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This work proposes a refractive index sensing concept of a Tamm plasmon (TP) device by using spectroscopic ellipsometry and phase detection. A TP device is generally composed of a 1-D photonic crystal (PC) with a metallic film on top of it. We found that the sensing performance can be improved by adjusting the parameters of the incident angle of polarized light, the top layer thickness, and the central wavelength of the PC. By designing proper parameters, it was found that the change of the phase difference of p-polarized and s-polarized lights, δ∆, can reach 34° when the ambient environment is changed from air (n = 1.00028) to carbon dioxide (n = 1.00045). A sensitivity of δ∆/δn ~2 × 105 °/RIU can then be obtained for the proposed TP device.
© 2017 Optical Society of America
1. Introduction
Plasmonics has been a rapidly developing topic in photonics. It has provided many applications in biophotonics and chemistry [1,2]. A conventional surface plasmon (SP) polaritons are formed with a TM polarization at the boundary of metallic and dielectric media by using dispersion-matching devices, like gratings or prisms [3]. Tamm plasmon (TP), formed by a high refractive index/low refractive index alternate-layered photonic crystal (PC) coated with a metallic film, can be easily excited by both the TE and TM polarization without using additional dispersion optics [4], therefore it is more convenient for practical applications. TP has been applied in many photonic devices, such as optical switches and semiconductor lasers [5,6]. Recently, a novel method of refractive index sensing using a high-refractive-index-contrast TP structure is proposed theoretically by Zhang et. al. [7]. The presence of air layers in their proposed TP structure, an air/dielectric alternate-layered PC, increases the refractive index contrast of the PC and greatly enhances the sensor sensitivity by measuring the shift of resonance wavelength with the change of ambient refractive index. However, the air layers in TP structure are not easy to fabricate for practical applications. A complicated approach by using mesoporous multilayers has also been proposed recently to solve this issue [8]. Recently, the TM polarized hybrid mode formed as a consequence of coupling between TP polariton and SP polariton has been proposed and it exhibits a sensitivity ~900 nm/RIU [9]. Conventional SP resonance (SPR) has been extensively explored for sensors based on detection of amplitude characteristics [10]. In order to improve the detection sensitivity, the phase-sensitive SPR has been adopted due to the existence of an abrupt phase change under suitable SPR parameters [11]. Several techniques based on phase-sensitivity measurements have been demonstrated, such as SPR polarimetry and optical heterodyning [11,12].
In this work, the approach of spectroscopic ellipsometry (SE) was applied to measure the phase difference of p-polarized and s-polarized lights with the ambient refractive index for a TP device. By using a commercial software for theoretical modeling, it was found that the change of phase difference of p-polarized and s-polarized lights can reach 34° when the ambient environment is changed from air (n = 1.00028) to CO2 (n = 1.00045) [13–15].
2. Structure design and analysis
The schematic of the proposed TP device and the apparatus for reflectance spectra measurement are shown in Figs. 1(a) and 1(b), respectively. A TP device is applied, using a standard quarter-wavelength PC composed of eight pairs of TiO2 (n~2.30 at 590 nm [16]) and SiO2 (n~1.46 at 590 nm [16]) with central wavelength λc ~730 nm. The thicknesses of the high (tH) and low (tL) refractive index films are given by tH = λc/4nH and tL = λc/4nL, where nH and nL are the indices of refraction of the high and low index films, respectively. The TiO2 and SiO2 layers were deposited onto a glass substrate by the electron beam evaporation with the ion beam assisted deposition (Kingmate Tech. Co.). The thicknesses of TiO2 and SiO2 were ~78 and ~125 nm, respectively. The top-layer thickness of the TiO2, tTiO2, was ~239 nm. A gold film ~41 nm (n = 0.24, k = 3.00 at 590 nm [16]) was applied on the PC to form a TP device by using a thermal evaporator. For the measurement of reflectance spectra at normal incident, a white light illuminates the TP device from the metal side as shown in Fig. 1(b).
Fig. 1 (a) The schematic structure of the TP device, and (b) the apparatus for reflectance measurement.
