A periodic dielectric configuration having a lattice constant smaller than the wavelength of light can be considered a homogeneous anisotropic material in which the electromagnetic wave propagation is feasible [1]. This is the case of the so-called subwavelength gratings (SWGs), first described in [2–4] as an alternative type of silicon waveguides and later on extended to all kind of integrated photonic applications [5,6]. More recently, SWG structures have been reported in the literature for refractive index (RI) sensing [7], providing very high bulk and surface sensitivities due to a stronger light–matter interaction with the surrounding media than for conventional waveguides. As a consequence, several sensor configurations such as ring resonators have been redesigned using SWG structures [8–11], exhibiting a superior performance in terms of both the sensitivity and limit of detection. Moreover, SWG also offer additional dispersive properties [12] that can be exploited to develop, for instance, broadband directional couplers [13], beam splitters [14], polarization controllers, [15] and densely integrated waveguides [16]. Within this context, we proposed in a previous work the use of a bimodal SWG waveguide as a spectral-interrogation-based sensor [17], where high-sensitivity values were theoretically obtained as a result of the inherent dispersive behavior of SWG structures. On the other hand, similar single-channel interferometers in homogeneous structures have been extensively studied and validated for biosensing purposes [18–20]. In these cases, the sensing performance has been determined by measuring the phase shift, which scales directly with the sensor length, and with the main drawback that large dimensions are required to reach high sensitivities.

In this Letter, we experimentally demonstrate for the first time, to the best of our knowledge, the use of SWG bimodal waveguides as high-performance single-channel interferometric sensors. The underlying idea is to take advantage of the SWG dispersion properties to enhance the spectral shift of a certain interference dip in the spectra. As a result, we show an experimental bulk sensitivity of 2270 nm/RIU for a compact SWG bimodal device being only $\sim 125\mathrm{\mu m}$ long.

The sketch of the proposed configuration is depicted in Fig. 1(a), where a single transverse electromagnetic (TE) mode waveguide, acting as the input port, excites the first two TE modes of the bimodal SWG waveguide. Similarly, these two modes will contribute to the excitation of the fundamental mode of the output single-mode waveguide. At this point, the transferred power will depend on the phase shift between the propagating modes of the SWG structure, creating an interference pattern in the transmission spectrum. By tracking the position of a certain spectral dip in the spectrum, caused by a destructive interference between both modes, we can determine the sensitivity of the sensor under different bulk RI variations. In this kind of spectral-interrogation-based sensors, bulk sensitivity can be mathematically expressed as follows [17]:

 

Fig. 1. (a) Sketch of the proposed bimodal SWG sensor and its design parameters. (b) Dispersion diagram of even and odd modes with $w=1400\mathrm{nm}$, $h=220\mathrm{nm}$, ${\mathrm{\Lambda }}_1=260\mathrm{nm}$, and $w_i=160\mathrm{nm}$. (c) Phase shift “$\mathrm{\Delta }\phi =L*({\beta }_{\mathrm{even}}-{\beta }_{\mathrm{odd}})$” between the even and odd modes as a function of wavelength for ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ configurations, and $N=480$ elements. (d) Electric field energy density of the TE even and odd modes excited in the SWG bimodal region. They are depicted over a SEM image of the fabricated structure. (e) SEM image of the interface between the SWG bimodal waveguide and the single-mode access waveguide, showing an input–output displacement distance of $d=350\mathrm{nm}$.

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For the experimental demonstration, the sensor was accessed in and out with a single-mode waveguide of width $w_s=450\mathrm{nm}$. Due to symmetry conditions of the modes field distribution [see Fig. 1(d)], the access single-mode waveguides must be displaced a certain distance “$d$” with respect to the $x=0$ point to excite the odd parity mode in the SWG region [see Fig. 1(e)]. A displaced distance $d=350\mathrm{nm}$ was used for an optimal excitation of both SWG modes.

