Transverse energy flows in vectorial fields of paraxial beams with singularities

Abstract A general study of transverse energy flows (TEF) as physically meaningful and informative characteristics of paraxial light beams’ spatial structure is presented. The total TEF can be decomposed into the spin and orbital contributions giving rise to the spin and orbital angular momentums, correspondingly. Definitions and properties of these constituents are discussed in relation with the optical field representation through linear and circular orthogonal polarization bases. With the help of model examples, the results are applied to investigation of TEF singularities in connection with the usual polarization morphology characteristics of paraxial optical fields. An analysis of TEFs near singular points has been carried out; in particular, the behavior of TEF and its partial contributions near polarization singularities ( C -points) has demonstrated the special role of a boundary flow in the origin of the spin angular momentum. The analytical and experimental applicability of the introduced concepts are discussed.

[1]  William B. McKnight,et al.  From Maxwell to paraxial wave optics , 1975 .

[2]  I. Mokhun,et al.  Behavior of the transversal component of the Poynting vector in the area of interference trap , 2006, International Conference on Correlation Optics.

[3]  M V Berry,et al.  Phase vortex spirals , 2005 .

[4]  Freund Saddles, singularities, and extrema in random phase fields. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Zofia Bialynicka-Birula,et al.  Beams of electromagnetic radiation carrying angular momentum : The Riemann-Silberstein vector and the classical-quantum correspondence , 2005, quant-ph/0511011.

[6]  Michael V Berry,et al.  Geometry of phase and polarization singularities illustrated by edge diffraction and the tides , 2001, Other Conferences.

[7]  Spatial evolution of the morphology of an optical vortex dipole , 2004 .

[8]  A. Bekshaev,et al.  An optical vortex as a rotating body: mechanical features of a singular light beam , 2004 .

[9]  John F Nye,et al.  Natural focusing and fine structure of light: caustics and wave dislocations , 1999 .

[10]  D. Lenstra,et al.  Light transmission through a subwavelength slit: waveguiding and optical vortices. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  L. W. Chubb,et al.  Polarized Light , 2019, Light Science.

[12]  M. Dennis LETTER TO THE EDITOR: Phase critical point densities in planar isotropic random waves , 2001 .

[13]  Mark R. Dennis,et al.  Phase singularities in isotropic random waves , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Cleve Moler,et al.  Mathematical Handbook for Scientists and Engineers , 1961 .

[15]  M S Soskin,et al.  Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  M. Berry Riemann-Silberstein vortices for paraxial waves , 2004 .

[17]  I. Bialynicki-Birula,et al.  Vortex lines of the electromagnetic field , 2003, physics/0305012.

[18]  Kishan Dholakia,et al.  The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization , 2004 .

[19]  D. Lenstra,et al.  The diffraction of light by narrow slits in plates of different materials , 2004 .

[20]  M. Soskin,et al.  Topological networks of paraxial ellipse speckle-fields , 2004 .

[21]  M. Vasnetsov,et al.  Wavefront motion in the vicinity of a phase dislocation: “optical vortex” , 2000 .

[22]  I. Mokhun,et al.  The behavior of the pointing vector in the area of elementary polarization singularities , 2006, International Conference on Correlation Optics.

[23]  Mark R. Dennis,et al.  Topological Singularities in Wave Fields , 2001 .

[24]  M. Tabor Chaos and Integrability in Nonlinear Dynamics: An Introduction , 1989 .

[25]  Mark R. Dennis,et al.  Polarization singularities in paraxial vector fields: morphology and statistics , 2002 .

[26]  M. Soskin,et al.  The relationship between topological characteristics of component vortices and polarization singularities , 2002 .

[27]  M. S. Soskin,et al.  Chapter 4 - Singular optics , 2001 .

[28]  Y. Anan'ev,et al.  Laser Resonators and the Beam Divergence Problem , 1992 .

[29]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[30]  Stephen M. Barnett,et al.  Orbital angular momentum and nonparaxial light beams , 1994 .

[31]  M. Soskin,et al.  Experimental optical diabolos. , 2006, Optics letters.

[32]  Miles J. Padgett,et al.  IV The Orbital Angular Momentum of Light , 1999 .

[33]  Mikhail V. Vasnetsov,et al.  Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system , 2002 .

[34]  Dan Cojoc,et al.  Orbital angular momentum of inhomogeneous electromagnetic field produced by polarized optical beams , 2004, SPIE Optics + Photonics.

[35]  E. M. Lifshitz,et al.  Classical theory of fields , 1952 .

[36]  E. Wolf,et al.  Energy Flow in the Neighborhood of the Focus of a Coherent Beam , 1967 .

[37]  Mark R. Dennis,et al.  Local properties and statistics of phase singularities in generic wavefields , 2001, Other Conferences.

[38]  Michael V. Berry,et al.  Paraxial beams of spinning light , 1998, Other Conferences.

[39]  Norman R. Heckenberg,et al.  Topological charge and angular momentum of light beams carrying optical vortices , 1997 .

[40]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

[41]  Filippus S. Roux,et al.  Distribution of angular momentum and vortex morphology in optical beams , 2004 .

[42]  I. Mokhun,et al.  Singularities of the Poynting vector and the structure of optical field , 2006, International Conference on Correlation Optics.

[43]  G. Kaiser Helicity, polarization and Riemann–Silberstein vortices , 2003, math-ph/0309010.

[44]  Mikhail V. Vasnetsov,et al.  Description of the morphology of optical vortices using the orbital angular momentum and its components , 2006 .

[45]  A. Bekshaev,et al.  Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons. , 2006, Optics letters.

[46]  B. Krauskopf,et al.  Proc of SPIE , 2003 .

[47]  Mikhail V. Vasnetsov,et al.  Transformation of higher-order optical vortices upon focusing by an astigmatic lens , 2004 .

[48]  M. Soskin,et al.  Elliptic critical points in paraxial optical fields , 2002 .

[49]  Miles J. Padgett,et al.  The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density , 2000 .