Coupling of plasmon modes in graphene microstructures

Abstract

A variety of different graphene plasmonic structures and devices have been proposed and demonstrated experimentally. Plasmon modes in graphene microstructures interact strongly via the depolarization fields. An accurate quantitative description of the coupling between plasmon modes is required for designing and understanding complex plasmonic devices. Drawing inspiration from microphotonics, we present a coupled-mode theory for graphene plasmonics in which the plasmon eigenmodes of a coupled system are expressed in terms of the plasmon eigenmodes of its uncoupled sub-systems. The coupled-mode theory enables accurate computation of the coupling between the plasmon modes and of the resulting dynamics. We compare theory with experiments performed on the plasmon modes in coupled arrays of graphene strips. In experiments, we tune the coupling by changing the spacing between the graphene strips in the array. Our results show that the coupling parameters obtained from the coupled-mode theory and the plasmon frequency changes resulting from this coupling agree very well with experiments. The work presented here provides a framework for designing and understanding coupled graphene plasmonic structures.Graphene, a single layer of carbon atoms arranged in honeycomb lattice, has emerged as an important material for plasmonics [1][2][3][4][5][6][7][8]. The high carrier mobility and the widely tunable conductivity in graphene together with the ability to fabricate graphene microstructures of different sizes implies that plasmons in graphene structures can have high quality factors and frequencies tunable from a few THz to more than 100 THz. Graphene plasmonic structures have the potential to form building blocks for novel THz/IR devices such as detectors, emitters, oscillators, switches, filters, and sensors. Several theoretical works have explored techniques to compute the modes in individual as well as in arrays of graphene plasmon resonators [9][10][11][12][13][14]. In order to realize the full potential of graphene plasmonics, and develop the ability to combine several graphene plasmonic resonators and engineer complex device structures, suitable techniques are needed model the interactions between plasmonic resonators in simple, yet effective and accurate, ways. In the field of microphotonics, the equivalent role is played by coupled-mode theories [15,16]. In coupled-mode theories, the field of a coupled system is expanded in terms of the fields of the eigenmodes of its uncoupled subsystems [15,16]. Accurate computation of the coupling parameters and the response of the coupled system without detailed first-principles electromagnetic simulations are few of the main benefits of coupled-mode theories. Coupled-mode theories have proven to be extremely effective tools in designing and understanding complex optical integrated structures [17]. In the field of graphene plasmonics, complex devices incorporating several coupled plasmonic resonators have been proposed and demonstrated for various applications [1,2,[18][19][20][21]...

Strong and Broadly Tunable Plasmon Resonances in Thick Films of Aligned Carbon Nanotubes

“…Thick-film-nanotube plasmon resonators are notably blueshifted from those in thin films 6 with the same L. This shift can be understood as a coupled antenna effect 30,31 , in which charges in a given nanotube are accelerated by the electric field deriving from plasmons in neighboring nanotubes. In one of our thickest films (t = 220 nm, L = 200 nm), the plasmon resonance frequency reaches 7000 cm -1 (Fig.…”

Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: An analytical approach

“…That foundational publication paved the way for the emergence of many experimental and theoretical works that soon followed, thereby establishing the field of graphene plasmonics [17][18][19][20][21][22][23][24]. As of today, GSPs have been realized in a number of systems, ranging from patterned grids of graphene ribbons [26,27,38,40,[48][49][50][51][52][53], disks [51,[54][55][56][57], and rings [54,55], periodic antidot lattices [57][58][59], resonators [60,61], and hybrid graphenemetal nanoantennas [43,44,[62][63][64], among others [65][66][67][68][69][70][71][72][73][74].…”

“…For extended graphene, these volumes can be about α 3 ≈ 10 −6 times smaller (where α denotes the fine-structure constant) than the volume characterized by the free-space light's wavelength (i.e., λ −3 0 ). Typical strategies to couple light to graphene plasmons involve the patterning of pristine graphene into gratings and related nanostructures [26,27,38,40,[48][49][50][51][51][52][53][54][55][56][57][57][58][59], the use of dielectric gratings [65,66], light scattering from a conductive tip [71][72][73][74], and even nonlinear three-wave mixing [69,70].…”

Photonic and Plasmonic Guided Modes in Graphene–Silicon Photonic Crystals

“…One of the challenges for surface plasmon polaritons excitation in graphene is the phase (optical 𝑘-vector) mismatch with the incident electromagnetic wave. Graphene nanostructures, such as one-dimensional (1D) nanoribbons array 11,12,20 or two-dimensional (2D) rectangular resonator array 21 , dots 7 and antidots lattices 22,23 and plasmonic crystals 24 are straightforward means for light coupling to graphene plasmons. However, plasmons excited in this way are limited by severe damping pathway due to the patterned edges with atomic scale roughness 11,25 .…”