Numerical study of a highly sensitive surface plasmon resonance sensor based on circular-lattice holey fiber

Jian-Fei Liao(廖健飛) Dao-Ming Lu(盧道明) Li-Jun Chen(陳麗軍) and Tian-Ye Huang(黃田野)

1School of Mechanical and Electrical Engineering,Wuyi University,Wuyishan 354300,China

2School of Mechanical Engineering and Electronic Information,China University of Geosciences(Wuhan),Wuhan 430074,China

3College of Physics and Electronic Information,Gannan Normal University,Ganzhou 341000,China

Keywords: surface plasmon resonance,holy fiber,fiber optics sensor

1. Introduction

In recent years,surface plasmon resonance(SPR)sensors based on photonic crystal fiber(PCF)or holey fiber(HF)have attracted considerable interests due to their excellent sensing characteristics including high detection accuracy, level-free and real-time detection.[1–11]In PCF-based SPR sensing technology,the crucial factor is that the phase matching condition between the fiber core mode and the surface plasmon mode is fulfilled. However,the phase matching condition is always difficult to achieve since the difference of the refractive index between these two modes is usually large. Furthermore, the sensing property is highly dependent on the plasmon active metal materials since the optical properties of the metal materials have a large influence on the sensing performance,and in general,gold and silver are adopted.[12–17]

Nowadays, for the purpose of realizing the SPR effect and improving the sensing performance, a large number of PCF-SPR sensors with various novel designs have been investigated.Several PCF-based SPR sensors with typical structures are as follows. Rifatet al.designed a PCF-SPR sensor by employing a hexagonal-lattice structure.[18]Their simulation results showed that a maximum wavelength sensitivity of 3000 nm/refractive index unit(RIU)and a resolution of 2.4×10-5RIU was achieved. In 2014,Otupiriet al.designed a PCF-SPR sensor with a slotted structure.[19]The resolution values of thex-polarized andy-polarized modes were up to 5×10-5RIU and 6×10-5RIU, respectively. Moreover, the amplitude sensitivities of these two polarized modes can be as high as 3×10-5RIU and 4×10-5RIU,respectively. In 2015,Rifatet al.designed a new type of PCF-SPR sensor by keeping the metallic film outside of the sensor structure.[20]The refractive index resolution of the sensor can reach to 2.5×10-5RIU.In 2016, Huang designed a PCF-SPR sensor by using a Dshaped fiber structure.[21]The results showed that a high sensitivity of 6000 nm/RIU was realized through optimizing the sensor design. In 2017,Liuet al. designed a PCF-SPR sensor with two open-ring channels.[22]The resonance wavelength of the sensor lied in(2.55,2.9)μm.The sensor maximum resolution and average wavelength sensitivity were 7.69×10-6RIU and 5500 nm/RIU, respectively. In 2018, Tonget al. proposed a PCF-SPR sensor with muti-core design.[23]An average wavelength sensitivity of 3435 nm/RIU with a resolution of 2.91×10-6RIU was achieved. In 2020, Wanget al.designed a PCF-SPR sensor with dual fiber structure.[24]The maximum spectral sensitivity and index resolution were as high as 17500 nm/RIU and 5.71×10-6RIU correspondingly.However, in order to induce the efficient SPR effect, most of PCF-based SPR sensors are coated with gold or silver,which have several obvious limitations. On the one hand, the resonance bandwidth of these sensors coated with gold is always so broad that decreases the sensing performance because gold has a large absorption coefficient. Meanwhile,chemical properties of silver is unstable and is easily oxidized, which also destroys the detection accuracy.

In this paper,with the aim of overcoming the above limitations, a new type of SPR sensor based on circle lattice HF coated with indium tin oxide (ITO) is designed. By using of the full-vector finite element method,the sensing characteristics of our proposed sensor including wavelength sensitivity,wavelength interrogation resolution,and amplitude sensitivity are numerically investigated carefully. The results show that the SPR effect can be efficiently enhanced by using a groove design,and the maximum wavelength interrogation sensitivity can reach to 1.76×104nm/RIU.

2. Fiber design and theory

The structure diagram of our proposed HF-based SPR sensor is given in Fig. 1. The proposed sensor design includes two layers of air holes arranged in a circular lattice and a groove. For the purpose of enhancing the interaction between the core-guided mode and the SPP mode, there is a layer of ITO film located at the bottom of the groove. The main parameters of our proposed sensor are inner air hole diameterd1, outer air hole diameterd2, the pitch in the inner ringR1,the pitch in the outer ringR2,the spacing between the bottom of the groove and the central of the HFh, the width of the groovew,and the thickness of the ITO layert. The refractive index (RI) of analyte isna. As the host material, the chromatic dispersion of silica is obtained by using the Sellmeier equation.[25]The permittivity of ITO is calculated by employing the Drude model[21]

whereεis the permittivity of ITO,ε∞=3.9 is the high frequency permittivity,ωis the angular frequency,ωpis the plasma frequency,Γ=1.8×1014rad/s is the electron scattering rate,m*=0.35m0,m0=9.1×10-31kg is the rest mass of electrons,n= 1.8×1021cm-3is the carrier concentration of ITO, andeis the electron charge. Note that our proposed HF can be drawn by using the stack-and-draw technology while the groove structure can be achieved by using the focused ion-beam milling technology. The ITO layer can be deposited by employing the high-pressure chemical vapor deposition method.

