Surface Plasmon Resonance (SPR), a unique optical phenomenon arising from optical excitation of charge-density oscillations localized at the interface between a micro-nano metal medium and dielectric surface^[1], has become a hot research topic in optical sensing especially in the detection of liquid Refractive Indexes (RIs), environmental humidity, environmental temperature, and magnetic fields. Recent advances have spurred the development of micro-nano optical devices and materials such as filters^[2-4], beam splitters^[5-7], couplers^[8], lenses^[9], logic gates^[10], functional artificial metamaterials^[11], and so on. In the 1990s, researchers began to combine SPR with optical fibers and fiber sensors based on SPR were proposed^[12-14]. Photonic Crystal Fiber (PCF) with controllable air holes has since garnered much interest. The advantages of this type of sensor include a light weight, miniaturization potential, real-time monitoring, high sensitivity, and strong anti-interference ability.

In order to enhance the sensitivity of PCF-SPR sensors, it is important to strengthen coupling between the core guided mode and plasmonic mode by optimizing the air hole arrangement in the PCFs^[15] as well as the location of the metal layer or filling in the voids. For example, the metal layer can be formed inside the air hole but this approach needs higher processing accuracy and it is difficult to coat the metal on the small surface area of an arc^[16-18]. In order to solve this problem, PCFs with metal coatings on the outer surface have been proposed^[19-20]. However, since the metal layer is far away from the core, coupling between the core guided mode and plasmonic mode is relatively weak resulting in lower sensitivity. The D-shaped structure PCF can overcome these problems. By polishing the fiber to form a plane, the distance between the metal layer and core can be shortened so that SPR is strengthened^[21-27]. However, the traditional D-shaped fiber is ground to nearly half of its original diameter thereby affecting the mechanical strength and making the fiber brittle as well. In this respect, the eccentric core^[28-29] and quasi-D-shaped PCFs have been recently combined to form PCF-SPR sensors^[30-33]. However, the sensitivity of this kind of PCF-SPR sensor is still not satisfactory. Therefore, the Photonic Quasi-crystal Fiber (PQF) which is a special PCF with low constraining loss, a wide band, ultra-high birefringence, and flat dispersion has also been studied as an SPR sensor^[34-35].

In this work, a ten-fold eccentric core quasi-D-shaped PQF-SPR sensor is designed and numerically analyzed. The distance between the metal layer and core is shortened to enhance resonance between the core mode and Surface Plasmon  Polariton (SPP) mode. In this structure, the low-cost Indium Tin Oxide (ITO) layer can be readily deposited by Chemical Vapor Deposition (CVD)^[36] or DC magnetron sputtering. By performing optimization using the Finite Element Method (FEM), the wavelength sensitivity and resolution are demonstrated to be 60,000 nm/RIU and 1.67×10⁻⁶ RIU, respectively. The new design and results described here reveal a viable strategy to design a highly sensitive RI sensor.

The schematic diagram of the PQF-SPR sensor is shown in Fig. 1(a) (Color online). The sensor is based on the ten-fold quasi-crystal structure (Fig.1(b), Color online) by removing two red air holes to construct the eccentric core and green air holes to form the quasi-D-shaped plane. The core is filled with air holes to restrict light transmission. The lattice constant of the PQF is Λ = 5 μm. The diameters of the cladding air holes and central air holes are d₁ = 2.4 μm and d₂ = 5.0 μm respectively. The polished quasi-D-shaped plane is H = 16.5 μm from the center and the ITO layer is coated on the surface. It is noted that the area requiring polishing is reduced greatly compared to traditional D-shaped sensors. The length L_ITO and thickness T_ITO of the ITO layer are 14 μm and 70 nm respectively. The analytical fluid is placed outside the structure and the radii r₁ and r₂ are 18 μm and 22 μm respectively. The structure is made of silica and wrapped by a Perfectly Matching Layer (PML) with a radius of 27 μm.

The relationship between the refractive index of silicon dioxide and its wavelength is derived by Sellmeier’s equation^[37]:

$ {n^2}(\lambda ) = 1 + \frac{{{A_1}{\lambda ^2}}}{{{\lambda ^2} - {B_1}}} + \frac{{{A_2}{\lambda ^2}}}{{{\lambda ^2} - {B_2}}} + \frac{{{A_3}{\lambda ^2}}}{{{\lambda ^2} - {B_3}}} \quad, $ (1)

where A₁ = 0.696166300, A₂ = 0.407942600, A₃ = 0.897479400, B₁ = 4.67914826×10⁻³ μm², B₂ = 1.35120631×10⁻² μm², and B₃ = 97.9340025 μm² where λ represents the wavelength of the incident light in vacuum. The Drude model is adopted to describe the relationship between the dielectric constant and wavelength of ITO^[38]:

$ {\varepsilon _{\text{m}}}(\lambda ) = {\varepsilon _\infty } - \frac{{{\lambda ^2}{\lambda _c}}}{{{\lambda ^2}_p({\lambda _c} + i\lambda )}}\quad , $ (2)

where λ_p = 5.6497×10⁻⁷ m and λ_c = 11.21076×10⁻⁶ m are the plasmonic and collision wavelengths of ITO, respectively and ε_∞ = 3.80 is the dielectric constant for the infinite value of the frequency of ITO.

