Fundamentals of Optical Fibers

by Buck, John A.

• ISBN13: 9780471221913
• ISBN10: 0471221910
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-04-27
• Publisher: Wiley-Interscience

Summary

Fundamentals of Optical Fibers, Second Edition offers readers a timely and consistent introduction to the fundamental principles of light propagation in fibers. In it, the author reviews, in depth, fundamental wave guiding concepts, the influence of various fiber structures and materials on light transmission, nonlinear light propagation effects occurring in fibers, and various measurement techniques. Since the chief application of optical fibers is in communication systems, throughout the book the focus is on topics, which pertain to that domain.

Author Biography

JOHN A. BUCK received his PhD in electrical engineering from the University of California at Berkeley in 1982. He then joined the faculty of the School of Electrical and Computer Engineering at the Georgia Institute of Technology, where he is now at the rank of professor. His research areas have included ultrafast switching, nonlinear optical materials characterization, and nonlinear propagation in fibers.

Table of Contents

Preface	xiii
Introduction	xv
Chapter 1. Selected Topics in Electromagnetic Wave Propagation	1	(21)
1.1. Maxwell's Equations and the Fundamental Fields	1	(1)
1.2. Electromagnetic Wave Propagation in Sourceless Media	2	(4)
1.2.1. Wave Equations in Simple Media	3	(1)
1.2.2. Time-Harmonic Field Solutions	3	(2)
1.2.3. Vector Helmholtz Equations and the Uniform Plane Wave	5	(1)
1.2.4. E and H as Related Through the Intrinsic Impedance	5	(1)
1.3. Power Transmission	6	(2)
1.3.1. Computation of the Time-Average Power Density	6	(1)
1.3.2. Standing Wave Power	7	(1)
1.4. Group Velocity	8	(2)
1.4.1. Propagation of a Wave Containing Two Frequencies	8	(1)
1.4.2. Group Velocity Definition	9	(1)
1.5. Reflection and Transmission of Waves at Plane Interfaces	10	(3)
1.5.1. Reflection Geometry	10	(1)
1.5.2. Applying the Field Boundary Conditions	11	(2)
1.5.3. Special Cases: Total Transmission and Total Reflection	13	(1)
1.6. Material Resonances and Their Effects on Wave Propagation	13	(6)
1.6.1. The Classical Electron Oscillator Model and the Electric Susceptibility	14	(2)
1.6.2. Wave Propagation in Media with Complex Susceptibilities	16	(2)
1.6.3. Off-Resonance Behavior and the Sellmeier Equation	18	(1)
1.6.4. Time Domain Analysis	18	(1)
Problems	19	(2)
References	21	(1)
Chapter 2. Symmetric Dielectric Slab Waveguides	22	(29)
2.1. Ray Analysis of the Slab Waveguide	22	(7)
2.1.1. Guided Mode Requirements and Mode Types	23	(2)
2.1.2. Plane Wave Field Representations	25	(1)
2.1.3. Surface Waves and the Reflective Phase Shift	26	(2)
2.1.4. Transverse Resonance and the Eigenvalue Equations	28	(1)
2.2. Field Analysis of the Slab Waveguide	29	(3)
2.2.1. Solving for the Longitudinal Field Components	29	(2)
2.2.2. Obtaining the Transverse Field Components	31	(1)
2.3. Solutions of the Eigenvalue Equations	32	(2)
2.3.1. Graphical Solution Method	32	(1)
2.3.2. Interpreting the Graphical Solution	33	(1)
2.4. Power Transmission and Confinement	34	(6)
2.4.1. Power Computation and the Confinement Factor	35	(1)
2.4.2. Mode Orthogonality	36	(1)
2.5. Leaky Waves	36	(2)
2.5.1. TE and TM Polarization	38	(1)
2.5.2. Power Loss in Leaky Wave Transmission	38	(2)
2.6. Radiation Modes	40	(2)
