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Abstract
Optical metasurface based refractive index (RI) sensors find applications in chemical, environmental, biomedical, and food processing industries. The existing RI sensors based on metals suffer from the plasmonic loss in the optical regime; in contrast, those based on Fano-type resonances generated by dielectric materials are either polarization-sensitive or are based on complex geometrical structures prone to fabrication imperfections that can lead to severe performance degradation. Here, we demonstrate that careful engineering of resonance modes in dielectric metasurfaces based on simple symmetric meta-atoms can overcome these limitations. More specifically, we have designed low-loss high-performance RI sensors using all-dielectric metasurfaces composed of TiO2 based nanostructures of three different shapes (i.e., cylindrical, square and elliptical) operating at near-infrared (NIR) wavelengths, which are robust against the perturbations of geometric parameters. In terms of physics, this work reports sensor structures achieving sharp resonant dips of high Q-factor in the transmission spectra corresponding to multiple dielectric resonance modes (i.e., electric quadrupole, magnetic dipole, and electric dipole) with superior performance as compared to the state-of-the-art. Four absolute liquids (water, ethanol, pentanol, and carbon tetrachloride) with a refractive index ranging from 1.333 to 1.453 are used to numerically validate the performance, and a maximum sensitivity of 798 nm/RIU with FOM up to 732 has been achieved.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
A material is recognized by its refractive index which defines its response to electromagnetic (EM) waves. For that reason, the measurement of refractive index found its various industrial applications in the fields of biological sensing, quality control, environmental monitoring, chemical and food industry and many more. Many methods can be found in the literature for the measurement of refractive index such as photonic crystals [1], ring resonator sensor, and optical fiber system [2]. But since the advent of metamaterials, they have become a perfect candidate for refractive index (RI) sensing.
Metamaterials are artificially arranged arrays of small scatterers for desired manipulation of light [3–6]. For the last two decades, metamaterial based devices are finding numerous practical applications. Metasurfaces are two-dimensional arrays of metamaterials which have found wide range of applications in different fields; for example, directive and efficient antennas, EM absorbers, superlenses to enhance resolution capabilities in optical imaging, invisibility cloaks, and in RI sensors which are being used in the fields of agriculture, biomedical, food sciences and chemical industry [7–10]. In refractive index sensing applications, metamaterials are integrated in the form of compact sensors working on the principle of changing resonance dips by changing medium around the sensor thus altering resonance characteristics of the overall structure.
Sensitivity and figure of merit (FOM) are the two important yardsticks to analyze the performance of an RI sensor; Sensitivity is defined as change in resonance wavelength per refractive index unit, whereas FOM is defined as the ratio of sensitivity and FWHM (full width at half maximum). Initially, metallic nanostructures have been used for sensing applications due to their unique optical properties [11]. One such sensor was proposed by Kabashin et al. [12] using gold nanorods, with high sensitivity up to 32000nm/RIU, but due to wide FWHM (full width at half maximum), its FOM (figure of merit) was reduced to 330. Another RI sensor was proposed by Liu et al. [13], using gold nanodisks with sensitivity up to 400 nm/RIU and figure of merit 87. A comprehensive review of plasmonic sensors was provided by Tong et al. [14]. Cheng et al. [15] proposed a dual band plasmonic absorber for RI sensing applications with high sensitivity of 1518 nm/RIU but a low FOM of 16.54. Recently Wang et al. [16] reported a sensor based on gold nanodisks with a sensitivity of 853 nm/RIU, and FOM 76.6. Some other metal based RI sensors have also been reported in literature [17–21]. Due to ohmic losses in metal based RI sensors, all-dielectric metasurfaces are being considered preferable [22–24]. Hu et al. [25] proposed an all-dielectric polarization-insensitive metasurface for refractive index sensing with a maximum sensitivity of 306 nm/RIU, but due to high FWHM, it has a low FOM of 16.76. Recently, another polarization insensitive all-dielectric metasurface was proposed by Ollanik et al. [26] with sensitivity up to 323 nm/RIU and a small FOM of 5.4 only.
