1. Introduction

Surface plasmon resonance (SPR) [1] has been widely applied in optical sensing [2], especially in chemical and biomedical detections [3, 4]. Among these SPR sensors, fiber sensor (FS) has attracted much attention due to their simplicity and portability, while solid core based SPR FS has already been extensively studied [5–10]. Compared with the solid one, hollow FS shows more convenience since the sensed medium, generally liquid, flows inside the fiber and requires less space. Therefore, hollow fiber is more practical and applicable in optical sensing, and hollow core based SPR FS has also been realized [11–13].

However, a necessary condition for SPR is, the refractive index (RI) of incident medium must be larger than the RI of insulator layer in order to realize attenuated total reflection. And for conventional SPR configuration, such as Otto configuration and Kretschmann configuration, once the total reflection condition is not satisfied, no resonance can be observed, which limits the detection range of SPR based sensors.

Similar to conventional SPR configuration, the metal cladding waveguide [14], which consist of metal-insulator-metal (MIM) layered structure, can also support the excitation of surface modes. Moreover, it can additionally support the excitation of guided modes. If the total reflection condition is satisfied, surface mode can be excited. Otherwise, guided mode resonance can be observed. These characteristics of MIM waveguide have already be applied in optical sensing [15–18], but only limited to conventional prism-coupling configurations. So far, no effort has been paid to apply the characteristics of MIM waveguide in hollow FS.

In this work, we propose a modified hollow FS based on the metal cladding waveguide configuration, which supports the propagation of both surface modes and guided modes, to extend the detection range of RI. The proposed FS can be realized by coating an MIM triple layer on the inner surface of the hollow fiber. Due to the dispersion characteristics of the MIM waveguide, the designed FS can work in surface mode when detecting liquid with a higher RI than the insulator, and in guided mode when detecting liquid with a lower RI than the insulator.

2. Metal cladding waveguide

The basic structure of metal cladding waveguide is depicted in Fig. 1. An intermediate insulator layer with thickness $d_i$, is sandwiched by identical metal layers. Note that, while the thickness of the metal reaches several hundred nanometers, the light will be almost totally absorbed due to the high loss of the metal, so the structure is equivalent to an insulator layer surrounded by two infinite metal in this circumstance.

 

Fig. 1 Schematic of metal cladding waveguide.

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Denote the dielectric constant of the insulator and metal as ${\epsilon }_i$ and ${\epsilon }_m$, respectively. The dispersion equation of the symmetrical MIM waveguide for transverse magnetic (TM) polarization can be generally expressed as [19]

Here $k_i=\sqrt{{\epsilon }_i{k}_0^2-{\beta }^2}$ refers to the perpendicular wave vector in the insulator, while ${\alpha }_m=\sqrt{{\beta }^2-{\epsilon }_m{k}_0^2}$ represents the attenuation factor in the metal. $\beta$ is the propagation constant of the waveguide and $k_0$ is the wave vector in the vacuum. $m$ denotes the order of mode.

Assume the structure is a silver coated silica waveguide. The optical properties of silver and silica can be estimated by Drude model and Sellmeier relation, respectively, as mentioned in reference [5] and [12]. Then we can numerically obtain the dispersion curves of TM modes according to Eq. (1), as is presented in Fig. 2.

 

Fig. 2 Dispersion curves of silver-silica-silver waveguide. Blue solid lines represent the dispersion of corresponding modes, while red dashed lines indicate the light line in silica waveguide. (a) Dispersion relation presented in ω-β relationship. The thickness of the silica layer here is 700 nm. (b) Dispersion relation presented in d_i-β relationship. The wavelength here is 632.8 nm.

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Figure 2(a) shows the dispersion curves of the waveguide in a relationship, where the thickness of silica layer is set as 700 nm. The red dashed line represents the light line in the silica, which is determined by $\beta =n_i\omega /c$, where $c$ denotes the speed of light in the vacuum, and $n_i$ denotes the RI of silica. The light line actually defines a boundary between surface modes and guided mode. The modes below the light line are surface modes, while others are guided modes. Therefore, from the curves we can identify that, TM₀ mode is totally a surface mode, since it is always below the light line, while TM₁ mode is a guided mode before crossing the light line, and become a surface mode after the intersection point. In addition, TM₀ and TM₁ modes tend to coincide as the frequency increases. Other high order TM modes are all pure guided modes, since they are all above the light line.