These designed SWG structures were fabricated on a silicon-on-insulator (SOI) wafer with an upper silicon layer thickness of 220 nm and a buried silica layer of 2 μm. Electron beam lithography, with an acceleration voltage of 30 KeV and an aperture size of 30 μm, was used in the exposure process on an HSQ negative resist, and inductively coupled plasma etching of the top silicon layer was employed to transfer the resist patterns into the SOI wafer. Scanning electron microscope (SEM) images of the fabricated SWG sensors are depicted in Figs. 1(d) and 1(e).

The optical characterization of the fabricated sensors was carried out using a coherent TE polarized light from a tunable laser (Keyshight 81980) vertically coupled into the chip using grating couplers. Light collected at the output is measured using an optical power meter (Keyshight 81636B) synchronized with the laser sweep. A LabVIEW application was programed to continuously save the spectrum data, and thus being able to perform time evolution experiments.

First results of the transmission spectra are shown in Fig. 2(a) for a SWG structure of $N=480$ elements, normalized with respect to a uniform reference waveguide in dB units. The sensor was covered with pure deionized water (DIW) and with a dilution of 6% ethanol (EtOH) volume in DIW, added gradually on the initial pure DIW dilution to obtain the desired concentrations. The dilutions were directly dropped onto the sample and measured afterwards. According to [22], the RI of these dilutions can be linearly approximated (in mass) for these working conditions ($\lambda =1550\mathrm{nm}$ at 25°C), obtaining a value of $n_{\mathrm{DIW}}=1.3173$ and $n_{\mathrm{EtOH}(6\%)}=1.3205$. The experimental data present a ripple, as a consequence of the Fabry–Perot resonances produced in the SWG discontinuities, that could have a negative effect on the limit of detection since the minimum of the spectral response could not be easily tracked in future biosensing experiments. For that reason, a Lorentzian fitting was applied to the raw data of each spectral dip to better follow the evolution of the minimum. As it was theoretically predicted in [17], the spectral dips are shifted toward lower wavelengths when the RI of the dilution increases [see Fig. 2(a)]. In addition, it can be seen how the absolute wavelength shift of the spectra for ${\mathrm{\Lambda }}_1=260\mathrm{nm}$ is higher than that obtained for the spectra of ${\mathrm{\Lambda }}_2=280\mathrm{nm}$. This is due to the lower phase shift slope as a function of wavelength obtained for the ${\mathrm{\Lambda }}_1$ configuration in comparison with the ${\mathrm{\Lambda }}_2$ configuration, and for our experimental wavelength range, as previously described. In addition, note that the spectral shift in both configurations is lower as we decrease the wavelength, which indicates a high dependence of the sensitivity with the dip spectral position.

 

Fig. 2. (a) Experimental normalized transmission spectra with respect to a reference waveguide, obtained for a bimodal SWG sensor of $N=480$ elements, ${\mathrm{\Lambda }}_1=260\mathrm{nm}$, and $w_i=160\mathrm{nm}$ (upper blue graph), and ${\mathrm{\Lambda }}_2=280\mathrm{nm}$, $w_i=180\mathrm{nm}$ (lower red graph). A Lorentzian fitting is also depicted over the spectral dips to ease the determination of the minimum location. (b) Experimental comparison between the numerical simulations and the absolute wavelength shifts of each spectral dip for a refractive index change of $3.2\times {10}^{-3}\mathrm{RIU}$ as a function of wavelength, and for the periods of ${\mathrm{\Lambda }}_1=260\mathrm{nm}$ and ${\mathrm{\Lambda }}_2=280\mathrm{nm}$. The lines show the numerical simulations for a continuous range of wavelengths, and the markers show the experimental values of each spectral dip located at a certain wavelength.

