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In this paper, we investigate the propagation dynamics of circular Airy beams (CAB) in a medium with radial parabolic potential both analytically and numerically. Our results show that CAB will exhibit periodic abruptly autofocusing behavior under the action of radial parabolic potentials. Within every period, we interestingly observe a novel autodefocusing behavior, which manifests that optical peak intensity abruptly decreases by several orders of magnitude. In particular, such unique “autofocusing-to-autodefocusing” effect can lead to the formation of a series of elegant periodic optical bottles having paraboloidal shapes during the whole propagation process. Our findings indicate that CAB is expected to provide a unique tool in optical micromanipulation and optical trapping.

In this paper, we derive an analytical solution of linearly chirped Airy beams (CAB) propagating in strongly nonlocal media with focusing and defocusing nonlinearity. Our analytical results show the periodic evolution pattern of CAB supported by strongly nonlocal focusing nonlinearity is made to be gradually reshaped each other between Airy distribution and conventional standard Gaussian distribution. Meanwhile, we further disclose how initial chirp affects the periodic evolution of optical beam. It is found that we can change ballistic trajectory gradually from conventional parabolic to trigonometric shapes through increasing initial chirp; however the corresponding period is only determined by the degree of nonlocality but independent on the former. Moreover, another interesting property is that initial chirp will lead to a positive or negative transverse displacement of the resulting Gaussian distribution depending on the direction of input beam, but does not affect its shape and longitudinal location. On the other hand, for defocusing nonlinearity, CAB is found to exhibit the conventional nonperiodic self-accelerating behavior, which direction is decided by the initial chirp. Our analytical results agree with the existing results and can be confirmed by numerical prediction.

In this paper, we propose a new family of circular Airy beam (CAB) through introducing a cone angle. We investigate the autofocusing properties of such conical circular Airy beam (CCAB) both analytically and numerically, particularly focusing on the novel behaviors different from the case of the conventional CAB. Under the action of positive cone angles, the autofocusing effect of CCAB is greatly strengthened, and the focal length is remarkably reduced, as compared to the case of conventional CAB. On the other hand, the autofocusing effect may be weakened or even completely eliminated, and the focal length is largely extended under the action of negative cone angles. Therefore, such dramatic enhancement or suppression of abruptly focus can be effectively controlled through adjusting the cone angle. The novel autofocusing properties will make CCAB more powerful in various applied fields including optical trapping and particle manipulation.

In this paper, we first derive a modified two-dimensional non-linear Schrodinger equation including high-order diffraction (HOD) suitable for the propagation of optical beam near the low-diffraction regime in Kerr non-linear media with spatial dispersion. Then, we apply our derived physical model to a designed two-dimensional configuration filled with alternate layers of a left-handed material (LHM) and a right-handed media by employing the mean-field theory. It is found that the periodic structure including LHM may experience diminished, cancelled, and even reversed diffraction behaviours through engineering the relative thickness between both media. In particular, the variational method analytically predicts that close to the zero-diffraction regime, such periodic structure can support stable diffraction-management solitons whose beamwidth and peak amplitude evolve periodically with the help of HOD effect. Numerical simulation based on the split-step Fourier method confirms the analytical results.

In this paper, we investigate the behavior of modulation instability(MI) induced by nonlinear diffraction (NLD) resulting from the vectoral effect in metamaterials with simultaneous Kerr-type electric and magnetic nonlinearity, trying to unfold some novel properties different from those in conventional positive-index media(CM). First, NLD in metamaterials differs from CM mainly in that its value is able to be positive or negative, which provides greater flexibility for us to control the dynamical behavior of MI. Then, we further show that NLD exerts strong influence upon the MI scenario for both defocusing and focusing nonlinear cases, depending on its magnitude and sign. Moreover, we demonstrate NLD can make MI possible even in metamaterials with focusing nonlinearity of negative diffraction case. Finally, we observe NLD under certain limits can open up a new modulation window with an infinite modulation frequency range unseen in conventional MI scenario. Our results denote that NLD in metamaterials can provide us a more powerful strategy to engineer the behavior of MI, as compared with the counterpart in CM.

In this paper, we propose a new kind of circular Airy beam whose spectrum is imposed an initial quadratic phase modulation (QPM). Unlike common abruptly autofocusing beams, we find that such modulated circular Airy beams (MCAB) at image plane, i.e., initial plane, may be morphed into conventional Airy patterns or Bessel-like patterns in spatial regime, depending on the magnitude of QPM. We further investigate the propagation characteristics of the MCAB both analytically and numerically. It is found that the focal intensity, as well as the size of focal spot, do not change with the QPM, but the latter greatly affects the focal trajectory and the focal position of MCAB. In particular, we show that, for the case of Airy pattern, MCAB will exhibit a dual abruptly focusing behaviors having the same focal intensity as well as size of focal spot, where there is one focus behind the image plane, and the another one is in front of it. On the other hand, for the case of Bessel-like pattern, the dual abruptly foci are simultaneously observed behind the image plane for positive QPM but in front of it for negative QPM, thus leading to the formation of an elegant optical bottle with paraboloidal shape. Such novel dual focusing behaviors are expected to be applied in the field of optical trapping and particle acceleration.

