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Abstract
In this paper, a novel kind of sensors for simultaneous measurement of refractive index and temperature based on all-dielectric metasurfaces is proposed. The metasurfaces are constructed by an array of silicon nanoblocks on top of the bulk fused silica substrate. We used three-dimensional full wave electromagnetic field simulation by finite integral method to accurately calculate the transmission spectrum of the metasurfaces. Two transmission dips corresponding to the electric and magnetic resonances are observed. Both dips shift as the ambient refractive index or the temperature changes. Simulation results show that the sensing sensitivities of two dips to the refractive index are 243.44 nm/RIU and 159.43 nm/RIU, respectively, while the sensitivities to the temperature are 50.47 pm/°C and 75.20 pm/°C, respectively. After introducing four holes into each silicon nanoblock, the electromagnetic field overlap in the surrounding medium can be further promoted, and the sensitivities to the refractive index increase to 306.71 nm/RIU and 204.27 nm/RIU, respectively. Our proposed sensors have advantages of polarization insensitive, small size, and low loss, which offer them high potential applications in physical, biological and chemical sensing fields.
© 2017 Optical Society of America
1. Introduction
The measurement of refractive index (RI) and temperature are essential in various fields, such as chemical industry, biological sensing, environmental monitoring, food science, and so on. In most cases, the refractive index of the object under detection varies with the temperature. Therefore, simultaneous measurement of the temperature and the refractive index is important for many sensing applications.
Many methods have been used for simultaneous detection of the temperature and the refractive index, such as silica bottle resonator sensor [1], plasmonic waveguide system [2] and optical fiber sensors. A lot of fiber structures have been proposed, such as fiber Bragg gratings (FBGs) [3, 4], long period fiber gratings (LPFGs) [5], Fabry-Perot cavities in optical fiber micro-tips [6], kinds of Mach-Zehnder interferometer (MZI) like air cavity with taper structure [7], thinned fiber [8], peanut-shape structure [9], no-core fiber and FBG [10], and double cladding fibers [11], as listed in Table 1. Most of them possess the sensitivity to the RI of about 100 nm/RIU, and the sensitivity to the temperature of dozens of pm/°C.
Table 1. Comparison of the Existing dual-parameter sensors
Metasurface [12–16] is an artificial layered material with a thickness less than the wavelength, which have garnered particular attention due to their advantages of smaller physical footprint, simpler fabrication and lower losses compared to their bulk counterparts. Metasurfaces, served as a remarkably versatile platform for light manipulation, have realized applications ranging from polarization conversion [17], antireflection coating [18], sensing of minute analyte quantities [19], nonlinear optics [20], spectrally selective thermal emission [21], and so on. Someone also combine metamaterials with quantum gain [22]. Dielectric metasurfaces [23, 24] are new research hot topics because they replace lossy ohmic currents with low loss displacement current and have lower absorption loss compared with metal metasurfaces [25, 26].
In this paper, we explore the possibility of using ultrathin dielectric metasurface sensors for simultaneous detection of the refractive index and temperature. Although metasurface has been used for the detection of various substances, to the best of our knowledge, it has not been investigated for simultaneous measurement of at least two external parameters. Simulation results confirm our design and good sensitivities to both the RI and the temperature are achieved. The proposed metasurface sensors are small, easy to fabricate and have low loss.
2. Sensor principle and discussion
The schematic diagram of the proposed metasurface sensor is shown in Fig. 1(a). The structure is an array of silicon (n = 3.7 at 20 °C) nanoblocks on the bulk fused silica substrate (n = 1.48 at 20 °C), which is called metasurface sensor 1. Silicon is an earth-abundant material and its fabrication is compatible with standard CMOS process of semiconductor industry. An enlarged view of part of the metasurface is shown in the lower right corner of Fig. 1(a). The length a and the thickness t of the silicon nanoblocks are 0.6 μm and 0.22 μm, respectively. The period px and py in x and y directions are both 0.8 μm. We used three-dimensional full wave electromagnetic field simulation by finite integral method. Finite integral technique (FIT) provides a universal spatial discretization scheme, applicable to various electromagnetic problems. Unlike most numerical methods, FIT discretizes Maxwell’s equation in an integral form rather than the differential ones [27]. Periodic boundary conditions are both utilized in the x and y directions, while perfectly matched layers are used in the wave propagating direction z. The incident electromagnetic field with a wave vector of ki is assumed to be a plane wave, propagating along z axis, with electric and magnetic fields polarized along y and x axes, respectively, as shown in lower left corner of Fig. 1(a). After propagating through the ultrathin metasurface sensor, the transmission light with a wave vector of kt is then collected. The calculated transmission spectrum, as shown in Fig. 1(b), has a strong dependence on the incident wavelength and two resonant dips around 1.42 μm and 1.63 μm are observed. For the wavelengths off the resonances, most of the incident electromagnetic energy is transmitted, which confirms the low loss nature of this metasurface sensor. According to the Mie resonance theory [28, 29], each dielectric particle can be equivalent to a magnetic dipole near the dip 1 with shorter wavelength or a electric dipole around the dip 2 with longer wavelength. To further investigate the origin of these two dips, the cross-sectional distributions of the electric and magnetic fields in one unit cell are depicted in Figs. 1(c)–1(f). At the wavelength of 1.42 μm (dip 1), the electric field is vortex and the magnetic field is almost linearly parallel to the x axis, indicating a magnetic dipole behavior, as shown in Figs. 1(c) and 1(d). This mode is corresponding to the TE011 mode of the Mie resonance and working as the magnetic activity resulted from the enhancement of the displacement current inside each nanoblock, which gives rise to a macroscopic bulk magnetization of the composite [30]. While at the other resonant wavelength of 1.63 μm (dip 2), Figs. 1(e) and 1(f) show the linearly parallel electric field and the vortex-like magnetic field, corresponding to the electric dipole characteristic. These correspond to the TM011 mode of the Mie resonance and lead to electric dipole behavior at far field [30].