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Conversely, a greater number of spectral dips is experimentally observed in Fig. 2(a) for the configuration with ${\mathrm{\Lambda }}_2=280\mathrm{nm}$ compared to the other with ${\mathrm{\Lambda }}_1=260\mathrm{nm}$, in the same range of wavelengths. This is explained by the higher phase shift slope obtained for the ${\mathrm{\Lambda }}_2$ configuration that produces more destructive interferences than the ${\mathrm{\Lambda }}_1$ configuration in the same bandwidth. As a consequence, the spectral dips will be narrower for the ${\mathrm{\Lambda }}_2$ configuration and thus easier to track in future sensing experiments. More specifically, for the ${\mathrm{\Lambda }}_2=280\mathrm{nm}$ configuration, the full width at half maximum (FWHM) of the most sensitive spectral dip located at 1580 nm is twice that for the lowest dip at 1523 nm. Therefore, a trade-off between sensitivity and narrower spectral dips is observed, although the FWHM of the most sensitive dips could be reduced by increasing the number of elements N.

To compare the results with simulations, the dispersion relations of both SWG modes were computed under different cladding RI scenarios of pure DIW and 6% ethanol volume in DIW. The computed absolute wavelength shift of each spectral dip and the experimental results are depicted in Fig. 2(b) for both configurations, showing a good agreement between theory and measurements for a RI increment of $3.2\times {10}^{-3}\mathrm{RIU}$. Moreover, it should be noted again that in Fig. 2(b) the shift is strongly dependent on wavelength because of the nonlinear phase shift behavior of the SWG structure. This fact provokes higher sensitivities for those spectral dips located at higher wavelengths.

Likewise, several time evolution measurements were carried out by covering the SWG sensor with different ethanol dilutions. To this end, real-time spectrum data were collected for 35 min and subsequently processed to properly track the minimum of each spectral dip over time. Figure 3(a) shows the tracking of the spectral dip located at 1580 nm for ${\mathrm{\Lambda }}_1=260\mathrm{nm}$ and ${\mathrm{\Lambda }}_2=280\mathrm{nm}$ configurations. Ethanol dilutions of 2%, 4%, and 6% in DIW were considered for the experiments, corresponding to a RI of 1.3183, 1.3194, and 1.3205, respectively. The absolute wavelength shift versus RI variations is depicted in Fig. 3(b) for both configurations. In this graph, we obtain a bulk sensitivity of 2270 nm/RIU for the SWG configuration with ${\mathrm{\Lambda }}_1=260\mathrm{nm}$ and a value of 1253 nm/RIU for the SWG with ${\mathrm{\Lambda }}_2=280\mathrm{nm}$. These results are in good agreement with the numerically simulations previously calculated and consistent with the phase shift slopes presented in Fig. 1(c). Note that there is a period of time that the measurements take to stabilize, and this is due to the RI variations occurring when new ethanol dilutions are added.

 

Fig. 3. (a) Time evolution of the spectral dips located at 1580 nm with $N=480$ elements for ${\mathrm{\Lambda }}_1=260\mathrm{nm}$, $w_i=160\mathrm{nm}$ (blue curve) and ${\mathrm{\Lambda }}_2=280\mathrm{nm}$, $w_i=180\mathrm{nm}$ (red curve) under three different dilutions of 2%, 4%, and 6% of ethanol volume in DIW. (b) Representation of the absolute wavelength shift of the spectral dips under different RI variations. The linear fitting represents the bulk sensitivity experimentally obtained for both configurations.

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In comparison with the literature, SWG spectral-based sensors such as multi-box ring resonators [23] have shown an experimental bulk sensitivity of 580 nm/RIU, and other configurations like slot ring resonators [24] have been experimentally demonstrated for RI sensing with sensitivities up to 1300 nm/RIU, as well as slotted photonic crystal sensors [25] with a reported sensitivity of 1538 nm/RIU. On the other hand, similar bimodal interferometers [26] using homogeneous waveguides have been presented as spectral-based sensors with sensitivity values of 789 nm/RIU. Therefore, our proposed sensor presents a markedly higher bulk sensitivity than previous examples, while keeping a very low structural complexity, thus confirming the high potential of SWG bimodal waveguides as a promising alternative for sensing applications in CMOS-compatible integrated devices.

