Focusing of vector beams with fractional-order azimutal polarization

2021 ◽  
Author(s):  
Vladislav Zaitcev ◽  
Sergey S. Stafeev ◽  
Victor Kotlyar
Keyword(s):  
Fractional Order ◽  
Vector Beams

scholarly journals Focusing fractional-order cylindrical vector beams

2021 ◽  
Vol 45 (2) ◽  
pp. 172-178
Author(s):  
S.S. Stafeev ◽  
V.D. Zaitsev
Keyword(s):  
Fractional Order ◽  
Energy Flux ◽  
Energy Flow ◽  
Focal Spot ◽  
Numerical Aperture ◽  
Vortex Beam ◽  
Incident Wavelength ◽  
Spot Center ◽  
Vector Beams ◽  
Linearly Polarized

By numerically simulating the sharp focusing of fractional-order vector beams (0≤m≤1, with azimuthal polarization at m=1 and linear polarization at m=0), it is shown that the shape of the intensity distribution in the focal spot changes from elliptical (m=0) to round (m=0.5) and ends up being annular (m=1). Meanwhile, the distribution pattern of the longitudinal component of the Poynting vector (energy flux) in the focal spot changes in a different way: from circular (m=0) to elliptical (m=0.5) and ends up being annular (m=1). The size of the focal spot at full width at half maximum of intensity for a first-order azimuthally polarized optical vortex (m=1) and numerical aperture NA=0.95 is found to be 0.46 of the incident wavelength, whereas the diameter of the on-axis energy flux for linearly polarized light (m=0) is 0.45 of the wavelength. Therefore, the answers to the questions: when the focal spot is round and when elliptical, or when the focal spot is minimal -- when focusing an azimuthally polarized vortex beam or a linearly polarized non-vortex beam, depend on whether we are considering the intensity at the focus or the energy flow. In another run of numerical simulation, we investigate the effect of the deviation of the beam order from m=2 (when an energy backflow is observed at the focal spot center). The reverse energy flow is shown to occur at the focal spot center until the beam order gets equal to m=1.55.

Tight focusing cylindrical vector beams with fractional order

2021 ◽  
Vol 38 (4) ◽  
pp. 1090
Author(s):  
S. S. Stafeev ◽  
A. G. Nalimov ◽  
V. D. Zaitsev ◽  
V. V. Kotlyar
Keyword(s):  
Fractional Order ◽  
Tight Focusing ◽  
Vector Beams

Stability in a Discrete Fractional Order Prey Predator System with Functional Response

2017 ◽  
Vol 7 (5) ◽  
pp. 630-633 ◽  
Author(s):  
A. George Maria Selvam ◽  
◽  
R. Janagaraj ◽  
Britto Jacob. S ◽  
◽  
...  
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Predator System

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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