Fig.1. The cross-structure of the proposed HF-based SPR sensor.

With the aim of investigating the sensing performance precisely, the sensor loss CL, wavelength sensitivitySλ, detectable index resolutionRand amplitude sensitivitySaare calculated by adopting the following formulas:[21]

whereλand Im(neff) are the wavelength and the imaginary part of theneff, correspondingly. Δλpeakstands for the resonance wavelength variation. Δnadenotes the RI changes.Δλminis the wavelength resolution of the instrument. ΔCL is the sensor loss changes while CLinitialis the sensor loss at initial state.

3. Simulation results and discussion

For the purpose of calculating the electric field distribution and its modal effective index, we use a full-vector finite element method with the PML boundary conditions to solve Maxwell equations on the fiber structure and output the complex eigenvalues,and then the complex modal effective index can be obtained. The real part of the complex modal effective index(Re(neff))represents the modal dispersion property while the imaginary part of the complex modal effective index stands for the modal loss. Note that there are 118715 degrees of freedom over the whole holey fiber cross-section. Furthermore, the triangular and edge elements are 16934 and 1281,respectively. Firstly,we study the resonance properties of the sensor with parametersd1=1 μm,d2=2 μm,R1=2.5 μm,R2=5.5 μm,w=2.6 μm,h=2.86 μm,t=70 nm,na=1.34,and the simulation results indicate that onlyy-polarized fundamental mode can effectively interact with the surface plasmon polaritons (SPP) mode. Hence, the coupling properties between these two modes are investigated in this work. Figure 2 gives the modal profiles at different wavelength and dispersion properties of our proposed sensor. It is apparent from this figure that the real part of the refractive index of they-polarized mode (Re(ny)) is much smaller than that of the SPP mode(Re(nspp))in the short wavelength region. However,if the incident light wavelength increases to 1.555 μm,we can find that Re(ny)=Re(nspp)since the SPR effect can modulate the phase of the electromagnetic wave. It means the phase-matching condition of the sensor is met. This resonance phenomenon can also be proved by the loss curve of they-polarized mode,which exists a sharp loss peak at 1.555 μm. Moreover, the coupling property of the sensor can be studied from the mode distributions of they-polarized fundamental and SPP modes,which are inserted in Fig. 2. Such as whenλ= 1.47 μm,these two modes can not interact with each other because the phase-matching condition is not met. But at 1.555 μm, the mode energy of they-polarized mode is largely transferred into the SPP mode. Further increasing the light wavelength to 1.62 μm, these two modes become decoupled again since the coupling condition is destroyed.

Fig. 2. The real parts of the effective indices and loss with na =1.34.Insets are the electronic field profiles of two resonance modes.

Fig.3. Loss of the y-polarized fundamental mode by changing na from 1.31 to 1.33 when t=65 nm and 75 nm.

Secondly,the effect ofton the sensing property with parametersd1=1 μm,d2=2 μm,R1=2.5 μm,R2=5.5 μm,w= 2.6 μm, andh= 2.86 μm is investigated. According to Fig. 3(a), it indicates that the resonance wavelength shifts to the longer wavelength by increasingnafrom 1.31 to 1.33 whent=65 nm. For instance, the resonance wavelength is 1.364 μm atna=1.31 while the resonance wavelength moves to 1.442 μm atna= 1.33. This is because Re(nspp) increases with the increment ofnawhile Re(ny) almost keeps unchanged. Thus the phase matching point moves to the longer wavelength region. On the contrary, the peak loss decreases with increasingnafrom 1.31 to 1.33 whentis equal to 65 nm. The reason is that the interaction strength between they-polarized fundamental mode and SPP mode decreases with the increment ofna, and then less mode energy of they-polarized mode is coupled into the SPP mode. Figure 3(b)gives the resonance property of our proposed sensor att=75 nm whennaincreases from 1.31 to 1.33. One can learn that the resonance and loss properties att=75 nm is similar to that of att=65 nm. However,compared Figs.3(a)with 3(b),it can be found that the resonance wavelength at the samenashifts to the longer wavelength iftchanges from 65 nm to 75 nm. According to Eq. (4), the wavelength sensitivities of 3800 nm/RIU and 4400 nm/RIU att=65 nm are obtained whennachanges from 1.31–1.32 and 1.32–1.33,respectively.But iftincreases to 75 nm,the wavelength sensitivities of the sensor increases to 4500 nm/RIU and 5500 nm/RIU whennachanges from 1.31–1.32 and 1.32–1.33,respectively.

