1. Introduction

Optical Metasurfaces (OMs), made of plasmonic nanostructures of sub-wavelength feature sizes, have shown enormous potential to detect extremely minute quantities (<1 nanomole) of analytes [1,2]. The plasmonic nanostructures confine light very strongly near their vicinity, resulting in electromagnetic hot- spots. These electromagnetic hot- spots are incredibly susceptible to any change in local refractive index— induced by minute quantities of analytical loading, thereby resulting in their optical detection [3]. Most biological macromolecules such as proteins, nucleotides, carbohydrates, enzymes form the building blocks of life. Such macromolecules exhibit molecular vibrations in the mid-infrared (MIR) regions. These vibrations are used as signatures/fingerprints to detect their presence [4,5]. Identification of the spectral signatures of these organic molecules is crucial in various applications, including disease theranostics, pandemic screening, and drug development [6–8]. By fabricating OMs with their electromagnetic hot- spot resonance coinciding with the molecular vibration (signatures) of biological macromolecules, it is possible to attain enhanced detection. Plasmonic OMs have been shown to confine the field down to molecular dimensions enabling molecular detection with high sensitivity [9,10]. Unfortunately, plasmonic OM biosensors suffer from high ohmic losses due to their constituent metal. The electromagnetic field confined in the hot-spots decays very rapidly at MIR. It is also insensitive towards detecting biological molecules such as proteins and hormones due to their lower molecular weight and low polarizability [11,12]. Recently discovered two-dimensional (2D) materials such as graphene offer a solution to this problem as it has a high surface-to-volume ratio and low ohmic losses, thereby increasing the sensitivity towards molecular detection at MIR [13,14]. Hybrid metasurfaces consisting of plasmonic metals in combination with highly tunable graphene have been used as biosensors where the shift in surface plasmon resonance (SPR) has been observed along with vibrational signatures [15,16]. Despite these promising results, surface plasmon polaritons (SPPs) suffer from ohmic losses in the mid-IR range, which deteriorates the surface wave’s quality factor and propagation length. However, one can circumvent these issues by adopting phonon polariton instead of plasmon polaritons. Phonon polaritons are the collective oscillations of the incident photons with the optical phonons (quanta of lattice vibrations) in polar dielectrics [17]. Strong phonon polaritons can be achieved in van der Waals crystals such as hexagonal boron nitride (hBN).

The hBN is a natural hyperbolic material that can be exfoliated to a few or even one atomic thick layer. Such atomic thick layer materials have boosted the nanophotonics field, including negative refraction, sub-diffraction imaging, and optical biosensing [18–20]. The phonon polaritons in hBN fall in mid-IR region, which shows hyperbolic response, therefore they are called hyperbolic phonon polaritons (HPhPs). The HPhPs are a superior alternative to plasmon polaritons, as they strongly confine within the material volume and thus exhibit low ohmic losses, propagates with large momentum, possess sub-diffraction confinement, and enhanced lifetime in comparison to plasmons [21–23]. These properties of HPhPs in hBN make it a strong candidate for optical biosensing of small-sized lower molecular weight organic molecules like proteins in MIR. Optical biosensors based on surface-enhanced infrared absorption (SEIRA) spectroscopy have the ability for ultrasensitive detection of samples (less than 50 nm thick), with the added advantage of being label-free and non-destructive in the MIR region, and thus can be used for point of care (POC) diagnostics [24,25]. Optical biosensors based on HPhPs using SEIRA have been developed recently, showing detection of vibrational fingerprints of the organic molecules due to strong field confinement and enhancement in these phononic nanostructures [26,27]. Though HPhPs based sensors showed an enhanced optical response, yet their practical implementation in and out-of-laboratory environment is greatly limited due to lack of tunability of their resonance response. Once OM is fabricated, it displays a fixed electromagnetic resonance response. To add tunability to the OM based sensors, we have selected graphene in combination with hBN to create van der Waals heterostructure-based optical metasurfaces (VOMs) for biosensing applications. By adding 2D materials (especially graphene) on top of OMs, it is possible to tune the overall SPR response of the whole system by electrostatic gating since its optical and electrical property is highly tunable [28]. It was also demonstrated that graphene plasmon resonances could be tuned over a broad frequency range from Terahertz (THz) to MIR by changing micro-ribbon width and in situ electrostatic doping [29–31]. The electromagnetic fields of graphene IR plasmons display highly spatial confinement, which will be suitable for strong light-matter interaction. When a graphene couples with hBN, a strong plasmon phonon coupling occurs, yielding manifold enhancement in the light-matter interaction at the nanoscale [32,33].

