About: Reflection (physics) is a research topic. Over the lifetime, 45189 publications have been published within this topic receiving 510226 citations. The topic is also known as: reflexion & mirroring.
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Abstract: Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
TL;DR: In this article, a two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint phase discontinuities on propagating light as it traverses the interface between two media.
Abstract: Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.
Abstract: Light propagation can be controlled with plasmonic interfaces that introduce abrupt phase shifts along the optical path. Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.
TL;DR: In this article, the authors present a two-dimensional wave equation and simple solutions for the wave equation with respect to the two dimensions of the wave and the two types of vibrations.
Abstract: Fundamentals of Vibration. Transverse Motion: The Vibrating String. Vibrations of Bars. The Two--Dimensional Wave Equation: Vibrations of Membranes and Plates. The Acoustic Wave Equation and Simple Solutions. Reflection and Transmission. Radiation and Reception of Acoustic Waves. Absorption and Attenuation of Sound. Cavities and Waveguides. Pipes, Resonators, and Filters. Noise, Signal Detection, Hearing, and Speech. Architectural Acoustics. Environmental Acoustics. Transduction. Underwater Acoustics. Selected Nonlinear Acoustic Effects. Shock Waves and Explosions. Appendices. Answers to Odd--Numbered Problems. Index.
TL;DR: In this article, two-and three-dimensional boundary value problems are studied for two-dimensional waveguides with Cylindrical Conducting Boundaries (CCLB).
Abstract: Stationary Electric Fields. Stationary Magnetic Fields. Maxwell's Equations. The Electromagnetics of Circuits. Transmission Lines. Plane-Wave Propagation and Reflection. Two- and Three-Dimensional Boundary Value Problems. Waveguides with Cylindrical Conducting Boundaries. Special Waveguide Types. Resonant Cavities. Microwave Networks. Radiation. Electromagnetic Properties of Materials. Optics. Appendices. Index.