Analytical calculation of beam profile and orbital angular momentum spectrum of Laguerre Gaussian beams reflected from a graphene plasmonic structure.

Abstract

In this paper, Laguerre Gaussian (LG) beams with different topological charges are used for excitation of surface plasmon polaritons (SPPs) through a graphene layer inserted in the Otto-configuration. By utilizing the angular spectrum representation (ASR) and Lorenz-gauge vector potential, an explicit analytical expression is derived for the electromagnetic fields of the reflected beam. At the optimal excitation state of graphene SPPs, the reflected beam exhibits a distinctive field profile characterized by two identical crescent-shaped lobes separated by a vertical strip with null intensity. Furthermore, in the absence of external magnetic field, the orbital angular momentum (OAM) spectrum of the reflected beam at the optimal excitation of SPPs reveals the annihilation of central OAM mode and the generation of two equal OAM sidebands, regardless of the incident OAM topological charge. Furthermore, the phase distributions of electric field of the reflected beam confirm the existence of OAM sidebands in the vicinity of optimal SPPs excitation. As the system is taken away from the optimal excitation of SPPs by introduction of an external magnetic field or increasing the chemical potential or increasing the incident angle, both central and sideband modes appear in the OAM spectrum of the reflected beam. In this case, when the topological charge of the incident wave increases, the weight of central OAM mode decreases while the weight of sidebands increases. In contrast, in the presence of external magnetic field, at the optimal excitation of SPPs, both central OAM and sidebands modes exist in the reflected beam such that the weight of central modes increases with the external magnetic field. This effect is also confirmed by plotting the phase distributions of the reflected beam at different external magnetic fields and for different incident topological charges. Therefore, the manipulation of graphene plasmons characteristics leads to the control of OAM sideband generation.