The ellipsometry spectra of the TP device placed in an ambient environment was measured by an ellipsometer (alpha-SE, J.A. Woollam Co.), and the light source illuminates the Tamm device from the metal side. The angle of incidence, θi, can be set at 65°, 70° or 75°. Ellipsometry is a very sensitive technique that applies p-polarized and s-polarized lights to characterize the thin films. The polarization of light changes upon reflection. Then, the ellipsometry parametersψ, describing the amplitude ratio, and the ∆, describing the phase difference of p-polarized and s-polarized lights are defined as
where rs (rp) is the s (p)-polarized complex reflection coefficient, and δs (δp) is the s (p)-polarized phase. The ψ and ∆ can be measured by an ellipsometer. A commercial software, the Essential Macleod, is applied to simulate the SE parameters in this work. It has been shown that the resonance wavelength λTP of the TP device depends on the central wavelength of PC, λc, the tTiO2, and the metallic film [17–19]. It is worth to note that the sample structure, including the thickness and refractive index, cannot be identical between the theoretical design and the fabricated results. Although the λTP is changed with the thickness and refractive index of each film, we can determine the λTP from experimental results and design the measurement apparatus at proper conditions to improve the detection sensitivity with the aid of simulation. The contribution of this work is to discuss the effect to sensitivity from each different parameter and able to conclude a design rule to general TP sensors. The simulation was also applied to determine the apparent thickness for each film.3. Results and discussion
Figure 2 shows the simulated and experimental reflectance spectra of the TP device at normal incidence. It is observed that λTP is at ~760 nm. The simulation shows good agreement to the experimental results. The deviation in resonance bandwidth is because of the optical loss in metal while doing thermal evaporation, like roughness and detects [17].
Fig. 2 Reflectance spectra of the simulation and experimental results for the TP device at normal incidence.
The experimental and simulation results of reflectance spectra, ψ and ∆ for the TP device in the air environment at θi = 65° are shown in Fig. 3, and a slight difference ~10 nm between them is observed. The difference of λTP, ~20 nm, between p and s polarized lights is also existed due to their different reflection properties. Two resonances in ψ are observed at about 660-700 nm, and two phase jumps in Δ take place at the same spectral points, corresponding to the two resonance minimums. The phase jump usually happens in the region of drop of light intensity where phase is not defined, while the sharpness of phase jump is determined by the intensity of light in the resonance [11,12]. The sharp peak in Fig. 3(c) is because of the phase range is limited in 2π in the software. Therefore, at the λTP, the large ∆ change will cause the step-like
Fig. 3 Experimental and simulation results of (a) reflectance spectra (b) ψ and (c) ∆ for the TP device in the air environment at θi = 65°.
results. The dependences of Au thickness and θi on λTP, ψ and ∆ are simulated and shown in Fig. 4 and Fig. 5, respectively. The results show that the 5 nm uncertainty for 40 nm Au film results in the uncertainties of ~5 nm, ~10° and ~40° for λTP, ψ and ∆, respectively, as shown in Fig. 4, and the 2° uncertainty for θi = 65° results in the uncertainties of ~6 nm, ~1° and 10° for λTP, ψ and ∆, respectively, as shown in Fig. 5. Therefore, the uniformity of Au thickness and the systematic error of θi may contribute to the different λTP, ψ and ∆ between the experimental and simulation results shown in Fig. 3. The λTP also depends on metal's plasma frequency [19]. Therefore, other than the thickness and the measuring angle divergence, the dielectric constant of Au could also be a factor to cause the deviation from measurement to simulation results. However, the deposited gold film could be slightly different from the database.
Fig. 4 The simulation results of (a) reflectance spectra (mean of p and s) (b) ψ and (c) ∆ for the TP device in the air environment with different Au thicknesses at θi = 65°.
Fig. 5 The simulation results of (a) reflectance spectra (mean of p and s) (b) ψ and (c) ∆ for the TP device in the air environment at different incident angles.
The changes of ψ and ∆, δψ and δ∆, with the ambient environment changed from air to CO2 at θi = 65° are simulated as shown in Figs. 6(a) and 6(b), respectively. δ∆ and δψ have the maximum absolute values ~1.5° and ~0.25°, respectively. δ∆ shows a better sensitivity for detecting the change of ambient index than δψ. Therefore, we use the δ∆ for further detection application. The δ∆ also depends on the wavelength, and the wavelength with the maximum value of δ∆, λmax, is chosen for studying the sensitivity. The maximum absolute value of δ∆ is ~1.5° at λmax = 672 nm as shown in Fig. 6(b).