Fig. 1 (a) Schematic of the metasurface sensor 1. The incident light is a plane wave of transverse electric (TE) mode. (b) Transmission spectrum of the metasurface sensor 1 showing two dips for magnetic (λM ≈1.42 μm) and electric (λE ≈1.63 μm) resonances. (c) Electric field distributions at λM ≈1.42 μm in a unit cell in the y-z plane. (d) Magnetic field distributions at λM ≈1.42 μm in a unit cell in the x-z plane. (e) Electric field distributions at λE ≈1.63 μm in a unit cell in the y-z plane. (f) Magnetic field distributions at λE ≈1.63 μm in a unit cell in the x-z plane. The arrows indicate the direction of the electric and magnetic fields.
We also explore the effect of structural parameters on the locations of electrical resonance and magnetic resonance spectroscopy, respectively, and the results are shown in Fig. 2. In Fig. 2(a), we can see electric resonance shifts faster than magnetic resonance as the side length of the nanoblocks varies. Figure 2(b) shows the relationship between the resonant wavelengths of the electric and magnetic dipoles with the thickness of the nanoblocks. Figures 2(c) and 2(d) reveal the effect of the transverse and longitudinal period px and py on the resonant wavelengths, respectively. The former mainly affects the resonant wavelength of the electric dipole, while the latter mainly affects that of the magnetic dipole.
Fig. 2 The relationship between the resonant wavelength of the electric and magnetic dipoles with the structural parameters of (a) the side length a, (b) the thickness t, (c) the transverse period px, and (d) the longitudinal period py. The fitting equations are also shown in the figures.
To realize a dual-parameter sensor, these two well-separated resonant spectrum dips in Fig. 1 are utilized. Considering the response of the sensor to temperature is due to combination of following effects: the change of the RI and the geometrical parameters of sensor material, and the RI change of ambient media induced by the temperature. Then the shift of spectral dips caused by the changes of the ambient RI and temperature can be expressed as [11]:
where i refers to the dip 1 and dip 2 of transmission spectrum in Fig. 1(b). The first term in the left of Eq. (1) refers to the spectrum shift induced by independent variation of the RI of ambient medium, and the second term refers to the spectrum shift induced by the ambient media thermo-optic effect, dn/dT is the thermo-optic coefficient, the third term refers to the spectrum shift induced by independent variation of temperature. After taking the inverse operation, we can obtain the variation of temperature and RI simultaneously by:Where Kn,1, Kn,2, KT,1, KT,2 are sensitivity coefficients. The Eq. (2) indicates that the temperature variation can be determined from the coefficient matrix, which is independent of the ambient RI variation and dn/dT. Therefore, we can measure the variation of temperature and total ambient RI () simultaneously. Besides, dn/dT is the thermo-optic coefficient which can be learned in advance. As for an unknown media, in a calibration process, the variation of solution RI only depends on dn/dT, namely △n = 0. From Eq. (2), the thermo-optic coefficient of the ambient media can be calculated as:As a result, △n and △T can be measured simultaneously by using Eq. (2). The next thing now is to determine the sensitivity coefficients (Kn,1, Kn,2, KT,1, KT,2).Then assuming the temperature is kept at 20 °C, the metasurface sensor is covered with different materials with RI ranging from 1.33 to 1.49, and the calculated transmission spectra are shown in Fig. 3(a). Both resonance dips shift in the long wavelength direction. In order to estimate the sensing property, the relationship between the two dip wavelength shifts and different RI are shown in Fig. 3(b). After linear fitting, the sensitivities of these two dips towards RI are determined to be 243.44 nm/RIU and 159.43 nm/RIU, respectively. In addition, the fitting degrees are 0.9995 and 0.99884, exhibiting good linear responses.