In order to have narrow dips and high FOM, sensors exhibiting Fano-resonance are used. Fano-resonance was originally observed in atomic physics [27], One of the principle highlights of the Fano-resonance is its asymmetric nature. The asymmetry starts from a nearby concurrence of resonant transmission and reflection and can be decreased to the communication of a discrete (localized) state with a continuum of transmitting modes [28]. A sensor based on periodical asymmetric paired bars exhibiting the Fano-resonance phenomenon was proposed by Zhang et al. [29], with a sensitivity of 370 nm/RIU and FOM of 2846. Another split-ring metasurface based sensor showing Fano-resonance was proposed by Liu et al. [30] with FOM of 56.5. However, Fano-resonant metasurfaces are mostly based on asymmetric nanostructures which means these kinds of sensor will be polarization-sensitive causing inconvenience during measurements. One such simulation based sensor having Fano-resonance and polarization-insensitive behavior was reported by Liu et al. [31] with a sensitivity of 186.96 nm/RIU and FOM up to 721. Moreover, structures with Fano-resonances are highly sensitive to geometrical changes and even a minor fabrication imperfection can change the performance of the device. So, there is a dire need to explore RI sensors based on such structures and materials which have low-loss, high sensitivity and Q-factor, and are least sensitive to the geometrical changes.
In this work, we present low-loss high-performance refractive index (RI) sensors using all-dielectric metasurfaces composed of TiO2 based nanostructures of three different shapes (i.e., cylindrical, square and elliptical nanodisks) operating at near-infrared (NIR) wavelengths. In terms of physics, the proposed sensor geometries can achieve sharp resonant dips in the transmission spectra corresponding to different resonance modes (i.e., electric quadrupole, magnetic dipole, and electric dipole) with superior performance as compared to the state-of-the-art. We demonstrate that all-dielectric metasurfaces based on simple symmetric meta-atoms can be used to design high-performance sensors, solving the problem of plasmonic loss in metallic metasurfaces, and of polarization sensitivity as well as complicated geometry in Fano-resonant metasurfaces. Each considered structure gives rise to three sharp dips with highest sensitivity and FOM of 798 nm/RIU and 732, respectively, which is higher as compared to previously reported polarization-insensitive dielectric RI sensors. Moreover, our proposed sensor is least sensitive to geometrical changes which can occur during fabrication process; thus, our proposed sensor designs are small, low-loss, easy-to-fabricate, and practical.
In section 2 of this paper detailed design of our proposed sensor is discussed. Section 3 focuses on the numerical results and performance analysis of proposed design. Finally, a conclusion of the presented work is given in section 4.
2. Design and simulations
Figure 1 shows the unit cells of the proposed RI sensors. The dielectric material used for these nanostructures is TiO2 with thickness t = 260 nm. The wavelength dependent refractive index of TiO2 film was taken from reported experimental data [32]. The substrate used is glass with n = 1.5. The periodicity of the unit cell for all structures in x and y direction is Px = Py = 800 nm. Figure 1(a) shows the geometrical parameters for cylindrical nanodisk with inner radius r = 161 nm and outer radius R = 235 nm. Square nanodisk with dimensions s = 260 nm, L = 400 nm and elliptical nanodisk with dimensions A = 250 nm, a = 200 nm, B = 155 nm, b = 100 nm are shown in Figs. 1(b) and 1(c), respectively. These are the optimized dimensions in order to excite same resonance modes for cylinder, square and elliptical nanodisks. Moreover, these designs are based on a physical theory that when there is a hole in the nanodisk a higher proportion of the electric field will interact with the surrounding medium, due to the conservation of normal displacement field [25]. This phenomenon accounts for the higher Q-factors and FOM of the RI sensor, by controlling the hole size we can control the Q-factor and FOM of the sensor.
Fig. 1. Schematics of unit cell of proposed RI sensors. (a) Cylindrical nanodisk. Perspective view (left). Top view (right) (b) Square nanodisk. Perspective view (left). Top view (right) (c) Elliptical nanodisk. Perspective view (left). Top view (right)
Full wave electromagnetic solver CST Microwave Studio is used for performing the numerical simulations [33]. Electromagnetic waves are impinged at normal incidence on periodic structure with periodic boundary conditions applied in x and y directions and open (add space) in z- direction.
3. Results and discussion
The transmittance spectra for each nanostructure (cylindrical, square and elliptical) evaluated with surrounding medium having refractive index n = 1.333 (water) is shown in Fig. 2. All of these structures are optimized in such a way to achieve three sharp resonance dips at nearly the same wavelength corresponding three different resonance modes i.e., Electric Quadrupole (EQ), Magnetic Dipole (MD), and Electric Dipole (ED) marked on each dip. Moreover, the high transmission efficiency is clearly depicting the low-loss nature of the proposed sensors.
