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| Lorenz beam | |
|---|---|
| Name | Lorenz beam |
| Type | Optical beam |
Lorenz beam The Lorenz beam is a class of structured optical field notable for non-diffracting or self-reconstructing properties under certain conditions. It appears in theoretical and experimental studies alongside concepts in wave optics, diffraction theory, and singular optics and has been explored in contexts connected to laser propagation, atmospheric optics, and optical trapping.
The Lorenz beam is defined within wave optics as a solution to scalar or vector wave equations that exhibits localized intensity distributions and particular phase singularity structures, linking it to studies by researchers working on Hans Lorenz-associated formalisms and to developments in Gustav Kirchhoff-inspired diffraction theory, Augustin-Jean Fresnel methods, James Clerk Maxwell-based formulations, and modern treatments in Eugene Hecht textbooks. Its basic properties include modal stability, parameter-dependent transverse profiles, and invariance under certain propagation transforms, as characterized in literature associated with Institute of Optics, Max Planck Institute for the Science of Light, École Polytechnique, Imperial College London, and Massachusetts Institute of Technology. Experimental reports and reviews connecting Lorenz-beam behavior cite intersections with techniques developed at Bell Labs, IBM Research, Rikagaku Kenkyūsho (RIKEN), National Institute of Standards and Technology, and Optical Society of America conferences.
Mathematically, Lorenz beams are formulated as particular solutions of the Helmholtz equation and paraxial wave equation, employing expansions in terms of special functions that relate to work by Bernhard Riemann, Lord Rayleigh, Karl Schwarzschild, Arthur Eddington, and modern formulations by researchers at CERN, Stanford University, Caltech, and University of Cambridge. Representations often use Fourier transforms, Bessel functions, Hankel transforms, and angular spectrum methods anchored in analyses from Joseph Fourier, John von Neumann, Norbert Wiener, Paul Dirac, and Eugene Wigner; eigenmode decompositions reference orthogonal bases familiar from Erwin Schrödinger-style modal theory and operator methods seen in Niels Bohr-inspired quantizations. Boundary conditions and aperture functions enter via integral kernels similar to those in studies by Vladimir Fock, Ludwig Prandtl, Theodore von Kármán, and applied in numerical implementations developed at Los Alamos National Laboratory and Lawrence Berkeley National Laboratory.
Generation of Lorenz beams has been achieved using laser sources, spatial light modulators, diffractive optical elements, and interferometric setups developed in laboratories at University of Rochester, University of Glasgow, University of Tokyo, ETH Zurich, and industrial R&D at Thorlabs, Coherent, Inc., and NKT Photonics. Experimental realization procedures draw on techniques refined in the context of Dennis Gabor's holography, David G. Grier's optical micromanipulation, Nicolas Gisin's photonics, and implementations reported at CLEO, SPIE Photonics West, European Conference on Lasers and Electro-Optics, and Frontiers in Optics. Characterization utilizes cameras and wavefront sensors associated with efforts at National Aeronautics and Space Administration, European Space Agency, JPL, and metrology approaches standardized by International Organization for Standardization committees and national metrology institutes.
Propagation characteristics include limited-diffraction ranges, resilience to partial obstruction, and energy concentration patterns; these traits position Lorenz beams for applications in optical trapping, microscopy, free-space optical communication, remote sensing, and laser machining, linking applied research at Optical Society of America, IEEE Photonics Society, National Institutes of Health, Wellcome Trust, and industry projects with Google and Microsoft Research. Specific applications map to technologies such as optical tweezers pioneered by Arthur Ashkin, super-resolution microscopy advanced by Erwin Müller-related work, LIDAR systems used by Velodyne Lidar, and imaging modalities developed at Massachusetts General Hospital and Johns Hopkins University. Adaptations to turbulent media reference atmospheric optics studies by Carl Sagan-adjacent teams, propagation modeling by Phoebus Levene-style groups, and mitigation strategies from research at Naval Research Laboratory and Defense Advanced Research Projects Agency.
Lorenz beams are related to other structured beams including Bessel beams, Airy beams, Gaussian beams, Laguerre–Gaussian beams, Hermite–Gaussian beams, Mathieu beams, and accelerating beams, with conceptual and mathematical links to work by J. D. Jackson, M. V. Berry, N. V. Zabusky, Frank Wright, L. Allen and groups at University of Rochester and Queen Mary University of London. Comparative analyses appear in context with nondiffracting solutions developed by Durnin and accelerating-wave research associated with Michael Berry and experimental platforms at California Institute of Technology, University of Ottawa, and University of Strathclyde.
The historical development of Lorenz-beam concepts traces through early wave optics and diffraction theory contributions by Augustin-Jean Fresnel, George Gabriel Stokes, Hendrik Lorentz, and Hans Lorenz-era formalisms, later expanded by 20th-century figures such as Max Born, Emil Wolf, Dennis Gabor, Arthur Ashkin, M. V. Berry, and contemporary groups at University of Oxford, University of Sydney, Tsinghua University, Peking University, and Kavli Institute for Theoretical Physics. Conferences and symposiums at Royal Society, National Academy of Sciences, American Physical Society, European Physical Society, and publications in journals like Physical Review Letters, Optics Letters, Journal of the Optical Society of America A, and Nature Photonics document the evolving theoretical, numerical, and practical work.
Category:Optical beams