Preface.Introduction.Chapter 1. Selected Topics in Electromagnetic Wave Propagation.1.1. Maxwell's Equations and the Fundamental Fields.1.2. Electromagnetic Wave Propagation in Sourceless Media.1.3. Power Transmission.1.4. Group Velocity.1.5. Reflection and Transmission of Waves at Plane Interfaces.1.6. Material Resonances and Their Effects on Wave Propagation.Problems.References.Chapter 2. Symmetric Dielectric Slab Waveguides.2.1. Ray Analysis of the Slab Waveguides.2.2. Field Analysis of the Slab Waveguides.2.3. Solutions of the Eigenvalue Equations.2.4. Power Transmission and Confinement.2.5. Leaky Waves.2.6. Radiation Modes.2.7. Wave Propagation in Curved Slab Waveguides.Problems.References.Chapter 3. Weakly-Guiding Fibers with Step Index Profiles.3.1. Rays and Fields in the Step Index Fiber.3.2. Field Analysis of the Weakly-Guiding Fiber.3.3. Eigenvalue Equation for LP Modes.3.4. LP Mode Characteristics.3.5. Single Mode Fiber Parameters.3.6. Derivation of the General Step Index Fiber Modes.Problems.References.Chapter 4. Loss Mechanisms in Silica Fiber.4.1. Basic Loss Effects in Transmission.4.2. Fabrication of Silica Fibers.4.3. Intrinsic Loss.4.4. Extrinsic Loss.4.5. Bending Loss.4.6. Source-to-Fiber Coupling.Problems.References.Chapter 5. Dispersion.5.1. Pulse Propagation in Media Possessing Quadratic Dispersion.5.2. Material Dispersion.5.3. Dispersion in Optical Fiber.5.4. Chromatic Dispersion Compensation.5.5. Polarization Dispersion.5.6. System Considerations and Dispersion Measurement.Problems.References.Chapter 6. Special Purpose Index Profiles.6.1. Multimode Graded Index Fiber.6.2. Special Index Profile Optimization.Problems.References.Chapter 7. Nonlinear Effects in Fibers I: Non-Resonant Processes.7.1. Nonlinear Optics Fundamentals.7.2. Nonlinear Phase Modulation on Pulses.7.3. The Nonlinear Schrodinger Equation.7.4. Additional Non-Resonant Processes.Problems.References.Chapter 8. Nonlinear Effects in Fibers II: Resonant Processes and Amplification.8.1. Raman Scattering.8.2. Stimulated Brillouin Scattering.8.3. Rare-Earth-Doped Fiber Amplifiers.Problems.References.Appendix A: Properties of Bessel Functions.Appendix B: Notation.Index.

Fundamentals of optical fibers

We describe the design trade-offs that are at stake when optimizing few-mode fibers (FMFs) that support a high number ( $\ge$ 6) of LP modes. We particularly detail the design of 6-LP-mode fibers that allow to multiply the capacity by a tenfold factor (two modes being spatially non-degenerate and four modes being two times spatially degenerate). For low-differential-mode-group-delay (low-DMGD) FMFs adapted to strongly-coupled mode-division-multiplexed systems, trench-assisted graded-index-core profiles can be optimized to have Max $\vert$ DMGD $\vert$ 1.0 × 10 $^{-3}$ ) to limit mode coupling and $A_{\rm eff}$ >∼100 μm $^2$ to limit intra-mode non-linearity with good mode robustness. For such weakly-coupled FMFs, sensitivity to process variability is small and main characteristics do not significantly change when variations are within the manufacturing tolerances. We also briefly discuss experimental validations.

Few-Mode Fibers for Mode-Division-Multiplexed Systems

The present invention embraces a multimode optical fiber that includes a central core having an alpha-index profile, an inner cladding, a depressed trench, and an outer cladding (e.g., an outer optical cladding). Typically, the central core's alpha-index profile has a minimum refractive index at the central core's radius that corresponds to a refractive index difference with respect to the outer cladding. The optical fiber achieves reduced bending losses and a high bandwidth with a reduced cladding effect for high-data-rate applications.

High-Bandwidth Multimode Optical Fiber Having Reduced Bending Losses

The present invention embraces an optical fiber that includes a central core having an alpha-index profile with respect to an outer cladding. The optical fiber also includes an inner cladding, a depressed trench, and an outer cladding. Typically, the alpha-index profile of the central core is interrupted at a point having a positive refractive index difference with respect to the outer cladding. The optical fiber achieves reduced bending losses and a high bandwidth with a reduced cladding effect for high-data-rate applications.