In this work, we propose a fully tunable OM based on hBN/graphene van der Waal’s heterostructure (VOM) for multimolecular sensing using SEIRA. The HPhPs are high momentum propagating electromagnetic waves, which are excited when momentum matching between the incident photon and the phonon polaritons satisfies [34]. In our case, we use silver grating nanostructure to excite HPhPs in hBN. A graphene layer is sandwiched between hBN and the silver grating, constituting hBN/graphene van der Waal’s heterostructure. This provides tunability and enhanced absorption to the proposed sensor. We have used finite element method (FEM) simulations for the calculation of absorption and electric field response of the device. Furthermore, we have shown the influence of the chemical potential of graphene on the absorption spectrum of the proposed structure. Finally, we have numerically demonstrated the multimolecular selective and quantitative sensing of the proposed VOMs using 4,4’-bis(N-carbazolyl)−1,1’-biphenyl (CBP) and nitrobenzene (Nb) [${C_6}{H_5}N{O_2}$], as two different analytes and targeted its different vibrational peaks for accurate detection.

2. Design and numerical simulations

The schematic of the proposed architecture is shown in Fig. 1. The proposed metasurface consists of hBN/Graphene van der Waals heterostructure on top of the silver grating. Our structure is periodic in x-direction and infinite in y-direction, light is incident along z-direction normal to x-y plane with TM polarization, i.e., electric field is in x-direction. The periodicity of the structure taken here after optimization is p = 4.2 µm, height of the trench h = 1.5 µm, width of the trench is w = 0.15 µm, height of the substrate is taken of same silver metal with thickness more than its skin depth, thickness of hBN slab d = 30 nm. When the momentum matching occurs between photons and HPhPs, the normally incident light generates high wavevector phonon polaritons in the volume of hBN as shown by the artistic wave in the schematic.

 

Fig. 1. Schematic of the hBN/Graphene van der Waals heterostructure on silver grating. Light is incident normally in z direction with its electric field in x direction as shown. Due to the momentum matching of incident photons with the HPhPs of hBN, the phonon polaritons are produced within the volume of hBN as shown by artistic waves.

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The hBN is a highly anisotropic material, where permittivity along two orthogonal crystal directions (in-plane and out-of-plane) is opposite in signs [35,36]. The phonon polariton modes in hBN exists in a frequency range for which light propagation is forbidden. These forbidden frequency ranges are called the Reststrahlen band (defined as the region between transverse and longitudinal optical phonon frequencies, ${\omega _{TO}}$ and ${\omega _{LO}}$ respectively), where the real part of the permittivity becomes negative [34]. It contains two kinds of hyperbolic responses, viz-Type I hyperbolicity in the lower Reststrahlen band (760–825 $c{m^{ - 1}}$) with Re (${\epsilon _{||}}$) <0, Re (${\epsilon _ \bot }$) >0 and Type II hyperbolicity in upper Reststrahlen band (1,360–1,610 $c{m^{ - 1}}$) with Re (${\epsilon _ \bot }$) <0, Re (${\epsilon _{||}}$) >0 where ${\epsilon _ \bot },\; {\epsilon _{||}}$ are in plane permittivity in x-y direction and out of plane permittivity in z direction respectively. We have modeled hBN analytically with anisotropic permittivity as given by Lorentz oscillator model [37].

 

Fig. 2. (a) hBN permittivity in both type I and type II hyperbolic region (b) Dispersion plot of hBN with varying thickness suspended in air.

