Design of a porous cored hexagonal photonic crystal fiber based optical sensor with high relative sensitivity for lower operating wavelength

In this article, highly sensitive and low confinement loss enriching micro structured photonic crystal fiber (PCF) has been suggested as an optical sensor. The proposed PCF is porous cored hexagonal (P-HPCF) where cladding contains five layers with circular air holes and core vicinity is formed by two layered elliptical air holes. Two fundamental propagation characteristics such as the relative sensitivity and confinement loss of the proposed P-HPCF have been numerically scrutinized by the full vectorial finite element method (FEM) simulation procedure. The optimized values are modified with different geometrical parameters like diameters of circular or elliptical air holes, pitches of the core, and cladding region over a spacious assortment of wavelength from 0.8 µm to 1.8 µm. All pretending results exhibit that the relative sensitivity is enlarged according to decrement of wavelength of the transmission band (O+E+S+C+L+U). In addition, all useable liquids reveal the maximum sensitivity of 57.00%, 57.18%, and 57.27% for n=1.33, 1.354, and 1.366 respectively by lower band. Moreover, effective area, nonlinear coefficient, frequency, propagation constant, total electric energy, total magnetic energy, and wave number in free space of the proposed P-HPCF have been reported recently.


Introduction
Photonic crystal fiber (PCF) is a novel invention of optical fiber technology which has ensured an immense advancement in telecom and nonlinear devices applications [1]. It consists of an arbitrary order [2] of tiny air holes which trip along the entire length of the fiber or periodic array [3]. Indexed guiding (IG) and photonic band gap (PBG) are two principal types of photonic crystal fibers according to propagation characteristics of light. In index guiding (IG), PCF has sustained superior refractive index than the cladding region with a solid core [4,5]. In addition, light is instructed by photonic band gap principle with a large air core in PBG PCF [6]. In 1996, Knight et al. [7] first fabricated a [4], liquid sensors [24], pressure sensors [25], temperature sensors [26], mechanical sensors [27], chemical sensors, and P H sensors [28] are the broad range implementation of PCF sensors. According to fascinate attraction in chemical and biomedical [28,29] applications, the evanescent wave based PCF sensors are expanding quickly. The evanescent field of PCFs is prevalently entangled in gas sensing with chemical and bio sensing [28][29][30] and different index materials [23]. In addition, the bacteria sensor [30] is accustomed with the evanescent wave based PCF sensor. To subdue the safety problem in the industrial adaptation [31] particularly for perception of toxic and flammable chemicals, noble sensitive chemical (liquid and gas) sensors are performed a significant rule. PCF based sensors are also attracted much concentration of researchers in environmental and safety monitoring [23,31] applications.
In order to maximize the relative sensitivity and reduce confinement loss at adequate degree in liquid [24] or chemical sensing [28] applications, the researchers has been reported plenty of articles by replacing distinctive geometric parameters of the PCF. Lee and Asher [28] sensed echanical sensors [27], chemical sensors, and P H level and ionic strength by using a PCF based chemical sensor. In 2001, Hansen et al. [32] reported a highly birefringence index guiding PCF which depicted a little bit higher birefringence contrast with conventional fibers. A hybrid-PCF structure is constituted by three rings cladding of circular air holes and micro structured core with elliptical air holes which depicts high birefringence, and sensitivity and low confinement loss was proposed by Asaduzzaman et al. [10]. In [33], it was recommended that lower confinement loss, dispersion, and nonlinear effect are pointed out by a nanostructure index guiding PCF.
In this article, a porous cored hexagonal photonic crystal fiber (P-HPCF) has been suggested which reveals high sensitivity and low confinement loss for three thermo optical coefficient like water (n=1.330), ethanol (n=1.354), and benzene (n=1.366). Our proposed P-HPCF is formed by five layered circular air holes based cladding and two layered porous cored with elliptical air holes. The geometrical parameters have been diverse with both the optimized structure core and cladding territory of proposed P-HPCF and improved the relative sensitivity with low confinement loss at the same time compared with prior PCFs [10,34,35].

