Pulse Propagation In Metamaterials Research Articles

Novel Optical Soliton Waves in Metamaterials with Parabolic Law of Nonlinearity via the IEFM and ISEM

Here, the miscellaneous soliton solutions of the generalized nonlinear Schrödinger equation are considered that describe the model of few-cycle pulse propagation in metamaterials with parabolic law of nonlinearity. The novel analytical wave solutions to the mentioned nonlinear equation in the sense of the nonlinear ordinary differential transform equation are obtained. The techniques are the improved exp − Γ ϖ function method and the improved simple equation method. The nonlinear ordinary transform to concern the generalized Schrodinger equation to convert it for a solvable integer-order differential equation is used. After the successful implementation of the presented methods, the exact solitary wave solutions in the form of trigonometric, rational, and hyperbolic functions are obtained. Hence, the presented methods are relatable and efficient to solve nonlinear problems in mathematical physics.

Impact of fractional effects on modulational instability and bright soliton in fractional optical metamaterials

In this paper, we have derived the fractional nonlinear Schrödinger equation modeling pulse propagation in metamaterials under nonlocal time evolution. We have investigated the influence of the fractional effects on both modulational instability (MI) gain and bright soliton. A negative group velocity (GV) is one of the necessary characteristic signatures of a left-handed material. The negativity of GV is observed for some fractional parameters α. MI occurs when the signs of first and second order dispersion are opposed. The results show that the fractional parameters can control the MI gain as well as the amplitude and the width of pulse.

Analysis of solitonic pulse propagation in metamaterials implemented in photonic crystals

ABSTRACT In this paper we present the analysis of soliton propagation in photonic crystal metamaterials. Current analysis considers the case of the complex refractive index for double negative (DNG) materials and for regular metamaterials. The analytical solution of the nonlinear Schrödinger (NLS) partial differential equation is realized through the traveling wave model. The analysis reveals the existence of soliton pulse propagation under specific constraint conditions necessary for the existence of the soliton solutions. The analytical solutions are validated by the results obtained through simulations. The analysis results give design guidance of waveguide structures able to support undistorted soliton wave propagation.

Miscellaneous new traveling waves in metamaterials by means of the new extended direct algebraic method

In this paper, we investigate miscellaneous new traveling wave solutions of the generalized nonlinear Schrödinger equation modeling few-cycle pulse propagation in metamaterials by the new extended direct algebraic method. As a result, we construct various hyperbolic and trigonometric functions solutions and for some appropriated parameters we obtain exact solutions including kink, antikink, breathers, dark and bright solitons.

Chirped dark solitons in optical metamaterials

The ultrashort pulse propagation in metamaterials that is governed by the generalized nonlinear Schrödinger equation with pseudoquintic nonlinearity and self-steepening effect is investigated. By adopting a nonlinear chirp anstaz, we obtain an elliptic differential equation with a fifth-degree nonlinear term describing the evolution of the wave amplitude in the metamaterial. We present a variety of exact chirped dark soliton solutions for the model in the presence of the self-steepening term. The obtained results show that the corresponding chirp is proportional to the field intensity and depends on the self-steepening parameter. Parametric conditions on the metamaterial parameters for the existence of the dark structures as well as the nonlinear chirp associated with each of these optical pulses are also presented.

Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects

We have investigated modulation instability (MI) in metamaterials (MM) with both cubic and quintic nonlinearities, based on a model appropriate for pulse propagation in MM with cubic–quintic nonlinearities and higher order dispersive effects. We have included loss into account in our analysis and found that loss distorts the sidebands of the MI gain spectrum. We found that the combined effect of cubic–quintic nonlinearity increases the MI gain. The role of higher order nonlinear dispersive effects on MI has also been discussed.

Spatiotemporal electromagnetic soliton and spatial ring formation in nonlinear metamaterials

We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.

DARK SOLITON SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION FOR ULTRASHORT PULSE PROPAGATION IN METAMATERIALS

The nonlinear Schrödinger equation for ultrashort pulse propagation in metamaterials with a nonlinear polarization is solved by an extended tanh function expansion method, and the dark solitary wave solutions for various conditions are obtained. The role of the dispersive magnetic permeability, which manifests itself as self-steepening and higher order nonlinear dispersion terms in the nonlinear Schrödinger equation in dark solitary wave propagation, is identified. It is found that the negative self-steepening effect in metamaterials makes the solitary wave move to the leading side, opposite to that in ordinary materials, in which the self-steepening effect is always positive. Most importantly, due to the role of the second order nonlinear dispersion, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear group velocity dispersion, different from the conditions for dark soliton formation in ordinary materials.