Generation of optical vortices by fractional derivative

Preda, L.

doi:10.1016/j.optlaseng.2013.09.013

Cited by 13 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The unperturbed Green function G In our case, λ(k) is the dispersion given by Eq. ( 8) and because of its complexity, it is not possible to obtain a closed form expression for G 13), (12) for the bound state energies and bound state amplitudes. Now, it turns out that G (0) mn is not quite the Green function we need.…”

Section: The Modelmentioning

confidence: 99%

“…where, 0 < α < 1. This unorthodox formalism with its definitions of a fractional integral and fractional derivative, has found application in several fields: fluid mechanics [5], fractional kinetics and anomalous diffusion [6][7][8], optics [9][10][11][12][13][14], strange kinetics [15], Levy processes in quantum mechanics [16], fractional quantum mechanics [17,18], plasmas [19], electrical propagation in cardiac tissue [20], biological invasions [21], and epidemics [22]. It has proven most useful in describing the behavior of systems with nonlocal interactions and systems with memory effects.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional nonlinear surface impurity in a 2D lattice

Molina

2021

Preprint

View full text Add to dashboard Cite

We study the formation of localized modes around a generalized nonlinear impurity which is located at the boundary of a semi-infinite square lattice, and where we replace the standard discrete Laplacian by a fractional one, characterized by a fractional exponent 0 < α < 1 where α = 1 marks the standard, non-fractional case. We specialize to two impurity cases: impurity at an "edge" and impurity at a "corner" and use the formalism of lattice Green functions to obtain in closed form the bound state energy and its mode amplitude. It is found that, for any fractional exponent and for impurity strengths above a certain threshold, there is always a single bound state for the linear impurity, while for the nonlinear (cubic) case, up to two bound states are possible. At small fractional exponents, the energy of the impurity mode becomes directly proportional to the impurity strength.

show abstract

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional nonlinear surface impurity in a 2D lattice

Molina

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…where, 0 < s < 1. This fractional formalism has found applications in several fields: Levy processes in quantum mechanics [27], strange kinetics [28], optics [29][30][31][32][33][34], fluid mechanics [35], quantum mechanics [36,37], electrical propagation in cardiac tissue [38], epidemics [39] and biological invasions [40].…”

Section: Introductionmentioning

confidence: 99%

Fractional electrical impurity

Molina

2024

New J. Phys.

View full text Add to dashboard Cite

We examine the localized mode and the transmission of plane waves across a capacitive impurity of strength $\Delta$, in a 1D bi-inductive electrical transmission line where the usual discrete Laplacian is replaced by a fractional one characterized by a fractional exponent $s$. In the absence of the impurity, the plane wave dispersion is computed in closed form in terms of hypergeometric functions. It is observed that the bandwidth decreases steadily, as $s$ decreases towards zero, reaching a minimum width at $s=0$. The localized mode energy and spatial profiles are computed in closed form v\`{i}a lattice Green functions. The profiles show a remnant of the staggered-unstaggered symmetry that is common in non-fractional chains. The width of the localized mode decreases with decreasing $s$, becoming completely localized at the impurity site at $s=0$. The transmission coefficient of plane waves across the impurity is qualitatively similar to its non-fractional counterpart ($s=1$), except at low $s$ values ($s\ll 1$). For a fixed exponent $s$, the transmission decreases with increasing $\Delta$.

show abstract

“…The synthesis of the optical fields with a uniform polarization state is relatively straightforward, as it only involves shaping the phase and intensity of the beam. It can be achieved, for example, by using various types of holograms [ 10 , 11 , 12 , 13 ], spiral phase plates [ 14 ], digital micro-mirrors devices [ 15 ], or spatial light modulators (SLM) [ 16 ], which can provide almost any modulation of phase and amplitude. The above approaches rely mainly on expensive and advanced techniques involving a bulky setup comprising many different optical components.…”

Section: Introductionmentioning

confidence: 99%

A Gaussian to Vector Vortex Beam Generator with a Programmable State of Polarization

et al. 2022

View full text Add to dashboard Cite

We study an optical device designed for converting the polarized Gaussian beam into an optical vortex of tunable polarization. The proposed device comprised a set of three specially prepared nematic liquid crystal cells and a nano-spherical phase plate fabricated from two types of glass nanotubes. This device generates a high-quality optical vortex possessing one of the multiple polarization states from the uniformly polarized input Gaussian beam. Its small size, simplicity of operation, and electrical steering can be easily integrated into the laboratory and industrial systems, making it a promising alternative to passive vortex retarders and spatial light modulators.

show abstract

Generation of optical vortices by fractional derivative

Cited by 13 publications

References 17 publications

Fractional nonlinear surface impurity in a 2D lattice

Fractional nonlinear surface impurity in a 2D lattice

Fractional electrical impurity

A Gaussian to Vector Vortex Beam Generator with a Programmable State of Polarization

Contact Info

Product

Resources

About