Geometries of the proposed P-HPCF
The schematic cross sectional scenery of the proposed P-HPCF is presented in Fig. 1 this figure is plainly outlined the entire geometrical structure of the PCF. The proposed P-HPCF structure is hexagonal where the core is porous shaped. In the cladding region, the vertices of the attaching air cavities contain a 60 angle that forms hexagonal shape. The first, second, third, fourth and fifth layers are restrained with 6, 12, 18, 24, and 30 air cavities, respectively. Pitch can be determined by the distance between the two air holes (at cladding) for entire types of fibers and procedures which are denoted by  1 and  2 . The diameters of air cavities in every layer of cladding are presented by d 1 and d 2 .
At the core territory, the vertices of the adjoining 6 elliptical air holes of the first layer contain a 60 angle which is arranged in a porous shape. Due to the second layers, the vertices of the adjoining elliptical air holes contain a 30 angle, and the number of elliptical air holes is 12. All elliptical air holes in the core region are arranged in a 135 angle perspective to original position. As a result, the proposed PCF design cannot be collapsed. Utilizing the Sellmeier equation's [36] refractive index (n) and absolute silica as background, material has been chosen for all kinds of fibers. The diameter and pitch of the complementary elliptical air holes of porous cored are marked by d c1 , d c2 , and , respectively. All supplementary elliptical air holes are filled with three different thermo optic coefficients like water (n=1.33), ethanol (n=1.354), and benzene (n=1.366) respectively at the core territory.

Synopsis of numerical method
All numerical results of the proposed P-HPCF can be examined by applying the full vectorial finite element method (FEM). To model and improve photonic ingredients or devices for engineers, perfectly matched layers (PML) boundary condition is referred as the most effective numerical approach [37][38][39][40][41]. According to the boundary condition, PML is fixed at 10% of the entire diameter of the proposed P-HPCF [42]. The thickness of circular PML is chosen as 1.1 m. The propagation characteristics such as relative sensitivity and the confinement loss are obtained from Maxwell's equations [43].
The power of light can be infiltrated of the cladding territory from the core because the finite number of air cavities of a photonic crystal fiber is considered as the confinement loss which is denoted by L c . Kaneshima et al. [44] expressed the confinement loss (dB/m) by where k 0 =2;  is the wavelength of light, and Im[n eff ] is known as the imaginary part of the refractive index. The relative sensitivity coefficient r can be computed by the mutual action between light and the analyte [45]. To estimate the relative sensitivity, coefficient r is enforced by the following equation: where n r and n eff are marked as the refractive index of sensed material within the air cavities and the modal effective index. The fraction of air cavity power and the absolute power percentage can be calculated through (3) and represented by f: where E x and H x represent the diagonal electric field Photonic Sensors 58 and magnetic field. E y and H y represent the longitudinal electric field and magnetic field. The FEM is implemented to procure the mode field pattern E x , H x , E y , H y , and formal effective index n eff correspondingly. The effective area A eff [46] of a PCF can be calculated by the following equation: where optical power is denoted by E. A small effective area is caused for high optical power density which also indicates the nonlinear effect. Equation (5) is utilized to calculate the nonlinear coefficient () [46]   where C, n, and  present the velocity, frequency, and wavelength of light, respectively. The nonlinearindex coefficient n 2 in the nonlinear part of the refractive index is  n = n 2 |E| 2 .

Numerical results and discussion
In this section, the guiding properties of the reported P-HPCF have been examined in agreement with assorted geometrical parameters. The complementary elliptical air cavities of core region is satiated by three thermo optic coefficients such as water (n=1.330), ethanol (n=1.354), and benzene (n=1.366). Numerical investigation into the P-HPCF has been carried out at a wide range of wavelength from 0.8 m to 1.8 m. The extensive pretending procedure has been performed by COMSOL Multiphysics 4.2 versions. The convergence error of the proposed P-HPCF is very low which is approximately at 1.5010 -8 % for the optimum parameters.
