1. Introduction

Since optical Tamm plasmon (OTP) was first proposed by A. V. Kavokin et.al. in 2005 [1], studies on OTP are flourishing, such as forming OTP in different structures, coupling of OTP with quantum well excitons, and enhancing nonlinearity through OTP. OTP is a kind of interface modes, which locates in the interface of two different media. Usually, it can be observed in one-dimensional photonic crystal hetero-structure or metal-dielectric distributed Bragg reflector (DBR) [2–5]. As a special type of surface Plasmon (SP), OTP can be excited by both TE and TM –polarized light without using additional dispersion-matching devices, which is different from common SP [2–4]. Moreover, OTP even shows much stronger light-trapping ability than SP [6,7]. Taking advantages of these characteristics, OTP has been applied in many occasions, such as optical switch, bistable logic control [8,9], new kind of metal/semiconductor lasers [10,11], and enhancement of broad-band absorption and optical nonlinearity [12–14]. Besides the above-mentioned applications, optical sensing using OTP is also supposed to be a promising way to enhance sensing performance like sensors based on surface plasmon resonance (SPR).

Recently, optical sensors based on SPR have been widely studied for chemical, biomedical and environmental monitoring [15–17], wherein trigger of SP requires specific injection conditions (i.g., polarization and injection angle) due to the momentum mismatch between light and SP at the same frequency. Besides, the measurement range of refractive index sensor is relatively narrow. In this paper, we propose a novel method of refractive index sensing using a high-refractive-index-contrast OTP structure. The structure is formed by an air/dielectric alternate-layered DBR [18] coated with silver film. The presence of air layers increases refractive index contrast of the DBR, therefore much fewer layers are enough to form OTP. Moreover, the air layers expose the optical field to the outer environment, enhancing the sensor sensitivity greatly [19]. Our numerical results indicate that both the reflectivity change (in intensity interrogation) and wavelength shift (in wavelength interrogation) of the reflection dip related to OTP are sensitive to change of ambient refractive index within a large variation range.

2. Structure design and analysis

The schematic of the proposed structure is given in Fig. 1. For comparison, two types of OTP structures are considered. In structure-1 (S1), Si/SiO₂ alternate-layered DBR is covered by a silver film. In structure-2 (S2), Si/air alternate-layered DBR is used. In fact, S2 can be made from S1 by etching or laser processing. The central wavelength, λ₀, of the DBRs is set at 400 nm. Thickness of each DBR layers is λ₀/4n, where n is the refractive index of a certain layer. For air, SiO₂ and Si, value of n is 1, 1.47 and 3.42, respectively. In our study, periods of the DBRs are assumed to be 4, and the injected light is TE-polarized if no additional introductions are given. Using a modified transfer matrix method proposed in our previous works [8,9], the structures in Fig. 1 can be analyzed numerically.

 

Fig. 1 Scheme diagram of the OTP structures.

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Sensing principle of the proposed structure is that the intensity and eigen wavelength of OTP is sensitive to variation of ambient refractive index, n_a. On the other hand, formation of OTP generates a dip in the reflection spectrum of the structure. Thus, reflectivity and wavelength of the dip is proportional to n_a, which can be used to measure the value of n_a.

The reflection spectra and field distributions of S1 and S2 are shown in Fig. 2. In the reflection spectra, a sharp dip is observed at 538 nm for S1, and at 580 nm for S2. This dip locates within the band gap of the DBRs, seeing Figs. 2(a) and 2(b). Its appearance corresponds to excitation of OTP [2], i.g., light at wavelength that is in resonance with the OTP eigen wavelength will penetrate the structure, while light at other wavelength will be reflected. Figure 2(c) shows the field distribution of light at different wavelengths. It is found that field intensity at the OTP eigen wavelength (i.e., wavelength of the reflection dip) is dominant in the structure. Besides, the maximum field intensity is near the metal-DBR interface, which is a typical characteristic of interface mode. Figure 2(d) gives the field distribution of light at the dip wavelength. It is observed that the maximum field intensity is enhanced 50 times in S2, which is five times larger than that in S1.

 

Fig. 2 Reflection spectra and field distributions of S1 and S2. (a) Reflection spectra of S1 and S2 without metal; (b) Reflection spectra of S1 and S2; (c) Power distribution of S1 and S2; (d) Power distribution corresponding to OTP excitations of S1 and S2, the left and right vertical lines correspond to the metal-DBR interface and the first Si-Air interface, respectively. In the simulation,θ = 0°, d = 50 nm.

