Foundations for GuidedWave OpticsISBN: 9780471756873
462 pages
November 2006

This text offers an indepth treatment of integrated and fiber optics, providing graduate students, engineers, and scientists with a solid foundation of the principles, capabilities, uses, and limitations of guidedwave optic devices and systems. In addition to the transmission properties of dielectric waveguides and optical fibers, this book covers the principles of directional couplers, guidedwave gratings, arrayedwaveguide gratings, and fiber optic polarization components.
The material is fully classroomtested and carefully structured to help readers grasp concepts quickly and apply their knowledge to solving problems. Following an overview, including important nomenclature and notations, the text investigates three major topics:
 Integrated optics
 Fiber optics
 Pulse evolution and broadening in optical waveguides
Each chapter starts with basic principles and gradually builds to more advanced concepts and applications. Compelling reasons for including each topic are given, detailed explanations of each concept are provided, and steps for each derivation are carefully set forth. Readers learn how to solve complex problems using physical concepts and simplified mathematics.
Illustrations throughout the text aid in understanding key concepts, while problems at the end of each chapter test the readers' grasp of the material.
The author has designed the text for upperlevel undergraduates, graduate students in physics and electrical and computer engineering, and scientists. Each chapter is selfcontained, enabling instructors to choose a subset of topics to match their particular course needs. Researchers and practitioners can also use the text as a selfstudy guide to gain a better understanding of photonic and fiber optic devices and systems.
1. Brief review of Electromagnetics and Guided Waves.
1.1 Introduction.
1.2 Maxwell's equations.
1.3 Uniform plane waves in isotropic media.
1.4 State of polarization.
1.5 Reflection and refraction by a planar boundary between two dielectric media.
1.5.1. Perpendicular polarization.
1.5.1.1 Reflection and refraction.
1.5.1.2 Total internal reflection.
1.5.2. Parallel polarization.
1.5.2.1 Reflection and refraction.
1.5.2.2 Total internal reflection.
1.6 Guided waves.
1.6.1 TE modes.
1.6.2 TM modes.
1.6.3 Waveguides with constant index regions.
References.
Problems.
List of Figures.
2. Stepindex Thinfilm Waveguides.
2.1 Introduction.
2.2 Dispersion of stepindex thinfilm waveguides.
2.2.1 TE modes.
2.2.2 TM modes.
2.3 Generalized parameters.
2.3.1 a, b, c, d and V.
2.3.2 bV diagram.
2.3.3 Cutoff thickness and cutoff frequencies.
2.3.4 Number of guided modes.
2.3.5 Birefringence in thinfilm waveguides.
2.4 Fields of stepindex thinfilm waveguides.
2.4.1 TE modes.
2.4.2 TM modes.
2.5 Cover and substrate modes.
2.6 Timeaverage power and confinement factors.
2.6.1 Timeaverage power transported by TE modes.
2.6.2 Confinement factor of TE modes.
2.6.3 Timeaverage power transported by TM modes.
2.7 Phase and group velocities.
References.
Problems.
List of figures.
3. Gradedindex Thinfilm waveguides.
3.1 Introduction.
3.2 TE modes guided by linearly graded dielectric waveguides.
3.3 Exponentially graded dielectric waveguides.
3.3.1 TE modes.
3.3.2 TM modes.
3.4 WKB method.
3.4.1 Auxiliary function.
3.4.2 Fields in the R Zone.
3.4.3 Fields in the L Zone.
3.4.4 Fields in the transition zone.
3.4.5 The constants.
3.4.6 The dispersion relation.
3.4.7 An example.
3.5 Hocker and Burns’ numerical method.
3.5.1 TE modes.
3.5.2 TM modes.
3.6 Stepindex thinfilm waveguides vs. gradedindex dielectric waveguides.
References.
Problems.
List of figures.
4. Propagation Loss in Thinfilm Waveguides.
4.1 Introduction.
4.2 Complex relative dielectric constant and complex refractive index.
4.3 Propagation loss in stepindex waveguides.
4.3.1 Waveguides having weakly absorbing materials.
4.3.2 Metalclad waveguides.
4.4 Attenuation in thick waveguides with stepindex profiles.
4.5 Loss in TM0 mode.
4.6 Metalclad waveguides with graded index profiles.
References.
Problem.
List of Figures.
5. Threedimensional Waveguides with Rectangular Boundaries.
5.1 Fields and modes guided by rectangular waveguides.
5.2 Orders of magnitude of fields.
5.2.1 modes.
5.2.2 modes.
5.3 Marcatili's method.
5.3.1 modes.
5.3.1.1 Expressions for H_{x}.
5.3.1.2 Boundary conditions along horizontal boundaries, y = ±h/2, x
5.3.1.5 Transverse wave vector K_{y}.
5.3.1.6 Approximate dispersion relation.
5.3.2 modes.
5.3.3 Discussions.
5.3.4 Generalized guide index.
5.4 Effective index method.
5.4.1 A pseudo waveguide.
5.4.2 An alternate pseudo waveguide.
5.4.3 Generalized guide index.
5.5 Comparison of methods.
References.
