Simulated Study of High-Sensitivity Gas Sensor with a Metal-PhC Nanocavity via Tamm Plasmon Polaritons

Abstract

An optical configuration was designed and simulated with a metal-photonic crystal (PhC) nanocavity, which had high sensitivity on gas detection. The simulated results shows that this configuration can generate a strong photonic localization through exciting Tamm plasmon polaritons. The strong photonic localization highly increases the sensitivity of gas detection. Furthermore, this configuration can be tuned to sense gases at different conditions through an adjustment of the detection light wavelength, the period number of photonic crystal and the thickness of the gas cavity. The sensing routes to pressure variations of air were revealed. The simulation results showed that the detection precision of the proposed device for gas pressure could reach 0.0004 atm.

1. Introduction

A high-sensitivity method of gas sensing is increasingly necessary through the development of a measurement technique. Recently, optical sensors have played an important role in the high-sensitivity sensing of various targets due to the development of photonic and laser technologies [1,2,3]. Tamm plasmon polaritons (TPPs) based optical sensors present many advantages [4,5]. TPPs, traditionally formed at the interfaces between photonic crystal and metal film, can be excited with both transverse electric (TE) and transverse magnetic (TM) polarized lights without the assistance of external structures [6,7]. Meanwhile, TPPs can selectively transform the energy of a specific wavelength light into an electromagnetic mode and can generate optical field enhancement. Their easy excitation mode and high optical field localization make TPPs attractive for many types of research fields, including sensors [4,5,8], photodetection [9,10,11], thermal emission [12], solar cell [13,14], confined laser [15,16], nonlinear optical effects [17,18], perfect absorption [19,20], and tunable filters [21,22,23]. Benefiting from the increasingly mature preparation technology, simple Tamm structures have been experimentally studied and have garnered plenty of results that matched well with theoretical studies [24,25,26,27,28,29]. These results demonstrate the value and the potential of TPPs-based devices. Recently, we found that a metal-PhC cavity could also generate TPPs, as the cavity could be used as gas channel. In this work, we designed an optical sensor based on a Ag-PhC nanocavity, that could allow for the high-sensitivity detection of gas.

2. Structure and Methods

The structure of an Ag-PhC nanocavity is shown in Figure 1a, and mainly contains PhC, gas nanocavity and Ag film. The preparation of an Ag-PhC nanocavity can be processed as discussed. Firstly, by preparing Ag film on silica substrate and etching a gas nanocavity on the Ag film. Then, by preparing a PhC structure on another silica substrate. Finally, by combining the etched Ag film and the PhC structure. The selected alternate dielectric layers of the PhC structure are silicon dioxide (SiO₂) and titanium dioxide (TiO₂), two common periodic structure materials. The thicknesses of SiO₂ and TiO₂ are set as 245 nm and 160 nm, respectively. The thickness of the gas nanocavity is set as 50 nm.

Both the reflection and absorption spectra of this configuration are theoretically investigated by the transfer matrix approach. There are two different matrices in this method, which are the transmission matrix (TM) and propagation matrix (PM), that can be described as:

$$T{M}_k=\frac{1}{t_k}\left[\begin{array}{cc}1& r_k\\ r_k& 1\end{array}\right], P{M}_k=\left[\begin{array}{cc}\exp \left(-i{\phi }_k\right)& 0\\ 0& \exp \left(-i{\phi }_k\right)\end{array}\right].$$

(1)

Here, t_k and r_k are the transmission and reflection coefficients of light transmission from the (k − 1)-th layer to the k-th layer. φ_k is the phase of light propagating in the k-th layer. Thus, the total transfer matrix can be represented as:

$$M=T{M}_{1}P{M}_1\cdots T{M}_{20}P{M}_{20}T{M}_{g}P{M}_{g}T{M}_s.$$

(2)

Here, TM_g refers the transmission matrix for the interface of the TiO₂ layer and the gas nanocavity, PM_g refers the propagation matrix of the gas nanocavity, TM_s refers the transfer matrix for the interface of the gas nanocavity and the Ag film. The transmission intensity will increase when the thickness of the Ag film is thinner than 60 nm. This will influence the intensity of the reflection light. In this study, the thickness of Ag film is set as 150 nm. Thus, the transmittance of the Ag-PhC nanocavity is near zero and negligible. The reflectance and absorptance of the structure can be expressed as R = |M₂₁/M₁₁|² and A = 1 − R. M₂₁ refers the first matrix element in the second row of M. M₁₁ refers the first matrix element in the first row of M.

