Optical phase-modulated nonlinear waves in a graphene waveguide

The different mechanisms that bring about the creation of optical nonlinear waves in a waveguide containing a graphene monolayer (or graphene-like two-dimensional material) are studied in the general case when resonant and nonresonant nonlinearities are simultaneously included. The conditions for the formation of optical hybrid, nonresonant, and resonant phase-modulated breathers in graphene, for waveguide transverse electric modes, are presented. It is shown that the characteristic parameters of these optical nonlinear waves depends on the graphene Kerr-type third-order susceptibility, the graphene conductivity, the reciprocal of Beer's absorption length, and the initial values of the ensemble of the atomic system and/or the semiconductor quantum dots that are embedded in the transition layer. In the case of the amplifier (active atomic system) transition layer, the conditions for the existence of a dark (topological) breather and the conditions when a nonlinear wave cannot be formed are determined. An explicit analytical expression for the profile of an optical nonlinear wave is also presented.

Figure 1

The waveguide TE mode is traveling along the $z$ axis. The vector of the magnetic field, $\vec{H}$, of the waveguide TE mode lies in the $xz$ plane. The vector of the electric field of the pulse, $\vec{E}$, is parallel to the $y$ axis. The transition layer, of thickness $h\ll \lambda$, contains the two-level atoms or SQDs, where $\lambda$ is the optical wavelength of the waveguide TE mode. The graphene monolayer are sandwiched between infinite half-space $({\mathrm{medium}}_3$, located at $x>d+h)$ and waveguide $({\mathrm{medium}}_2$, located at $0<x<d)$, where $d$ is the thickness of the waveguide. Below ${\mathrm{medium}}_2$, at $x<0$, is a ${\mathrm{medium}}_1$.