Role of the anomalous self-steepening effect in modulation instability in negative-index material

Abstract

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.

Waves in hyperbolic and double negative metamaterials including rogues and solitons

“…In the simulations presented later in this section the parameters that are considered are self-steepening and the use of a range of magnetooptic parameters that are used to adjust the effect of self-steepening in the metamaterial. It should be noted that the self-steepening coefficient S in equation (6.1) involves very specific properties of the metamaterials which has been pointed out by previous authors [12,122] however here the self-steepening term is that laid out in equation (2.21) of [120] which is arrived at via a different approach and the result is less restrictive than other approximations.…”

“…For example, it soon becomes apparent that the sign of the self-steepening [12] parameter can be changed through frequency management. This has a dramatic impact upon modulation instability (MI) and short pulse propagation [13][14][15][16].…”

Raman solitons in nanoscale optical waveguides, with metamaterials, having polynomial law non-linearity

“…This model equation has studied for five forms of nonlinear media by the aid of ansatz method (5,29), travelling wave hypothesis (33) as well as mapping methods (22) and collective variables approach (28). This paper will employ the travelling wave hypothesis to secure solutions to the model (1) that is with polynomial law non-linearity.…”

[INVITED] Soliton propagation through nanoscale waveguides in optical metamaterials

“…However it is always a challenge to compensate for the loss when engineering these types of waveguides using metamaterials. The theoretical results showed that metamaterials enhance nonlinearity by confining electrical field in a small region that allows more light-matter interaction [11,17,19,20]. In metamaterials, linear and nonlinear coefficients of the propagation equation can be tuned to achieve any combination of signs that is not possible in regular materials.…”