Fig. 6 Simulation results of SE parameters ψ and ∆ for the TP device at θi = 65° when the ambient environment is changed from air to CO2.
Because the applied ellipsometer has the limited resolutions in wavelength and θi, we investigate the sensitivity of the proposed TP devices theoretically for the following discussion. The sensitivity δ∆ can be improved by properly selecting several parameters, such asθi and PC structure. Simulation results of δ∆ as a function of wavelength at different θi are shown in Fig. 7, where λc = 730 nm and tTiO2 = 239 nm. It is seen that when the ambient environment is changed from air to CO2, the maximum δ∆ depends on the θi. The δ∆ and the corresponding λmax as a function of wavelength at different θi are shown in Fig. 8. A maximum value δ∆ ~2.0° at λmax = 703 nm is obtained when θi is near 50°. We also found that the structure of the PC, including tTiO2 and λc, produces an influence on the sensitivity. Simulation results of δ∆ and the corresponding λmax as a function of tTiO2 are shown in Fig. 9, where θi = 65° and λc = 730 nm. The maximum value of δ∆ is ~12° at λmax = 664 nm when tTiO2 = 230 nm.
Fig. 7 δ∆ as a function of the wavelength at different incident angles, where λc = 730 nm and tTiO2 = 239 nm.
Fig. 8 δ∆ and the corresponding λmax as a function of the incident angle, where λc = 730 nm and tTiO2 = 239 nm.
The λc can be adjusted by varying the thicknesses of the nH and nL films [19]. Simulation results of δ∆ and the corresponding λmax as a function of λc are shown in Fig. 10, where tTiO2 = 239 nm and θi = 65°. The maximum value of δ∆ is ~34° at λmax = 706 nm as λc is 810 nm. The deposited thickness of each film in TP device may not be identical to the theoretical design due to the uncertainty of fabrication depending on the applied facility. If there is ± 1% error in the final result of λc (λc = 810 nm), the δ∆ falls in the range between ~34° and ~20° according to Fig. 10. Therefore, a sensitivity (δ∆/δn = 20°−34°/0.00017) in the range between 1.2 × 105 °/RIU and 2 × 105 °/RIU is obtained for the proposed TP device when the ambient environment is changed from air to CO2. The resolutions of the commercial rotational stage and spectrometer are better than 0.1° and 0.1 nm, respectively. Therefore the influences of the uncertainties from θi and wavelength on sensitivity is less than 10% according to the Figs. 8 and. 10.
Phase-sensitive SPR and the detection limits are well described in the recently published articles [11,12]. The sensitivity of SPR depends on many factors, such as measurement geometry and instrumental and environmental noises [12]. Our applied commercial ellipsometer has noisy characteristics in terms of their stability, ~0.2°. Based on this phase stability, the refractive index resolution of ~10−6 RIU (0.2°/(~2 × 105 °/RIU)) for the present design is obtained if only the instrumental noise is considered. The RI resolution can be further improved if the phase resolution of an instruments can be improved to ~0.001° by special designed low-noisy schemes [11,12,20].
4. Conclusions
In summary, a refractive index sensing concept of a TP device by using SE is proposed. The sensing performance can be designed and improved by adjusting the λc, the tTiO2 and θi. A detection sensitivity of ~2 × 105 °/RIU can be obtained for the proposed TP device when the ambient environment is changed from air to carbon dioxide, where λc = 810 nm, tTiO2 = 239 nm, and θi = 65°. The main scientific contribution of this work is to provide the design rule for TP phase sensor. Comparing to Kretschmann–Raether prism geometry, TP sensor has the advantage in fabrication, low cost, and easy set-up.
Funding
Ministry of Science and Technology of Taiwan (MOST 103-2112-M-009-013-MY3 and MOST 105-2221-E-009-096-MY2).
Acknowledgments
We thank the anonymous reviewers for their constructive comments.
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