The influence of silica thickness on the dispersion of the waveguide is also presented in Fig. 2(b), which is calculated under a typical wavelength, 632.8 nm. As can been seen, for any mode higher than TM₀, there is a cutoff thickness, and a higher order of mode corresponds to a larger cutoff thickness. Therefore, the larger the silica thickness is, the more modes the waveguide contains. But note that, TM₀ mode has no cutoff thickness, which means this mode always exists in the waveguide, with any thickness. Moreover, as silica thickness increases, TM₀ and TM₁ mode gradually degenerate and become two isolated SPPs.

As Fig. 3(a) depicts, a prism-coupling configuration is generally adopted to excite the optical modes in the waveguide. The spectrum of the waveguide can be calculated through transfer matrix method [20], which gives the reflection coefficient of the system as

 

Fig. 3 (a) Prism-coupling configuration to realize mode resonance in metal cladding waveguide. (b) The spectra of the configuration presented in Fig. 3(a). Blue line and red line refers to the spectrum while the incident angle equals 5° and 40.5°, respectively.

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Presume the prism is made up of widely used 2S2G chalcogenide glass, and the thickness of silver layer and silica layer is respectively 40 nm and 700 nm. Following Eq. (2), we calculate the spectrum of the configuration, as is shown in Fig. 3(b).

The red line and blue line in Fig. 3(b) refer to the spectra of the configuration with different incident angles. For the red line, the incident angle is 40.5°, which is larger than the critical angle between prism and silica. Therefore, the two dips of the red line are induced by surface mode resonance, and the one with longer wavelength corresponds to TM₀ mode, while the one with shorter wavelength indicates TM₁ mode. For the blue line, the incident angle is 5°, which is much smaller than the critical angle. Thus, the dips in the spectrum all represent guided mode resonance. From the comparison between the two spectra, it is obvious that the resonance width of guided mode is much smaller than the surface mode, though the surface mode is more sensitive. These features will be utilized in designing MIM waveguide based FS.

3. Hollow fiber sensor

In the above section, we have analyzed the dispersion characteristics of MIM waveguide, and presented the resonance properties. Next, we are going to apply this structure in hollow FS.

As is shown in Fig. 4, the proposed model is a hollow fiber with a silver-silica-silver triple layer coated on the inner surface, where the first silver cladding is several hundred nanometers and can be regarded as infinite. The hollow core is filled with sensed liquid, while the light propagates in the hollow core and interact with the sensed liquid. The length and inner diameter of the hollow fiber is denoted as $L$ and $D$, respectively. The silver layer can be coated with chemical deposition method, while the silica layer can be coated with liquid phase coating method. The detailed fabrication method has been described in our previous works [12, 21].

 

Fig. 4 The structure of hollow fiber sensor based on metal cladding waveguide.

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Since the bore size of hollow fiber is generally much larger than the wavelength of input light, here we employ a geometrical optical model to calculate the transmission spectrum of the hollow fiber, which gives the transmissivity of the hollow FS as [22]

Here ${\phi }_0$ represents the divergence angle of the input Gaussian beam, while $R(\phi )$ denotes the reflectivity at angle $\phi$, which is also calculated through aforementioned transfer matrix method. $N=L\cot \theta /D$ refers to the times of reflection, where $\theta$ represents the real incident angle of light in the fiber.

We design the FS with length $L=5\text{cm}$, diameter $D=0.7\text{mm}$. The thickness of the silica layer here is 900 nm, while the thickness of the inner silver layer is 20 nm. The divergence angle of the input light is 5°. This is an appropriate parameter setup according to our analysis.

3.1 High RI liquid

We firstly evaluate the sensing characteristics of the designed FS when filled with high RI liquid. Representative high RI liquids include benzene and carbon disulfide, with RI around 1.50 and 1.60, respectively. So here we select 1.53 as a reference RI for the detection. The calculated spectrum of the fiber under this condition is shown in Fig. 5.

 

Fig. 5 Performance of the designed fiber sensor when detecting liquid with RI = 1.530. (a) The spectrum of the fiber. (b) The dependence of resonance wavelength on the RI of sensed liquid. The red circles and blue triangles represent TM0 and TM1, respectively.

