High Quality Factor Silicon Membrane Metasurface for Intensity-Based Refractive Index Sensing

Abstract

We propose a new sensing device based on all-optical nano-objects placed in a suspended periodic array. We demonstrate that the intensity-based sensing mechanism can measure environment refractive index change of the order of $1.8\times {10}^{-6}$, which is close to record efficiencies in plasmonic devices.

1. Introduction

Optical sensing has become very important in applications ranging from chemistry to biology, since it is a noninvasive approach and can provide a very fast response time [1,2,3]. In particular, metallic nanoparticles (NPs) have been extensively used for optical sensing because of their localized surface plasmon resonance [4,5]. Indeed, the latter property offers a strong enhancement of the electric field in proximity of the NPs, magnifying the system sensitivity to the environment refractive index changes. Hence, the nature of the analyte placed in proximity of the metallic NP can be disclosed by analyzing the sensor optical response. Recently, a plethora of sensors based on plasmonic structures have been presented [4,6,7] and proved to selectively detect cadmium ions and bacteria when jointly operated with optical fibers [8,9,10]. Although plasmonic sensors can offer a very good performance in terms of sensitivity, analyte selectivity and versatility, they may be plagued by strong ohmic losses due to light absorption in the metallic parts. This fact could yield an important temperature increase in the system, ultimately triggering unwanted chemical reactions or altering the analytes, which may provoke serious consequences for inflammable detection of gases such as methane or propane. Keeping the sensor temperature under control, by avoiding Joule heating occurring in plasmonic devices, is also of paramount importance in biological applications since even temperatures below 80 ${}^{\circ }$C may cause permanent damages in in-vivo applications.

In order to contain the losses, a valuable alternative is the design of optical sensors based on dielectric materials [11]. Nanostructures made with dielectric materials with high refractive index support Mie-type resonances that provide localized field enhancement. This resonant behavior can be obtained in the spectral region where the optical absorption of the material is negligible. In this regard, optical sensing in the environment of all-dielectric nanostructures was reported in [12,13,14,15,16,17]. In particular, silicon nanoresonator-based biosensors with good sensitivity were devised. The latest results show that all-dielectric optical sensing—a relatively unexplored field up to now—is promising for the conception of new generation sensors.

In this context, we propose a new sensing device based on all-optical nano-objects arranged in a suspended periodic array similar to what was reported in [18]. In particular, we consider a metasurface made of two suspended sheets of nanocylinders (NCs) held together by crossed spokes and separated by a small air gap. The NCs are made of silicon, a material endowed with a high refractive index, a crucial feature for a strong electric field confinement, and characterized by well-established nanofabrication techniques. Unlike many of the proposed sensors in literature, our device is not based on the shift of the resonant wavelength but rather on the change of reflectivity at a single wavelength [19]. In the following, we show that a single wavelength approach leads to an improved sensitivity with respect to the refractive index in the surrounding environment. This approach is advantageous for applications since it does not require additional components such as the spectrometer and the broadband light source, which are necessary for a sensor based on the resonance spectral shift. The single wavelength approach and the possibility to suspend the sensor allows to immediately apply the metasurface as a cheap and compact pressure sensor in ultra high vacuum systems. Moreover, our sensor does not require a substrate and it can be placed anywhere.

2. Results and Discussion

The device studied here is represented in Figure 1 and is composed of two arrays of silicon NCs held together by thin spokes. We start our treatment considering simpler geometries, i.e., a metasurface of NCs suspended in air and one made by two NCs separated by a tiny gap. We show that introducing a gap is fundamental to improve the sensitivity. In order to achieve this goal, we perform finite element method simulations to engineer the device geometrical parameters and study their behavior when the refractive index of the surrounding medium changes.

