Graphene based hyperbolic metamaterial for tunable mid-infrared biosensing

Abstract

Plasmonic biosensors, operating in the mid-infrared (mid-IR) region, are well-suited for highly specific and label-free optical biosensing. The principle of operation is based on detecting the shift in resonance wavelength caused by the interaction of biomolecules with the surrounding medium. However, metallic plasmonic biosensors suffer from poor signal transduction and high optical losses in the mid-IR range, leading to low sensitivity. Here, we introduce a hyperbolic metamaterial (HMM) biosensor, that exploits the strong, tunable, mid-IR localization of graphene plasmons, for detecting nanometric biomolecules with high sensitivity. The HMM stack consists of alternating graphene/Al₂O₃ multilayers, on top of a gold grating structure with rounded corners, to produce plasmonic hotspots and enhance sensing performance. Sensitivity and figure-of-merit (FOM) can be systematically tuned, by varying the structural parameters of the HMM stack and the doping levels (Fermi energy) in graphene. Finite-difference time-domain (FDTD) analysis demonstrates that the proposed biosensor can achieve sensitivities as high as 4052 nm RIU^-1 (refractive index unit) with a FOM of 11.44 RIU^-1. We anticipate that the reported graphene/Al₂O₃ HMM device will find potential application as a mid-IR, highly sensitive plasmonic biosensor, for tunable and label-free detection.

Fig. 1. (a) Schematic representation of the proposed HMM biosensor stack on top of a gold grating structure (b) graphene/Al₂O₃ HMM stack with N = 11 bilayers and a graphene layer on top (c) top and side view of a unit cell used in the simulation (d) real and imaginary parts of effective permittivity of graphene/Al₂O₃ HMM, with 11 bilayers, determined with effective medium theory. Hyperbolic dispersion occurs when λ > 3.58 μm. Here, p, g, d, and h denote the period, radius of the rounded corner, width, and height of the grating structure, respectively.

Fig. 2. Reflectance spectra of the grating coupled graphene/Al₂O₃ HMM structure for varying (a) angles of incidence θ, with g = 30 nm, N = 11 and p = 820 nm. Enlarged view shows blue shift of the resonance wavelength, with increasing θ for BBP5 (b) radius (g) of the rounded corners in the grating, with θ = 35°, N = 11, and p = 820 nm (c) number of graphene/Al₂O₃ bilayers (N), with θ = 35°, g = 30 nm, and p = 820 nm (d) grating period (p) with θ = 35°, g = 30 nm, and N = 11. In all cases, E_F = 0.64 eV.

Fig. 3. (a) Reflectance spectra of grating coupled graphene/Al₂O₃ HMM stack for different values of graphene Fermi energy E_F, showing all five BPP modes (b) real part of in-plane permittivity, ε_‖, with varying E_F. Here, θ = 35°, g = 30 nm, N = 11 and p = 820 nm.

Fig. 4. (a–e) Reflectance spectra of the graphene/Al₂O₃ HMM biosensor, detecting biomolecules with different RIs. (f–j) Corresponding linear fitting of resonant wavelength versus ambient RI. In all cases, E_F = 0.64 eV, θ = 35°, g = 30 nm, N = 11, and p = 820 nm.

Fig. 5. (a–e) Sensitivity of graphene/Al₂O₃ HMM biosensor for detecting biomolecules, represented by their respective RIs. The reference RI = 1.33 (water). In all cases, E_F = 0.64 eV, θ = 35°, g = 30 nm, N = 11, and p = 820 nm (f) sensitivity of graphene/Al₂O₃ HMM biosensor, for the BPP5 mode, at different E_F of graphene, when RI = 1.33.

Fig. 6. (a–e) FOM values of graphene/Al₂O₃ HMM biosensor for detecting biomolecules as represented by their respective RIs. In all cases, E_F = 0.64 eV, θ = 35°, g = 30 nm, N = 11, and p = 820 nm. The reference RI = 1.33 (water).

Fig. 7. The distribution of electric field intensity, for BPP4, with (a) background RI = 1.33 and (b) background RI = 1.41. In all cases, E_F = 0.64 eV, θ = 35°, g = 30 nm, N = 11, and p = 820 nm.