Figure 1b shows the reflection and absorption spectra of the Ag-PhC nanocavity when the period number of PhC is set as 10. The refractive indices of SiO₂ and TiO₂ can be set as 1.45 and 2.13 [23]. The permittivity of the Ag film is described by the Lorentz-Drude model [30]. It can be seen that the proposed structure has a narrow-band absorption of almost 1550 nm. The reflection spectrum shows a narrow valley at the corresponding wavelength. Meanwhile, the red line in Figure 1a shows the electric field distribution of light at 1550 nm, at which a high localization in the PhC exists. These results reveal the generation of TPPs in the Ag-PhC nanocavity.

3. Results and Discussion

The intensity of the reflection light (I) and the intensity of the light source (I₀) can be detected using an optical power meter. We can simulate I/I₀ by calculating the reflectance of the Ag–PhC nanocavity. The influence of the gas refractive index (n) on the reflectance of the Ag–PhC nanocavity is shown in Figure 2, in which the period number of the PhC (N) is set as 10. As shown in Figure 2a, we can find that the reflection valley blue-shifts from ~1552 nm to ~1548 nm as n varies from 0.97 to 1.03. We derived the reflectance of the Ag–PhC nanocavity at 1548 nm, 1550 nm and 1552 nm, as shown in Figure 2b–d. It can be observed that the reflection has high selectivity on the light wavelength. For 1548 nm light, the reflectance decreases from ~0.7 to near zero as n varies from 0.97 to 1.03, which increases from almost zero to ~0.7 for 1552 nm light. To clearly study the sensitivity to n, we plotted the derivative of the reflection with n, as the dotted lines in Figure 2b–d. It can be observed that the absolute value of derivation reaches ~15, which means the reflectance of the Ag–PhC nanocavity will change by ~15 times the I₀ as n changes 1. The maximum absolute value of derivation appeared at a medium value of the reflectance, which is disparate for different light wavelengths. That means we can tune the sensitivity of gas nanocavity by selecting the wavelength of light source.

After this, we investigated the influence of N (the period number of PhC), as shown in Figure 3. The wavelength of the light source is set as 1550 nm. It can be observed that the minimum value of reflectance is lowest when N is 10, which is near zero. This minimum value of reflectance appears at a lower n as N increases. Meanwhile, we calculated the derivation of lines in Figure 3a, as shown in Figure 3b. It can be seen that the maximum value of derivation increases with an increase of N. Meanwhile, the position of this maximum sensitivity appeared at different n for different N. These results reveal that the sensitivity of the Ag–PhC nanocavity on the gas nanocavity can be adjusted using the period number of PhC.

Furthermore, the influence of the thickness of the nanocavity (d_g) was investigated. We found a series of d_g could lead to the TPPs reflectance valley at 1550 nm, such as 50 nm, 825 nm, 1600 nm, 2375 nm and so on. These thicknesses of the nanocavity satisfy n_g·∆d_g = λ/2. Furthermore, n_g refers the refractive index of the cavity. λ refers the wavelength of light. The generation of TPPs must satisfy the phase matching condition that can be deduced as [6,7]:

$$r_{\mathrm{PhC}}{r}_{\mathrm{Ag}} \exp (2i{\phi }_g)=1$$

(3)

