Design and Simulation of Photonic Crystal Fiber Based Surface Plasmon Resonance Biosensor for Cancer Diagnosis


 A surface plasmon resonance (SPR) sensor based on photonic crystal fiber (PCF) was designed and gold metal was used as a sensitive plasmonic layer. Performance of this sensor was investigated using the finite element method (FEM) for refractive indexes (RI) of 1.33 to 1.41. This sensor has a sensitivity for the defined refractive indexes range between 2600 to 28921 nm/RIU at wavelengths of 650 to 1400 nm and has the highest resolution and best FOM with a value of 3.46×10 -6 RIU, 222.45 RIU -1 , respectively. Diagnosis of cancer by examining blood samples is one of the advantages of this sensor. Due to the simple structure of this sensor and its good performance, it can be used as a good diagnostic tool for analytes with different refractive index.


1-Introduction
The oscillations of the electrons at the interface between the dielectric and the metal are called surface plasmon. These oscillations are caused by the collision of light with electrons. If the frequency of the emitted light is the same as the natural frequency of the electron, the surface plasmon wave propagates along with the dielectric-metal interface, which is called the surface plasmon resonance (SPR) [1]. SPR technology provides access to ultra-compact detection sensors and electronic devices [2]. Due to the sensitivity of SPR sensor to refractive index and label-free sensing capability, this sensor as a direct measuring device has many applications, such as environmental monitoring [3], food health [ 4], biological material detection [5], and film thickness monitoring [6].
Conventional optical sensors made using the SPR phenomenon had problems that were mostly solved with the advent of photonic crystal fiber (PCF) and the use of their advantages such as smaller size, easier light transmission and single-mode light emission. Sensitivity in PCF-based SPR sensors can be adjusted in PCF by using the number of rings and air-hole dimensions [7]. The SPR phenomenon is created using gold, silver, copper and aluminum in most PCF-based sensors today. Among them, gold is more compatible with organic environments [8]. PCF-based SPR sensors are generally divided into two categories. In the first category, metal layer coating is selectively placed inside the air holes created in the PCF and the analyte material is optionally placed in the same holes. In the second category, metal coating is placed in the outer layer of PCF and the analyte material is placed on it. The first category is less favorite since the placement of the metal layer inside the air holes is difficult, but the second category is used more because the placement of the metal layer on the outer surface is easier and has a good sensitivity [9][10][11]. However, so far sensors have been designed that have used the first type of fabrication method [12,13]. In 2019, for example, Chao Liu et al. proposed an SPR sensor that used a gold nanowire as a plasmonic sensitive layer and achieved a sensitivity of 14200 [14]. In another paper, Zhenkai Fan (2019) presented a structure, which used a gold ring inside the PCF as a plasmonic layer and was able to achieve a sensitivity of 2150 [15]. Also, Suoda Chu et al. (2020) proposed a PCF-based SPR sensor that used two silver nanowires in air holes. At best, the sensor offered a sensitivity of 3400 and a resolution of 2.5 [16].
One of the applications that has always been suggested for SPR sensors is its use as a diagnostic tool. Among diseases, leukemia is one of the most common diseases in the world today, which has different types and kills thousands of people every year.
However, accurate and quick diagnosis can help a lot in its treatment. Biosensors made using PCF can be used in research on cancer cells [17][18].
This paper presents a PCF-based SPR sensor. The performance of this proposed sensor was evaluated using LUMERICAL software in the refractive index range of 1.33 to 1.41. In addition, the function of this sensor for detection of several types of cancer was evaluated.

2-Sensor design and numerical simulation
A schematic of the proposed PCF-based SPR biosensor is shown in Figure 1. The PCF sensor can be fabricated by the die-cast and stack-and-draw methods [19,20] As shown in the figure, this biosensor consists of a regular hexagon composed of air holes on the bed of Fused Silica with a diameter of 16 µm , and the diameter of the air holes d2, d3, d4 and d5 is .8 µm, 1.2µm, 1.6µm, and 2µm, respectively. The distance between the air holes is called the lattice pitch and is denoted by A, which is equal to 3µm. A layer of gold with a thickness of 40nm and a length of 7µm is used as a surface plasmon excitation layer. The distance from the gold layer to the center of the core is 4.4µm. The thickness of the analyte layer in part d1 is equal to 1.6µm.

