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 engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics." —Michael Berry, University of Bristol, UK "The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts...." —Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University "a firm and comprehensive grounding both for those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." —Miles Padgett, Kelvin Chair of Natural Philosophy and Vice Principal (Research), University of Glasgow This book focuses on the various forms of wavefield singularities, including optical vortices and polarization singularities, as well as orbital angular momentum and associated applications. It highlights how an understanding of singular optics provides a completely different way to look at light. Whereas traditional optics focuses on the shape and structure of the non-zero portions of the wavefield, singular optics describes a wave’s properties from its null regions. The contents cover the three main areas of the field: the study of generic features of wavefields, determination of unusual properties of vortices and wavefields that contain singularities, and practical applications of vortices and other singularities.

This book includes high-quality research papers presented at the Fourth International Conference on Innovative Computing and Communication (ICICC 2021), which is held at the Shaheed Sukhdev College of Business Studies, University of Delhi, Delhi, India, on February 20–21, 2021. Introducing the innovative works of scientists, professors, research scholars, students and industrial experts in the field of computing and communication, the book promotes the transformation of fundamental research into institutional and industrialized research and the conversion of applied exploration into real-time applications.

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."