Here, r_PhC and r_Ag refer the reflection coefficients from the gas cavity to the PhC and the Ag layer, respectively. φ_g = 2πn_gd_g/λ is the phase of light propagating in the gas cavity. As seen in Equation (4), the variation of φ_g needs to be an integral number of π, which corresponds well with the above results. The influence of d_g on the reflectance spectrum is investigated, as shown in Figure 4a. It can be found that the full width of half maximum (FWHM) of the TPPs valley becomes narrower with an increase of d_g. The FWHM of the TPPs valley is 5.38 nm (d_g = 50 nm), 3.14 nm (d_g = 825 nm), 2.22 nm (d_g = 1600 nm), 1.71 nm (d_g = 2375 nm), respectively. Additionally, the derivative of reflection on the gas refractive index is also investigated, as shown in Figure 4b. It can be seen that the maximum value of derivation dramatically increases with an increasing d_g, which reaches ~800 for d_g = 2375 nm. However, the detection range of the gas refractive index decreases with an increase of d_g. We can set the monotone increasing section in Figure 4b as the detection range. For d_g = 50 nm, the detection range is ~0.04. For d_g = 2375 nm, the detection range decreases to ~0.0001. Thus, we can select the applicable thickness of the gas cavity based on practical necessity.

To discuss the detection precision of the proposed structure, we calculated the wavelength of the reflectance valley at different d_g. From Figure 5, we found that the wavelength of the reflectance valley linearly red-shifts when the refractive index of the gas cavity increases. For the proposed structure, the detection sensitivity can be set as S = ∆λ/∆n. It can be deduced that S reaches 1057 nm/RIU when d_g = 2375 nm. The figure of merit (FOM) is also an important parameter to characterize the sensing ability, which can be defined as FOM = S/FWHM. It can be deduced that FOM reaches 618.1/RIU when d_g = 2375 nm. These parameters of detection sensitivity can be further enhanced by increasing the thickness of the gas cavity. This can be explained by the phase matching condition, for which the TPPs wavelength is related to φ_g. The refractive index of the gas will have a greater influence on φ_g when the thickness of the gas cavity increases. To assess the detection ability of the proposed configuration, sensitivities of different TPP-based gas sensors are listed in

Table 1. Sensitivities of different Tamm plasmon based gas sensors.

Structure	S (nm/RIU)	FOM (/RIU)
PhC-Au-Gas [31]	55	-
Ag-Gas/Si PhC [4]	83.3	-
Graphene-Gas-PhC [32] (in terahertz band)	-	142
This work	1057	618.1

. It can be seen that the proposed structure in this paper has a relatively high sensitivity on the refractive index of gas.

4. Simulation Sensing of Gas Pressure

To clearly demonstrate the high sensitivity of the Ag–PhC nanocavity on gas, we simulated the detection of air at different gas pressures. The sensing route is shown in Figure 6a. The 1550 nm laser passes through a splitter into the Ag-PhC nanocavity. The reflection laser of the Ag–PhC nanocavity is reflected by the splitter. Finally, the laser reflected from the splitter is detected by an optical detector, which can obtain the intensity of signal light I. The gas cavity is exposed to the outside, in which the gas pressure is consistent with the environment. The relationship between gas pressure and the gas refractive index can be expressed as [33]:

$$n=1+\frac{p(n_0-1)}{96095.43}\times \frac{1+p(0.613-0.00998t)\times {10}^{-8}}{1+0.003661t}$$

(4)

Here, n is the gas refractive index and n₀ is the gas refractive index of standard air, which equals 1.00012438 for 1550 nm light. p is the gas pressure and t is the temperature.

We set a standard intensity of the signal light I_s at 1.0 atm and 25 °C. Based on the above formula, we plotted the intensity variation of the signal light (normalized by I_s) with different gas pressures as shown in Figure 6b. It can be seen that I is greatly influenced by the gas pressure, has and that they have a significant linear relationship. The variation rate of normalized light intensity on gas pressure reaches ~2.5 per atm, which means that ∆pI/∆I is ~0.4 atm if we set the detection precision of optical power meter as a thousandth of the detection range. Thus, the detection precision of gas pressure can reach 0.0004 atm.

5. Conclusions

In summary, TPPs were generated in an Ag-PhC nanocavity. Based on the Ag-PhC nanocavity, an optical sensor for gas was designed. The simulated results revealed that the detection sensitivity for the gas refractive index could reach 1057 nm and the FOM is able to reach 618.1/RIU. Meanwhile, the simulated results demonstrated that the detection precision of the Ag–PhC nanocavity on gas pressure could reach 0.0004 atm. The proposed configuration can also be used for many other applications, such as concentration sensing and composition detecting.