Defect Modes of Defective Parity-Time Symmetric Potentials in One-Dimensional Fractional Schrödinger Equation

Zhan, Ke; Zhang, Jiao; Jia, Yulei; Xu, Xianfeng

doi:10.1109/jphot.2017.2761826

Cited by 8 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although, in comparison to the standard Schrodinger equation, the fractional one just contains the fractional Laplacian operator instead of the common one, this change can lead to significant differences in the wave function characteristics. In the space-fractional Schrödinger formalism, optical solitons, self-focusing, and wave collapse 46 , Hermite–Gaussian-like solitons 47 , solitons in a 1D array of rectangular ferroelectric nanoparticles 48 , nontrivial wave-packet collision and broadening 49 , parity-time-symmetric lattice potentials 50 , defect modes 51 , modulation instability of Co-propagating optical beams 52 , propagation characteristics of ring Airy beams 53 , transmission through locally periodic potentials 54 , localization and Anderson delocalization of light 55 , quantum information entropies 56 , etc. have thus far been studied.…”

Section: Introductionmentioning

confidence: 99%

Fractional Young double-slit numerical experiment with Gaussian wavepackets

Ghalandari

Solaimani

2020

Sci Rep

View full text Add to dashboard Cite

In the present work, we consider the transmission properties of a Gaussian wavepacket when transmits through few double and multi-slit systems in a fractional medium. For this purpose, we have solved the two-dimensional fractional Schrodinger equation utilizing a split-step Fourier method. Then, we have investigated the effects of different parameters such as the number of slits, slit width, barrier width, layer width, layer heights, fractional order, and wavepacket width on the transmission coefficient, and wavepacket evolution.

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional Young double-slit numerical experiment with Gaussian wavepackets

Ghalandari

Solaimani

2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In fractional nonlinear regime, a series of interesting phenomena have been reported by many investigations, such as propagation of super-Gaussian beam [31], propagation and interaction of Airy beams [32][33][34], evolution of Bessel-Gaussian beam [35], Nonlinear conical diffraction [36], and different types of optical solitons [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Although 1D DSs have been studied in FNLSE with defective parity-time symmetric potential [52] and Kerr nonlinearity [53], properties of 1D and 2D DSs with saturable nonlinearity in FNLSE remain to be studied in detail.…”

Section: Introductionmentioning

confidence: 99%

Defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation

Wang

Xia²,

Chen

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

We address the existence, stability, and propagation dynamics of both one- and two-dimensional defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation. Under the influence of fractional effect, in one dimension, solitons exist stably in limited regions in the semi-infinite bandgap with high and low power both for a negative and positive defect lattice. In the first bandgap, solitons are stable for negative defect lattice, while unstable for positive defect lattice. In the second bandgap, only stable solitons can propagate in small regions for the positive defect lattice. With increasing the Lévy index from 1 to 2, the power of the defect solitons decreases in the semi-infinite bandgap and increases in the first bandgap. Linear stability analyses show that, the domains of stability for defect solitons strongly depend on the Lévy index, defect strength and different bandgaps. In two dimension, defect solitons can exist stably at high and moderate power regions in the semi-infinite bandgap and all regions in the first bandgap with negative defect lattice, while they are stable at high, moderate and low power regions in the semi-infinite bandgap and unstable in the first bandgap with positive defect lattice.

show abstract

“…This provided possibility to control optical beam propagation by using the fractional effect. After that, the beam dynamics modeled by FSE has drawn much attention and more intriguing phenomenon have been observed, such as zigzag propagation trajectory of optical beams [33], diffraction-free beams and conical diffraction [34], optical Bloch oscillation [35], optical Zener tunneling [36], beam propagation management [37], potential barrier-induced dynamics of FEABs [38], and many types of solitons in nonlinear fractional Schrödinger equation [39][40][41][42][43][44][45][46]. Moreover, recent works have also studied propagation of Gaussian and super-Gaussian beams modeled by FSE [47,48], interaction of FEABs in FSE with Kerr-type nonlinearity or a linear potential [49,50], and propagation dynamics of FEABs with different light field structure in FSE [51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation

2021

View full text Add to dashboard Cite

We investigate theoretically and numerically the interaction of Airy beams modeled by fractional nonlinear cubic-quintic Schrödinger equation. By considering fractional diffraction effect, when the initial beam interval between the two Airy beams is large enough, it is found that two in-phase Airy beams attract and repel each other, and two out-of-phase beams repel each other. This is different from the interaction of two Airy beams with large interval in standard nonlinear Schrödinger equation, where the two beams display a weak interaction. For smaller interval, single breathing soliton and symmetric breathing soliton pairs are formed in the in-phase and out-of-phase cases, respectively. As the Lévy index decreases, for the single breathing soliton, the oscillation becomes stronger, the mean peak intensity increases, and the soliton width decreases, for the symmetric breathing soliton pair, the width becomes narrower, and the repulsion between the two Airy components becomes stronger. Besides, the quintic defocusing strength will modulate the interaction of Airy beams. When the strength coefficient increases, the width of the breathing soliton formed in the in-phase case becomes wider, the repulsion between the two beams in the out-of-phase case increases, as well as the width of the soliton pair becomes wider. The work may provide new control methods on the interaction of Airy beams.

show abstract

Defect Modes of Defective Parity-Time Symmetric Potentials in One-Dimensional Fractional Schrödinger Equation

Cited by 8 publications

References 16 publications

Fractional Young double-slit numerical experiment with Gaussian wavepackets

Fractional Young double-slit numerical experiment with Gaussian wavepackets

Defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation

Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation

Contact Info

Product

Resources

About