Title: From Bessel beam to complex-source-point cylindrical wave-function

This investigation shows that a scalar Bessel beam can be transformed into the non-paraxial complex-source-point cylindrical wave (CSPCW). High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically. Moreover, partial-derivatives of the high-order CSPCW solutions satisfy the Helmholtz equation. In addition, the CSPCW solutions satisfy the nonrelativistic Schrödinger equation within standard quantum mechanics, thus, the results can be used in the description of elementary particle/matter motion and related applications in quantum scattering theory. Furthermore, the analysis is extended to the case of vector beams in which the components of the electromagnetic (EM) field are obtained based on different polarizations of the magnetic and electric vector potentials, which exactly satisfy Maxwell’s vectorial equations and Lorenz’ gauge condition. An attractive feature of the high-order solutions is the rigorous description of strongly focused (or strongly divergent) cylindrical wave-fields without any approximations, nor the need for numerical methods. Possible applications are in beam-forming design using high-aperture or collimated cylindrical laser/electron quasi-Gaussian beams in imaging microscopy, particle manipulation, optical tweezers, and the study of the scattering, and radiation forces on objects. - Highlights: • Bessel beam is transformed into the non-paraxial cylindrical complex-source-point. • Exact high-order tightlymore » focused solutions are derived without any approximations. • The exact solutions also satisfy the nonrelativistic Schrödinger equation. • Electromagnetic beams are obtained as solutions of Maxwell’s vectorial equations. • Applications are in laser/electron beam imaging, tweezers, and radiation force.« less

Journal Name: Annals of Physics; Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTRON BEAMS; EXACT SOLUTIONS; MAXWELL EQUATIONS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; WAVE FUNCTIONS