The electric field distributions for (a) xpolarization and (b) y-polarization at an activation wavelength of 1.33 m have been presented in Fig. 2. The mode field is firmly restricted in the core vicinity which increases the sensitivity of the proposed P-HPCF. As a result, the leakage loss of the fiber is very low.   [10,34,35] due to the fact that those articles achieved high sensitivity with the increment of wavelength. The relative sensitivity of proposed P-HPCF is 57%, 57.18%, and 57.27%, respectively for three liquids like water (n=1.330), ethanol (n=1.354) and benzene (n=1.366) at 1.33 m wavelength. Besides, confinement loss of the fiber is 2.1510 -10 dB/m, 1.1110 -11 dB/m, and 1.9710 -11 dB/m, respectively in the same condition. In addition, the degree of freedom is d 1 =1.80 m, 30 m, and =0.80 m for the optimum structure.
The optimization of the proposed P-HPCF has done following a simple technique [35]. The first cladding region is optimized.  Figure 4 demonstrates the effect on the relative sensitivity to fluctuate the cladding air-hole diameters (d 1 and d 2 ) of +4% with the optimum values when other parameters are kept same for the proposed P-HPCF. The sensitivity of 56.52%, 57.82%, and 57.96% and the confinement loss of 3.1310 -10 dB/m, 5.9510 -10 dB/m, and 2.510 -10 dB/m correspondingly have gained at 1.33 m wavelength. Now it is clearly visualized that sensitivity has increased for two liquids except water (n=1.330) compared with the optimum value. Figure 5 shows the impact on the relative sensitivity, +8% variation with the optimum values of cladding air-hole diameters (d 1 and d 2 ) when other parameters have remained constant for the proposed P-HPCF. The sensitivity of 58.37%, 58.51%, and 58.59% accordingly has been reported for three analytes at 1.33 m wavelength which is little bit high compared with the optimum value. Besides, the confinement loss of the order of 1.9210 -9 dB/m, 5.8010 -11 dB/m, and 4.7910 -11 dB/m accordingly has also been achieved for desired liquids but it is also high compared with the optimum value. Same results have been found for +12% increment of cladding diameters which is shown in Fig. 6. All examined results are shown in Figs. 4, 5, and 6. It has been signified that relative sensitivity of the proposed P-HPCF is enlarged when we increase the values of d 1 and d 2 with the optimum value. . But to avoid fabrication complexity, d 1 =1.80 m and d 2 = 1.96 m have been selected as an optimum value in the cladding region. Figure 7 demonstrates the influence on the relative sensitivity for decreasing the cladding airhole diameters (d 1 and d 2 ) of -4% with the optimum values when other parameters are remained the same for the proposed P-HPCF. The sensitivity of 56.23%, 56.43%, and 56.52% and confinement loss of 1.9210 -9 dB/m, 5.8010 -11 dB/m, and 4.7910 -11 dB/m respectively have been achieved at 1.33 m wavelength. Now it is clearly visualized that sensitivity has decreased due to -4% variations with the optimum value for three liquids. Similar results have been found for -8% decrement of cladding diameters in Fig. 8. After completing all investigations from Figs. 7 and 8, it has been indicated that propagation characteristics like sensitivity of the reported P-HPCF is diminished due to a decrease in the optimum values of cladding air-hole diameters (d 1 and d 2 ). Next the core territory is optimized. Figure 9 represents the effect on the relative sensitivity of the proposed P-HPCF for interchanging the air-hole diameters (d c1 and d c2 ) of core vicinity with the optimum values. After completing this procedure, the sensitivity and confinement loss are turned into little bit changes. The sensitivity of 56.90%, 57.19%, and 57.14% and confinement loss of 2.7910 -10 dB/m, 4.3910 -10 dB/m, and 1.8110 -11 dB/m correspondingly are obtained at 1.33 m wavelength for three thermo optic coefficients. Since the relative sensitivity is slightly decreased with exchanging core air-hole diameters, d c1 =0.40 m and d c2 = 0.30 m are chosen as the optimum values of airhole diameters in the core region.     After finishing all examinations from Figs. 10, 11, and 12, it has been revealed that the high relative sensitivity and low confinement loss are achieved for =0.79 m due to applying three chemicals like water (n=1.330), ethanol (n=1.354), and benzene (n=1.366) at 1.33 m wavelength. To evade cost and complexity during the fabrication process, = 0.80 m is selected as the optimum pitch value of the core vicinity.
