The mechanism of the PCF-based SPR is shown in Figure 1(a). This kind of photonic crystal fiber made of PMMA, whose structure design is based on [18,19], has only one layer of air holes (6 μm in diameter) near the edge of the fiber and one single hole (14.4 μm in diameter) in the core region, and the whole fiber diameter is 250 μm. We chose PMMA as the background material of polymer PCF because biomolecules can be attached directly to the surface of the holes of the fiber [14], and in a PMMA PCF, the thickness of the sensor layer can be reduced to 10 nm (the thickness of the antigen layer only) compared to a silica microstructured optical fiber (MOF) for a biosensor, since intermediate functionalization layers can be avoided. Markos et al. calculated the sensitivity for both thicknesses of ts = 40 nm and ts = 10 nm and they found the difference to be small [20]. In this paper, we choose the thickness of the film ts = 40 nm.

Silver film of 40 nm thickness is deposited on the outer side of the fiber, which is surrounded by an aqueous sample, which can reduce the refractive index contrast between cladding-core, thus enabling single-mode operation of the fiber above 500 nm [20]. The FEM with a perfectly matched layer (PML) is chosen to calculate the effective indices of fiber modes supported by the sensor, and more accurate confinement loss of the fiber can be obtained. Figure 1(b) represents field distribution of the fundamental mode. Refractive index of the PMMA fiber can be determined by the Sellmeier equation: n = C₁ + C₂λ² + C₃λ⁻² + C₄λ⁻⁴ + C₅λ⁻⁶ + C₆λ⁻⁸, where C₁ = 2.399964, C₂ = −8.308636E−2, C₃ = −1.919569E−1, C₄ = 8.720608E−2, C₅ = −1.666411E−2, C₆ = 1.169519E−3 [21]. The relative permittivity of silver (or refractive index) is obtained from an optical handbook [22].

As shown in Figure 2(a), a relationship between wavelength and confinement loss constant of the fundamental mode is obtained, in which the black and red curves representing the refractive indices of the samples are 1.33 and 1.335, respectively. This diagram presents that a sharp loss peak in the range of 470–490 nm for each curve. That is because the resonance between the core mode and the surface plasmon makes great energy loss of light field in the core.

The attenuation constant of the fundamental mode is calculated for different incident light wavelengths. The wavelength with maximal transmission loss can be identified. It is easy to prove that the optical fiber transmission loss coefficient α_loss is: (1) α loss = 10 lg e ⋅ α = 10 lg e ⋅ 2 k 0 Im ( n eff ) = 8.686 ⋅ 2 π λ ⋅ Im [ n eff ] ( d B / m )where k₀ is the wave number (k₀=2π/λ),n_eff align is the mode effective refractive index.

When the refractive index of the sample changes from 1.33 to 1.335 (Δn_a = 0.005), the resonance peak shifts toward longer wavelength, and the amount of shift is about 6 nm (Δλ_peak). If the instrumental peak-wavelength resolution is assumed to be Δλ_min = 0.1 nm, the refractive index resolution of the corresponding sensor can be obtained as: (2) R = Δ n a Δ λ min / Δ λ peak = 8.33 × 10 − 5 RIU

Another detection method is known as the power detection at a fixed single wavelength, which is also known as amplitude-based detection method. Assume that the wavelength of the light is λ, and the transmission length is L, and then the power detection sensitivity for the refractive index variation Δn_a can be defined as: (3) S ( λ ) = ( P ( L , λ , n a + Δ n a ) − P ( L , λ , n a ) ) / P ( L , λ , n a ) / Δ n a

The sensor length L is typically limited by the modal transmission loss. A reasonable choice of a sensor length is L = 1/α(λ,n_a). Such choice of a sensor length results in a simple definition of sensitivity for the small changes in the analyte refractive index [23]: (4) S ( λ ) = 1 / P ( L , λ , n a ) ⋅ ∂ P ( L , λ , n a ) / ∂ n a = 1 / α ( λ , n a ) ⋅ ∂ α ( λ , n a ) / ∂ n a

In Figure 2(b) we present the amplitude sensitivity curve of the computed PCF-based SPR sensor. As can be seen in the diagram, the maximal sensitivity of about 106 RIU⁻¹ is achieved around 495 nm. It is typically a safe assumption that a 1% change in the transmitted intensity can be detected reliably, which leads to a sensor resolution of 9.43 × 10⁻⁵ RIU.

