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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 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 put forward a novel method for the management of optical collapse through controlling anomalous nonlinear diffraction (NLD) originating from the vectoral effect in metamaterials with simultaneous cubic electric and magnetic nonlinearity, particularly focusing on the unusual behaviors different from those in ordinary positive-index materials. First, NLD in metamaterials can be positive or negative, which makes it possible for us to offer greatly enhanced design freedom to manipulate the behavior of optical collapse at will. Then, it is further demonstrated that the negative NLD can arrest the catastrophic self-focusing of optical wave; however, the positive NLD will lead to the acceleration of its occurrence, as opposed to the case in ordinary positive-index materials. Our analysis is performed by directly numerically solving the nonlinear Schrödinger equation, as well as by using the modulation theory, both showing consistent results. These findings show that NLD in metamaterials can provide a more powerful tool in controlling the collapse of optical wave when compared with the corresponding case in ordinary positive-index materials.

Spatiotemporal instability (STI) in metamaterials (MMs) with a Kerr-type nonlinear polarization is investigated. A general expression for instability gain, taking account of the effects of arbitrary high-order linear and nonlinear dispersions, is derived. Special attention is paid to the general features of instability induced by nonlinear dispersion effects originating from the combination of dispersive magnetic permeability and nonlinear polarization. It is shown that, just like their linear counterparts, all even-order nonlinear dispersions not only deform the original instability regions, but also may lead to the appearance of new instability regions. However, all odd-order nonlinear dispersions always suppress STI irrespective of their signs, quite different from their linear counterparts which exert no influence on instability. Moreover, we find that, unlike the linear dispersions, the nonlinear dispersions lead to the dependence of gain peak on the spatial modulation frequency. The role of the firs...

We report on the generation of superbroad spectrum bunched noise-like pulses from a passively mode-locked erbium-doped fiber laser, in which the cavity is made of purely anomalous dispersion fibers. The maximum 3 dB spectral bandwidth of the pulse is about 98 nm. We show numerically that the superbroad spectrum of the pulse is caused by the fiber birefringence.

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.

In this paper, we in detail investigate the dynamic behavior of pulse splitting in metamaterials (MMs) with a Kerr nonlinear polarization, focusing on the anomalous propagation properties associating with the unique and engineerable electromagnetic properties of such materials. The numerical results show that, the pulse symmetric splitting in MMs will occur for the case of defocusing nonlinearity with anomalous dispersion due to the negative refractive index; while it will appear for the case of focusing nonlinearity with normal dispersion in ordinary materials. Moreover, our further analysis shows that, like the case in ordinary materials, the inclusion of self-steepening (SS) effect with positive value gives rise to the asymmetry between the leading and trailing pulses, but the relative magnitudes of the two peaks are reversed, namely, the leading pulse is higher than the trailing pulse. However, the negative SS does opposition.

We investigate modulation instability (MI) in a nonlinear oppositely directed coupler with a quadratic nonlinearity, where one channel is made from a positive-index material (PIM) and another channel is fabricated from a negative-index material (NIM), trying to identify the different MI properties from those in a conventional parametric gap system with grating. Both the analytic continuous wave (CW) solutions and dispersion relation are obtained. By using standard linear instability we in detail discuss how the ratio of the backward to forward propagating wave’s power, the phase mismatch, and the coupled coefficient influence the dynamical behavior of MI. Large stable regions are found if the fundamental harmonics (FH) falls in the normal dispersion when compared to the case in the conventional Bragg grating with a quadratic nonlinearity where the CW solutions are unstable in most cases. In addition, we also observe the large stable regimes of the CW solutions even when the coupled strength for the second harmonics (SHs) is weaker than that of the FH. These findings suggest that the oppositely directed coupler with a NIM channel provides more ways to manipulate the MI and soliton.

The dynamic propagation of the finite-energy Airy pulse (FEAP) is studied numerically in the presence of higher-order effects, including Raman scattering, self-steepening (SS), and third-order dispersion (TOD). It is shown that the Raman-induced frequency shift (RIFS) of a FEAP can be tailored by varying the truncation coefficient of the FEAP. In particular, the combined effects of Raman scattering and SS (or TOD) on the nonlinear propagation of a FEAP are identified. It is found that both TOD and SS effects tend to slow down the RIFS during the nonlinear propagation of a FEAP. In addition, the simultaneous contributions of Raman, TOD, and SS effects to the nonlinear propagation of FEAP are further discussed. Compared to the conventional symmetric pulses, such as Sech pulses, the FEAP can generate a broadening spectrum that is extended toward the blue side, in addition to the conventional red-shifted components. These results demonstrate that the FEAP can be used for supercontinuum generation and broadband sources.