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As can be seen, the two dips in Fig. 5(a) respectively represents the resonance of surface mode, TM₀ and TM₁. For TM₀ mode, the resonance wavelength (RW) is about 710.3 nm, while the full width at half maximum (FWHM) is about 69.4 nm. For TM₁ mode, the RW is about 547.8 nm, while the FWHM is about 50.6 nm. The transmissivity at the RW of TM₀ and TM₁ is 61.42% and 19.00%, respectively.

The relationship between RWs and the RI of sensed liquid is presented in Fig. 5(b). As the RI of sensed liquid increases from 1.520 to 1.540, the RW of TM₀ mode decreases from 755.9 nm to 674.5 nm, while the RW of TM₁ mode decreases from 576.3 nm to 523.9 nm. Therefore, the average sensitivity of resonance dip of TM₀ and TM₁ in the discussed range is about 4070 nm/RIU and 2620 nm/RIU, respectively. As a result, the FOM, defined as sensitivity divided by FWHM, is approximately 58.6 RIU⁻¹ and 51.8 RIU⁻¹, respectively.

Compared with other SPR based sensors [12], the designed sensor retains the high sensitivity, which is an important advantage for wavelength interrogation.

3.2 Low RI liquid

The proposed FS can also detect liquid with low RI. The most common used low RI liquid is generally water solution, so here we select the RI of water, which is about 1.330, as our low RI for detection.

The spectrum of designed FS when filled with water is presented in Fig. 6. As can be seen, there are three resonance dips in the spectrum, denoted as dip 1 dip 2 and dip 3. As the RI of the liquid is lower than the silica layer, all the dips refer to the guided modes resonance. It should be noted that the number of the dip here does not correspond to the order of guided mode, since we only consider the dips in the presented wavelength range. The sensing properties of the three resonance dips observed in the spectrum are shown in Table 1.

 

Fig. 6 Spectrum of the fiber sensor when detecting liquid with RI = 1.330.

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Table 1. The sensing properties of resonance dips presented in Fig. 6.

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Generally, with the increase of the order of mode, both FWHM and sensitivity of resonance dip decrease. As presented in Table 1, while the sensitivity of the dip of guided mode maintains an acceptable level, the width is much smaller, leading to a large FOM for sensing. The FOM of the dip increases from 92.4 RIU⁻¹ to 237.7 RIU⁻¹, which is very high compared with the surface mode resonance. Meanwhile, the minimum transmissivities (MTs) of all the three dips keep a low level, being about 14.70%, 20.98% and 32.37%, respectively, which additionally enhances the sensing performance.

Since the FOMs of the dips are very high, it would be very effective to utilize these guided modes for intensity interrogation. Therefore, we calculate the relationship between transmissivity and the RI of sensed liquid for each dip, as presented in Fig. 7. The wavelength of input light in each case is the initial RW of the corresponding dip, i.e. 664.2 nm, 449.4 nm or 345.2 nm. As we can see in Fig. 7, transmissivities dramatically change as the RI changes. For example, as the RI of liquid decreases from 1.330 to 1.329, the transmissivity of the three dips respectively increases to 24.45%, 44.96% and 67.24%, and the difference is respectively 9.75%, 23.98% and 34.87%, which indicates the transmissivity is very sensitive to the RI. As the guided mode with a higher order has a larger FOM, the change in transmissivity is also larger. The high dependence of transmissivity on the RI of sensed liquid consequently leads to a high resolution, which is very significant for intensity interrogation. Note that, although the wavelengths of the monochromatic input lights used here are not among commonly used laser sources, the wavelength location of resonance dip can be easily adjusted to be fit for those lasers by adopting appropriate dielectric layer thickness.

 

Fig. 7 Transmissivities varying with the refractive index of the sensed liquid. Blue, black and red line respectively represents the situation of dip 1, dip 2 and dip 3 in Fig. 6, and the corresponding wavelength is respectively 664.2 nm, 449.4 nm and 345.2 nm.

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4. Conclusion

We have demonstrated that, by applying metal cladding waveguide configuration in hollow HS, the detection range of RI of liquid can be significantly extended. Under an appropriate parameter setup, the performance of the proposed FS is analyzed and discussed. The results show that, when filled the hollow fiber with high RI liquid, surface modes can be excited, with large sensitivities. And when filled the fiber with low RI liquid, guided modes can be excited, with large FOMs. We hope this work could promote the application of hollow FS for optical detections.