Multimode Optical Fiber with Low Bending Losses and Reduced Cladding Effect

We present the fundamentals of multiple-input, multiple-output (MIMO) signal processing for mode-division multiplexing (MDM) in multimode fiber (MMF). As an introduction, we review current long-haul optical transmission systems and how continued traffic growth motivates study of new methods to increase transmission capacity per fiber. We describe the key characteristics of MIMO channels in MMF, contrasting these with wireless MIMO channels. We review MMF channel models, the statistics derived from them, and their implications for MDM system performance and complexity. We show that optimizing performance and complexity requires management of channel parameters-particularly group delay (GD) spread and mode-dependent loss and gain-by design of transmission fibers and optical amplifiers, and by control of mode coupling along the link. We describe a family of fibers optimized for low GD spread, which decreases with an increasing number of modes. We compare the performance and complexity of candidate MIMO signal processing architectures in a representative long-haul system design, and show that programmable frequency-domain equalization (FDE) of chromatic dispersion (CD) and adaptive FDE of modal dispersion (MD) is an attractive combination. We review two major algorithms for adaptive FDE of MD-least mean squares (LMS) and recursive least squares (RLS)-and analyze their complexity, throughput efficiency, and convergence time. We demonstrate that, with careful physical link design and judicious choice of signal processing architectures, it is possible to overcome MIMO signal processing challenges in MDM systems.

MIMO Signal Processing for Mode-Division Multiplexing: An overview of channel models and signal processing architectures

PROBLEM TO BE SOLVED: To provide multimode optical fibers in which the differential in the mode delay of a high order mode is reduced for bending insensitive MMF. SOLUTION: The result is preservation of low differential mode delay and high bandwidth is achieved, while low bend loss is achieved. The designs are based on choosing a combination of a core profile and a cladding structure with a negative trench positioned at a radius position related to the core profile. The feature of the preferable embodiments is a core with a hybrid refractive index profile. The hybrid refractive index profile is essentially a combination of a standard alpha profile and a step-like profile at the outer edge of the alpha profile. COPYRIGHT: (C)2011,JPO&INPIT

Equalizing modal delay of high order modes in bend insensitive multimode fiber

This chapter gives an overview of design and optimization of few-mode optical fibers (FMF) for space-division multiplexed transmission. The design criteria are outlined, along with performance limitations of the traditional step-profile and graded-index profiles. The trade-offs between number of usable optical modes (related to total channel capacity), differential group delay, differential mode attenuation, mode coupling, and the impact on MIMO (multiple-input and multiple-output) receiver complexity are outlined. Improved fiber designs are analyzed which maximize channel capacity with foreseeable next-generation receiver technology. FMF measurement technology is overviewed.

Few-Mode Fiber Technology for Spatial Multiplexing

The specification describes modified step index and GRaded INdex (GRIN) fibers with low core relative delta (near 0.8%) which have desirable properties for transmission. These lower delta fibers have lower attenuation losses due to reduced Rayleigh scattering, which is desirable to improve performance in multiple mode multiplexing. The fiber designs include optimized raised triangle profiles, and depressed cladding profiles, to support two and four LP modes.

Multiple lp-mode fiber designs for mode-division multiplexing

A few-mode optical fiber comprises a core surrounded by a cladding, having a graded index profile that is structured to support propagation of a plurality of desired signal-carrying modes, while suppressing undesired modes. The core and cladding are configured such that the undesired modes have respective effective indices that are close to. or less than, the cladding index such that the undesired modes are leaky modes. The index spacing between the desired mode having the lowest effective index and the leaky mode with the highest effective index is sufficiently large so as to substantially prevent coupling therebetween.

Graded-index few-mode fiber designs for spatial multiplexing

Optical fiber refractive index profile designs having an alpha core profile and a negative index trench to control bend loss, are modified by truncating the edge of the alpha core profile and adding a ledge to the truncated core The result is low bend loss and preservation of low differential mode delay and high bandwidth

Yi Sun

Papers

Equalizing modal delay of high order modes in bend insensitive multimode fiber

Few-Mode Fiber Technology for Spatial Multiplexing

Multiple lp-mode fiber designs for mode-division multiplexing

Graded-index few-mode fiber designs for spatial multiplexing

Dmd performance in bend optimized multimode fiber