2.1. Metasurface Design

In order to achieve spectrally narrow resonances, we exploit quasi-bound states in the continuum (quasi-BIC). These are obtained from geometrical perturbations of BICs that are resonant states localized within the continuum radiation of the spectrum, yielding zero energy decay [20]. They were first introduced in quantum mechanics in 1929 by von Neumann and Wigner [21] and are now attracting a lot of interest in many fields of physics [20,22,23,24]. BICs are characterized by zero-linewidth spectral features, which is connected with the impossibility to directly couple with the impinging radiation. However, BICs are only a mathematical idealization, and in practice, we deal with quasi-BIC, which are characterized by a high but finite quality factor (Q-factor). We engineer a quasi-BIC starting from the eigenmode of a single isolated NC shown in Figure 2a. The related far-field radiation pattern is reported in Figure 2b, where it is clear that there is no emission along the vertical z-axis direction. This is due to destructive interference between the electric field radiated by the top and the bottom of the NC. In an infinite periodic array, when the periodicity is smaller than the mode wavelength, all the radiation channels, except the 0th diffraction order, are closed [22]. Since the mode is not emitting along the normal direction, as the isolated NCs become closer, the mode of the isolated NC evolves in a symmetry-protected BIC. In Figure 2a, the NC radius and height are 250 and 563 nm. The geometrical parameters of the metasurface, and consequently the BIC wavelength, were chosen by performing a parametric sweep in the range of dimensions accessible with well-established fabrication techniques for the most common dielectric materials [25,26]. The eigenmode wavelength can be arbitrarily tuned by changing the height of the cylinder. The eigenmode calculation for a single array of NCs suspended in air and periodicity P = 850 nm confirms that the selected mode is a BIC since the frequency imaginary part is zero. However, as explained before, it is not possible to couple to such a mode from a beam propagating in free-space and exploit very narrow features in the spectrum. To this goal, we introduce a 15 nm gap in the middle of the isolated NC (see Figure 2c). The gap in the NC induces a small phase shift along the vertical direction across the cylinder and thus the mode has finite radiation in the vertical direction. This enables the mode of the NC array to radiate in the (0,0) diffraction mode, transforming the BIC in a quasi-BIC. Hence, the modified geometry is now made of two arrays of NCs, separated by a small gap of 15 nm. The radius of the NCs is kept fixed at 250 nm, and the height of each NC is 274 nm. As a consequence, the height of the nanostructure with two arrays equals the height of the nanostructure with one array discussed before. The refractive index in the gap equals the one of the environment. We note that the gap size can be tailored to adjust the Q-factor of the mode by increasing or decreasing the interference between the field radiated from the top and bottom NC, as shown in Figure 2d, since it decreases when the gap size increases.

The electric field distribution with fixed period is almost unchanged and yields a finite, but very small, imaginary part of the eigenfrequency (see Figure 2d). Hence, it is possible to couple with an incident plane wave. Furthermore, the presence of the small gap in between the NCs is fundamental not only to couple light to the quasi-BIC but also for the operation of our sensor, since in order to maximize the sensitivity, the analytes to be sensed must be placed in a region where field confinement is strong.

2.2. Sensing Mechanism

Once we have optimized the structure, we can analyze its sensing performance. The traditional sensing mechanism relies on the frequency shift of resonance as the environment refractive index varies. In this context, the sensitivity (S) is defined as [6,27]:

$$S=\frac{\Delta {\lambda }_{res}}{\Delta n_{env}},$$

(1)

where $\Delta {\lambda }_{res}$ is the shift of the resonant wavelength and $\Delta n_{env}$ is the perturbation of the refractive index of the environment. In Figure 3, we report the spectral response of the sensor with double NC arrays without spokes as $n_{env}$ changes, and we obtain a sensitivity of 170 nm/RIU. This value is much lower than in plasmonic structures and comparable with previous results obtained in dielectric platforms [19]. Although the response is linear in the range $1\le n\le 1.01$, the resonance shift is insufficient, resulting in limited sensitivity. However, in an intensity-based refractive index sensor, it is possible to exploit narrow resonances even if the wavelength shift is small. In analogy to [19], we define $S_I$ as:

$$S_I=\frac{dR}{d{n}_{env}},$$

(2)

