Design and analysis of highly sensitive solid core gold-coated hexagonal photonic crystal fiber sensor based on surface plasmon resonance

Abstract. A surface plasmon-based hexagonal photonic crystal fiber sensor is numerically computed and studied covering a large span of analyte refractive index from 1.33 to 1.40. Structural design parameters are optimized to improve the sensor performance. Investigation of sensor sensitivity has been performed by analyzing the electromagnetic behavior of light using finite element method-based mode solver. The studied sensor yields the maximum amplitude sensitivity of 3958.84  RIU  −  1 at analyte RI of 1.39 and moderate wavelength sensitivity of 8000  nm RIU  −  1 at analyte RI of 1.40. The observed results are also presented by changing the gold layer thickness, lattice period, and air hole diameter. The reported plasmonic sensor is an appealing aspirant in the field of biochemical sensing, biomolecule detection, and biological sample recognition.


Introduction
Sensors are essential devices that detect the component amount of an estimation article and convert this amount into a readable signal, which is shown on an instrument. Furthermore, detecting technology is an innovation that utilizes sensors to gain data by sensing the physical, chemical, and biological properties and converting them into coherent signal. In recent years, optical sensing technique (OST) gained attention due to its numerous applications in different aspects of science and technology from industry to real life. 1,2 In the present era, surface plasmon resonance (SPR)-based photonic sensors have become the primary technique in OST. 3 Furthermore, SPR has been an important research subject for recent 20 years due to its accommodation in real-time sample detection, nonobtrusive, high affectability, and label-free handling. 4 Initial prism-based SPR sensor 5 and optical fiber-based SPR sensor 6 had some limitations in terms of numerical aperture and complexity in fabrication. SPR sensors using photonic crystal fiber (PCF) are used to overcome these limitations and become popular because of appealing properties, such as design flexibility, tunable dispersion and birefringence, tight light confinement, and single-mode function. 7 These SPR-PCF sensors are proving themselves as a suitable candidate in various areas such as water testing, salinity testing, 8 gas, liquid, and drug detection, 9 food safety, 10 biochemical sample recognition, and blood component detection. 11 Internal coating and external coating are two well-known approaches for plasmonic material coating. In internal coating, metal is coated at the inner layer of the air hole. 12 Although this approach provides high sensor performance, it has two major drawbacks: first, the uniform metal deposition during fabrication is a challenging task, and second, the analyte injection into the micron-sized air hole limits its real-time application. 13 The external coating approach has been utilized to resolve these drawbacks, 14 where metal layer is circulated on the external boundary of the PCF. The analyte layer is in direct contact with plasmonic metal layer. In general, detecting attributes of sensors rely upon the selection of plasmonic materials. Gold, copper, silver, and graphene are a few plasmonic materials that have been used in the recent research work related to photonic sensors. [15][16][17][18] Hossain et al. presented a hexagonal PCF biosensor utilizing an external sensing approach. This silver-coated PCF ensures the highest wavelength sensitivity (WS) of 21;000 nm RIU −1 with amplitude sensitivity (AS) in the order of 2456 RIU −1 . 19 Shakib et al. demonstrated a structure of PCF biosensor to acquire the extreme WS in value of 16;000 nm RIU −1 and an AS to 780 RIU −1 . In the proposed model, outer ring air holes are cut to make slots, which are difficult to fabricate. 20 A number of cores also affect the performance of the sensor. A double-core SPR-PCF sensor is designed and analyzed by Shakib et al. 21 It offers a WS of 8000 nm RIU −1 and a high value of AS of 700 RIU −1 with a figure of merit of 138 RIU −1 . Shafkat proposed a PCF sensor to display the WS of 10;700 nm RIU −1 with a suitable AS of 1770 RIU −1 . This goldcoated duplex-core model has fewer air holes of different diameters, which increases the fabrication complexity. 22 Rifat et al. 23 illustrated a PCF plasmonic biosensor and achieved a high sensor resolution with high sensitivities of 4000 nm RIU −1 and 478 RIU −1 . Akter et al. 24 demonstrated an open channel PCF sensor to acquire a WS of 5000 nm RIU −1 and an AS of 396 RIU −1 for near to visible transmission range. Chakma et al. 25 displayed a gold-deposited PCF-SPR biosensor and presents a WS in the order of 9000 nm RIU −1 and high resolution with AS to 318 RIU −1 . Hasan et al. demonstrated a spiral shape PCF to provide an AS of 420.4 RIU −1 with a moderate WS of 4300 nm RIU −1 for vertical-polarized mode. 26 All SPR-PCF sensors discussed above are unable to achieve AS in the thousands and have some restrictions for fabrication due to complex geometry. Proposed sensor provides high amplitude sensitivities over a large span of analyte refractive index (ARI) (1.33 to 1.40) as shown in Table 1. Another advantage is ease of fabrication because of its simple structure. PCF sensor design and modeling is elaborated in the second section. Optimized sensor performance and the effects of design parameters on sensitivity are analyzed in Sec. 3 followed by conclusion in Sec. 4. Figure 1 shows the transverse representation of an investigated gold-coated PCF sensor. All the circular air holes (d ¼ 1.2 μm) are patterned in a hexagonal manner in the presented sensor geometry. Gold, an inactive and less oxidized metallic material, is circulated on the PCF's outer surface. 27 One small-size air hole is inserted in the center, and one air hole from the second layer is omitted to make a solid core for light confinement. Three air holes near the solid core are kept small to reduce the air gap between the metal and core area. This arrangement is suitable to

