Benzene Shape Photonic Crystal Fiber Based Plasma Sensor: Design and Analysis

A novel benzene core photonic crystal fiber (BC-PCF) is proposed for plasma sensing applications. The proposed BC-PCF parameters have been tuned to gain high sensitivity, high numerical aperture (NA), and low confinement loss, and modality over the extensive variety of 0.7 µm to 1.9 µm wavelength. The explored results for the ideal structure have exhibited the high sensitivity up to 77.84% and negligible confinement loss of 7.9 × 10-3 dB/m at 1.3 µm wavelength. The V-barometer remains under 2.405 over the whole working wavelength. So the proposed BC-PCF is a single mode fiber, which advances the long partition correspondence applications. Furthermore, high numerical aperture (NA) makes the fiber potential candidate in medical imaging applications. The plan of the sensor is to find out the creative potential outcomes in sensing applications.


Introduction
Nowadays, looking for the scientific research it is detectable that logical research is going with optical fiber innovation by managing photonic crystal fiber (PCF). In contrast with regular optical fiber, PCFs are contributing to advancing optical detecting and in addition, optical correspondence by demonstrating some indistinguishable properties like additional guiding opportunity, low confinement loss, high sensitivity, high center power division, high numerical aperture (NA), vast powerful zone, high nonlinearity, high birefringence, and ultra-flattened dispersion [1][2][3][4][5][6][7][8][9][10][11]. Additionally, PCF likewise assumes a fundamental part in modern, biomedical, and natural detecting applications. Sensing can be communicated as the common activity amongst analysts and passing light through the fiber. PCF based sensors have turned out to be excessive mainstream by scientists because of its flexibility and adaptability. With the assistance of innovative headway, the optical sensors, for example, gas sensor, compound sensor, temperature sensor, pressure sensor, biosensor, twist sensor, strain sensor, refractive index sensor, vibration sensor, DNA sensor, protein sensor, dampness sensor, and pH sensor are refreshing quickly [12][13][14][15][16][17][18][19][20][21][22][23]. Be that as it may, outlining an adaptable and dependable sensor is a testing issue because of the absence of proficient detecting and additionally other directing properties.
Last few decades ago, to get scrumptious optical properties, different geometric shapes, for example, hexagonal, octagonal, circular, decagonal, porous, spiral, and hybrid cladding, were presented. In 2016, Ahmed et al. [24] proposed hexagonal, square, and octagonal shape PCFs for sensing applications. At 1.33 m wavelength, the octagonal PCF increased most extreme sensitivity of 46.87% for ethanol analyte. But they did not mention any other parameters without sensitivity and confinement loss. The same authors [25] proposed a micro structure octagonal PCF for liquid sensing applications and improved the sensitivity of 47.35% and confinement loss of 2.40 × 10 -4 dB/m at 1.33 m wavelength.
In 2016, Asaduzzaman et al. [26] enhanced the sensitivity up to 49.17% and confinement loss of 2.75 × 10 -10 dB/m by presenting hybrid cladding PCF. The authors did not specify the modality and NA properties with the exception of sensitivity and confinement loss. In last 2016, Paul et al. [27] enhanced the sensitivity up to 64.19% for S-band by proposing folded cladding PCF. In addition, they showed and picked up the NA of 0.36 for U-band. In 2017, same authors enhanced the sensitivity of 1.06 times for identification liquor from drinks [28]. However, they didn't demonstrate the other pivotal parameters. Moreover, still now there is no published articles for the PCF based plasma sensor. So in light of the past writing articles, there is still gigantic space to outline plasma sensors to accomplish better guiding properties.
In this article, a circular-cladding and benzene-core based PCF has been proposed for proficient conveyance of sensing applications. The research has uncovered the extreme sensitivity and confinement loss of 77.23% and 5.15 × 10 -3 dB/m, respectively. In addition, the ideal structure has likewise picked up the high NA. The proposed fiber is applicable in detecting plasma as well as biomedical imaging applications.

Geometries of the proposed P-HPCF
The end-faced view of the proposed benzene core photonic crystal fiber (BC-PCF) is presented in Fig. 1. At BC-PCF, the microstructure benzene shaped core is infiltrated with plasma (n = 1.350). The circular five layers air hole surrounded by the core acts as a cladding region. The core region has three-layer-microstructure air holes where the radius of the core is homogenous except 6 corner air holes. The microstructure core with benzene shape contains 6 air holes in a benzene manner. The diameters of the air holes in the core region are denoted by D co , and the distance between holes (pitch) is denoted by Λ co . The diameter of 6 corner air holes is 0.8 m where the other air holes' diameter is 0.3 m. The cladding is arranged with five layers of the air holes which remain the same with the structures different in the core region. The air filling ratio (AFF) is a very critical factor in the fabrication process. In the proposed BC-PCF, the AFF remains below 90% both for the core and cladding regions. So the proposed BC-PCF can be easily fabricated using any well-known techniques. The diameters of the air holes at cladding are denoted by D cld , and the pitch of the two adjacent air holes between the two different layers of air holes is denoted by Λ cld . Silica is used as hosting material for the better optical guiding properties for a wider wavelength range [29]. The COMSOL multi-physics 4.2 software has been employed to simulate and design the proposed structure. An outer boundary known as perfectly matched layer (PML) has been applied for diminished nonphysical scattering with a thickness of 10% following the articles [30][31][32][33]. Figure 1(c) visualizes the modal intensity of the proposed structure and it is nicely exhibited that light is tightly confined through the core region.