Fig. 3 (a) The transmission spectra of the metasurface sensor 1 covered with different RI materials. (b) Linear fit of the relationship curves between the wavelength shift of two resonance dips and the external refractive index. (c) The transmission spectra of the metasurface sensor 1 with different temperature. The insets are partial enlarged details of two dips. (d) Corresponding linear fit to the relationship curves between the wavelength shift of two dips and the external temperature.
Then the metasurface sensor is covered with water and heated in the range from 0 °C up to 100 °C. As we know, the RI of the water decreases when the temperature increases, and the thermo-optic coefficient of the pure water is K [31]. On the other hand, the RI and geometrical parameters of sensor will also change as temperature changes. Therefore, the thermal expansion coefficients (TEC) and thermal-optic coefficients (TOC) of the silicon nanoblock and the silica substracte should be considered. The TEC of silicon and silica is [32] and [6] respectively. And the TOC of silicon and silica is [33] and [6], respectively. The transmission spectra at different temperatures are presented in Fig. 3(c), and Fig. 3(d) shows the linear fit of the wavelength shift versus temperature, the sensitivities to the temperature are calculated to be 25.64 pm/°C at dip 1 and 58.94 pm/°C at dip 2. Good linear performances are observed with all fitting degree R2 almost equal to 1. However, we should note that the simulation above-mentioned about response to temperature have considered not only the spectrum shift induced by independent variation of temperature, but also the spectrum shift induced by the ambient solution thermo-optic effect. In other words, the coefficient of the temperature above is the sum of the direct contribution of the temperature change and the indirect contribution of the induced change of the RI of the water. Therefore, the real coefficient of the temperature can be linearly approximated as:
where i refers to the dip 1 and dip 2 of transmission spectrum in Fig. 1(b), and is the real coefficient of the temperature which we want, is the coefficient we obtain by linear fitting. Then the pure coefficient of the temperature can be calculated from Eq. (4) as 50.47 pm/°C and 75.20 pm/°C.Then based on the above calculated parameters, substituting the calculated sensitivity values into Eq. (2), we gain the following matrix:
Therefore, after obtaining the wavelength shifts of both resonance dips, simultaneous measurement of RI and temperature is realized, which confirm the feasibility of our proposed all-dielectric metasurface sensor.
In addition, the sensing performance of the metasurface sensor 1 can be further evaluated by a figure of merit (FOM), which is the ratio of the sensitivity value to the full width at half maximum (FWHM) of the resonance dips. In view of the two resonance dips and the two parameters, we define that
where S refers to the sensitivity, i refers to the ordinal of the dips, and j is n or T, which represents the temperature or the refractive index of the ambient environment. The FWHM1 of the metasurface sensor 1 is about 78.15 nm and the FWHM2 is about 22.41 nm, so the FOM1, n and FOM2, n are 3.12 and 7.11, respectively. As for FOM1, T and FOM2, T, they are far less than 1 because of the sensitivities to the temperature are in the picometer level.3. Further investigation
Higher sensitivity is always desired in optical sensing. One simple way to improve the sensitivity to the RI is to increase the contact surface with the surrounding media. To accomplish this, four holes are engraved in each silicon nanoblock unit as shown in Fig. 4(a), which is call the metasurface sensor 2, and the right side of Fig. 4(a) is the enlarged image of the circled region. Normal incidence light is considered to propagate through the dielectric metasurface, and then the transmission light is collected. The dimension of the four square holes in each silicon nanoblock unit is the same, as b = 0.13 μm, and the width of the gap in between is g = 0.14 μm. Other structural parameters of the metasurface sensor 2 are the same with the above mentioned metasurface sensor 1, i.e. px = py = 0.8 μm, a = 0.6 μm, t = 0.22 μm. The calculated transmission spectrum, as shown in Fig. 4(b), has a strong dependence on the incident wavelength and two resonant dips around 1.30 μm and 1.54 μm. The cross-sectional distributions of the electric and magnetic field in one unit cell are shown in Figs. 4(c)–4(f), which are similar to the metasurface sensor 1 and indicate a magnetic dipole behavior and an electric dipole characteristic, respectively.
Fig. 4 (a) Schematic of the metasurface sensor 2. (b) Transmission spectrum of the metasurface sensor 2 showing two dips for magnetic (λM ≈1.30 μm) and electric (λE≈1.54 μm) resonances. (c) Electric field distributions at λM≈1.30 μm in a unit cell in y-z plane. (d) Magnetic field distributions at λM≈1.30 μm in a unit cell in the x-z plane. (e) Electric field distributions at λE≈1.54 μm in a unit cell in y-z plane. (f) Magnetic field distributions at λE≈1.54 μm in a unit cell in x-z plane. The arrows indicate the direction of the electric and magnetic fields.