where we employ the metasurface reflectivity R instead of the scattering intensity, the latter being typically used to characterize isolated antennas. The device works at a single wavelength, and the surrounding refractive index is changed. We report in Figure 4 the reflectivity as a function of $n_{env}$. For the case of a double NC array without spokes (black curve), the operating wavelength is 1382 nm, corresponding to the resonance for the nanostructure immersed in air. We highlight that the reflectivity halves for refractive index variations ∼1 $\times {10}^{-4}$ (black line). According to our definition, $S_I$ is 5548 per RIU. In contrast to the traditional sensing mechanism, the intensity-based sensor is linear for a smaller range of refractive index variation. In the region $3\times {10}^{-4}\le \Delta n_{env}\le 1\times {10}^{-3}$, the sensor response is not linear and the sensitivity reduces for larger refractive index perturbations. We note that highly sensitive sensors operating with the traditional mechanism have a similar linearity region with respect to refractive index variations [28].

Since we defined S in two different ways, depending on the sensing mechanism, in order to compare the two approaches and evaluate the sensor performance, we should consider the smallest appreciable variation of the refractive index that can be detected. High-end spectrometers can have resolutions of $0.1$ nm, and the reported record sensitivity for a wavelength-dependent sensor is ∼$(140\pm 6)\times {10}^3$ nm/RIU [28], which results in a minimum $\Delta n_{env}$ in the order of $8\times {10}^{-7}$. With the same sensing mechanism, our device can detect $\Delta n_{env}$ in the order of $6\times {10}^{-4}$. However, when the sensor operates in the intensity-based configuration, assuming a minimum measurable reflectivity variation of $0.01$, then the minimum detectable refractive index change by our device is $1.8\times {10}^{-6}$. It is worth noting that it is easier to experimentally detect reflectivity variations than wavelength shifts since this paradigm requires only a laser source and a photodiode.

2.3. Practical Structure Design

For the sake of simplicity, up to now, we have considered arrays of free-standing NCs. However, these configurations are not experimentally realizable. To overcome this limitation, one may introduce four spokes per disk to sustain the silicon cylinders in air and achieve a geometry that can be fabricated and realistically employed. Each spoke has a rectangular cross section, whose height equals the one of each NC, and the width is 20 nm. (see Figure 1). One may expect that the spokes are enough to introduce a defect in the single NCs array and thus allow to couple the external radiation to the metasurface. However, as can be seen in Figure 4, the sensing performance of the single NCs geometry with spokes (blue line) is very poor compared to the double disk geometry (black line), which is almost unaffected by the introduction of the spokes (red dashed line). This comparison provides direct evidence of the importance of the air gap in the sensing mechanism, which is fundamental to exploit the high electric field enhancement inside the high-index contrast structures.

3. Conclusions

In this work, we designed a dielectric metasurface composed of two arrays of NCs suspended by spokes and numerically investigated their sensing application. We compared two different ways of operating the device, which are based on the resonant wavelength shift and the change of the reflectivity at fixed wavelengths, respectively. We demonstrated that the intensity-based sensing mechanism can measure the environment refractive index changes of the order of $1.8\times {10}^{-6}$, which is close to record efficiencies in plasmonic devices ($8\times {10}^{-7}$). We also prove the importance of the air gap between the two slabs to open a radiation channel that allows to couple the incident plane wave to the sensor by judiciously reducing the Q-factor and by also allowing to place the analytes in a region characterized by strong field confinement. Both these factors are fundamental since the introduction of the spokes, which are inserted in order to complete the definition of a fabricable device, is not enough to provide sensible variations of the reflectivity when the refractive index is changed.

4. Materials and Methods

All the simulations were performed employing the commercial software Comsol Multiphysics. The isolated NCs were simulated, introducing a spherical domain surrounded by perfectly matched layers and an eigenmode solver with a fixed refractive index $n=3.49$ for silicon. The metasurfaces were simulated, imposing Floquet boundary conditions on the sides of the simulated domain and perfectly matched layers below and above the structure. We excited the nanostructures by using an impinging plane wave at normal incidence, and we changed the refractive index of the environment to investigate the sensing capabilities of the structure. The simulations of the incident linearly polarized plane wave take into account the dispersion of the silicon refractive index [29].