Interferometric.Structures.............................................................74
2.7. Problems........................................................................................................................74
References................................................................................................................................76
3. 3D Integrated Optical Waveguides....................................................................................79
3.1. Introduction..................................................................................................................79
3.2. Marcatili’s.Method.......................................................................................................80
3.2.1. Field.and.Modes.Guided.in.Rectangular.Optical.Waveguides...............81
3.2.1.1. Mode.Fields.of.H .Modes...............................................................81
x
3.2.1.2. Boundary.Conditions.at.the.Interfaces........................................84
3.2.2. Mode.Fields.of.E.Modes................................................................................85
y
3.2.3. Dispersion.Characteristics.............................................................................86
3.3. Effective.Index.Method...............................................................................................86
3.3.1. General.Considerations..................................................................................86
3.3.2. A.Pseudo-Waveguide.....................................................................................90
3.3.3. Finite.Difference.Numerical.Techniques.for.3D.Waveguides..................91
3.4. Non-Uniform.Grid.Semivectorial.Polarized.Finite.Difference.Method.for.
Optical.Waveguides.with.Arbitrary.Index.Profile..................................................91
3.4.1. Propagation.Equation.....................................................................................91
3.4.2. Formulation.of.Non-Uniform.Grid.Difference.Equation..........................92
3.4.2.1. Quasi-Transverse.Electronic.Mode...............................................93
3.4.2.2. Inverse.Power.Method....................................................................98
Contents ix
3.4.3. Ti:LiNbO .Diffused.Channel.Waveguide.................................................100
3
3.4.3.1. Refractive.Index.Profile.of.the.Ti:LiNbO .Waveguide.............100
3
3.4.3.2. Numerical.Simulation.and.Discussion......................................104
3.5. Mode.Modeling.of.Rib.Waveguides........................................................................112
3.5.1. Choice.of.Grid.Size.......................................................................................115
3.5.2. Numerical.Results.........................................................................................118
3.5.3. Higher.Order.Modes....................................................................................118
3.6. Conclusions.................................................................................................................121
3.7. Problems......................................................................................................................123
References..............................................................................................................................123
4. Single-Mode Optical Fibers: Structures and Transmission Properties...................127
4.1. Optical.Fibers..............................................................................................................127
4.1.1. Brief.History..................................................................................................127
4.1.2. Optical.Fiber:.General.Properties...............................................................128
4.1.2.1. Geometrical.Structures.and.Index.Profile.................................128
4.1.3. Fundamental.Mode.of.Weakly.Guiding.Fibers........................................130
4.1.3.1. Solutions.of.the.Wave.Equation.for.Step.Index.Fiber...............130
4.1.3.2. Gaussian.Approximation.............................................................132
4.1.3.3. Cutoff.Properties...........................................................................135
4.1.3.4. Power.Distribution........................................................................136
4.1.3.5. Approximation.of.Spot.Size.r .of.a.Step.Index.Fiber................138
0
4.1.4. Equivalent.Step.Index.(ESI).Description...................................................138
4.1.4.1. Definitions.of.Equivalent.Step.Index.Parameters.....................139
4.1.4.2. Accuracy.and.Limits.....................................................................140
4.1.4.3. Examples.on.Equivalent.Step.Index.Techniques......................140
4.1.4.4. General.Method.............................................................................141
4.2. Nonlinear.Optical.Effects.........................................................................................141
4.2.1. Nonlinear.Self.Phase.Modulation.Effects.................................................142
4.2.2. Self.Phase.Modulation.................................................................................142
4.2.3. Cross.Phase.Modulation..............................................................................143
4.2.4. Stimulated.Scattering.Effects......................................................................144
4.2.4.1. Stimulated.Brillouin.Scattering...................................................144
4.2.4.2. Stimulated.Raman.Scattering......................................................145
4.2.4.3. Four-Wave.Mixing........................................................................146
4.3. Optical.Fiber.Manufacturing.and.Cabling.............................................................147
4.4. Concluding.Remarks.................................................................................................148
4.5. Signal.Attenuation.and.Dispersion.........................................................................148
4.5.1. Introductory.Remarks..................................................................................149
4.5.2. Signal.Attenuation.in.Optical.Fibers.........................................................151
4.5.2.1. Intrinsic.or.Material.Attenuation................................................151
4.5.2.2. Absorption.....................................................................................151
4.5.2.3. Rayleigh.Scattering.......................................................................151
4.5.2.4. Waveguide.Loss.............................................................................152
4.5.2.5. Bending.Loss..................................................................................152
4.5.2.6. Microbending.Loss.......................................................................152
4.5.2.7. Joint.or.Splice.Loss........................................................................153
4.5.2.8. Attenuation.Coefficient................................................................154