In this paper, we apply the conventional method of linear stability to investigate the dynamical behaviors of spatiotemporal instability in a periodic structure consisting of negative-index materials and positive-index materials. It is found that the high-order diffraction (HOD) originating from spatial dispersion in such physical setting not only leads to the appearance of new instability regimes, but also may exert significant influence on the original instability, depending on the combined signs of both diffraction and dispersion. In the conventional positive diffraction regime, the most notable property is that HOD shrinks the regime of the original instability for the normal dispersion case through suppressing the higher-frequency components growth while it leads to the appearance of new instability regimes in addition to deforming the original instability for the anomalous dispersion case. However, in the negative diffraction regime, HOD may lead to the occurrence of spatiotemporal instability even for the normal dispersion case while it mainly shrinks the regimes of the original instability for the anomalous dispersion case.

In this article, we put forward a novel strategy to realize the management of wave collapse through designing probe–pump configuration where probe wave is assumed to propagate in the positive-index region of metamaterials (MMs), while pump wave is assumed to propagate in the negative-index region. We disclose that cross-phase modulation (XPM) in MMs as a new physical mechanism that can be used to arrest the collapse of probe wave in the positive-index region by copropagating it together with pump wave in the negative-index region. Further, we observe that pump wave will evolve into a ring while probe wave will develop a side lob in the wings during the course of coupled waves propagation, different from the corresponding counterpart in the ordinary positive-index materials (OMs) where they simultaneously exhibit the catastrophic self-focusing behavior. Meanwhile, we also discuss how to control the collapse of probe wave by adjusting intensity-detuned pump wave. Our analysis is performed by directly numeri...

In this paper, we investigate the dynamical behaviors of the modulation instability (MI) of copropagating optical beams in fractional coupled nonlinear Schrodinger equations (NLSE) with the aim of ...

In this paper, we propose a scheme consisting of alternating layers of a slab of a negative-index material and a slab of positive-index material. By employing the mean-field theory, we show that the sign of standard diffraction can be made either positive or negative, or even zero, in this layered structure. Subsequently, we demonstrate that close to the zero-diffraction regime, the high-order diffraction (HOD) strongly affects the dynamical behavior of the transverse instability, just like the corresponding high-order dispersion in optical fibers. Specifically speaking, HOD not only deforms the original instability regions in the positive-diffraction regime with focusing nonlinearity, but also may lead to the appearance of new instability regions even in the negative-diffraction regime with focusing nonlinearity or in the zero-diffraction regime. Meanwhile, we also disclose some novel features of the transverse instability for defocusing Kerr nonlinearity as well as non-Kerr nonlinearity. Our findings denote that the temporal modulation instability induced by high-order dispersion in optical fibers can find its transverse instability counterpart resulting from HOD in such a diffraction-management structure.

The additional dispersive magnetic permeability in metamaterials (MMs) described by the Drude model is able to generate the anomalous self-steepening (SS) effect which can be positive, negative even zero. This provides more great flexibility for us to control ultrashort pulse propagation, when compared with the corresponding case in naturally positive-index materials (PIMs). In this paper, we theoretically investigate the self-accelerating control of Airy pulse through such anomalous SS effect in MMs with a cubic nonlinearity. The emphasis is given to the counterintuitive dynamical behavior different from those in PIMs. It is shown that positive SS in MMs acts to promote the self-acceleration of such pulse and the corresponding spectral features exhibits a broad redshifted behaviors, as it does in PIMs; while the negative SS gives rise to the appearance of the opposite situation. That is to say, the self-acceleration of Airy pulse will be delayed through broadening the spectrum toward blue side. Meanwhile, the effect of the specific truncation coefficient imposed on Airy pulses in MMs also be discussed under the roles of positive and negative SS, respectively. Our findings show that the SS effect in MMs can provide a more powerful tool in controlling the self-accelerating of Airy pulse when compared with the corresponding case in PIMs.

We present a numerical study of the propagation dynamics of accelerating and decelerating truncated Airy pulses (TAPs) in the anomalous dispersion region of optical fibres, with inclusion of the Raman scattering effects, by analysing their cross-correlation frequency resolved optical gating traces. We identify the differences between the evolution dynamics of a decelerating and accelerating TAP. It is shown that the main lobe of the pulse is capable of shedding solitons, which are delayed due to the Raman effects. For the decelerating pulse, however, the soliton is dragged from the original pulse and never meets the input oscillatory Airy tail due to the deceleration of both the pulse and the soliton. The rest of the decelerating pulse rebuilds a new Airy waveform with a stronger degree of truncation compared with that of the incident pulse. For the accelerating TAP, the soliton collides continuously with the tail of the pulse and thus gains further energy by means of their nonlinear interaction. As a consequence, the remaining pulse cannot develop a new Airy waveform. In addition, under the same conditions, the Raman-induced frequency shift of the accelerating TAP is much larger compared with that of the decelerating one.