Optical Waveguide Theory

Non-Gaussian beam profiles such as Bessel or an- nular beams enable novel approaches to modifying materials through laser-based processing. In this review paper, proper- ties, generation methods and emerging applications for non- conventional beam shapes are discussed, including Bessel, an- nular, and vortex beams. These intensity profiles have important implications in a number of technologically relevant areas includ- ing deep-hole drilling, photopolymerization and nanopatterning, and introduce a new dimension for materials optimization and fundamental studies of laser-matter interactions.

Bessel and annular beams for materials processing

1. Semiconductor Laser Diodes 2. Basic Concepts 3. Free-Carrier Theory 4. Coulomb Effects 5. Many-Body Gain 6. Band Mixing and Strain in Quantum Wells 7. Semiclassical laser Theory 8. Multimode Operation 9. Quantum Theory of the Laser 10. Propagation Effects 11. Beyond Quasiequilibrium Theory, Appendices A-e, Index

Semiconductor-Laser Physics

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

Over the last dozen years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations, but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing) and are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing, among others.

Airy beams and accelerating waves: an overview of recent advances

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

Hollow Gaussian beams and their propagation properties.

We investigated the propagation dynamics of the Circular Airy Beams (CAB) with optical vortices (OVs) by numerical calculation. Comparing to the common CAB, the maximum intensity of CAB with vortices can be increased greatly at the focal plane and its focal intensity profile is doughnut-shaped when an on-axis vortex is imposed. The case for an off-axis OV and multiple OVs have been investigated as well. We demonstrate that two opposite OVs will annihilate exactly at the focal plane, with the focal intensity is highly increased.

Propagation dynamics of abruptly autofocusing Airy beams with optical vortices

The radiation force of circular Airy beams (CAB) on a dielectric Rayleigh particle is investigated in this paper. Our results show that the CAB can be used to trap the particle whose refractive index is larger than the ambient at different positions along the beam axis. Comparing with the Gaussian beam under the same conditions, the longitudinal and the transverse gradient force of CAB on the Rayleigh particle are increased, and the particle can be trapped more stable. Our analyses also demonstrate that the trapping properties of CAB can be modulated by controlling corresponding parameters of CAB.

Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle

Propagations of coherent and partially coherent flat-topped beams through a focusing optical system are formulated. The radiation force on a Rayleigh dielectric sphere induced by focused coherent and partially coherent flat-topped beams is investigated theoretically. It is found that we can increase the transverse trapping range at the planes near the focal plane by increasing the flatness (i.e., beam order) of the flat-topped beam, and increase the transverse and longitudinal trapping ranges at the focal plane by decreasing the initial coherence of the flat-topped beam. Moreover the trapping stiffness of flat-topped beam becomes lower as the beam order increases or the initial coherence decreases. The trapping stability is also analyzed.

Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle

We report the experimental generation of a high-quality partially coherent dark hollow beam (DHB) by coupling a partially coherent beam into a multimode fiber (MMF) with a suitable incidence angle. The interference experiment of the generated partially coherent DHB passing through double slits is demonstrated. It is found that the coupling efficiency of the MMF, the quality, and the coherence of the generated partially coherent DHB are closely controlled by the coherence of the input beam.

Xuanhui Lu

Papers

Hollow Gaussian beams and their propagation properties.

Propagation dynamics of abruptly autofocusing Airy beams with optical vortices

Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle

Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle

Generation of a high-quality partially coherent dark hollow beam with a multimode fiber