Modulation Instability In Metamaterials Research Articles

Tunable modulation instability in metamaterials with pseudo-quintic nonlinearity, self-steepening effect and delayed Raman response

Modulation instability (MI) in metamaterials induced by pseudo-quintic nonlinearity, self-steepening effect along with delayed Raman response (DRR) is investigated and expression for MI gain is presented by linear stability method. Compared to the previous results with saturable nonlinearity, it is found that the MI without DRR may occur in four primary cases with different threshold behaviors depending on the combination of dispersion and nonlinearity and the competition of pseudo-quintic nonlinearity and self-steepening effect. This implies that we may manipulate or tune the MI by adjusting the power and frequency of incident waves at will. In addition, we consider the influence of DRR on MI and find that the DRR leads to additional regions where it entirely governs the MI gain, besides the primary ones where the self-steepening and the pseudo-quintic nonlinearity dominate the MI gain. Moreover, the DRR makes MI happen in three new cases exhibiting monotonous growth with perturbation frequency, which means that it is possible to observe MI at arbitrary high frequency. Finally, we confirm the analytical results by numerical simulations. The obtained results may be useful for manipulating or tuning the MI in metamaterials and provide more ways to generate ultrashort pulses with ultrahigh repetition rate.

Modulation instability in metamaterials with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.

负折射介质中非线性色散效应对调制不稳定性的影响

负折射介质中非线性色散效应对调制不稳定性的影响

Modulation instability in metamaterials with saturable nonlinearity

We analyze modulation instability (MI) in metamaterials with saturable and focusing nonlinearity according to the propagation model, including the self-steepening (SS) parameter and the second-order nonlinear dispersion (SOND). A detailed discussion on the common role of saturable nonlinearity, SS, and SOND terms on the MI is presented. It is found that MI is irrespective of the sign of the SS parameter and dependent on the sign of SOND. Generally, SS and saturable nonlinearity suppress the MI generation, and SOND promotes the MI in the anomalous group-velocity dispersion (GVD) region. Moreover, linear stability analysis predicts that MI may occur in both the abnormal GVD and normal GVD regime, even at the zero-GVD point, which is to say that some interesting MI phenomena appear involving the additional excited SOND term induced by the dispersive magnetic permeability. In particular, the saturable nonlinearity changes the generation condition of MI seriously. Finally, the numerical simulation is performed to confirm the theoretical predictions.

Influence of dispersive magnetic permeability on modulation instability in metamaterials

The influence of dispersive magnetic permeability on propagation of untrashort pulses in metamaterials is mainly in that it leads to the appearance of the pseudo-χ(5), self-steepening (SS) and second-order nonlinear dispersion terms in the propagation equations. In this paper, the role of dispersive magnetic permeability in modulation instability (MI) in metamaterials is identified based on the Drude model. It is found that in the anomalous dispersion regime, the pseudo-χ(5) nonlinear parameter, which is always negative, increases the MI frequency and growth rate, which is opposite to that in ordinary positive-index materials; the SS tends to suppress MI regardless of its sign, while the second-order nonlinear dispersion effect tends to stimulate MI in the positive-index region and suppress MI in the negative-index region. In the normal dispersion regime, in which MI cannot occur in the ordinary materials, MI can occur due to the role of the second-order nonlinear dispersion, suggesting a new way of generating solitons or ultrashort pulse trains in the normal dispersion regime.

Influence of nonlinear dispersion on modulation instability of coherent and partially coherent ultrashort pulses in metamaterials

The combination of dispersive magnetic permeability with nonlinear polarization leads to a series of nonlinear dispersion terms in the propagation equations for ultrashort pulses in metamaterials. Here we present an investigation of modulation instability (MI) of both coherent and partially coherent ultrashort pulses in metamaterials to identify the role of nonlinear dispersion in pulse propagation. The Wigner–Moyal equation for partially coherent ultrashort pulses and the nonlinear dispersion relation for MI in metamaterials are derived. Combining the standard MI theory with the unique properties of the metamaterial, the influence of the controllable first-order nonlinear dispersion, namely self-steepening, and the second-order nonlinear dispersion on both coherent and partially coherent MI, in both negative-index and positive-index regions of the metamaterial for all physically possible cases is analyzed in detail. For the first time to our knowledge, we demonstrate that the role of the second-order nonlinear dispersion in MI is equivalent to that of group-velocity dispersion (GVD) to some extent, and thus due to the role of the second-order nonlinear dispersion, MI may appear in the otherwise impossible cases, such as in the normal GVD regime.