The cross-section model of the proposed the sensor is shown in Fig. 1 (a). The background material is fused silica, which is used to absorb radiation energy [15]. Inside the perfect matching layer (PML) is the analyte layer, which is assumed to have a thickness of 3.5 µm and the thickness of the PML is 1.5 µm. Inside the analyte layer is a ITO layer of thickness t. In the coverage area of the background material, there are four air holes with diameter d arranged in a square, and the distance between air holes is Λ. The large air holes can better confine the light from the fiber core and guide the light to the surface of the ITO layer, so that they can interact each other. Figure 1 (b-e) show the core fundamental mode and SPP mode in the two polarization modes.

The dispersion relationship of the proposed sensor with the refractive index of 1.39 is shown in Fig. 2. It can be seen from Fig. 2 that the resonance wavelength in the two polarization modes is the same at 1865 nm. Because the structure is symmetrical, the mode fields and loss spectrum are similar for both polarization modes. Therefore, in the subsequent parameter optimization process, the y-polarization mode of the structure is selected for analysis. It can be seen from Fig. 2 when the incident wavelength is shorter than the resonance wavelength, the energy of the fundamental mode is well confined in the fiber core. As the wavelength of the incident light increases, the fundamental mode gradually couples with the SPP mode. There is a sudden change in Re(neff) for both modes when the wavelength reaches the resonance wavelength, the energy of the fundamental mode of the fiber core transferred to the SPP mode.

The dispersion relationship of the fused silica is calculated by Sellmeier equation [16]:

$${n^2}(\lambda )=1+\frac{{{B_1}{\lambda ^2}}}{{{\lambda ^2} - {C_1}}}+\frac{{{B_2}{\lambda ^2}}}{{{\lambda ^2} - {C_2}}}+\frac{{{B_3}{\lambda ^2}}}{{{\lambda ^2} - {C_3}}}$$

1

In this expression, *B**1*, *B**2*, *B**3*, *C**1*, *C**2* and *C**3* are 0.6961663, 0.4079426, 0897479400, 0.0046791486, 0.0135120631 and 97.9340025, respectively. Here, *λ* is the incident light wavelength in vacuum.

The dielectric constant of ITO is expressed by Eq. 2 [17]:

$${\varepsilon _m}(\lambda )={\varepsilon _\infty } - \frac{{{\lambda ^2}{\lambda _c}}}{{\lambda _{p}^{2}({\lambda _c}+i\lambda )}}$$

2

In this expression, *λ**p* = 5.6497×10–7 m and *λ**c* = 11.21076×10–6 m are the plasmonic wavelength and collision wavelength of ITO, respectively, *ε**∞* = 3.80 is the dielectric constant for the infinite value of the frequency of ITO, and *λ* is the operating wavelength in micron.

The confinement loss of this sensor can be expressed by Eq. 3 [18]:

$$Loss(dB/cm)=8.686 \times {k_0} \times \operatorname{Im} ({n_{eff}}) \times {10^4}$$

3

In this expression, *k**0* *= 2π/λ* is the wave number, *λ* is in micron. *Im[n**eff**]* is the imaginary part of the effective refractive index.

The sensitivity of this sensor can be expressed by Eq. 4 [19]:

$${S_\lambda }(nm/RIU)=\frac{{\vartriangle {\lambda _{peak}}}}{{\vartriangle n}}$$

4

In this expression, *Δλ**peak* is resonance peak offset, *Δn* is the refractive index variation value.

The resolution is this sensor can be expressed by Eq. 5 [20]:

$$R(RIU)=\vartriangle n\frac{{\vartriangle {\lambda _{\hbox{min} }}}}{{\vartriangle {\lambda _{peak}}}}$$

5

In this expression, *Δλ**min* represents the offset of the wavelength.