Fig. 2. Transmittance spectra of sensors with y-polarized light normally incident on sensors, (insets showing the magnified views at resonance dips). The refractive index of the surrounding medium is 1.333(water). (a) Cylindrical nanodisk (b) Square nanodisk. (c) Elliptical nanodisk
For cylindrical RI sensor, the resonance dips occur at λ=908.9 nm, λ$\mathrm{\lambda }$. = 988.76 nm and λ=1090 nm as can be seen from the inset of Fig. 2(a). The FWHM for first, second and third resonance dips are 0.76, 0.9, and 3 respectively. For square RI sensor these resonances occur at λ=908.46nm with FWHM 0.87, λ=990.98nm with FWHM 1, and λ=1088.6nm with FWHM 3.4, which are very similar to the dips we discussed for cylindrical sensor. Similarly, the resonance wavelengths for elliptical sensor are λ=911.4nm, λ=994.5nm and λ=1099nm with FWHM 1.03, 1.9, and 3.9, respectively. The higher value of FWHM for elliptical sensor as compared to those of cylindrical and square is due to the lesser E-field distribution.
To gain further insight into the resonance phenomena we investigate the cross-sectional distribution of electric field for TM mode at each resonance dip. Figure 3 shows the electric field vectors in the xz-plane at y=0 for the three resonance dips of cylindrical nanodisk Figs. 3(a1)–3(a3)], square nanodisk [Figs. 3(b1)–3(b3)], and elliptical nanodisk [Figs. 3(c1)–3(c3)]. In cylindrical nonodisk, at resonance wavelength λ=908.9 nm we observe higher-order mode i.e., electric quadrupole (EQ). The higher-order modes usually exhibit sharper resonance peaks which are clearly depicted in Fig. 2 and have more zero field lines in the cross-sectional distribution of field lines as shown in Fig. 3(a1). At λ=988.76 nm, electric field lines make a vortex which infers a magnetic dipole (MD) behavior as shown in Fig. 3(a2). At the third resonance dip λ=1090 nm, the electric field lines are in parallel with x-axis thus confirming the electric dipole (ED) nature of this resonance as shown in Fig. 3(a3). By optimizing the geometries we are able to excite the similar resonance modes as that of cylindrical nanodisk for square and elliptical nanostructures. It can be seen from Figs. 3(b1) to 3(b3) and from Figs. 3(c1) to 3(c3) that EQ, MD, and ED are being formed at λ = 908.46 nm, λ = 990.98 nm and λ = 1088.6 nm for square nanodisk and at λ = 911.4 nm, λ = 994.5 nm and λ = 1099 nm for elliptical nanodisk, respectively. The magnitude for E-field distribution is higher for cylindrical nanodisk which means that there is higher E-field interaction for cylinderical whereas, for elliptical it is lowest among the three proposed design because of the smallest inner hole area.
Fig. 3. Cross-sectional distribution of Electric field in the xz-plane. (a1-a3) Cylindrical nanodisk (a1) Electric quadrupole at $\mathrm{\lambda }$=908.9 nm (a2) Magnetic dipole at $\mathrm{\lambda }$=988.76 nm (a3) Electric dipole at $\mathrm{\lambda }$=1090 nm, (b1-b3) Square nanodisk (b1) Electric quadrupole at $\mathrm{\lambda }$=908.46 nm (b2) Magnetic dipole at $\mathrm{\lambda }$=990.98 nm (b3) Electric dipole at $\mathrm{\lambda }$=1088.6 nm. (c1-c3) Elliptical nanodisk. (c1) Electric quadrupole at $\mathrm{\lambda }$=911.4 nm (c2) Magnetic dipole at $\mathrm{\lambda }$=994.5 nm (c3) Electric dipole at $\mathrm{\lambda }$=1099 nm. The solid arrow indicates the direction of E-field.
3.1 Sensitivity analysis
For the verification of RI sensing, we simulated our proposed sensors with different surrounding medium with refractive index varying from 1.333 to 1.453. The chosen material-under-test (MUT) are absolute solutions of water (n=1.333), ethanol (C2H5OH, n=1.357), pentanol (C5H11OH, n=1.401) and carbon tetrachloride (CCl4, n=1.453). These absolute liquids are chosen because of their high usage in bio-chemical sensing in medical industry. Figures 4(a)–4(c) shows the good variation in resonance wavelength when the RI in the surrounding medium changes. It can be seen that keeping the transmittance spectra with n=1.333 as a reference, there is a redshift in resonance dips as the refractive index of surrounding medium increases. Thus, larger the value of ‘n’ with respect to that of water (n=1.333), more significant will be the shift in resonance.
Fig. 4. (a-c)Transmittance spectrum with different surrounding media of index ‘n’ (a) Cylindrical nanodisk (b) Square nanodisk (c) Elliptical nanodisk, (d-f)Shifts of the resonance wavelengths as a function of the refractive index(n) (d) Cylindrical nanodisk (e)Square nanodisk (f)Elliptical nanodisk.