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Graphene is modeled using a surface conductivity model for a 2D sheet resembling single-layer graphene, and its optical conductivity includes both interband and intraband transition. The surface conductivity of graphene ${\sigma _g}$ is related to radiation frequency $\omega $, chemical potential ${\mu _c}$ (Fermi level ${E_f}$), environmental temperature T and is given by [37]:

3. Simulation results and discussions

Magnetic polaritons (MP) in metal grating structures have been theoretically demonstrated to achieve near-perfect absorption on coupling with HPhPs in hBN [40,41]. In this work, we focus on type- II hyperbolicity where in-plane permittivity, i.e. Re (${\epsilon _x}$) = Re (${\epsilon _y}$) = Re (${\epsilon _ \bot }$) is negative and out of plane permittivity i.e Re (${\epsilon _z}$) = Re (${\epsilon _\textrm{||}}$) is positive. When light is normally incident upon structure consisting of hBN placed on a silver grating, the resonance of the silver grating strongly couples with the incident electromagnetic waves and gives rise to MPs in the narrow trench. Upon excitation, this MP induces a current loop in the trench, resulting in a high absorption peak near 7.3 µm, as shown in Fig. 3(a) (blue dashed line). Low absorption due to phonon resonance of 30 nm thick hBN suspended in air is shown near 7.2 µm in Fig. 3(a) (green dashed line) whose resonance wavelength coincides with the MP mode. The momentum of the incident EM wave is insufficient to launch HPhPs in hBN, but simply placing hBN on a silver grating structure provides sufficient in-plane momentum for the excitation of HPhP [42]. Electric field concentrated at the corners of metal grating possesses huge momentum, which is adequate to launch HPhPs in the two Reststrahlen bands of hBN. The HPhPs in hBN strongly couples with the MP of the grating and thus form hybrid plasmon phonon polaritons with dual-band near-perfect absorption peaks, as shown in Fig. 3(a) (red solid line). Two hybrid peaks are shifted from their initial positions as can be seen from Fig. 3(a) and possess entirely different normalized electric field distribution as shown in Fig. 3(b) & (c). The hybrid phonon peak occurs at 6.78 µm while the hybrid MP peak appears at 8.66 µm. The electric field is mainly absorbed in the hBN layer for the hybrid phonon peak lying in the upper Reststrahlen band as can be seen in Fig. 3(c). The electric field, uniquely propagates inside the hBN film in a zigzag pattern and gradually vanishes due to low losses of hBN, This zigzag pattern is due to the phonon polariton propagation angle $(\beta )$ inside the hBN, which is given [43] as:

 

Fig. 3. (a) Absorption peak of silver grating (dashed blue curve),30 nm hBN layer suspended in air (dashed green curve) and dual bands near perfect hybrid plasmon phonon polariton modes (solid red curve) with MP peak at 8.66 µm and hybrid phonon peak at 6.78 µm (b) & (c) Normalized electric field distribution near hybrid MP peak at at 8.66 µm and hybrid phonon peak at 6.78 µm respectively.

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The unique polariton propagation in low loss hBN allows for extended light-matter interaction as shown in Fig. 3(c) and thus high absorption, which can be used for optical sensing. For the hybrid MP peak lying outside the Reststrahlen band, the electric field is confined in the hBN layer at the corner of the grating, as shown in Fig. 3(b). The strong coupling between the HPhPs and MP can be understood by the LC circuit model [40], where L and C represent effective inductance and capacitance of hBN/Ag grating structure, and the resonance frequency is given by:

The hBN behaves like an inductor in the Reststrahlen band region, which is parallel to the grating inductance, resulting in reducing the effective inductance L making the hybrid phonon peak shift to higher frequencies. The resonant peak of the hybrid structure varies by varying periodicity p, the height of trench h, the width of trench w of the silver grating as shown in [40,41].

To demonstrate the sensing capabilities of the device, we consider a 50 nm thick film of the organic molecule 4,4’-bis(N-carbazolyl)−1,1’-biphenyl, known as CBP. This particular organic molecule CBP has three vibrational resonances at 6.65 µm, 6.77 µm, and 6.9 µm of very low intensity, as shown in the inset of Fig. 4. When the CBP analyte is bought in the vicinity of the hybrid structure (i.e., hBN on silver grating), the vibrational resonances of the analyte couple with the enhanced hybrid plasmon phonon polariton modes in the Reststrahlen band, yielding an improved fingerprint detection of the CBP molecule [44] as seen in Fig. 4.

