Theoretical analysis of a graphene quantum well hybrid plasmonic waveguide to design an inter/intra-chip nano-antenna

Design and Analysis of a Polarization-Insensitive VO2/Graphene Optical Modulator Using a 3D Heat Transfer Method

“…where ε 0 is the permittivity of free space, Δ is the effective thickness of monolayer graphene that is 0.34 nm, ω is the angular frequency of light, and σ is the complex conductivity of graphene. The conductivity of graphene is obtained from the Kubo formalism 5,44,45 je j ( )…”

“…The electromagnetic response of a single graphene layer can be described by its dielectric constant ε g as , where ε 0 is the permittivity of free space, Δ is the effective thickness of monolayer graphene that is 0.34 nm, ω is the angular frequency of light, and σ is the complex conductivity of graphene. The conductivity of graphene is obtained from the Kubo formalism ,, where σ intra and σ inter are, respectively, the intraband and interband conductivities, ℏ is the reduced Plank constant, e is the electron charge, μ c is the chemical potential, and τ is the relaxation time that is taken as 0.5 ps. The chemical potentials of graphene at the on state ( V bias = 0) are assumed to be μ c 1 = μ c 2 = 0.55 eV, which ensure that the graphene sheets are transparent at an operating wavelength of 1550 nm.…”

Controllable hybrid plasmonic integrated circuit

“…These thicknesses are selected based on the technological challenges and limits to be compatible with the SOI technology in order to avoid complexity of fabrication process. Moreover, the Si substrate is a bulk material with the thickness on the order of hundreds of micrometers in PICs, which can be considered as an infinite layer in comparison to the desired wavelength of 1550 nm (193.5 THz) 16 . Consequently, the thickness of 800 nm is considered for the Si layer to reduce the computation time and memory requirements.…”

“…The ratio of the received power to the transmitted power can be calculated from the Friis equation 16 : where is transmitter/receiver impedance mismatch, is polarization mismatch, and d link is the distance between the transmitter and receiver antennas. Also, and are complex unit vectors describing the polarization of the incident wave and the direction of the vector effective length of receiving antenna, respectively 16 . Based on the reciprocity theory, the gains of transmitter and receiver antennas are considered equal .…”

“…The relative permittivity of graphene is given as 16 : where is the graphene conductivity described by the Kubo formula. The absorbed power by the graphene layer reaches maximum value when .…”