Moreover, we have observed the same trend for cylindrical, square and elliptical RI sensors. For cylindrical RI sensor, the maximum shift of 94.35 nm was observed in 3rd resonance dip for n=1.453, while the minimum shift of 53.45 nm in 2nd resonance dip for n=1.453, as shown in Fig. 4(a). Similarly, square RI sensor undergoes the maximum shift of 95.82 nm in 3rd resonance dip for n=1.453 and the minimum shift of 53.64 nm in 2nd resonance dip for n=1.453 as shown in Fig. 4(b) and elliptical RI sensor experiences a maximum shift of 94.8 nm in 3rd resonance dip for n=1.453 nm and a minimum shift of 52.53 nm in 2nd resonance dip for n=1.453 as shown in Fig. 4(c).
To analyze the performance of RI sensors, two important metrics are sensitivity and figure of merit (FOM). Sensitivity (S) is defined as a change in resonance wavelength per refractive index unit:
In order to further characterize our design’s performance, we calculated the FOM for all the three resonance dips. FWHM for three resonance dips, in the case of cylindrical RI sensor is 0.76, 0.9, and 3. So their corresponding FOM comes out to be 732, 495 and 262. Similarly, the values of FOM for square RI sensor are 646, 447, and 235 and for elliptical RI sensor, the calculated values of FOM are 540, 230, and 202. The lower values of FOM for square and elliptical RI sensor are because of the higher FWHM of resonance dips as compared to the cylindrical RI sensor. By tuning the hole size of elliptical metasurface FOM can be improved further compared to those of cylindrical or square, but that will shift the resonance wavelength. Table 1 shows a comparison between our proposed sensors to that of previously reported metasurface sensors.
Table 1. Comparison of the existing refractive index sensors and proposed sensors
3.2 Parametric analysis to predict the effect of fabrication imperfection
We have calculated the rate of change in resonance dips which is the first derivative of resonance wavelength with respect to geometrical parameters (such as thickness, periodicity of all proposed RI sensors and outer and inner radii of circular and ellipse nanodisks and side lengths of square nanodisks) and tells about the slope of line fitting curve. For our proposed sensors to be independent of fabrication imperfections, the slope of the line should be minimum which means the change in geometrical parameters will produce a very small or negligible change in resonance wavelength. The effect of structural parameters on the EQ, MD, and ED resonances in order to predict the influence of fabrication imperfections on the performance is shown in Fig. 5. The shifts in resonance wavelengths of cylinder RI sensor due to change in geometrical parameters is shown in Figs. 5(a1)–5(a4). In Fig. 5(a1) resonance dips as a function of the outer radius are plotted, it can be seen that electric quadrupole and dipole (EQ, ED) shows the least dependence on the outer radius, whereas magnetic dipole (MD) is more sensitive with slope of 1.25. Similarly, line fitting between inner radius and resonance dips is shown in Fig. 5(a2), resonance dips shift towards left by increasing inner radius, with maximum slope of −0.99 of MD. Figure 5(a3) shows linear approximations between thickness of cylindrical nanodisk and resonance wavelength, with maximum slope of 0.75 of MD. Similarly, in Fig. 5(a4) sensors dependence on periodicity Px and Py is shown in contrast to other parameters resonance dips are more sensitive to periodicity especially electric quadrupole and dipole (EQ, ED) depends on periodicity with slopes 0.8 and 1.35 respectively. Figures 5(b1)–5(b4) shows the shift in the resonance wavelengths by changing the geometrical parameters of square RI sensor. Figure 5(b1) demonstrates shifting in resonance wavelengths by changing outer length ‘L/2’ of square nanodisk, it can be noted that shift in magnetic dipole (MD) is more than that of electric quadrupole and electric dipole (EQ, ED) with maximum rate of change $\textrm{d}\mathrm{\lambda }/\textrm{dL}$ = 0.74 of MD. Similarly, Fig. 5(b2) shows resonance shifting by changing inner length ‘s/2’, which is also about half times the resonance shifts in cylindrical nanodisk for all resonance dips. Contrary to L, increase in inner length produces blueshift and vice versa with maximum rate of change ${\Delta }\mathrm{\lambda }/\Delta \textrm{s}$ = −0.45 of MD. In Fig. 5(b3) change in resonance wavelengths by changing thickness of the square nanodisk is shown which is slightly more than as shown by cylindrical nanodisk with maximum rate of change ${\Delta }\mathrm{\lambda }/\Delta \textrm{t}$ = 0.76 of MD. Figure 5(b4) shows ${\Delta }\mathrm{\lambda }/\Delta \textrm{P}$ which is same as that of cylindrical nanodisk with maximum ${\Delta }\mathrm{\lambda }/\Delta \textrm{P}$ = 1.39 shown by ED. Elliptical nanodisk is least sensitive to small changes in geometrical parameters as shown in Figs. 5(c1)–5(c4).