 

Fig. 4. Detection of 50 nm of CBP analyte placed on hBN/silver grating structure, showing its three characteristic fingerprints marked by numbers at (1)6.65 µm, (2)6.77 µm and (3)6.9 µm. (Inset shows the native absorption spectrum of CBP)

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From the information of shift in the hybrid phonon resonance due to the presence of CBP and other simulation parameters, we have calculated the minimum number of analyte molecules ${N_a}$ that can be detected, using the equation [45,46]:

Further to enhance the capability in terms of tunability, we sandwich a graphene layer between hBN and silver grating. This creates a tunable van der Waals metasurface for optical biosensing in mid-IR range, as shown in the schematic Fig. 1. The absorption spectrum of the corresponding hybrid metasurface is shown in Fig. 5(a), with graphene having Fermi potential of 0.25 eV (solid blue curve) and without graphene (solid red curve). The plasmons in graphene affect both the dual-band absorption of hybrid phonon peak and hybrid MP peak. The hybrid phonon peak shows an increase in its absorption strength on varying Fermi potential ${E_f}$. On changing the Fermi potential of graphene, the carrier concentration increases which thereby enhances the conductivity ${\sigma _g}$ (see Eq. (3)) and hence increase in the imaginary part of the graphene permittivity ${\varepsilon _g}$. The permittivity of graphene can be expressed as:

 

Fig. 5. (a) Absorption spectra of the hBN/graphene van der Waals heterostructure with graphene ${E_f}$=0.25 eV (solid blue line) and without graphene (solid red line). Electric field plot at (b) hybrid phonon peak at 6.529 µm, (c) hybrid MP peak 8.124 µm. (d) Absorption spectra with varying ${E_f}$ between 0.1 eV- 0.5 eV.

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From Fig. 5(d), it is evident that the resonance peaks experience a blue shift as Fermi potential increases. We can understand this blueshift in the spectrum by ‘power law scaling’ which shows the dependence of graphene plasmon resonance (${\omega _p}$) on ${E_f}$ and its carrier concentration n, i.e., ${\omega _p}\; \; \alpha \; \; {|{{E_f}} |^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}} \right.}\!\lower0.7ex\hbox{$2$}}}}\; \; \; \alpha \; \; {n^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}} \right.}\!\lower0.7ex\hbox{$4$}}}}$ [29]. Therefore, the increase in Fermi potential causes the increase in the plasmon energy or plasmon resonance peak ${\omega _p}$, which induces the blue shift. Thus, we can achieve tunability in the device simply by varying ${E_f}$ between 0.1 eV- 0.5 eV, as shown in Fig. 5(d). The devices response can be scaled widely across the electromagnetic spectrum by changing its geometry and the fermi potential of graphene. However, the hybrid phonon resonance useful for biosensing of organic molecules can be tuned in the restsrahlen band of hBN which lies in the mid-IR region where most of the organic molecules show their vibrational fingerprint. The proposed van der Waals heterostructure offers a high wavevector of hybrid plasmon phonon polaritons in addition to the increased absorption and tunability. Additional dispersion provided by the metallic nature of graphene plasmons and silver substrate is responsible for this high wavevector. These advantages offered by the proposed structure can improve SEIRA-based detection of multiple molecular vibrational resonances in the mid-IR region.