The properties of the sensor are analyzed by the Finite Element Method (FEM) with the COMSOL multi-physics software. An artificial boundary condition is set to increase the computational accuracy and there is a Perfectly Matched Layer (PML) with a thickness of 5 μm to absorb the radiation energy. The mesh statistics of the structure include 11861 vertices, 23670 triangles, 1739 edge elements and 207 vertex elements. The domain units are as follows: the number of units is 23670, the unit area ratio is 2.875 × 10⁻⁴ and the grid area is 2284 μm².

The confinement loss which is the key parameter to evaluate the properties of the sensor can be calculated by the following equation^[39]:

$ {\alpha _{{\text{loss}}}} = 8.686 \times \frac{{2\text{π} }}{\lambda }{{\rm{Im}}} ({n_{{\rm{eff}}}}) \times {10^4}({\rm{dB}}/{\rm{cm}})\quad , $ (3)

where λ is the wavelength in micrometers and Im(n_eff )is the imaginary part of the effective refractive index of the core mode.

In the numerical simulation, the key step is to determine the phase-matching intersection of the core mode and SPP mode of the sensor. The liquid analyte RI is chosen to be 1.39 and the simulation results are presented in Fig. 2 (Color online). The effective refractive indices of the Y-polarized core mode and SPP mode are represented by the red solid dotted line and red hollow dotted line, respectively. At the phase-matching point, the strongest coupling occurs at a resonance wavelength of 2200 nm. The power of the core mode transferred to the SPP mode is shown in Fig. 3 (Color online). The Confinement Loss (CL) shows a maximum value which is described by the imaginary part of the effective index of the core mode. This peak wavelength is called the resonance wavelength. The loss spectrum of the Y-polarized core mode is described by the black circular dotted line. Similarly, the loss spectrum of the X-polarized core mode is calculated and shown by the blue circular dotted line. The Y-polarized mode shows a significant loss peak compared to the X-polarized mode due to the Y-direction polished plane. Therefore, the Y-polarized mode is employed to assess the sensing characteristics of the PQF-SPR sensor.

The RI sensitivity of the PQF-SPR sensor is analyzed with the analyte RI range between 1.35 and 1.40 as shown in Fig. 4(a) (Color online). The CL spectra of the sensor red-shifts and the resonance peaks increase with increasing analyte RIs. For an analyte RI of 1.4, the CL peak reaches a maximum indicating that a large amount of energy is transmitted from the Y-polarized core mode to the SPP mode. When the RI is greater than 1.4, the peak intensity decreases and the sensitivity decreases along with it.

The RI sensitivity is one of the important parameters of the sensor and can be expressed by the following equation^[40]:

$ {S_\lambda }(\lambda ) = \frac{{\Delta {\lambda _{{\rm{peak}}}}}}{{\Delta {n_a}}}({\rm{nm}}/{\rm{RIU}})\quad , $ (4)

where Δλ_peak is the peak wavelength shift and Δn_a is the RI variation of the analyte. As shown in Fig. 4(b) (Color online), the resonance peak shifts by about 150 nm as the RIs vary from 1.39 to 1.395, corresponding to the RI sensitivity of 30000 nm/RIU. Similarly, the maximum RI sensitivity is about 60000 nm/RIU which is observed in the range of 1.395~1.40 where the average sensitivity is about 17800 nm/RIU. Polynomial fitting of the resonance wavelengths indicates a continuous response and the ability to determine the analyte accurately with R² = 0.99991.

The amplitude sensitivity is an important parameter to evaluate the performance of a sensor and is defined as follows^[41]:

$ {S_A}({\rm{RI}}{{\rm{U}}^{ - 1}}) = - \frac{1}{{\alpha (\lambda ,{n_a})}}\frac{{\partial \alpha (\lambda ,{n_a})}}{{\partial {n_a}}}\quad. $ (5)

Here, α(λ,n_a) is the confinement loss and ∂α(λ,n_a) is the difference of two adjacent confinement loss spectra caused by the changing RIs. Fig. 4(c) (Color online) shows the amplitude sensitivity curves for different analyte RIs. The amplitude sensitivity increases from 102.424 RIU⁻¹ to 594.241 RIU⁻¹ as the analyte RIs vary from 1.35 to 1.4 indicating enhanced resonance of the core guided mode and SPP mode.

