Tunable Wide-Angle Tunneling in Graphene-Assisted Frustrated Total Internal Reflection

Abstract

Electrically tunable permittivity of graphene provides an excellent tool in photonic device design. Many previous works on graphene-based photonic devices relied on variable absorption in graphene, which is naturally small in the optical region, and resonant structures to enhance it. Here we proposed a novel scheme to control evanescent coupling strength by inserting two graphene layers to a frustrated total internal reflection (FTIR) configuration. The resulting structure behaves in a drastically different way from the original FTIR: optical transmission though the structure can be electrically controlled from ~10−5 to ~1 with little dependency on angle of incidence. This unique feature stems from the fact that the permittivity of doped graphene can be close to zero at a certain photon energy. The electrical controllability of evanescent coupling strength can enable novel design of optical devices. As a proof-of-concept, we designed a waveguide-type optical modulator of a novel operation principle: transmission modulation depends on the electrically controlled existence of a guided-mode of the waveguide, not the variation of the ohmic loss of graphene, resulting in a low insertion loss and a small device footprint.

Low-loss Electrically Controllable Vertical Directional Couplers

“…At the ENZ frequency for EF = 0.90 eV (red dash-dot horizontal line), the dispersion curves of the third-order (even; red) and second-order (odd; green) supermodes coincide at the same wave number, implying that those supermodes have the same effective index. This is because there is almost no coupling between waveguides at the ENZ frequency [11]. The first-order (even) supermode, associated with the ENZ mode [16] has an extremely large effective index, owing to strong field confinement in the graphene layers, such that it almost does not interfere with the other two modes.…”

“…The performance of the GA-FTIR degrades slightly, since the optical-isolation effect of ENZ graphene is somewhat lowered at a chemical potential of 0.54 eV (corresponding to the ENZ of graphene at 1.55 μm). However, this effect can be compensated by increasing the number of graphene layers, as previously discussed [11], so our proposed devices can also operate at the optical communication wavelength, without considerable performance degradation.…”

“…Our previous work [11] showed that the operation of the GA-FTIR scheme at the telecommunication wavelength of 1.55 μm is possible by changing the chemical potential of graphene correspondingly. The performance of the GA-FTIR degrades slightly, since the optical-isolation effect of ENZ graphene is somewhat lowered at a chemical potential of 0.54 eV (corresponding to the ENZ of graphene at 1.55 μm).…”

“…It was shown that the optical behavior of the GA-FTIR structure could be tuned drastically, from close to optical insulation (zero coupling) at the ENZ frequency, to near-perfect tunneling (perfect coupling) at a frequency slightly below than the ENZ point [11]. (The ENZ frequency is defined as the frequency at which the magnitude of the complex permittivity of graphene becomes minimal, which varies as a function of the chemical potential of graphene, EF [11].) Thus, if such a GA-FTIR configuration were applied to two coupled waveguides, it is expected that very different supermodes would form for the zero-and perfect-coupling regimes, enabling a very compact, electrically controllable directional coupler.…”

“…Recently, it has been numerically demonstrated that, by adding doped graphene layers to a frustrated total internal reflection (FTIR) structure, it is possible to directly control ISSN: 2508-7266(Print) / ISSN: 2508-7274(Online) DOI: https://doi.org/10.3807/COPP.2017.1.1.065 the evanescent coupling strength between the media by electrically controlling the epsilon of graphene in an epsilonnear-zero (ENZ) regime; this was dubbed a grapheneassisted (GA) FTIR structure [11]. It was shown that the optical behavior of the GA-FTIR structure could be tuned drastically, from close to optical insulation (zero coupling) at the ENZ frequency, to near-perfect tunneling (perfect coupling) at a frequency slightly below than the ENZ point [11].…”