Problems.
List of figures.
6. Optical directional couplers and their applications.
6.1 Introduction.
6.2 Qualitative description of the operation of directional couplers.
6.3 Marcatili’s improved coupled mode equations.
6.3.1 Fields of isolated waveguides.
6.3.2 Normal mode fields of the composite waveguide.
6.3.3 Marcatili’s relation.
6.3.4 Approximate normal mode fields.
6.3.5 Improved coupled mode equations.
6.3.6 Coupled mode equation in an equivalent form.
6.3.7 Coupled mode equation in an alternate form.
6.4 Directional couplers with uniform cross section and constant spacing.
6.4.1 Transfer matrix.
6.4.2 Essential characteristics of couplers with K_{1} = K_{2} = K.
6.4.3 3 dB directional couplers.
6.4.4 Directional couplers as electrically controlled optical switches.
6.4.5. Switching diagram.
6.5 Switched δβ directional couplers.
6.6 Optical directional couplers filters.
6.6.1 Directional coupler filters with identical waveguides and uniform spacing.
6.6.2 Directional coupler filters with nonidentical waveguides and uniform spacing.
6.6.3 Tapered directional coupler filters.
6.7 Intensity modulators based on directional couplers.
6.7.1 Electrooptic properties of lithium niobate.
6.7.2 Dielectric waveguide with an electrooptic layer.
6.7.3 Directional coupler modulator built on a Zcut LiNbO_{3} plate.
6.8 Normal mode theory of directional couplers with two waveguides.
6.9 Normal mode theory of directional couplers with three or more waveguides.
References.
Problems.
List of Figures.
7. Guidedwave Gratings.
7.1 Introduction.
7.1.1 Types of guidedwave gratings.
7.1.1.1 Static gratings.
7.1.1.2 Programmable gratings.
7.1.1.3 Moving grating.
7.1.2 Applications of guidedwave gratings.
7.1.3. Two methods for analyzing guidedwave grating problems.
7.2 Perturbation theory.
7.2.1 Waveguide perturbation.
7.2.2 Fields of perturbed waveguide.
7.2.3 Coupled mode equations and coupling coefficients.
7.2.4 Codirectional coupling.
7.2.5 Contradirectional coupling.
7.3 Coupling coefficient of a rectangular gratingan example.
7.4 Graphical representation of grating equation.
7.5 Grating reflectors.
7.5.1 Coupled mode equations.
7.5.2 Filter response of grating reflectors.
7.5.3 Bandwidth of grating reflectors.
7.6 Distributed feedback lasers.
7.6.1 Coupled mode equations with optical gain.
7.6.2 Boundary conditions and symmetric condition.
7.6.3 Eigen value equations.
7.6.4 Mode patterns.
7.6.5 Oscillation frequency and threshold gain.
References.
List of Figures.
8. Arrayedwaveguide Gratings.
8.1 Introduction.
8.2 Arrays of isotropic radiators.
8.3 Two examples.
8.3.1 Arrayedwaveguide gratings as dispersive components.
8.3.2 Arrayedwaveguide gratings as focusing components.
8.4 1x2 arrayedwaveguide grating multiplexers and demultiplexers.
8.4.1 Waveguide grating elements.
8.4.2 Output waveguides.
8.4.3 Spectral response.
8.5 NxN arrayedwaveguide grating multiplexers and demultiplexers.
8.6 Applications in WDM communications.
References.
List of Figures.
9. Transmission characteristics of stepindex optical fibers.
9.1. Introduction.
9.2. Fields and propagation characteristic of modes guided by stepindex fibers.
9.2.1 Electromagnetic fields.
9.2.2 Characteristic equation.
9.2.3 Traditional mode designation and fields.
9.3. Linearly polarized modes guided by weakly guiding stepindex fibers.
9.3.1 Basic properties of fields of weakly guiding fibers..
9.3.2 Fields and boundary conditions.
9.3.3 Characteristic equation and mode designation.
9.3.4 Fields of xpolarized LP0m modes.
9.3.5 Timeaverage power.
9.3.6 Single mode operation.
9.4. Phase velocity, group velocity and dispersion of linearly polarized modes.
9.4.1 Phase velocity and group velocity.
9.4.2 Dispersion.
9.4.2.1 Intermodal dispersion.
9.4.2.2 Intramodal dispersion.
9.4.2.3 Zero dispersion wavelengths.
References.
Problems.
List of Figures.
10. Input and output characteristics of weakly guiding stepindex fibers.
10.1 Radiation of LP modes.
10.1.1 Radiated fields in the Fraunhofer zone.
10.1.2 Radiation by a Gaussian aperture field.
10.1.3 Experimental determination of ka and V.
10.2 Excitation of LP modes.
10.2.1 Power coupled to LP mode .
10.2.2 Gaussian beam excitation.
References.
Problems.
List of Figures.