Sensor Design and Numerical Modeling
perfectly matched layer is employed as a final circulation for minimizing the unavoidable leakage from the cladding part of the PCF. 28 Due to simple structure of proposed sensor, conventional stack and draw procedure is appropriate to fabricate it, 29 and chemical vapor deposition method is suitable for making a gold metal layer with thickness of T g ¼ 30 nm. 27 Conventional silica is selected as a host material to get the high-performance sensor.
The dielectric constant is considered to get the complex refractive index of gold. Drude-Lorentz equation is used to determine this constant value as 27 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 3 8 1 where ε Gold is the gold permittivity, ε ∞ ¼ 5.9673 is the high-frequency permittivity, ω d ¼ 2113.6 × 2π THz is the plasma frequency, and γ d ¼ 15.92 × 2π THz denotes the decay frequency. The angular frequency ω ¼ 2πc∕λ at working wavelength λ, here c is the constant light velocity, has a value of 3 × 10 8 m∕s, and weighting factor Δε ¼ 1.09. Moreover, Ω L ¼ 650.07 × 2π THz is the oscillator strength and Lorentz's spectral width is referred as THz. 20 Sellmeier equation is defined for silica's refractive index as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 2 6 3 where D and E (μm 2 ) are taken as Sellmeier coefficients up to third-order and their values are The analyte layer with a thickness (t a ) of 1.2 μm is plated on the metal layer's outer surface to sense the molecules efficiently. The structure has been simulated for a large range of ARI (1.33 to 1.40). It is observed that for lower ARI (1.33 to 1.36), there is a slight variation in peak loss value as shown in Fig. 4(a). For high ARI (n a > 1.40), two resonant peaks are observed with high value of confinement loss (CL), it affects the sensor performance. Therefore, ARI values (n a ) of 1.38, 1.39, and 1.40 are considered to get the optimized sensor performance. The whole sensor structure is designed and simulated using software COMSOL Multi-physics. The finite element method is employed to get the desired simulated results under the finer mesh mapping.