Besides wavelength interrogation sensitivity, amplitude sensitivity is another important factor to evaluate its sensing quality. Therefore, we study the influence ofton the amplitude sensitivity according to Eq.(6),and the numerical results are given in Fig.4. Note that the sensor parameters are set tod1=1 μm,d2=2 μm,R1=2.5 μm,R2=5.5 μm,w=2.6 μm andh=2.86 μm. It is apparent from this figure that the value of the amplitude sensitivity is almost unchanged iftvaries from 65 nm to 75 nm. For example,the maximum amplitude sensitivity is 83.29 RIU-1att=65 nm while the maximum amplitude sensitivity is 82.39 RIU-1att=75 nm. This is because iftvaries from 65 nm to 75 nm,the coupling efficiency between these two modes is almost unchanged except that the coupling wavelength shifts to the longer wavelength,which is proved by Fig. 3. Moreover, the amplitude sensitivity curves move to the longer wavelength when the thickness of ITO film increases from 65 nm to 75 nm. Similar phenomena can be found in Refs.[26,27].

Fig.4. Influence of the thickness of ITO film on the amplitude sensitivity with na varying from 1.31 to 1.32.

Table 1. Comparison of the sensing quality within na range from 1.31 to 1.36 when t=65 nm,70 nm and 75 nm,respectively.

Table 2. Influence of h on the sensing quality when na varies from 1.31 to 1.36.

For the purpose of further investigating the sensing property of our proposed sensor,Table 1 gives the summary of several performance indexes withinnarange from 1.31 to 1.36 whent=65 nm, 70 nm, and 75 nm, respectively. One can find from this Table thatthas large influence on the peak wavelength, wavelength sensitivities and wavelength for the maximum amplitude sensitivity, but has small influence on the peak loss and maximum amplitude sensitivities. The resonance wavelength and the wavelength sensitivity of the designed sensor increase with increasingtfrom 65 nm to 75 nm whennalies in (1.31, 1.36). Such as whennais equal to 1.35, the peak wavelength and the wavelength sensitivity att=65 nm are 1.569 μm and 9800 nm/RIU while the peak wavelength and the wavelength sensitivity att=75 nm are up to 1.706 μm and 17600 nm/RIU, respectively. By using Eq.(5),we can obtain that the detectable index resolution can reach up to 5.68×10-6RIU if the wavelength resolution of the instrument is 0.1 nm. Moreover, the changing trend of the wavelength for the maximum amplitude sensitivity is the same as that of the peak wavelength. The main reason is that the maximum amplitude sensitivity is proportional to the maximum ΔCL, which always happens nearby to the resonance wavelength. Benefiting from its excellent sensing property,our designed sensor should be very suitable for chemical and biological sensing applications.Note that the other parameters are set tod1=1 μm,d2=2 μm,R1=2.5 μm,R2=5.5 μm,w=2.6 μm,andh=2.86 μm.

Finally, we study the effect ofhon the sensing performance with parametersd1=1 μm,d2=2 μm,R1=2.5 μm,R2=5.5 μm,w=2.6 μm, andt=70 μm whennavaries from 1.31 to 1.36, and the simulation results are given in Table 2. According to this Table,we can learn that the peak loss decreases with increasinghfrom 2.76 μm to 2.96 μm whennakeeps unchanged. The reason is that the interaction strength between these two modes becomes weaker ifhchanges from 2.76 μm to 2.96 μm. However,other performance parameters increase with the increment ofh, especially the wavelength sensitivity. For example, the wavelength sensitivity increases from 11900 nm/RIU to 13300 nm/RIU with the increment ofhfrom 2.76 μm to 2.96 μm whennachanges from 1.35 to 1.36.

Table 3. Comparison of other PCF-SPR sensor sensitivity.

Table 3 gives a comparison of other PCF-SPR sensor sensitivity. Commonly,high sensitivity and high-accuracy detection makes our proposed sensor much more competitive than these traditional PCF-based SPR sensors.[18,28]Compared to these grooved PCF-based SPR sensors coated with gold or silver film,[29–31]the cost of our proposed HF-based SPR sensor coated with ITO is much lower. Furthermore, although other designs including inner-coated PCF-based SPR sensors have high sensitivity,[32,33]our proposed open-groove structure has the obvious advantages that an open-groove design is easier to fabricate and has an open sensing channel, which makes it very suitable for the real-time sensing.

4. Conclusion

In this paper,a new type of SPR sensor based on circularlattice HF with an open sensing channel is proposed to achieve high sensitive sensing. The coupling resonance properties and sensing performance of our designed sensor are studied carefully. The research findings indicate that only theypolarized fundamental mode can effectively interact with the SPP mode,which can efficiently eliminate the crossing interference between two fundamental polarized core modes. Furthermore, the maximum wavelength sensitivity and the detectable index resolution can reach as high as 17600 nm/RIU and 5.68×10-6RIU, respectively. Benefiting from its excellent sensing characteristics,our proposed HF-based SPR sensor is of great potential for chemical and biological sensing applications.

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant No. 61765003) and the Scientific Research Foundation for the Wuyi University (Grant No.YJ202104).