In a selective manner, filling the air holes of photonic crystal fiber by analytes is referred as a dare job. The air cavities of PCF in either the core or cladding region can be satiated by distinctive analytes with the progress of nanotechnology. A number of technical skills have been reported by the researchers. In 2004, Huang et al. [47] proposed a unique technique to fill the micro structured air cavities of both the core and cladding vicinities with distinctive analytes which may be accustomed to reveal the functionality of the PCF applications. This filling adaptation takes place by compelling the ultraviolet-curable polymer within the PCF. Zhang et al. [48] suggested a method for practical exhibition and speculate pretending of a liquid filled core based PCF to improve the sensing application. All investigated results in Table 1 have been manifestly indicated that the relative sensitivity and confinement loss are slightly varied with the optimum parameters after all modifications. So we confirmed that no global effects can influence the reported structure afterwards the fabrication process.
We have also examined the optimum parameters of 1% and 2% replacement as global parameters of the proposed P-HPCF. Comparison of relative sensitivity and confinement loss among the optimum parameters and the change in global parameters for water (n=1.330), ethanol (n=1.354), and benzene (n=1.366) at =1.33 m has been revealed in Table 1. Table 2 demonstrates the comparison of the effective area and nonlinear coefficient of the optimum P-HPCF structure for three applied liquids such as water, ethanol, and benzene at =1.33 m.
Several numbers of guiding attributes like frequency, propagation constant, total electric energy, total magnetic energy, and wave number in the free space of the proposed P-HPCF have been shown in Table 3. After completing the calculation process, it has been seen that propagation constant, total electric energy, and total magnetic energy are changed with different refractive index chemicals such as water (n =1.330), ethanol (n=1.354), and benzene (n=1.366) except frequency and wave number in the free space.   The comparative performance analysis between the prior PCFs and proposed P-HPCF has been listed in Table 4. Comparing with the prior PCFs, our proposed PCF depicts upward relative sensitivity and low confinement for ethanol (n=1.354) analytes. The proposed P-HPCF is nobly improved the relative sensitivity approximately 2.41, 1.30, and 1.16 times compared with the previous PCFs [34], [35], and [10] respectively as well as diminishing the confinement loss from [34] and [10]. The fabrication procedure is a significant topic for all proposed photonic crystal fibers. So the fabrication process of the proposed P-HPCF may be not comfortable. The proposed P-HPCF includes two different types of holes in cladding regions. Due to the technological progress in the fabrication of PCFs, our reported structure can be feasibly fabricated. Various fabrication techniques have been advanced for micro structured PCF like extrusion [49], stack and draw [50], drilling [51], and sol-gel casting [52]. Extrusion method contributes exemption in design. To utilize this method, material losses are extremely high for soft glasses, which is regarded as key drawback of this technique. The drilling technique allows fitting both the holes size and spacing. But circular shape fiber is restricted to drilling technique. In 2012, Hamzaoui et al. [52] fabricated an ionic copper-doped micro structured optical fiber by a new fabrication method which is renowned as a sol-gel technique. This method provides the freedom to modify air holes size, shape, and pitches. So, the proposed P-HPCF will be successfully fabricated by sol-gel casting technique.

Conclusions
A micro structured porous cored hexagonal photonic crystal fiber (P-HPCF) formed by five layered cladding embracing circular air holes and two layered porous coredwith elliptical air holes is reported in this paper. The proposed P-HPCF is accustomed as a chemical sensor. The FEM and PML circular boundary conditions are enforced for numerically investigated variation of effects on propagation characteristics of the proposed P-HPCF. All examined outcomes show that the proposed P-HPCF exposes decent sensitivity and lower confinement loss compared with the prior PCFs at a wide scope of wavelength from 0.8 m to 1.8 m. The proposed PCF reveals the relative sensitivity 57.00%, 57.18%, and 57.27% correspondingly for water (n=1.33), ethanol (n=1.354), and benzene (n=1.366) analytes. In addition, the confinement losses of 2.1510 -10 dB/m, 1.1110 -11 dB/m, and 1.9710 -11 dB/m are gained for the same analytes. So it is apparent that the proposed P-HPCF based chemical sensor exhibits novel execution in industrial security intention at the lower band.
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