The wavelength resolution is determined by the following equation^[42]:

$ R({\rm{RIU}}) = \Delta {n_a} \times \Delta {\lambda _{\min }}/\Delta {\lambda _{{\rm{peak}}}}\quad , $ (6)

where Δλ_peak is the peak wavelength shift, Δn_a is the variation of the analyte RIs, and Δλ_min is the spectrometer resolution that can be set to 0.1 nm. The resolution is 1.67 × 10⁻⁶ RIU when the analyte RI is changed from 1.395 to 1.4. Table 1 shows the resonance wavelengths, peak intervals, wavelength sensitivities, amplitude sensitivities, wavelength resolutions, and amplitude resolutions of the sensor in relation with RIs. A comparison of the sensor in this paper and those reported in recently published literature is presented in Table 2.

The sensor is further optimized by adjusting the structural parameters because the plasma excitation intensity depends on the plasma materials. When the analyte RI is 1.4, the loss spectra for different ITO layer thicknesses are shown in Fig. 5(a) (Color online). The resonance wavelength red-shifts with increasing ITO layer thickness. For an ITO thickness of 70 nm, the loss peak reaches a maximum and then decreases sharply, at which point it is no longer suitable for measurement. Fig. 5(b) (Color online) shows the relationship between the wavelength sensitivity and ITO layer thickness. The wavelength sensitivity increases initially and then drops with increasing ITO thickness. Therefore, the optimal ITO layer thickness is 70 nm when considering the loss and wavelength sensitivity.

Fig. 6(a) (Color online) shows the influence of the length of the ITO layer on the loss spectra for RIs of 1.395 and 1.4 (indicated by the dotted lines and solid lines). The ITO layer length only changes the level of the loss peak but does not influence the resonance wavelength. Fig. 6(b) (Color online) shows the resonance wavelengths of different ITO lengths with refractive indexes of 1.395 and 1.4. The ITO length has little effect on the sensitivity because Re(n_eff) of the SPP mode increases while Re(n_eff) of the core mode does not change. Therefore, the influence of the length of the ITO layer on the performance of the sensor can be greatly reduced in the manufacturing process. After consideration of the various factors, the optimal ITO length L is 14 μm.

The air hole spacing Λ of the PQF is another important parameter that affects the sensing characteristics. Figs. 7(a) and (b) (Color online) show the loss spectra corresponding to the air hole space for refractive indexes of 1.395 and 1.4. The resonance peak shifts to a shorter wavelength. The resonant peak increases initially and then decreases with increasing Λ because the core mode field is limited for a smaller Λ, the coupling between the core mode and SPP mode is weakened. A larger Λ increases the transmission path of the fundamental mode energy to the metal oxide layer and so coupling between the core mode and SPP mode is enhanced. As Λ is increased further, more energy is concentrated in the core to weaken resonance coupling between the core mode and SPP mode. Fig. 7(c) (Color online) shows the variation in the resonance wavelength and peak loss for refractive indices of 1.395 and 1.4. The wavelength sensitivity reaches a maximum at Λ = 5.0 μm and the peak loss shows the desirable value. Therefore, the optimal air hole spacing is 5.0 μm.

Finally, the diameters of the air holes d₁ and d₂ are optimized. Fig. 8(a) (Color online) shows the effects of d₁ on the loss spectra when the refractive index is 1.4. The resonant wavelength red-shifts with increasing d₁ from 2.0 to 2.8 μm and the peak loss also changes. When d₁ is 2.4 μm or 2.6 μm, the spectra show higher peak loss but similar wavelength sensitivity, as shown in Fig. 8(b) (Color online). However, excessive loss is not advisable considering the measurement range of the spectrometer. Hence, the optimal diameter d₁ is 2.4 μm. The effects of the air hole diameter d₂ on the loss spectra are presented in Fig. 8(c) (Color online). The loss spectra are almost unchanged with increasing d₂ from 4.6 μm to 5.4 μm, because the mode field of the core mode is not influenced by the central air hole. This reduces the requirement for machining precision in the manufacturing process of the sensor. Therefore, d₂ = 5.0 μm is the optimal diameter of the central air hole. In summary, the optimal structural parameters are: d₁ = 2.4 μm, d₂ = 5.0 μm, Λ = 5.0 μm, L_ITO = 14 μm and T_ITO = 70 nm.

A liquid RI sensor based on the ITO-coated quasi-D-shaped PQF with ultra-high sensitivity is designed and analyzed. The quasi-D-shaped fiber maintains the mechanical strength of the fiber and mitigates the manufacturing difficulty in ITO deposition. The eccentric core structure enhances the coupling between the core mode and SPP mode to achieve high RI sensitivity. The maximum wavelength sensitivity of 60000 nm/RIU is realized in the analyte RI range between 1.395 and 1.4 and the maximum wavelength resolution is 1.67×10⁻⁶ RIU. Owing to its excellent sensing properties, the quasi-D-shaped PQF-SPR sensor has immense commercial potential.