11. Birefringence in Singlemode Fibers.
11.1 Introduction.
11.2 Geometrical birefringence.
11.3 Birefringence due to buildin stress.
11.4 Birefringence due to externally applied mechanical stress.
11.4.1 Lateral stress.
11.4.2 Bending.
11.4.2.1 Pure bending.
11.4.2.1 Bending under tension.
11.4.3 Mechanical twisting.
11.5 Birefringence due to externally applied electric and magnetic fields.
11.5.1 Strong transverse electric fields.
11.5.2 Strong axis magnetic fields.
11.6 Jones matrices of birefringent fibers.
11.6.1 Linearly birefringent fibers with stationary birefringent axes.
11.6.2 Linearly birefringent fiber with a continuous rotating axis.
11.6.3 Circularly birefringent fibers.
11.6.4 Linearly and circularly birefringent fibers.
11.6.5 Fibers with linear and circular birefringence and axis rotation.
Problems.
References.
12. Manufactured fibers.
12.1 Introduction.
12.2 Powerlaw index fibers.
12.3 Key propagation and dispersion parameters of graded index fibers.
12.3.1 Generalized guide index b.
12.3.2 Normalized group delay.
12.3.3 Group delay and the confinement factor.
12.3.4 Normalized waveguide dispersion.
12.3.5 An example.
12.4 Radiation and excitation characteristics of graded index fibers.
12.4.1 Radiation.
12.4.2 Excitation by a linearly polarized Gaussian beam.
12.5 Mode field radius.
12.5.1 Marcuse?s mode field radius.
12.5.2 First Petermann?s mode field radius.
12.5.3 Second Petermann?s mode field radius.
12.5.4 Comparison of three mode field radii.
12.6 Mode field radius and key propagation and dispersion parameters.
References.
Problems.
List of Figures.
13. Propagation of pulses in singlemode fibers.
13.1 Introduction.
13.2 Dispersion and group velocity dispersion.
13.3 Fourier transform method.
13.4 Propagation of Gaussian pulses in fibers.
13.4.1 Effects of? the first order group dispersion.
13.4.2 Effects of the second order group dispersion.
13.5 Impulse response.
13.5.1 Approximate impulse response function with β" ignored.
13.5.2 Approximate impulse response function with β" ignored.
13.6 Propagation of rectangular pulses in fibers.
13.7 Envelope equation.
13.7.1 Monochromatic waves.
13.7.2 Envelop equation.
13.7.3 Pulse envelop in nondispersive media.
13.7.4 Effect of the first order group velocity dispersion.
13.7.5 Effect of the second order group velocity dispersion.
13.8 Dispersion compensation.
References.
Problems.
List of Figures.
14. Optical Solitons in Optical Fibers.
14.1 Introduction.
14.2 Optical Kerr effect in isotropic media.
14.2.1 Electric susceptibility tensor.
14.2.2 Refractive index.
14.3 Nonlinear envelope equation.
14.3.1 Linear and thirdorder polarizations.
14.3.2 Nonlinear envelope equation for nonlinear media.
14.3.3 Selfphase modulation.
14.3.4 Nonlinear envelope equation for nonlinear fibers.
14.3.5 Nonlinear Schrödinger equation.
14.4 Qualitative description of solitons.
14.5 Fundamental solitons.
14.5.1 Canonical expression.
14.5.2 General expression.
14.5.3 Basic soliton parameters.
14.5.4 Basic soliton properties.
14.6 Higherorder solitons.
14.6.1 Secondorder solitons.
14.6.2 Thirdorder solitons.
14.7 Generation of solitons.
14.7.1 Integer A.
14.7.2 Noninteger A.
14.8 Soliton units of time, distance and power.
14.9 Interaction of solitons.
References.
List of Figures.
Appendix A: Brown Identity.
A.1 Wave equations for inhomogeneous media.
A.2 Brown identity.
A.3 Two special cases.
A.4 Effect of material dispersion.
References.
Appendix B: Twodimensional Divergence Theorem and Green’s Theorem.
Appendix C. Orthogonality and Orthonormality of Guided Modes.
C.1 Lorentz’ reciprocity.
C.2 Orthogonality of guided modes.
C.3 Orthonormality of guided modes.
References.
Appendix D: Elasticity, Photoelasticity and Electrooptic Effects.
D1 Strain tensors.
D1.1 Strain tensors in onedimensional objects.
D1.2 Strain tensors in twodimensional objects.
D1.3 Strain tensors in threedimensional objects.
D2 Stress tensors.
D3 Hook’s law in isotropic materials.
D4 Strain and stress tensors in abbreviated indices.
D5 Relative dielectric constant tensors and relative dielectric impermeability tensors.
D6 Photoelastic effect and photoelastic constant tensors.
D7 Index change in isotropic solids: an example.
D8 Linear electrooptic effects.
D9 Quadratic electrooptic effects.
References.
List of Figures.
Appendix E: Effect of mechanical twisting on fiber birefringence.
E1. Relative dielectric constant tensor of a twisted medium.
E2. LP modes in weakly guiding, untwisted fibers.
E3. Eigen polarization modes in twisted fibers.
References.
Appendix F: Derivation of (12.7), (12.8) and (12.9).
Appendix G: Two Hankel transform relations.
Index.