2.6.1. Physical Description of Radiation Modes	40	(1)
2.6.2. Summary of Wave Types	41	(1)
2.7. Wave Propagation in Curved Slab Waveguides	42	(5)
2.7.1. Basic Concepts of Curved Guiding	42	(1)
2.7.2. Criteria for Small Curvature Loss	43	(1)
2.7.3. Analysis of Curved Slab Waveguides Through Conformal Transformation	44	(3)
Problems	47	(3)
References	50	(1)
Chapter 3. Weakly-Guiding Fibers with Step Index Profiles	51	(41)
3.1. Rays and Fields in the Step Index Fiber	53	(3)
3.1.1. Ray Trajectories and Transverse Resonance	53	(2)
3.1.2. Relations Between Ray Paths and Mode Field Patterns	55	(1)
3.1.3. Weakly Guiding Fibers and the LP Modes	55	(1)
3.2. Field Analysis of the Weakly Guiding Fiber	56	(4)
3.2.1. Assumed Field Solutions and Wave Equations for LP Modes	56	(1)
3.2.2. Solving the Wave Equation	57	(2)
3.2.3. Evaluating the Coefficients	59	(1)
3.3. Eigenvalue Equation for LP Modes	60	(6)
3.3.1. Derivation of the Eigenvalue Equation	60	(2)
3.3.2. Graphical Solution Method	62	(3)
3.3.3. Cutoff Conditions and Mode Designations	65	(1)
3.4. LP Mode Characteristics	66	(7)
3.4.1. Intensity Patterns and Polarizations	66	(3)
3.4.2. Parameter Computation	69	(2)
3.4.3. Power Confinement	71	(2)
3.5. Single-Mode Fiber Parameters	73	(6)
3.5.1. Cutoff Wavelength	73	(2)
3.5.2. Gaussian Approximation for the LP01 Mode Field	75	(4)
3.6. Derivation of the General Step Index Fiber Fields	79	(8)
3.6.1. Mode Field Derivation	80	(1)
3.6.2. Mode Classification and the Eigenvalue Equation	81	(1)
3.6.3. The Eigenvalue Equation Under the Weak-Guidance Approximation	82	(2)
3.6.4. General Mode Fields Under the Weak-Guidance Approximation	84	(1)
3.6.5. LP Modes as Superpositions of General Modes	85	(2)
Problems	87	(3)
References	90	(2)
Chapter 4. Loss Mechanisms in Silica Fiber	92	(33)
4.1. Basic Loss Effects in Transmission	93	(1)
4.2. Fabrication of Silica Fibers	94	(3)
4.2.1. Preform Manufacturing Using MCVD	94	(1)
4.2.2. Dopants for Control of Refractive Index	95	(1)
4.2.3. Preform Completion and Fiber Drawing	96	(1)
4.3. Intrinsic Loss	97	(4)
4.3.1. Ultraviolet Absorption	97	(1)
4.3.2. Infrared Absorption	97	(1)
4.3.3. Rayleigh Scattering	98	(2)
4.3.4. Combined Intrinsic Losses	100	(1)
4.4. Extrinsic Loss	101	(2)
4.4.1. Metallic and Rare Earth Impurities	101	(1)
4.4.2. Loss Arising from OH	102	(1)
4.5. Bending Loss	103	(9)
4.5.1. Wave Theory of Macrobending Loss	104	(4)
4.5.2. Additional Factors That Influence Macrobending Loss	108	(1)
4.5.3. Microbending Loss	109	(3)
4.6. Source-to-Fiber Coupling	112	(8)
4.6.1. Single-Mode Fiber Splicing	113	(2)
4.6.2. Gaussian Beam Input Coupling	115	(2)
4.6.3. General Source Coupling to Multimode Fiber	117	(2)
4.6.4. Imaging Methods in Extended-Source Coupling	119	(1)
Problems	120	(2)
References	122	(3)
Chapter 5. Dispersion	125	(60)
5.1. Pulse Propagation in Media Possessing Quadratic Dispersion	126	(12)
5.1.1. Propagation of Transform-Limited Gaussian Pulses	126	(5)
5.1.2. Input Pulses with Initial Chirp	131	(2)
5.1.3. Gaussian Pulses Having Excess Bandwidth	133	(1)
5.1.4. Characterizing Arbitrarily Shaped Pulses	134	(2)
5.1.5. Cubic Dispersion	136	(2)
5.2. Material Dispersion	138	(7)
5.2.1. Group Delay and Group Index	138	(3)
5.2.2. Dispersion Parameter	141	(1)
5.2.3. Wavelength Domain Description of Cubic Dispersion	142	(3)
5.3. Dispersion in Optical Fiber	145	(8)
5.3.1. Group Delay in Step Index Fiber	145	(4)
