Abstract
We investigate the supermodes in arbitrary layers of graphene sheets, which are collective guided modes formed by coupling of surface plasmon polaritons (SPPs) in each graphene sheet. In terms of the dispersion relation, we analyse the effective indexes and mode profiles of the supermodes. Numerical simulations reveal that the supermodes can be well approximated by linear superposition of SPPs in individual graphene sheets. Among all the possible supermodes, there is an interesting one possessing both lowest propagation loss and shortest mode wavelength. The loss of the supermode decreases as the number of layers increases and saturates at about 5 layers. The graphene multilayers may find potential applications in low-loss plasmonic waveguides and so constructed optical devices.
Highlights
Surface plasmon polaritons (SPPs) are electromagnetic waves guided at the interface of two materials with opposite signs of dielectric constants [1, 2]
We borrow the concept of supermode to characterize the collective surface plasmon polaritons (SPPs) mode in the graphene multilayer, which stems from the evanescent coupling of SPPs in individual graphene sheets
We assume the transverse magnetic (TM) polarized SPPs propagate along the z direction in each graphene sheet, the magnetic field in the region between the (n−1)th and (n + 1)th graphene sheets can be written as the superposition of waves in opposite directions: H
Summary
Surface plasmon polaritons (SPPs) are electromagnetic waves guided at the interface of two materials with opposite signs of dielectric constants [1, 2]. The strong field confinement makes it possible to manipulate the light at nanoscale below the diffraction limit. They could find applications in integrated optics, transformation optics, biosensing, and solar cells [3, 4]. While the intrinsic material loss at visible regime, to some degree, have hindered the practical applications of metal-based SPPs [12]. The properties of graphene-based SPPs can be tuned by doping or gating, making them a promising platform for plasmonic applications [12, 16]. We borrow the concept of supermode to characterize the collective SPP mode in the graphene multilayer, which stems from the evanescent coupling of SPPs in individual graphene sheets. The influence of the graphene numbers and other parameters are considered in detail
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