Enhancing Graphene Plasmonic Device Performance via its Dielectric Environment

Amun Jarzembski, Michael Goldflam, Aleem Siddiqui, Isaac Ruiz, and Thomas E. Beechem

Phys. Rev. Applied 14, 034044 – Published 16 September 2020

Abstract

Graphene plasmons provide a compelling avenue toward chip-scale dynamic tuning of infrared light. Dynamic tunability emerges through controlled alterations in the optical properties of the system defining graphene’s plasmonic dispersion. Typically, electrostatic induced alterations of the carrier concentration in graphene working in conjunction with mobility have been considered the primary factors dictating plasmonic tunability. We find here that the surrounding dielectric environment also plays a primary role, dictating not just the energy of the graphene plasmon but so too the magnitude of its tuning and spectral width. To arrive at this conclusion, poles in the imaginary component of the reflection coefficient are used to efficiently survey the effect of the surrounding dielectric on the tuning of the graphene plasmon. By investigating several common polar materials, optical phonons (i.e., the Reststrahlen band) of the dielectric substrate are shown to appreciably affect not only the plasmon’s spectral location but its tunability, and its resonance shape as well. In particular, tunability is maximized when the resonances are spectrally distant from the Reststrahlen band, whereas sharp resonances (i.e., high- $Q$ ) are achievable at the band’s edge. These observations both underscore the necessity of viewing the dielectric environment in aggregate when considering the plasmonic response derived from two-dimensional materials and provide heuristics to design dynamically tunable graphene-based infrared devices.

Received 14 April 2020
Revised 6 July 2020
Accepted 30 July 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.034044

Physics Subject Headings (PhySH)

Dielectric properties Integrated optics Nanophotonics Optical phonons Optoelectronics Plasmonics

2-dimensional systems Graphene

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Amun Jarzembski ^1,*, Michael Goldflam¹, Aleem Siddiqui¹, Isaac Ruiz¹, and Thomas E. Beechem^1,2,†

¹Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
²Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

^*ajarzem@sandia.gov
^†tebeech@sandia.gov

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 14, Iss. 3 — September 2020

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The optical response of a graphene metasurface obtained by full-field EM simulations and analytic calculations. (a) The three-dimensional (3D) and 2D schematics of a patterned nanoribbon graphene metasurface, $W = 33.5 nm$ and $Λ = 100 nm$ , with topside air and variable substrate below, used in the full-field simulations. (b) The total simulation absorptance spectrum of the patterned graphene metasurface (top) suspended in air and (bottom) resting on a ${Si O}_{2}$ substrate, where the graphene Fermi level, $ε_{f}$ , is varied between 0.2 and 0.8 eV. (c) The fast Fourier transform (FFT) of the resonant $E$ -field magnitude, $| E |$ , along the graphene interface (line trace shown in the inset) illustrating the dominant plasmon-wavelength, $λ_{p}$ , component at $Λ$ . (d) The 3D and 2D schematics of a graphene sheet with topside air and variable substrate below, used in analytic calculation of the p-polarized (TM) reflection coefficient, $r_{p}$ . (e) $Im [r_{p}]$ spectra at $λ_{p} = 100 nm$ for graphene (top) suspended in air and (bottom) resting on a ${Si O}_{2}$ substrate, where $ε_{f}$ is tuned between 0.2 and 0.8 eV. The resonant plasmon (f) wave number, $ω_{p}$ , and (g) $Q$ factor, $Q = ω_{p} / γ$ , for suspended graphene, obtained from the poles of $Im [r_{p}]$ , full-field simulations, and Eq. (1). The graphene thickness in (a) and (d) is not to scale.
Reuse & Permissions
Figure 2
The effect of the substrate’s RB on the graphene plasmon dispersion. (a) The dispersion relation extracted from the poles in $Im [r_{p}]$ given a ${Si O}_{2}$ substrate, where $ε_{f}$ is tuned between 0.2 and 0.8 eV. Here, the presence of the RB centered at $ω_{RB,avg}$ splits the graphene plasmonic dispersion into two branches, upper and lower. The tuning range versus $ω_{RB,avg}$ of the (b) upper and (c) lower modes for common dielectric substrate materials given $λ_{p} = 500 nm$ . An expanded version of (c) is provided in the Supplemental Material [19] for improved visibility of the material names. The spectral locations of the upper (blue) and lower (green) graphene plasmon modes with respect to the RB (red) for common dielectric substrate materials at $λ_{p}$ of (d) 500 nm and (e) 100 nm. The bottom and top extent of the green and blue columns indicates the plasmon energy when $ε_{f}$ is 0.2 and 0.8 eV, respectively. (f) The effect of $ω_{RB,avg}$ on the average spectral location of the graphene plasmon between $ε_{f} = 0.2$ eV and 0.8 eV, $ω_{p, avg}$ . The dashed lines and shaded regions in (b), (c), and (f) are aids for the eye.
Reuse & Permissions
Figure 3
The effect of the substrate’s RB on the graphene plasmon $Q$ factor (Q). The Q of the upper-mode plasmon resonances at $ε_{f} = 0.2$ and 0.8 eV for $λ_{p}$ of (a) 500 nm and (b) 100 nm. $Q$ rapidly increases with an increased RB energy for $λ_{p} = 500$ nm and at $ε_{f} = 0.2$ eV for $λ_{p} = 100$ nm, but is relatively constant for $λ_{p} = 100$ nm and $ε_{f} = 0.8$ eV. The materials denoted in gray text within (a) indicate resonances that tune into the RB (i.e., the low-loss assumption loses validity) and as a result they are not used in the $Q$ -factor analysis. The red dashed lines are guides to the eye. An expanded version is provided in the Supplemental Material [19] for improved visibility of the material names.
Reuse & Permissions
Figure 4
The trade-off between the tuning range ( $T_{R}$ ) and $Q$ . The variation of $Q_{avg}$ with the tuning range achieved by the substrate dielectric materials under consideration. The bars signify the variation of $Q$ for $ε_{f}$ between 0.2 and 0.8 eV, and the red dashed line is used to guide the eye.
Reuse & Permissions
Figure 5
The origin of the tuning-range ( $T_{R}$ ) and Q dependence on the gate dielectric. (a) The tuning range and (b) $Q_{avg}$ of the graphene plasmon upper mode as a function of the proximity to the RB quantified by $β$ [See Eq. (3)]. The dashed vertical lines indicate the overlap criteria. (c) The tuning range and (d) $Q$ of the graphene plasmon upper mode compared with the high-frequency permittivity, $ϵ_{\infty}$ . The bars in (b) and (d) signify the variation of $Q$ for $ε_{f}$ between 0.2 and 0.8 eV, and the red dashed line in (b) is used to guide the eye.
Reuse & Permissions

Physical Review Applied