# High Sensitivity Photonic Crystal Fiber Refractive Index Sensor with Gold Coated Externally Based on Surface Plasmon Resonance

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}. Due to its high sensitivity, the proposed sensor can be used for practical biological and chemical sensing.

## 1. Introduction

^{−1}at the refractive index range of 1.390~1.395.

## 2. Structural and Theoretical Modeling

_{0}= 0.2 μm. The air holes in the first ring have a radius of r

_{1}= 0.4 μm, and they are arranged in a clockwise rotation of 60°. The distance between the center of the air holes and the center of the fiber is d = 2 μm. In the second ring, the air holes have a radius of r

_{2}= 0.6 μm and they rotate clockwise at 30°. The distance between the first layer and the second is $\mathsf{\Lambda}$ = 1.2 μm, and two holes are missing in the opposite vertices of the second ring. The thickness of the gold layer is t

_{g}= 35 nm. Outside the gold layer is the analytical layer.

_{1}= 0.6961663, B

_{2}= 0.4079426, B

_{3}= 0.8974764, ${\lambda}_{1}$ = 0.0684043 μm, ${\lambda}_{2}$ = 0.1162414 μm, ${\lambda}_{3}$ = 9.896161 μm.

_{g}. The dielectric constant of gold can be expressed as Drude-Lorentz [19], which is expressed as follows:

## 3. Simulation Results and Analysis

_{g}) on the confinement loss of the core-guided mode. It can be seen from the figure that when t

_{g}increases from 30 to 50 nm, the resonance intensity decreases and the resonance wavelength red-shifts. This is because the thicker the t

_{g}, the higher the damping loss. As a result, the core-guided mode has less energy penetration into the gold film and the coupling effect becomes weaker.

_{0}) on the confinement loss of the core-guided mode. It can be seen from the diagram that, when r

_{0}changes from zero to 0.25 μm, the resonance intensity increases, and the resonance peak becomes sharper and the resonance wavelength shifts red. This is because the change of r

_{0}affects the refractive index of the core-guided mode. Thus, the phase matching between SPP mode and the core-guided mode is affected, which in turn leads to a change in the resonance intensity, resonance peak, and the resonance wavelength. Therefore, we can change the size of r

_{0}to optimize the sensor performance.

_{1}) on the confinement loss of the core-guided mode. It can be seen that when r

_{1}increases from 0.34 to 0.42 μm, the resonance intensity increases slowly and the resonance wavelength shifts red. This is because the change of r

_{1}affects the refractive index of the cladding region, leading to the change of the phase matching condition. Figure 6 displays the influence of the size of the-second-layer air holes (r

_{2}) on the confinement loss of the core-guided mode. It can be seen that with the increase of r

_{2}(from 0.57 to 0.69 μm), the resonance intensity decreases, the resonance peak becomes sharper, and the resonance wavelength shifts blue.

^{−5}RIU.

_{a}, $\partial \alpha (\lambda ,{n}_{a})$ is the difference of confinement loss due to two adjacent refractive indexes of two analytes. When the refractive index of the analyte is 1.390, the maximum amplitude sensitivity of the sensor can reach 641 RIU

^{−1}at the wavelength of 0.893 μm.

## 4. Conclusions

_{0}= 0.2 μm, r

_{1}= 0.4 μm, r

_{2}= 0.6 μm, $\mathsf{\Lambda}$ = 1.2 μm, d = 2 μm, and t

_{g}= 35 nm. Additionally, the maximum wavelength sensitivity of the sensor can reach as high as 11,000 nm/RIU and the amplitude sensitivity 641 RIU

^{−1}at the refractive index range of 1.390~1.395. The proposed sensor is simple, reliable, easy to fabricate, and highly applicable, and it can be used for practical biological and chemical sensing.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**(

**a**) Dispersion relation between surface plasmon polaritons (SPP) mode and core-guided mode; optical field distribution of (

**b**) the core-guided mode, (

**c**) the SPP mode, and (

**d**) Optical field distribution in phase matching. $\left({n}_{a}=1.36,{r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 3.**The confinement loss of the core-guided mode for different thickness of the gold layer. $\left({n}_{a}=1.36,{r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m}\right)$.

**Figure 4.**The confinement loss of the core-guided mode for different size of the central air hole. $\left({n}_{a}=1.36,{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 5.**The confinement loss of the core-guided mode for different size of the-first-layer air holes. $\left({n}_{a}=1.36,{r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 6.**The confinement loss of the core-guided mode for different size of the-second-layer air holes. $\left({n}_{a}=1.36,{r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 7.**Loss spectral when increasing analyte RI from 1.350 to 1.395. $\left({r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 8.**The resonance peak when increasing analyte Re from 1.350 to 1.395. $\left({r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

**Figure 9.**Amplitude sensitivity when increasing analyte RI from 1.350 to 1.395. $\left({r}_{0}=0.2\mathsf{\mu}\mathrm{m},{r}_{1}=0.4\mathsf{\mu}\mathrm{m},{r}_{2}=0.6\mathsf{\mu}\mathrm{m},\mathsf{\Lambda}=1.2\mathsf{\mu}\mathrm{m},d=2\mathsf{\mu}\mathrm{m},{t}_{g}=35\mathrm{nm}\right)$.

The Structure of PCF | Detection RI Range | Maximum Sensitivity |
---|---|---|

Double core structure [2] | 1.35–1.36 | 2200 nm/RIU |

Graphene-Based structure [21] | 1.345–1.350 | 3400 nm/RIU |

Hollow-core silver coated structure [22] | 1.36–1.37 | 4200 nm/RIU |

Double core structure [23] | 1.33–1.34 | 4000 nm/RIU |

Double core structure [24] | 1.36–1.37 | 9000 nm/RIU |

Structure with Gold Coated Externally (our work) | 1.390–1.395 | 11,000 nm/RIU |

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**MDPI and ACS Style**

Li, X.; Li, S.; Yan, X.; Sun, D.; Liu, Z.; Cheng, T.
High Sensitivity Photonic Crystal Fiber Refractive Index Sensor with Gold Coated Externally Based on Surface Plasmon Resonance. *Micromachines* **2018**, *9*, 640.
https://doi.org/10.3390/mi9120640

**AMA Style**

Li X, Li S, Yan X, Sun D, Liu Z, Cheng T.
High Sensitivity Photonic Crystal Fiber Refractive Index Sensor with Gold Coated Externally Based on Surface Plasmon Resonance. *Micromachines*. 2018; 9(12):640.
https://doi.org/10.3390/mi9120640

**Chicago/Turabian Style**

Li, Xudong, Shuguang Li, Xin Yan, Dongming Sun, Zheng Liu, and Tonglei Cheng.
2018. "High Sensitivity Photonic Crystal Fiber Refractive Index Sensor with Gold Coated Externally Based on Surface Plasmon Resonance" *Micromachines* 9, no. 12: 640.
https://doi.org/10.3390/mi9120640