Sensor Performance Based on Simulated Results
The investigated SPR sensor works on dynamics of the interaction point of a solid core-clad zone, when light is incident on the dielectric metal part, then this lower index region absorbs some fraction of light and emits free electrons. These electrons start oscillating and generate surface plasmon wave. When confined core-mode index and the surface plasmon polariton (SPP) mode index are equivalent to each other and then produce a sharp peak loss in the reflecting light; this mechanism is referred as SPR. 3 Each sensor performance is discussed by calculating the CL (dB/cm), which is expressed as: 26 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 6 2 1 where Imðn eff Þ indicates an imaginary effective refractive index. An unknown sensing medium can be identified by observing the shift of resonant peaks wavelengths. The optical field distribution for confined core-mode, initial phase of resonance, and SPP mode are shown in Figs. 2(a)-2(c), respectively. The power is concentrated in the core area as shown in Fig. 2(a) and some of the confined light leaked out [shown in Fig. 2(b)] and start interacting with plasmonic material to generate SPP mode shown in Fig. 2(c). The dispersion relation is communicated in Fig. 3 for core and SPP-guided modes. Dash black line and dash red line describe the real effective index for confined core-mode and SPP mode, respectively.
At 680 nm, due to phase-matching condition, real n eff of confined core-mode and SPP mode intersect, and a sharp peak occurs in the CL curve (solid blue line). This peak is a clear indication  of maximum light transition from fiber guided core-mode to SPP mode, and that particular wavelength is assumed as resonance wavelength (RW). The peak value of CL 110.89 dB∕cm is acquired at an RW of 680 nm for the ARI of 1.38.

Sensor Performance for Different Value of n a (Analyte Refractive Index)
CL is the first factor that has a profound impact on sensor performance. This CL changes with the ARI value. From Fig. 4(a), it is clear when there is a change in ARI from 1.33 to 1.40 with a gap of 0.01; then peak is shifted from a smaller wavelength to higher wavelength as follows. ARI changes from 1.33 to 1.34, peak is shifted from 570 to 580 nm, from 1.34 to 1.35, peak is moved from 580 to 600 nm, from 1.35 to 1.36 peak is changed from 600 to 620 nm, from 1.36 to 1.37 peak is shifted from 620 to 640 nm, from 1.37 to 1.38 peak is moved from 640 to 680 nm, from 1.38 to 1.39 peak is shifted from 680 to 740 nm, from 1.39 to 1.40 peak is changed from 740 to 820 nm, respectively. The peak value of CL varies from 19.47 to 230.1 dB∕cm for the ARI range from 1.33 to 1.40. Based on these different CL values, WS is determined using wavelength interrogation (WI) technique defined as 22 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 5 4 3 S w ðnm∕RIUÞ ¼ Δλ P ∕Δn a ; (4) where Δλ P represents the wavelength difference between two adjacent peaks and Δn a is the difference between two adjacent ARIs. In this paper, it has a fix value of 0.01. The proposed sensor geometry shows Δλ P as a variation of 10, 10, 20, 20, 20, 40, 60, and 80 nm over the ARI variation from 1.33 to 1.40 with a gap of 0.01. Therefore, according to Eq. (4), the numerically computed WSs are 1000, 1000, 2000, 2000, 2000, 4000, 6000, and 8000 nm RIU −1 , correspondingly. In Fig. 4(b), wavelength sensitivities are plotted against ARI difference (1.36 to 1.40). WS increases gradually as it depends on shifted RW. When there is an increment in the ARI value, it reduces the RI difference between the confined core-mode and plasmonic mode. This phase enhances the resonance effect resulting in a strong mutual coupling, so phase-matching point shifts toward higher wavelength which increase the WS of the sensor. Wavelength resolution (WR) is also an essential factor to measure the sensing potential of a sensor for a minimum variation in the ARI as characterized in the literature: 24 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 3 6 7 WRðRIUÞ ¼ Δn a × Δλ min ∕Δλ P : the sensitivity in terms of amplitude at a specific wavelength. 30 Given expression explains the AS in Eq. (6): E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 4 8 2 where αðλ; n a Þ displays the CL and dαðλ; n a Þ signifies the CL difference. AS is determined and plotted in Fig. 5 at different values of wavelength range. The highest AS of 3958.84 RIU −1 is acquired at 740 nm wavelength with a n a value of 1.39. Besides, for lower value of n a 1. 33

