The surface plasmon is referred as the plasma oscillation which is localized at the surface or interface. “Plasmon” means quasi-particle representation of plasma frequency [1] . Plasma oscillation represents the phenomena that free electrons of the metal oscillate cooperatively from their equilibrium position [2] - [7] . In SPR measurement the change of refractive index change in nanometer range can be detected easily. For this reason SPR is used in different bio-sensing application such as detection of label-free antigen-antibody reaction.

In the last couple of years, SPR biosensor has been created a remarkable place from the other biosensors because of its high sensitivity and reliable procedure [8] . Kretschmann configuration [8] is widely used in which a very thin layer of metal is directly deposited on the surface of coupling prism. It is bulky in size and difficult to optimize. Furthermore, it cannot be used in remote sensing application. For removing this barrier of remote sensing optical fiber is used. Its advantage is that its core diameter is small that is why it can be used in small areas along with the capability of remote sensing. In the last decade, PCF has been contributed to different applications owing to its several properties [9] and several types of sensor have been designed using PCF. The PCF SPR sensor is worked on evanescent field principle and it is produced because of propagation of light in the core-cladding region [10] . Owing to changing of analyte local refractive index (RI), the RI of the surface plasmon polaritons (SPP) will be changed and finally, resonant wavelength will be also changed [10] .

R.C. Jorgenson has propounded in [11] , the very first optical fiber SPR sensor in where the core was coated by the Au film to exhibit plasmonic response. In [12] , Polymer selectively coated PCF structure has been put forth by J. N. Das and R. Jha. Moreover, in [13] J. N. Das and R. Jha used multiple graphene layers in birefringence control PCF structure for SPR sensor. Previously the multiple metal layers are exercised in PCF SPR sensor and liquid infiltration inside the air holes or core [14] . Recently PCF SPR biosensor is designed by keeping the metal as well as sensing absorbate outside the PCF structure [15] [16] .

Comprehensively as plasmonic material, gold and silver have been used. Among them, silver is preferable due to its most conductive nature, sharp peak and high detection accuracy compared to gold [17] - [25] But silver can be easily oxidized and detection accuracy will be reduced. Silver oxidization can be prevented by using a thin layer of graphene on the silver layer [26] [27] [28] . But gold is chemically immutable and shows larger wavelength shift in resonant wavelength. As a result detection accuracy to detect unknown analyte is raised [28] [29] [30] [31] [32] .

In this work, a regular hexagonal PCF SPR biosensor has been proposed where the metal (gold), as well as sensing absorbate, is placed outside the PCF structure. This reduces the fiber structure complexity and sensing process easier. The unknown analyte can be easily detected by flowing it or just placing it outside of the gold surface just in label-free detection mode. Our structure is easy to construct in terms of fabrication.

At the outer circle, six circles are omitted so that evanescent field can be flown to excite the metal surface. The cross section of our numerically proposed sensor has been shown in Figure 1. A simple three-ring, hexagonal PCF is designed for the SPR sensor.

According to the standard fiber drawing “stack and draw” technique, the proposed fiber can be constructed. In our core guided mode, the air holes in the

first ring act as low index cladding. It has been used to vacillate the phase matching with plasmonic mode by reducing the refractive index. Our sensor parameters are defined as pitch Λ = 1.7 µm, diameter of the first ring air hole (d1), the second air hole (d2) and the diameter of the centre air hole (dc) are 0.4 Λ, 0.55 Λ and 0.25 Λ respectively. Moreover, the thickness of the gold layer is defined to 40 nm and it is about the ideal case. The real part of the dielectric constant of the gold has been defined from the Drude-Lorentz model [16] . The RI of silica has been taken by using Sellmeir equation [16] .

n 2 ( λ ) = 1 + B 1 λ 2 λ 2 − C 1 − B 2 λ 2 λ 2 − C 2 − B 3 λ 2 λ 2 − C 3 (1)

where B₁ = 0.69616300, B₂ = 0.407942600, B₃ = 0.897479400, C₁ = 4.67914826 × 10⁻³ µm², C₂ = 1.35120631 × 10⁻² µm², C₃ = 97.9340025 µm² are the coefficients of Sellmier equation [16] and n is the RI of the silica and λ is the wavelength in µm. We use finite-element method (FEM) and also use scattering boundary condition (SBC) on the outest layer to determine mode confinement behavior.

The working fashion of the PCF based on SPR sensor is evanescent electromagnetics field. For plasmonic phenomenon efficient excitation is the key factor. At a definite frequency of the incident light which can excite the surface and produce resonance, The Finite Element Method (FEM) based software such as “Comsol Multiphysics 4.4” framework has been used to simulate and analyze our proposed structure. Although there exists both the horizontal and vertical polarization, we consider only horizontal polarization here because vertical polarization is lesser compared to the horizontal polarization.

Figure 2 shows, the horizontal polarization property of fundamental core mode and surface plasmon mode.

As the mode propagates through the core, plasmon mode at the metal sensing layer is excited by the core mode. Resonance occurs when the real part of the local RI of the core mode and the surface plasmon mode matches. At this specific point maximum modal loss is found. At maximum loss point imaginary value of

RI of the core guided mode reaches to largest value. After this point, it has been noticed, modal loss is started decreasing again between core mode and plasmon mode. The modal loss of the fundamental core guided mode is extracted by using the equation below [19] .

α = 8.686 × k 0 ⋅ Im [ n e f f ] dB / m (2)

where k_0 = 2 π⁄λ, λ are the wave number, wavelength in µm in free space.

Figure 3 shows that at 640 nm wavelength a very sharp peak is found. At that point real part of the core mode and SPP mode coincide. It defines that maximum power has transferred to fundamental core mode to SPP mode. Due to core cladding refractive index contrast sharp peak is found. Without influenced by other higher-order plasmonics one resonance is found for the fundamental mode. Sensing performance is indicated by the presence of resonance on the metal surface. At wavelength 640 nm phase matching phenomena is found where fundamental core mode, SPP mode and loss peak are well matched.

Our sensor is providing very sensitive results according to the analyte RI change. RI changing will change the phase matching phenomena between the core mode and SPP mode. RI change can be detected by measuring the loss spectra shift. By increasing the analyte RI loss spectra is shifted toward the higher wavelength. It is shown in Figure 4.

A numerically PCF based SPR biosensor has been proposed and studied. The FEM method has been adopted to model the computational domain of the proposed sensor and a circular perfectly matched layer has been used outside the structure to abolish radiation toward the surface. The proposed sensor shows wavelength sensitivity of 4000 nm/RIU with resolution of 2.5 × 10⁻⁵ RIU. Also, the sensor shows the amplitude sensitivity of 265 RIU⁻¹ with resolution of 3.7 × 10⁻⁵ RIU. As the sensor is easy to fabricate by using draw and Stack method. Due to promising result and simple sensing scheme we believe that this sensor can be a good candidate for biological and biochemical analyte detection.

The authors declare no conflicts of interest regarding the publication of this paper.

Hossain, Md.B., Hossain, Md.S., Moznuzzaman, Md., Hossain, Md.A., Tariquzzaman, Md., Hasan, Md.T. and Rana, Md.M. (2019) Numerical Analysis and Design of Photonic Crystal Fiber Based Surface Plasmon Resonance Biosensor. Journal of Sensor Technology, 9, 27-34. https://doi.org/10.4236/jst.2019.92003