These papers were taken from a conference on singular optics. They address topics such as: paraxial beams of spinning light; diffraction catastrophes and wave caustics of multimode fibres; and visualization of the phase singularities in wavefront sensors.

This memorial volume in honor of Dr Akira Tonomura is to commemorate his enormous contributions to fundamental physics in addition to the basic technology of electron microscopy. Dr Tonomura passed away on May 2, 2012 at the age of 70. He was Fellow of Hitachi, Ltd., Group Director of Single Quantum Dynamics Research Group of RIKEN, Principal Investigator of the FIRST Tonomura Project, and Professor of Okinawa Institute of Science and Technology Graduate University. The book consists of: 1) contributions from distinguished physicists, who participated in the OC Tonomura FIRST International Symposium on Electron Microscopy and Gauge FieldsOCO planned by Tonomura himself and held in Tokyo on May 9OCo10, 2012, and 2) reprints of key papers by Tonomura and his team. Invited speakers at this Symposium include Chen Ning Yang and other distinguished physicists such as Yakir Aharonov, Gordon Baym, Christian Colliex, Anthony J Leggett, Naoto Nagaosa, Nobuyuki Osakabe and Masahito Ueda. This OC memorialOCO Symposium was originally planned to commemorate the start of the Japanese-government-sponsored FIRST Tonomura Project to construct the 1.2 MV holography electron microscope capable of observing quantum phenomena in the microscopic world. In addition, the book includes contributions from participants of the past ISQM-Tokyo symposia held at Hitachi and from Tonomura''s longtime friends, including Michael Berry, Jerome Friedman, Hidetoshi Fukuyama, Joseph Imry, Yoshinori Tokura, Jaw-Shen Tsai, and Anton Zeilinger. The co-editors are Kazuo Fujikawa, Tonomura''s longtime friend, and Yoshimasa A Ono who is Tonomura''s associate at Hitachi Advanced Research Laboratory and now in the FIRST Tonomura Project. Contents: My Dream of Ultimate Holography Electron Microscope (Akira Tonomura); Biography of Akira Tonomura (April 1942 OCo May 2012) (Nobuyuki Osakabe); Tonomura FIRST International Symposium on OC Electron Microscopy and Gauge FieldsOCO (Yoshimasa A Ono); Recollections of Akira Tonomura: Thank You and Farewell to Tonomura-kun (Hidetoshi Fukuyama); Remembering Akira Tonomura (Michael Berry); Akira Tonomura: An Experimental Visionary (Anton Zeilinger); Dr. Akira Tonomura: Master of Experimental Physics (Kazuo Fujikawa); Gauge Theory and Aharonov-Bohm Effect: Topology and Gauge Theory in Physics (Chen Ning Yang); On the Aharonov-Bohm Effect and Why Heisenberg Captures Nonlocality Better Than SchrAdinger (Yakir Aharonov); How the Test of Aharonov-Bohm Effect was Initiated at Hitachi Laboratory (Nobuyuki Osakabe); Some Reflections Concerning Geometrical Phases (Anthony J Leggett and Yiruo Lin); Mesoscopic Aharonov-Bohm Interferometers: Decoherence and Thermoelectric Transport (Ora Entin-Wohlman, Amnon Aharony and Yoseph Imry); Spin Textures and Gauge Fields in Frustrated Magnets (Naoto Nagaosa and Yoshinori Tokura); Gauge Theory and Artificial Spin Ices: Imaging Emergent Monopoles with Electron Microscopy (Shawn D Pollard and Yimei Zhu); Do Dispersionless Forces Exist? (Herman Batelaan and Scot McGregor); Aharonov-Bohm Effect and Geometric Phases OCo Exact and Approximate Topology (Kazuo Fujikawa); A Brief Overview and Topological Aspects of Gaseous Bose-Einstein Condensates (Masahito Ueda); Application of Electron Microscopy to Quantum Mechanics and Materials Sciences: Mapping Electric Fields with Inelastic Electrons in a Transmission Electron Microscope (Christian Colliex); OC The Picture is My LifeOCO (Shuji Hasegawa); Direct Observation of Electronically Phase-Separated Charge Density Waves in Lu 2 Ir 3 Si 5 by Transmission Electron Microscopy (Cheng-Hsuan Chen); Basic Discoveries in Electromagnetic Field Visualization (Daisuke Shindo); Nanomagnetism Visualized by Electron Holography (Hyun Soon Park); Quantum Physics: Probing the Proton with Electron Microscopy (Jerome I Friedman); Hanbury BrownOCoTwiss Interferometry with Electrons: Coulomb vs. Quantum Statistics (Gordon Baym and Kan Shen); Vortex Molecules in Thin Films of Layered Superconductors (Alexander I Buzdin); Coherent Quantum Phase Slip (Jaw-Shen Tsai); Coherency of Spin Precession in Metallic Lateral Spin Valves (YoshiChika Otani, Hiroshi Idzuchi and Yasuhiro Fukuma); Transverse Relativistic Effects in Paraxial Wave Interference (Konstantin Y Bliokh, Yana V Izdebskaya and Franco Nori). Readership: Graduate students and researchers in physics, materials science and related fields."

An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

This book presents methods to improve information security for protected communication. It combines and applies interdisciplinary scientific engineering concepts, including cryptography, chaos theory, nonlinear and singular optics, radio-electronics and self-changing artificial systems. It also introduces additional ways to improve information security using optical vortices as information carriers and self-controlled nonlinearity, with nonlinearity playing a key "evolving" role. The proposed solutions allow the universal phenomenon of deterministic chaos to be discussed in the context of information security problems on the basis of examples of both electronic and optical systems. Further, the book presents the vortex detector and communication systems and describes mathematical models of the chaos oscillator as a coder in the synchronous chaotic communication and appropriate decoders, demonstrating their efficiency both analytically and experimentally. Lastly it discusses the cryptologic features of analyzed systems and suggests a series of new structures for confident communication.

Topology is the study of properties that remain unchanged under bending, twisting, and stretching of a system. Long important in other areas of physics, topology has recently become a vital tool in optics and photonics as well, leading to a broad range of unexpected phenomena such as knotted and linked optical vortices and topologically protected states that are immune to environmental disruption. Topology in Optics: Tying Light in Knots (Second Edition) covers the background needed to follow these developments and provides a brief survey of topological effects in optics. Assuming only a background in physics at the advanced undergraduate level, it requires no prior familiarity with topology. Revised and expanded with two new chapters. Topological Photonics and Optical Knots and Links, this will be an invaluable reference for undergraduate and graduate students as well as researchers and engineers in optics and related areas. Book jacket.