Fig. 5. Rate of change in resonance dips with respect to different geometrical parameters: (a1-a4) Cylindrical nanodisk. (b1-b4) Square nanodisk (c1-c4) Elliptical nano disk
Figure 5(c1) demonstrates shifting in resonance wavelengths by change in major axis of outer ellipse A, which is less than the shifting in resonance wavelength of a square nanodisk by change in outer length A. It can also be noted that shift in magnetic dipole (MD) is more than that of electric quadrupole and dipole (EQ, ED) with maximum rate of change ${\Delta }\mathrm{\lambda }/\Delta \textrm{A}$ = 0.36 of MD. Similarly, Fig. 5(c2) shows resonance shifting by changing major axis of elliptical hole B, which is also less than the resonance shifts in square nanodisk for all dips. Contrary to A, increase in elliptical hole produces left shift and vice versa with maximum rate of change
${\Delta }\mathrm{\lambda }/\Delta \textrm{B}$=−0.197 of MD. In Fig. 5(c3) change in resonance wavelengths by changing thickness of the nanodisk is shown which is slightly more than as shown by cylindrical and square nanodisks with maximum rate of change ${\Delta }\mathrm{\lambda }/\Delta \textrm{t}$=0.83 of MD. Figure 5(c4) shows ${\Delta }\mathrm{\lambda }/\Delta \textrm{P}$ which is almost same as square nanodisk with maximum slope of ${\Delta }\mathrm{\lambda }/\Delta \textrm{P}$=1.31 in ED. Table 2 shows the summary of our three proposed RI sensors. Thus, the performance of our proposed RI sensors is least dependent on structural parameters while maintaining high sensitivity and FOM as compared to other all-dielectric metasurface sensors.
Table 2. Comparison between all proposed structures.
3.3 Polarization and incidence angle dependence
Due to the fourfold symmetric nature of cylindrical, square along x and y axes, are polarization-insensitive, Therefore, whether square and cylindrical sensors are illuminated with x-polarized light or y-polarized light their performance will remain unaffected. Moreover, even if the incident light is circularly polarized, the transmittance will remain unchanged. Whereas due to lack of symmetric nature, elliptical nanostructures are polarization-sensitive. Figures 6(a)–6(c) shows the transmittance spectrum for y-polarized, x-polarized and RCP incident lights for the three proposed RI sensors. It can be seen that for different polarizations the transmittance of cylindrical and square sensors remains unaffected as shown in Figs. 6(a) and 6(b), whereas transmittance of elliptical nanodisks is different for y, x and RCP polarized lights as shown in Fig. 6(c). Figures 6(d)–6(f) demonstrates shift in resonance wavelengths by small variations in angle of incident. It can be seen electric dipole (ED) and electric quadrupole (EQ) shows a very small shift by increasing incident angle in all cases (cylindrical, square and ellipse) whereas magnetic dipole (MD) shows a variation of about 50 nm by a small change in incident angle (0°–5°) in all the three cases which means that MD resonance is highly dependent on incidence angle.
Fig. 6. (a-c) Transmittance spectra for input y-polarized, x-polarized and RCP. (a) Cylindrical nanodisk (b) Square nanodisk. (c) Elliptical nanodisk.. (d-f) Shift in resonance dips by changing incident angle. (d) Cylindrical nanodisk (e) Square nanodisk (f) Elliptical nanodisk.
4. Conclusion
We have demonstrated three all-dielectric metasurfaces based sensors for effective measurement of refractive index. The proposed sensors are made up of TiO2 nanostructures (cylinder, square and ellipse) on a glass substrate. The performance and feasibility of our device are presented theoretically by using four absolute liquids (water, ethanol, pentanol, and carbon tetrachloride) with refractive index ranging from 1.333 to 1.453. Each sensor gives three narrow highly sensitive resonance dips with sensitivity up to 798 nm/RIU, and high FOM up to 732. To the best of our knowledge, the performance of our design is superior as compared to reported polarization-insensitive all-dielectric metasurfaces in the literature. The minimum shift in resonance dips with respect to change in geometrical parameters is showing that our devices are least sensitive to fabrication error. Thus, the proposed metasurface sensors are polarization-insensitive, low-loss, easy to fabricate, more realizable and have potential applications in the fields of biochemistry, chemical industries, and agriculture sector.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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