scholarly journals Пучки Гельмгольца--Гаусса с квадратичной радиальной зависимостью

2022 ◽  
Vol 130 (2) ◽  
pp. 260
Author(s):  
А.Б. Плаченов ◽  
Г.Н. Дьякова
Keyword(s):  
Parabolic Equation ◽  
Helmholtz Equation ◽  
Fundamental Mode ◽  
Complex Surface ◽  
Optical Vortices ◽  
Arbitrary Solution ◽  
New Class ◽  
Localized Solutions ◽  
Gaussian Type ◽  
Amplitude Factor

A new class of localized solutions of paraxial parabolic equation is introduced. Each solution is a product of some Gaussian-type localized axisymmetric function (different from the fundamental mode) and an amplitude factor. The latter can be expressed via an arbitrary solution of the Helmholtz equation on an auxiliary two-sheet complex surface. The class under consideration contains well known and novel solutions, including those describing optical vortices of various orders.

scholarly journals Influence of attenuation on the generation of optical vortices in multihelicoidal optical fibers

2021 ◽  
Vol 2103 (1) ◽  
pp. 012149
Author(s):  
C N Alexeyev ◽  
S S Alieva ◽  
E V Barshak ◽  
B P Lapin ◽  
M A Yavorsky
Keyword(s):  
Optical Fibers ◽  
Fundamental Mode ◽  
Optical Vortex ◽  
Conversion Process ◽  
Exceptional Point ◽  
Optical Vortices ◽  
Attenuation Coefficients ◽  
Enhanced Sensitivity ◽  
Scalar Approximation ◽  
The Difference

Abstract In this paper we have studied influence of attenuation on conversion processes of the fundamental mode (FM) in multihelicoidal optical fibers (MHF) in the vicinity of the point of accidental spectrum degeneracy within the framework of the scalar approximation. To this end, we have obtained expressions for modes of the MHF, which consist of the FM and an optical vortex (OV), and shown that conversion of the FM into the OV takes place. The difference in the attenuation coefficients for the partial fields of MHF’s modes leads to deterioration in the conversion process even with an ideal system’s tuning. At sufficiently large values of attenuation coefficients the conversion of the incoming FM into the vortex vanishes. Also we have shown the presence of exceptional point (EP) in the spectra of modes of the MHF and demonstrated enhanced sensitivity of the fiber in the vicinity of the EP to perturbations.

scholarly journals Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Constantin P. Niculescu ◽  
Ionel Rovenţa
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Blow Up ◽  
Neumann Boundary ◽  
Semilinear Parabolic Equations ◽  
New Class ◽  
Large Solutions ◽  
Nonlocal Parabolic Equation ◽  
Work Done ◽  
Semilinear Parabolic

We consider a new class of nonlinearities for which a nonlocal parabolic equation with Neumann boundary conditions has finite time blow-up solutions. Our approach is inspired by previous work done by Jazar and Kiwan (2008) and El Soufi et al. (2007).

Optical vortices in fiber

Nanophotonics ◽  
2013 ◽  
Vol 2 (5-6) ◽  
pp. 455-474 ◽  
Author(s):  
Siddharth Ramachandran ◽  
Poul Kristensen
Keyword(s):  
Angular Momentum ◽  
Optical Fibers ◽  
Orbital Angular Momentum ◽  
Optical Vortex ◽  
Optical Vortices ◽  
New Class ◽  
Phase Singularities ◽  
Vortex Beams ◽  
Exotic Beams

AbstractOptical vortex beams, possessing spatial polarization or phase singularities, have intriguing properties such as the ability to yield super-resolved spots under focussing, and the ability to carry orbital angular momentum that can impart torque to objects. In this review, we discuss the means by which optical fibers, hitherto considered unsuitable for stably supporting optical vortices, may be used to generate and propagate such exotic beams. We discuss the multitude of applications in which a new class of fibers that stably supports vortices may be used, and review recent experiments and demonstration conducted with such fibers.

A FINITE DIFFERENCE SOLUTION TO THE HELMHOLTZ EQUATION IN A RADIALLY SYMMETRIC WAVEGUIDE: APPLICATION TO NEAR-SOURCE SCATTERING IN OCEAN ACOUSTICS

2008 ◽  
Vol 16 (03) ◽  
pp. 447-464 ◽  
Author(s):  
CATHERINE DE GROOT-HEDLIN
Keyword(s):  
Parabolic Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Helmholtz Equation ◽  
Mode Coupling ◽  
Analytic Solutions ◽  
Numerical Dispersion ◽  
Wide Angle ◽  
Complex Models ◽  
Finite Difference Solution

A finite difference (FD) method is developed and analyzed for the Helmholtz equation in a radially symmetric waveguide. The resulting algorithm can be used to solve for sound intensities in complex models that may include high material contrasts and arbitrary bathymetry. An analysis of the effect of grid discretization on the results indicates that numerical dispersion is significant within one-third of a wavelength from a point source and decreases beyond that. Numerical results are presented and compared to wide-angle parabolic equation (PE) solutions and analytic solutions, where available. Comparison with analytic results indicates that the FD method accurately solves for the acoustic wave field at all propagation angles and is more accurate than the PE method near the source. Results are also shown for models in which mode coupling occurs near the source.

A new class of inverse Gaussian type distributions

Metrika ◽  
2007 ◽  
Vol 68 (1) ◽  
pp. 31-49 ◽  
Author(s):  
Antonio Sanhueza ◽  
Víctor Leiva ◽  
N. Balakrishnan
Keyword(s):  
Inverse Gaussian ◽  
New Class ◽  
Gaussian Type
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