To investigate the dependence of the experimental sensitivity with the sensor length, the spectral shift of several dips with SWG configurations of $N=120$, $N=240$, $N=360$, and $N=480$ elements for a RI change of $5.39\times {10}^{-3}\mathrm{RIU}$ was also measured. The rest of the design parameters are the same used in the previous analysis ($w_s=450\mathrm{nm}$, $w=1400\mathrm{nm}$, $h=220\mathrm{nm}$, $d=350\mathrm{nm}$, ${\mathrm{\Lambda }}_2=280\mathrm{nm}$, and $w_i=180\mathrm{nm}$). Figure 4(a) depicts numerical simulations for the numerator and the denominator of Eq. (1), varying the number $N$ of SWG elements. In this graph, we can clearly see that the value of the numerator and denominator highly depends on $N$ and wavelength. However, when we apply Eq. (1) and divide both expressions, the theoretical sensitivity obtained remains constant for any value of $N$, although it still depends on wavelength. This theoretical sensitivity curve is shown in Fig. 4(b) as a function of wavelength. The colored bars represent the experimental sensitivity of each spectral dip obtained for different $N$ at a certain wavelength. All the measurements are in a good agreement with the simulations and remain on the line of Eq. (1). These results demonstrate that the bulk sensitivity, measuring the wavelength shift, does not depend on the sensor length, as it occurs in interferometric configurations when measuring the phase shift.

 

Fig. 4. (a) Color map representing the numerical derivative of the phase shift with respect to the cladding RI (upper graph) and wavelength (lower graph), for a different number of periods $N$ and wavelengths. (b) Comparison between the simulated sensitivity obtained using Eq. (1) (red curve) and the experimental results considering a different number of periods $N$ (colored bars). The SWG dimensions used for the simulation and experimental measurements are $w=1400\mathrm{nm}$, $h=220\mathrm{nm}$, $d=350\mathrm{nm}$, ${\mathrm{\Lambda }}_2=280\mathrm{nm}$, and $w_i=180\mathrm{nm}$.

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Despite this, as it has been explained before, the quality factor of the spectral dip increases with $N$ since it is more grouped in the spectrum, and narrower spectral features are obtained. As a result, longer SWG structures will facilitate the tracking of those dips and thus enhance the limit of detection of the sensor, although it will increase its footprint, which is not very suitable for integration purposes. Future optimized designs must be made to enhance the sensor limit of detection, and thus compare it to other existing devices in biosensing applications [27]. The obtained transmission spectra for a different $N$ were compared to the one recorded with a single-mode waveguide, with the aim of measuring the insertion losses of the sensor. A value around 1 dB was obtained for any number of elements $N$, which means that losses are mainly due to the coupling between the single-mode access waveguides and the bimodal SWG, and that propagation losses can be considered practically negligible, thus allowing the use of long bimodal SWG sections, if desired.

To conclude, in this Letter, we have demonstrated the use of bimodal SWG waveguides for RI sensing and studied their high-performance experimental features. The proposed mechanism relies on the dispersive behavior of SWG structures to critically enhance the wavelength shift of the spectral dips when varying the RI of the cladding. A complete comparison of experimental results and simulations is provided, as well as time evolution measurements to evaluate its bulk sensitivity. Values up to 2270 nm/RIU have been obtained for a SWG periodicity and element width of 260 nm and 160 nm, respectively. To the best of our knowledge, these experimental results are the highest reported in the literature for an integrated silicon RI sensor. Furthermore, its scalable properties allow us to design the sensor to work at the desired wavelength by simply changing the lattice period of the structure. Overall, its compact fully etched single-channel design and its outstanding sensitivity place it as a promising alternative for lab-on-a-chip devices in future work.