Sensor Performance Analysis on the Effect of Gold Layer Thickness
The gold metallic layer has a significant influence on sensor sensitivity. 27 CL and AS can be altered with the variation in metallic layer thickness T g . Here, the CL spectra for ARI of 1.38 and 1.39 with the variation in T g from 30 to 50 nm are shown in Fig. 6(a).   Figure 6(a) uncovers that the peak loss value is reduced by increasing the gold layer thickness. As per obtained CL values, AS of 2191.95 RIU −1 for T g ¼ 30 nm, 1548 RIU −1 for T g ¼ 40 nm, and 826 RIU −1 for T g ¼ 50 nm has been achieved for the ARI of 1.38 as shown in Fig. 6(b). Due to less penetration of light, the mutual coupling decreases between the metal and dielectric medium. This condition occurred when we increase the gold thickness. So, maximum AS is acquired at 30 nm T g , which is suitable for sensor performance analysis.

Sensor Performance Analysis on the Effect of Lattice Period
In this section, the effect of lattice period Λ on the CL values and corresponding AS has been simulated and plotted in Figs. 7(a) and 7(b), respectively. Variation in CL spectrum is plotted with the different values of Λ 1.7, 1.75, and 1.8 μm. Minimum and maximum loss peaks vary over the wavelength range from 660 to 780 nm. Peak RW shifted toward a lower wavelength while increasing the lattice period from 1.7 to 1.8 μm. The calculated AS variation has been displayed in Fig. 7(b). For Λ ¼ 1.7 μm observed AS is 1652 RIU −1 , for Λ ¼ 1.75 μm AS is as 2191 RIU −1 , and for Λ ¼ 1.8 μm AS is as 1342 RIU −1 for the analyte RI of 1.38. Therefore, from Fig. 7(b), the highest sensitivity is achieved with the lattice period of 1.75 μm.

Sensor Performance Analysis on the Effect of Small Air Hole Diameter
The impact of varying the dimension of small air hole d s on the sensor sensitivity has been analyzed. In Figs Fig. 8(b). 3 Polynomial fit is an important factor in analyzing the sensor performance. This relation is obtained between peak RW and respective ARI as shown in Fig. 9. Here, ARI is taken on the horizontal axis and dependent variable RW is taken on the vertical axis. When there is a slight change in the ARI (1.33 to 1.40), n eff of the SPP mode has been changed. Due to this, resonance (phase-matching) wavelength shifts toward higher wavelengths with high peak loss value, resulting in resonant wavelength is increasing with the ARI from 1.33 to 1.40. Polynomial fitting equation with R-value is shown in the inset of Fig. 9. Good polynomial fit suggests that the reported sensor is fit for ARI recognition. 20 The investigated PCF-SPR sensor performance has been compared with other published PCF sensors in Table 2. Sensors proposed in Refs. 23, 24, 26, and 27 have potential to recognize unidentified ARI but are less sensitive in comparison to the proposed sensor. Although the sensor investigated in Ref. 25 has high WS, its AS is very low, which makes it less cost effective than   the proposed sensor. With respect to this comparison, the suggested sensor design also offers enhanced simulated results in terms of sensing ability. In addition, the proposed high-sensitivity sensor can be helpful in cancer cell detection, which has refractive index span of 1.36 to 1.40. 31

Conclusions
A regular hexagonal solid core SPR-PCF sensor is proposed and studied in terms of sensitivity performance. The deposition of less oxidized gold plasmonic material surrounding the PCF geometry offers a compact structure for manufacturing and enhances the recognition process. Structural elements such as plasmonic layer thickness, lattice period, and air hole diameters are optimized to detect the ARI range from 1.33 to 1.40. Studied results present a maximum AS of 3958.84 RIU −1 with a resolution of 10 −5 RIU for ARI of 1.39. Obtained results make it competent for recognizing biological elements, chemical, and liquids samples. [32][33][34]