The proposed VOM with near-perfect absorption, as shown in Fig. 5(d), can be tuned for enhanced detection of CBP analyte by overlapping the analytes resonance peak with the hybrid phonon resonance peak. In Fig. 6(a), we have shown enhanced detection of CBP analyte of different thickness for a Fermi potential of 0.1375 eV. The magnified view of the absorption spectra at the CBP vibrational peak of 6.65 µm is shown in the inset. Figure 6(b) depicts the absorption spectra of another important analyte, nitrobenzene (Nb), which has its vibrational peak at 6.56 µm. This clearly indicates the efficacy of the proposed structure towards multianalyte molecular sensing. In Fig. 6(b), various absorption spectra correspond to different nitrobenzene layer thickness when brought in the vicinity of the structure at a Fermi potential of 0.25 eV. The inset shows the magnified version of the absorption spectrum of nitrobenzene at the vibrational peak of 6.56 µm. The presence of graphene increases the wavevector, which squeezes the polaritons into a small volume of hBN, providing an extremely small λ_p of 65 nm for E_f = 0.1375 eV and 81 nm for E_f = 0.25 eV for CBP and Nitrobenzene analyte respectively. From Eq. (6), the minimum number of the detectable molecule is estimated ∼ 390 molecules for 50 nm CBP (E_f=0.1375 eV) and 1990 molecules for 50 nm nitrobenzene (E_f=0.25 eV). The sensitivity of the proposed device to detect minimum number of molecules is attributed to the small modal volume of hBN phonon polariton hotspots ($\frac{{{\lambda _p}^3}}{\pi }$), which decreases further by adding graphene. The device’s sensitivity is limited by its Q factor, which is reduced in this case due to metallic plasmons and also with the increasing fermi potential of graphene. The ${N_a}$ detected for nitrobenzene increases mainly due to the reduction in the quality factor of the phonon-like peak with the increasing E_f. Due to the strong plasmon phonon coupling, the proposed device can detect a thin layer of CBP and nitrobenzene analyte of up to 10 nm, as shown in Fig. 6(a) &(b). The number of vibrational resonances that can be accommodated depends on the Q factor of the resonance peak. For SEIRA based sensing we need a broad resonance of low Q factor so that all the vibrational peaks can be detected separately. As for high Q resonance the different closely spaced vibrational peaks can overlap with each other leading to ambiguity in their detection. However much lower Q factor would result in difficulty in the detection of analytes fingerprint, as the absorption intensity won’t be enhanced enough to get detected. The Q factor of the device can be manipulated easily as per the requirements since it depends on the geometry of the metal grating and hBN thickness (d) [40].

 

Fig. 6. Absorption spectrum of the VOM for various thickness of (a) CBP analyte at ${E_f}$=0.1375 eV and (b) Nitrobenzene (Nb) at ${E_f}$=0.25 eV. The inset shows the magnified view of the of spectra at vibrational peak of CBP and Nb at 6.65 µm and 6.56 µm respectively.

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The proposed sensor described here is made up of three sub-systems 1) The Silver Nanostructured grating 2) Graphene layer and 3) hBN layer. To create such a system, the silver nanostructure grating could be fabricated using a combination of Electron Beam Lithography (EBL) technique, followed by electron beam metal evaporation and metal lift-off. Description of a similar fabrication process is given in our previous work of Ref. [3]. The layers of Graphene and hBN could be created using conventional Chemical Vapor Deposition (CVD) techniques and could be put on top of one another (and the silver grating) as the method described in Ref. [29]. The overall characterization of such a device (with and without analyte) for experimental validation could be done using a standard microscope enabled Fourier Transform Infrared (FTIR) Spectrometer.

4. Conclusion

To conclude our work, we have designed a tunable VOM and theoretically demonstrated its applicability as an optical biosensor. The proposed device utilizes the strong and long interaction of hyperbolic phonon polaritons in hBN. Phonons with long propagation length and very high momentum interact with incident radiation over a longer propagation distance. Moreover, when these phonons are placed over the silver grating structure, their momentum is further enhanced. A substantial overlap of the spectral response with the vibrational resonance of the analyte yields an enhance absorption, making SEIRA-based detection of the analytes possible. Numerical simulations suggest that it is possible to detect 626 CBP molecules in a small modal volume. The presence of graphene in the proposed hBN-silver grating structure imparts electrical tunability and turns the device into a multimolecular sensing device. The device can detect multiple analytes i.e., CBP and nitrobenzene.

Other than the tunability feature, graphene also helps in enhancing spectral absorption with small modal volume. The proposed biosensor can thus detect molecules as low as 390 for CBP and 1990 for nitrobenzene. Future works would require nanofabrication and characterization of such devices for their practical application in real-life scenarios.