Temperature-dependent effect of modulation in graphene-supported metamaterials

Abstract

We report on a novel effect of temperature-dependent modulation in graphene-supported metamaterials. The effect was observed during the theoretical analysis of a model graphene-supported electro-optical modulator having silicon dioxide (SiO2) or hafnium dioxide (HfO2) as a buffer dielectric layer. Comparative analysis of the two materials showed that they provide approximately the same maximum values for transmission and reflection modulation depths. However, in the case of a HfO2 buffer layer, a lower chemical potential of the graphene is required to achieve the maximum value. Moreover, theoretical calculations revealed that a lower gate voltage (up to 6.4 times) is required to be applied in the case of a HfO2 layer to achieve the same graphene chemical potential. The graphene layer was found to possesses high absorption (due to the additional resonance excitation) for some values of chemical potential and this effect is extremely temperature dependent. The discovered modulation effect was demonstrated to further increase the transmission modulation depth for the simple model structure up to 2.7 times (from 18.4 to 50.1 %), while for the reflection modulation depth, this enhancement was equal to 2.2 times (from 24.4 to 52.8 %). The novel modulation effect could easily be adopted and applied over a wide range of metadevices which would serve as a quick booster for the development of related research areas.

Discussion of temperature-dependent epsilon-near-zero effect in graphene

“…In other words, the isotropic graphene model has been considered applicable without any concerns for such kind of devices. However, willing to reveal the real nature of the temperature-dependent modulation effect shown in [23], in the present work we highlight that with the reduction of graphene effective temperature, the ENZ effect in the near-IR wavelength range becomes essential even for such kind of structures and can greatly affect their performance. This temperature-dependent behaviour was interpreted analytically within the approximation when the real part of the graphene dielectric constant is considered vanishingly small compared to the imaginary part (this condition is always satisfied at the ENZ point in graphene).…”

“…The original design of the graphene-based modulator considered in [3,23] is shown in figure 1. A plane wave with the electric field polarization along x-or y-axis (i.e., lying in the plane of the graphene layer) propagating in the negative direction along z-axis excites the structure.…”

“…A plane wave with the electric field polarization along x-or y-axis (i.e., lying in the plane of the graphene layer) propagating in the negative direction along z-axis excites the structure. In [23] it was shown that under specific values of the graphene effective temperature T and chemical potential μ c , the propagating wave acquires an increased absorption which allowed to increase the modulation depth of the device up to three times. However, the real nature of the modulation was not revealed, and (in accordance with the obtained results) the effect was attributed to an additional resonance excitation in the graphene layer (e.g., a plasmonic one).…”

“…Using the original design (shown in figure 1), it is extremely difficult to interpret results obtained in [23] due to the fact that it contains two slot lines (orthogonal to each other) that form a cross-shaped structure, and this cross-shaped structure is excited by the plane wave simultaneously all over the structure's surface. At the same time, due to the symmetry of the considered geometry, one of the slot lines (which is extended along the plane wave polarization) cannot qualitatively affect the observed results.…”

“…Besides, the optical properties of graphene were also theoretically studied considering it as an isotropic material [17,18]. At the same time, despite controversial results and still ongoing dispute if the ENZ effect can exist in graphene in reality [10,[19][20][21][22], the controversial nature of the isotropic graphene model has never been considered as an issue for devices designed to be used without TM-modes as fundamental/guided modes (i.e., devices with guided modes which electric field components lie in the plane of graphene layer)-this is due to the fact that under this condition ENZ effect in graphene is considered as neglectable and has been never observed in such kind of devices in the near-IR wavelength range at room temperatures [3,23]. In other words, the isotropic graphene model has been considered applicable without any concerns for such kind of devices.…”