Three-dimensional Extremely Short Optical Pulses in Graphene with Inhomogeneities

Authors N.N. Konobeeva , M.B. Belonenko

Volgograd State University, 400062 Volgograd, Russia

Issue Volume 11, Year 2019, Number 3
Dates Received 20 March 2019; revised manuscript received 20 June 2019; published online 25 June 2019
Citation N.N. Konobeeva, M.B. Belonenko, J. Nano- Electron. Phys. 11 No 3, 03026 (2019)
PACS Number(s) 42.65.Re, 78.67.Ch
Keywords Ultrashort pulse, Graphene (21) , Inhomogenity, Charge density.

We consider the Maxwell`s equations for an electromagnetic field, which propagates in impurity graphene with taking into account the spatial inhomogeneity. By heterogeneity, we mean the presence of a region of increased electron density. A particularly important case is inhomogeneity due to areas of increased concentration of conduction electrons due to the presence of impurities. According to this fact, it seems appropriate to investigate the impact of such inhomogeneity on the pulse propagation in impurity graphene. Due to the diversity of impurities and the nature of their interaction with the graphene subsystem, different approaches are possible in such problems. One of these approaches is to consider the scattering of ballistic electrons in graphene by impurities. Impurities are considered responsible for the occurrence of a disorder and a weak localization. In this case, they go beyond the limits of the self-consistent Born`s approximation and the renormalization-group approach is applied. In this paper, the electronic spectrum for the graphene subsystem is taken from the approach of the renormalization group, widely used in quantum field theory, when the transition from areas with lower energy to areas with more energy is caused by a change in the scale of consideration of the system. The main idea is that the Fermi velocity is renormalized, which begins to depend on the electron energy in a logarithmic way. Within the framework of the semi-classical approach, an effective equation for the vector-potential of the electromagnetic field is obtained and solved numerically. It is observed that three-dimensional extremely short optical pulses propagate unstablely with disturbed pulse shape. In this case, the introduction of a spatial inhomogeneity of the charge density into the medium makes it possible to reduce the pulse loss in the amplitude. The influence of the spatial parameters of the inhomogeneity on the propagation pattern of an extremely short optical pulse is also studied. It is shown that the depth and the width of the spatial inhomogeneity of the charge density do not have a significant impact on the pulse shape.