Then the sensitivities of this metasurface sensor 2 are calculated. Figure 5(a) shows the transmission spectra when the temperature is kept at 20 °C and covered with different material with the RI ranging from 1.33 to 1.49. And according to the linear fitting, as shown in Fig. 5(b), the sensitivities of the two resonance dips to the RI increase to 306.71 nm/RIU, and 204.27 nm/RIU. As for its response to variation of ambient temperature, the transmission spectra are presented in Fig. 5(c), and Fig. 5(d) shows the linear fit curve with sensitivities to the temperature are 4.17 pm/°C and 46.05 pm/°C for two dips, respectively. And then the pure coefficient of the temperature can be calculated from Eq. (4) as 35.45 pm/°C and 66.89 pm/°C. By substituting the calculated sensitivity value into Eq. (2), we gain the following matrix:
Fig. 5 (a) The transmission spectra of the metasurface sensor 2 covered with different RI materials. (b) Linear fit of the relationship curves between the wavelength shift of two resonance dips and the external refractive index. (c) The transmission spectra of the metasurface sensor 2 with different temperature. The insets are partial enlarged details of two dips. (d) Corresponding linear fit to the relationship curves between the wavelength shift of two dips and the external temperature.
The FWHM1 of the metasurface sensor 2 is about 30.39 nm and the FWHM2 is about 12.19 nm, so the FOM1, n and FOM2, n are 10.09 and 16.76, respectively. As for FOM1, T and FOM2, T, both of them are larger than that of the metasurface sensor 1, since the FWHM is smaller.
To investigate the sensitivity difference between metasurface sensor 1 and 2, the cross-sectional electric field distributions of one unit cell in x-y plane are calculated at their electric resonance wavelengths, as shown in Fig. 6. As revealed by the comparison between Figs. 6(a) and 6(b), when there are four holes in the silicon nanoblock, a higher proportion of the electric field will interact with the surrounding medium, due to the conservation of normal displacement field. This phenomenon accounts for the higher sensitivities to the RI of metasurface sensor 2. On the other hand, a less proportion of the electric field interacts with the sensor itself when the volume of silicon is cut down. This causes the decrease of the sensitivities to the temperature after introducing four holes into each silicon nanoblock. The simulation results of sensitivities are summarized in Table 1. The sensitivities of our sensors are better than most reported values, except for Ref [2] and [6], which are based on plasmonic waveguides or Fabry-Perot cavities. The plamonic waveguides involves silver, causing high loss in the visible and infrared wavelength bands. And the realization of F-P cavities is complicated. Comparatively speaking, our proposed sensors are compact and low loss.
Fig. 6 Calculated cross-sectional electric field distributions in one unit in the x-y plane of (a) metasurface sensor 1 and (b) metasurface sensor 2 at the electric resonance wavelength.
In the above numerical simulation, the electric and magnetic fields are assumed to be polarized along y and x axes, respectively. However, the simulation results will remain the same even if the polarization direction of the incident light is rotated 90 degrees due to the rotational symmetry of our proposed sensors. We also investigated the property of the metasurface sensors when the incident plane wave is polarized at different angles (0°, 15°, 30° and 45°) relative to the x axis. The transmission spectra are almost the same as shown in Fig. 7. The unit cells of both metasurface sensors are symmetric along the x and y axis. Therefore whether the electric field of incident light is polarized along x or y axis is undifferentiated. In addition, when the incident electric field is polarized at different angles, the transmittance remains unchanged because any input light can be divided into two orthogonal decompositions. This phenomenon demonstrates that the proposed sensors are polarization insensitive.
Fig. 7 Transmission spectra of metasurface sensor 2 at different polarization angle of incident light.
4. Conclusions
We have proposed a new type of sensors for simultaneous measurement of refractive index and temperature based on all-dielectric metasurfaces. The metasurfaces are constructed by an array of silicon nanoblocks on top of the bulk fused silica substrate. The feasibility and performance are demonstrated theoretically. Simulation results show that the sensing sensitivities of two dips to the refractive index are 243.44 nm/RIU and 159.43 nm/RIU, respectively, while the sensitivities to the temperature are 50.47 pm/°C and 75.20 pm/°C, respectively. After engraving four holes in each silicon nanoblocks, the sensitivities to the refractive index increase to 306.71 nm/RIU and 204.27 nm/RIU, respectively. The proposed sensors have advantages of polarization insensitive, small size, low loss, which offer them high potential applications in physical, biological and chemical sensing fields.
Acknowledgments
This work was supported by the Youth Innovation Promotion Association of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 61675226) and the National high level talent special support program Young top-notch talent project.
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