We investigate modulation instability (MI) in negative-index material (NIM) with a Kerr nonlinear polarization based on a derived (3+1)-dimensional nonlinear Schrödinger equation for ultrashort pulse propagation. By a standard linear stability analysis, we obtain the expression for instability gain, which unifies the temporal, spatial, and spatiotemporal MI. It is shown that negative refraction not only brings some new features to MI, but also makes MI possible in ordinary material in which it is otherwise impossible. For example, spatial MI can occur in the defocusing regime, while it only occurs in the focusing regime in ordinary material. Spatiotemporal MI can appear in NIM in the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in ordinary material in the same case. We believe that the difference between the MI in NIM and in ordinary material is due to the fact that negative refraction reverses the sign of the diffraction term, with the signs of dispersion and nonlinearity unchanged. The most notable property of MI in NIM is that it can be manipulated by engineering the self-steepening effect by choosing the size of split-ring resonator circuit elements. To sum up the MI in ordinary material and in NIM, MI may occur for all the combinations of dispersion and nonlinearity.

In negative-index materials (NIMs), the self-steepening (SS) effect is proven to be anomalous in two aspects: First, it can be either positive or negative, with the zero SS point determined by the size of split-ring resonator circuit elements. Second, the negative SS parameter can have a very large value compared to an ordinary positive-index material. We present a theoretical investigation on modulation instability (MI) to identify the role of the anomalous SS effect in NIM. We find that the first anomaly of SS doesn't influence MI, yet the controllable zero SS point can be used to manipulate MI, and thus manipulate the generation of solitons. The second anomaly, however, leads to significant changes in the MI condition and property, compared with the case of an ordinary positive-index material. Numerical simulations confirm the theoretical results and show that negative SS moves the center of generated pulse toward the leading side, and shifts a part of energy of the generated pulse toward the red side, opposite to the case of positive SS.

Topological insulators have been theoretically predicted as promising candidates for broadband photonics devices due to its large bulk band gap states in association with the spin-momentum-locked mass-less Dirac edge/surface states. Unlike the bulk counterpart, few-layer topological insulators possess some intrinsic optical advantages, such as low optical loss, low saturation intensity and high concentration of surface state. Herein, we use a solvothermal method to prepare few-layer Bi₂Te₃ flakes. By sandwiching few-layer Bi₂Te₃ flakes with polymethyl methacrylate (PMMA) polymer, a novel light modulation device had been successfully fabricated with high chemical and thermal stabilities as well as excellent mechanical durability, originating from the contribution of PMMA acting as buffer layers that counteract excessive mechanical bending within the fragile Bi₂Te₃ flakes. The incorporation of the as-fabricated PMMA-TI-PMMA as saturable absorber, which could bear long-term mechanical loadings, into the fiber laser cavity generated the stable dissipative soliton mode-locking with a 3-dB spectral bandwidth up to 51.62 nm and tunable wavelength range of 22 nm. Our work provides a new way of fabricating PMMA-TI-PMMA sandwiched composite structure as saturable absorber with promising applications for laser operation.

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