Synopsis of numerical method
Finite element method (FEM) is used for analyzing our proposed PCF structure which has been utilized for the electromagnetic simulation of the proposed chemical (Plasma) sensor PCF. We consider two very important parameters, sensitivity and confinement loss, which are very closely related to our PCF structure. We should solve the Maxwell equation by utilizing the circular perfectly matched boundary layer (PML). All numerical calculations have been done following the previously published articles [34].
The host material of the proposed PCF is pure silica. Silica has a refractive index dependency on wavelength followed by Sellmeier equation as where B 1 = 0.6961663, B 2 = 0.4079426, B 3 = 0.8974794, C 1 = 0.0684043, C 2 = 0.1162414, C 3 = 98.96161, and n() is the refractive index for corresponding operating wavelength  in m.
A powerful numerical simulation tool is the full vectorial finite-element method. Various photonic waveguide devices are numerically analyzed by FEM. FEM processes complex structure PCF in homogenous subspaces and then is computed with Maxwell's vector equation as where [S] is the PML matrix including PML parameters S x and S y , E is the electric field vector, and the wave number is k 0 which is a function of wavelength () followed as follows: During the simulations time, COMSOL solves the Maxwell's equation internally, and simulation outcomes provide the propagation constant of the operating wavelength. The real part produces the effective mode index, the imaginary part produces the confinement loss, and they are calculated as follows: eff 0 When the power flows through the fiber, some power penetrates into cladding region of the fiber, which causes confinement loss or leakage loss as follows: The effective mode area of the proposed PCF structure can be calculated by the propagating mode area as follows: The NA of the PCF can be calculated as follows:

Numerical results and discussion
The convergence error of any PCF is the defective modes in PCF with compactly supported perturbations. The convergence error of the proposed BC-PCF is very low. The value of convergence error is 5.28 × 10 6 . To get greater sensitivity, the core region and cladding region of the proposed structure are tuned by changing values of cladding diameter, cladding pitch, core diameter, and core pitch setting on the benzene shape core. In Fig. 2, the sensitivity is visualized as a function of wavelength for different cladding pitches by keeping all the parameters constant. It is nicely exhibited that there is no much variation of sensitivity for cladding pitch variation. From the graph, the optimum sensitivity of 73.25% is found at the wavelength of 1.3 m. In Fig. 3, the changing rate of sensitivity has been revealed by tuning cladding diameter. The optimum sensitivity of 73.25% is found at the wavelength of 1.3 m. Moreover, the higher air holes diameter enhances the sensitivity. These outcomes are high noticeable than that reported in [35].  In Fig. 4, the sensitivity is pictured as a component of wavelength for various core diameters to keep every parameter steady. It is shown that there is a variety of sensitivities for cladding pitch. From the diagram, the ideal sensitivity of 77.96% is found at the wavelength of 1.3 m. It is clearly pictured that the increment of core air holes diameter enhances the sensitivity. This outcome is exceedingly identical with that of the beforehand distributed articles [36][37][38]. The changing rate of sensitivity has been uncovered by tuning core pitch which is demonstrated in Fig. 5. The ideal sensitivity of 76.32% is found at the wavelength of 1.3 m. In addition, the sensitivity is enhanced by the lower value of pitch. These results are highly observable than those reported in previous articles [39][40][41]. From Fig. 1(c), it is noticeable that the light is well confined into the core region, so the leakage loss will be very low. The lower confinement loss of the proposed BC-PCF is shown in Fig. 6.
Powerful zone and nonlinearity decencies of photonic precious crystal fiber are driving the optical gadgets. In the correspondence territory, the information movement is expanding step by step. Subsequently, PCF with vast powerful territory is required if there should be an occurrence of high information movement transmission. Now the modality of any fiber can be checked by using (9). In Fig. 7, V-parameter stays under 2.405 over the entire working wavelength range. So the proposed PCF is a single mode fiber, which advances the long separation correspondence applications. 10  Tightly confinement of light into the core region introduces a smaller effective area and higher NA.
But it is noted that for silica based PCF the value of NA more than 0.4 is uncommon [42]. Figure 8 demonstrates the highest NA of 0.58 which makes the fiber a potential candidate in biomedical imaging applications. This value is highly noticeable than those in the previously reported articles [43].  Table 1 compares the simulation results in research papers. It is clearly visualized that compared with other papers, the sensitivity obtained in our paper is higher and the concentration loss is lower.

Conclusions
A novel benzene core photonic crystal fiber (BC-PCF) based plasma sensor has been introduced, and different guiding properties are pursued. After theoretical modeling and numerical simulation using COMSOL Multi Physics 4.2 version, high sensitivity of 77.84% and low confinement loss of 7.9 × 10 -3 dB/m at 1.3 m are obtained. In addition, the proposed BC-PCF plasma sensor is realizable by using any well-known fabrication technique. Furthermore, the maximum NA of 0.58 is obtained at 1.9 m wavelength which makes the fiber an essential candidate in medical imaging applications. For the whole operating wavelength, the proposed BC-PCF also behaves a single mode fiber and makes the fiber potential fiber in long-distance applications.
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