An important parameter of the PMMA-based SPR sensor is the confinement loss. From the contents mentioned above, we can see that the confinement loss of the proposed 250 μm PMMA fiber is very low if the core of the fiber is large enough. Low-loss fiber may be very beneficial for signal transmission, but not always for sensing applications. In order to increase the transmission loss appropriately, and improve the sensitivity of the sensor, the diameter is decreased (125 μm) and air holes (six) are introduced in the core of the PCF, which is shown in Figure 3. The refractive index of a core-guided mode is lowered by doing so, and this can facilitate phase matching with a plasmon.

The simulated results of the improved PMMA-based SPR sensor are shown in Figure 4. The relationship between wavelength (λ) and attenuation constant of the fundamental mode (α) is obtained and shown in Figure 4(a) in which the black and red curves represent the refractive indices of the samples (1.33 and 1.335, respectively). When sample refractive index changes from 1.33 to 1.335 (Δn_a = 0.005), the resonance peak shifts 6 nm (Δλ_peak) towards the longer wavelength, corresponding to the spectral detection resolution of 8.33 × 10⁻⁵ RIU. The maximal amplitude sensitivity is achieved at 493 nm and equals to 103 RIU⁻¹, as shown in Figure 4(b). That a 1% change in the transmitted intensity can be detected reliably is also assumed, leading to a sensor resolution of 9.43 × 10⁻⁵ RIU.

Compared with the first structure it is clear that the fiber loss is greatly increased when six big air holes are added in the core region of the fiber and the diameter is decreased, while maintaining similar sensitivity. We conclude that increasing the air holes, or reducing the fiber diameter can further increase the confinement loss of the PMMA PCF.

To improve the sensing properties, we add more air holes into the core of the PCF with the diameter of 125 μm, which is shown in Figure 5(a). The structure increases the transmission loss appropriately, and improves the sensitivity of the sensor. Figure 5(b) represents the fundamental mode field distribution, and the arrows indicate the polarization direction of the electric field.

The results of the improved PMMA-based SPR sensor are shown in Figure 6, which indicates that the fiber confinement loss is greatly increased again with the similar sensitivity. We can conclude that increasing the number of air holes with a smaller diameter can further increase the confinement loss of the PMMA PCF.

In order to optimize the structural parameters of the proposed PMMA PCF-based SPR sensor for high sensitivity, it is important to understand the effects these parameters have on the sensor properties. Considering the structure of Figure 5(a), the air holes of diameter d, has been employed to tune the phase matching conditions. In what follows, we will investigate the effect of size variation of the air holes. The diameter of the air holes was varied between 0.3Λ, 0.4Λ and 0.5Λ, while keeping all other structural parameters constant. Change in the confinement loss is shown in Figure 7(a) (n_a = 1.33), which shows that the loss increased with the decreasing diameter of the air holes. However the sensitivity ultimately reaches the same value, as shown in Figure 7(b).

In Figure 7, we can observe that the amount of air holes plays a significant role in the confinement loss reduction, but the diameter of the air holes almost has no influence on the PMMA PCF-based SPR sensor. The curves show that it ultimately maintains the same properties of the fundamental mode at the resonant wavelength with the changed diameters of the air holes. This is different from silica fiber structures, which is sensitive to structure changes. These properties are beneficial to the fabrication of PMMA PCFs, and it are an advantage for a polymer PCF sensor.

Surface plasmon waves, like the surface excitations, are very sensitive to the thickness of the metallic layer, so we investigated the influence on sensing properties of changes of the thickness of silver t_Ag, which is varied from 30 nm to 50 nm. As illustrated in Figure 8, the confinement loss spectra for the fundamental mode of the structure of Figure 5(a), in which the refractive index of the samples is 1.33 and other structural parameters are kept constant.

As shown in Figure 8, the resonant wavelength shifts to longer wavelengths as the thickness of the silver layer increases. The resonant wavelength shifts from about 1 nm to 2 nm for t_Ag values of 30 nm and 50 nm. In addition, the loss spectra shows a downward trend when the thickness of the silver layer increases. The electric field will be difficult to sense through the silver layer when the thickness is larger. Therefore, we should establish an appropriate t_Ag for the corresponding sensing regimes.