Fig. 1. Cross-section of the proposed PCF-based SPR biosensors
The function of this sensor is that the analyte solution is in contact with the smooth and polished surface of gold, and when light is concentrated in the center of the core, some losses occur in the gold layer. Because the analyte refractive index is varied, the peak of these losses occurs each time at a specific wavelength. In this way, a spectrum can be obtained by optical spectrum analysis (OSA).
Fused Silica is used as the core coating material and its refractive index is calculated from the Sellmeier equation [21], n(λ) 2 = 1+ + + Where the values of B 1 , B 2 , B 3 , C 1 , C 2 , C 3 , are 0.691663, 0.407943, 0.897479, 0.004679µm 2 , 0.013512µm 2 , and 97.934003µm 2 , respectively; and λ is the wavelength of light emitted in the center of the fiber core. Also, the dielectric constant of the gold layer is calculated using the Drude model [21].
ε= ε ∞here ε ∞ = 9.75 is the high frequency dielectric function of gold; while w p = 1.36 × 10 16 rad/s and w c = 1.45 × 10 14 rad/s are the plasma frequency of the metal and scattering frequency of the electrons, respectively. The air refractive index is considered one [21].
To evaluate the performance of this biosensor, the finite element method (FEM) is used by LUMERICAL software.

3-Results and discussion
The principle of operation of PCR-based SPR sensor is based on the interaction between electrons on the surface between the metal and the insulation and the field created around it. When a light wave propagates through the PCF core, a field is created which, when it collides with an electron on the surface of the metal layer, creates a surface plasmon wave (SPW). If the fundamental mode (FM) frequency of the light guided in the nucleus coincides with the surface plasmon polariton (SPP) mode frequency, phase matching occurs and a peak of losses occurs at that frequency [22,23]. In this sensor, the perimeter of the metal layer is filled with analyte, and when there are small changes in the refractive index of the analyte around the metal layer, the position of the effective refractive index changes according to the wavelength, resulting in peak losses in the phase shift mode.
The simulation results for the proposed PCF-based SPR sensor are shown in Figure 2.
As you can see, Figure 2 shows  showing that the highest energy transfer from FM mode to SPP mode occurs at this wavelength and causes resonance and production of surface plasmon. The performance of this sensor is mainly determined by structural parameters, such as resonance wavelength, losses, and sensitivity [24,19]. The sensitivity of the biosensor can be obtained by the interrogation method in terms of nm/RIU by the following formula [21]:  Where, S is sensor sensitivity and FWHM denotes full bandwidth at half-maximum. a higher value of FOM responsible to a better detection limit. The relationship between FOM and refractive index is shown in Figure 6.  Table 1 shows the resonance wavelengths, sensitivity, resolution, and FOM for this sensor at different refractive indexes.    To evaluate the overall performance of this sensor, Table 3 compares the properties of the proposed PCF-based SPR biosensor with the structures found in other articles. In this comparison, the sensitivity, refractive index measurement range, resolution, and FOM of the sensor are considered. As can be seen from the table, the proposed SPR PCF sensor performs better in terms of sensitivity, resolution and FOM. 222.45

4-Conclusion
In this paper, we propose a D-shaped PCF-based SPR sensor for measuring analytes with a refractive index of 1.33 to 1.41. In this sensor, gold metal was used as a sensitive plasmonic layer. The simulation results show that the maximum sensitivity for this sensor in the tested range is 28921 nm/RIU . Also, its maximum resolution and best FOM is 3.46 × 10 -6 RIU and 222.45 RIU -1 , respectively . The proposed sensor has the ability to distinguish a person with cancer from a healthy person by testing a blood sample.