5.3.2. Group Dispersion in Single-Mode Fiber	149	(4)
5.4. Chromatic Dispersion Compensation	153	(8)
5.4.1. Dispersion-Compensating Fiber	153	(1)
5.4.2. Gires-Tournois Interferometer	154	(5)
5.4.3. Chirped Fiber Bragg Grating	159	(2)
5.5. Polarization Dispersion	161	(11)
5.5.1. Wave Polarization in Single-Mode Fiber	162	(2)
5.5.2. Differential Group Delay and Polarization Mode Dispersion in the Intrinsic Regime	164	(2)
5.5.3. Polarization Mode Dispersion in the Coupled Regime	166	(6)
5.6. System Considerations and Dispersion Measurement	172	(6)
5.6.1. Linear System Model-Fiber Bandwidth	173	(1)
5.6.2. Dispersion Limits	174	(2)
5.6.3. Dispersion Measurement	176	(2)
Problems	178	(5)
References	183	(2)
Chapter 6. Special-Purpose Index Profiles	185	(43)
6.1. Multimode Graded Index Fiber	185	(13)
6.1.1. Ray Optics Picture	186	(2)
6.1.2. Field Analysis	188	(6)
6.1.3. Index Profile Optimization	194	(4)
6.2. Special Index Profiles in Single-Mode Fiber	198	(25)
6.2.1. The Equivalent Step Index Method	198	(9)
6.2.2. Index Profiles for Control of Loss and Dispersion	207	(7)
6.2.3. Polarization-Maintaining Fiber	214	(5)
6.2.4. Photonic Crystal Fiber	219	(4)
Problems	223	(2)
References	225	(3)
Chapter 7. Nonlinear Effects in Fibers I: Nonresonant Processes	228	(39)
7.1. Nonlinear Optics Fundamentals	229	(12)
7.1.1. The Role of Medium Polarization in Wave Propagation	229	(1)
7.1.2. The Nonlinear Polarization	230	(2)
7.1.3. The Structure of the Nonlinear Susceptibility	232	(3)
7.1.4. Symmetries in the Third-Order Susceptibility Tensor	235	(2)
7.1.5. Example: Third Harmonic Generation	237	(4)
7.2. Nonlinear Phase Modulation on Pulses	241	(4)
7.2.1. Nonlinear Refractive Index	241	(2)
7.2.2. Self-Phase Modulation	243	(2)
7.3. The Nonlinear Schrödinger Equation	245	(10)
7.3.1. Development of the Nonlinear Schrödinger Equation from the Wave Equation	246	(3)
7.3.2. Normalized Form of the Nonlinear Schrödinger Equation	249	(2)
7.3.3. Optical Solitons	251	(4)
7.4. Additional Nonresonant Processes	255	(8)
7.4.1. Cross-Phase Modulation	258	(2)
7.4.2. Four-Wave Mixing	260	(3)
Problems	263	(2)
References	265	(2)
Chapter 8. Nonlinear Effects in Fibers II: Resonant Processes and Amplification	267	(48)
8.1. Raman Scattering	268	(17)
8.1.1. Basic Theory of Stimulated Raman Scattering	268	(6)
8.1.2. Raman Gain in Silica Fiber	274	(2)
8.1.3. Stimulated and Spontaneous Raman Scattering in Fiber	276	(3)
8.1.4. Multiple Stokes Orders and Raman Cross-Talk	279	(3)
8.1.5. Raman Fiber Amplifiers	282	(3)
8.2. Stimulated Brillouin Scattering	285	(8)
8.2.1. Stimulated Brillouin Scattering as a Third-Order Process	286	(1)
8.2.2. The Acoustic Displacement Equation	287	(1)
8.2.3. The Nonlinear Polarizations and Coupled Equations for Stimulated Brillouin Scattering	288	(2)
8.2.4. Brillouin Amplification	290	(2)
8.2.5. Adapting the Theory to Optical Fibers	292	(1)
8.3. Rare-Earth-Doped Fiber Amplifiers	293	(16)
8.3.1. Basic Theory of Amplification by Stimulated Emission	294	(2)
8.3.2. Absorption and Emission Characteristics of Erbium-Doped Fiber	296	(6)
8.3.3. Erbium-Doped Fiber Amplifier Fabrication, Configuration, and Operating Regimes	302	(2)
8.3.4. Gain Flattening and Noise	304	(1)
8.3.5. Other Rare-Earth-Doped Systems	305	(4)
Problems	309	(2)
References	311	(4)
Appendix A. Properties of Bessel Functions	315	(4)
Appendix B. Notation	319	(6)
Index	325