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Figure 3(a) shows the dip wavelength, λ_d, as a function of n_a. It is observed that λ_d of S2 shifts to longer wavelength as n_a increases from 1 to 2. The average sensitivity of refractive index measurement through wavelength interrogation is about 0.012/nm, which is much more sensitive than that of S1. This is because that S2 uses high-refractive-index-contrast structure, which can enhance the field intensity more efficiently, and the air layers expose more portion of optical field to the ambient. In addition, effective thickness (i.e., physical length times refractive index) of the air layers increases with ambient refractive index, which further shift the OTP eigen wavelength. Figure 3(b) shows the dip reflectivity, r_d, as a function of n_a. The dip reflectivity of S2 varies much more obviously with n_a than that of S1. Besides, an inflection point exists when n_a = 1.38. For n_a smaller (larger) than this inflection point, r_d decreases (increases) with n_a increasing, and the average sensitivity of intensity interrogation is 0.009/dB (0.012/dB). This value can be larger if n_a only varies near the inflection point.

 

Fig. 3 The dip wavelength and reflectivity as a function of n_a. (a) Dip wavelength as a function of n_a; (b) Dip reflectivity as a function of n_a. In the simulation, θ = 0°, d = 50 nm.

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We can find from Fig. 3 that λ_d various monotonously with n_a, which guarantees a large measuring range of n_a though wavelength interrogation. Though r_d various non-monotonously with n_a, the intensity interrogation has a large measuring sensitivity, especially for n_a near the inflection point. For practical applications, wavelength and intensity variations can be interrogated together to enhance the measuring range and the sensitivity simultaneously. In the following discussions, influence of metal thickness, d, and injection angle, θ, on sensing performance of S2 is studied.

Figure 4(a) repeats the plot of Fig. 3(a) for different values of d. The curve of λ_d versus n_a changes slightly with d, indicating that the relationship between dip wavelength and ambient refractive index is changed little by varying metal thickness. Figure 4(b) repeats the plot of Fig. 3(b) for different values of d. When d increases (decreases), the inflection point in Fig. 4(b) moves to smaller (larger) value of n_a. Thus, by proper choosing the metal thickness, r_d can change monotonously with n_a in a wide range of n_a.

 

Fig. 4 Dip wavelength/reflectivity versus n_a for different metal thickness. (a) Dip wavelength versus n_a for different metal layer thickness; (b) Dip reflectivity versus n_a for different metal layer thickness. In the simulation, θ = 0°.

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Figure 5 shows the case when two optimized thicknesses of metal layer are considered. We can see that both λ_d and r_d increase monotonously with n_a. For d = 31 nm (56 nm), the average sensitivity of wavelength interrogation is 0.012/nm (0.011/nm), and the average sensitivity of intensity interrogation is 0.036/dB (0.025/dB).

 

Fig. 5 The dip wavelength and reflectivity as a function of n_a for d = 31 or 56 nm. (a) Dip wavelength as a function of n_a ; (b) Dip reflectivity as a function of n_a. In the simulation, θ = 0°.

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Figure 6(a) shows the values of λ_d as a function of n_a for different value of θ. The red shift of the dip wavelength becomes smaller and smaller when θ increases from 0 to 45 degree, and becomes blue shift when θ is larger than 45 degree. Figure 6(b) shows the values of r_d as a function of n_a for different value of θ. The inflection point of the curve moves to larger value of n_a when θ increases. This indicates that measuring range and sensitivity of the proposed structure can be controlled and optimized by injection angle.

 

Fig. 6 Dip wavelength/reflectivity versus n_a for TE-ploarized injection of different injection angle. (a) Dip wavelength versus n_a for different injection angle; (b) Dip reflectivity versus n_a for different injection angle. In the simulation, d = 50 nm.

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Figure 7 repeats the plot of Fig. 6 except that the injected light is TM-polarized. Previous studies have verified that OTPs related to TM and TE -polarized injection have different dispersion curves [1,20], which induces polarization dependence of sensing. In Fig. 7(a), the curve of λ_d versus n_a moves to shorter wavelength when θ increases, however, the slope efficiency of the curve keeps almost unchanged. In Fig. 7(b), the inflection point moves to smaller value of n_a when θ increases, which is reverse to the case of Fig. 6(b). Thus, the polarization is also another usable parameter to control the sensing performance.

 

Fig. 7 Dip wavelength/reflectivity versus n_a for TM-ploarized injection of different injection angle. (a) Dip wavelength versus n_a for different injection angle; (b) Dip reflectivity versus n_a for different injection angle. In the simulation, d = 50 nm.

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3. Conclusion

In conclusion, a novel refractive index sensing concept using OTP is proposed. The high-refractive-index-contrast OTP structure helps to trap light more intensively and to enhance interaction of the light field with outer environment. Thus, ambient refractive index can be tested with a large measuring range and high sensitivity. Besides, the sensing performance can be designed or optimized by adjusting the metal layer thickness or the injection angle. The influences of metal thickness and injection angle also depend on the polarization of injection light, owning to different dispersion characteristics of OTP under TE and TM –polarized injection. It is also worth mentioning that the refractive index response of the proposed sensor is not strictly linear, because a relative wide measuring range is considered in the simulation. In practical applications, refractive index often changes within a much smaller range, so good linearity is obtainable. In addition, the thickness of Si/air layers is not restricted to λ/4, and it can be optimized [1] according to a specific measurement. The proposed planar structure can also be made in optic fibers to simplify light injection and collection.