Open AccessFormation of required distributions on the basis of decomposition by vortex eigen functions of a bounded non-paraxial propagation operator
Author(s) -
С. Н. Хонина,
S. G. Volotovskiy,
Mikhail S. Kirilenko
Publication year - 2019
Publication title -
kompʹûternaâ optika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 29
eISSN - 2412-6179
pISSN - 0134-2452
DOI - 10.18287/2412-6179-2019-43-2-184-192
Subject(s) - eigenfunction , paraxial approximation , diffraction , mathematics , superposition principle , mathematical analysis , bounded function , operator (biology) , eigenvalues and eigenvectors , physics , optics , quantum mechanics , beam (structure) , biochemistry , chemistry , repressor , transcription factor , gene
The solution of the problem of overcoming the diffraction limit based on the representation of an optical signal in the form of a superposition of communication modes matched with the vortex eigenfunctions of a bounded (in the object and spectral regions) nonparaxial propagation operator in free space is considered. Nonparaxial propagation of laser beams is described using an expansion in terms of conic waves based on the m-th order Fourier-Hankel transform. The eigenfunctions of such an operator, which have near-unity eigenvalues, determine the number of degrees of freedom and characteristics of an optical signal transmitted without distortion over a given distance. Based on the considered approach, a parametric method was developed for solving the inverse diffraction problem, including overcoming the diffraction limit.