Design and Numerical Analysis of a Novel Rectangular PCF (R-PCF)-Based Biochemical Sensor (BCS) in the THz Regime

A novel PCF-based sensor has been presented in this paper to sense different chemicals and biocomponents. ,e proposed biochemical sensor (BCS) comprises a simple arrangement of rectangular holes. ,e competence of this BCS in detecting analytes is evaluated employing the full-vector finite element method (FEM). Performance metrics prove the competence of this BCS in sensing various analytes that have a refractive index in the range of 1.33–1.48.,e proposed BCS shows ultralower values for both the bulk absorption and confinement loss. ,is BCS attains a maximum of about 95.82% relative sensitivity at 2.5 THz. Also, the dispersion for this sensor is only 0.12± 0.011 ps/THz/cm at the same point of interest. ,ese results prove that the proposed BCS will play a key role in sensing toxic chemicals, illegal drugs, biocomponents, etc. Besides, the simple rectangle-based PCF structure ensures the feasibility of fabrication by practicing the existing fabrication strategies.


Introduction
e terahertz (THz) band is gaining high popularity as an apposite operating region for diverse application fields like spectroscopy, sensing, astrophysics, hereditary, biomedical, and telecommunication [1][2][3][4][5][6][7][8]. is band offers a broad frequency band extending from 0.1 to 10 THz. An entire THz system requires 3 basic elements that include the waveguide, source, and detector. e development of THz source and detector elements in recent years has accelerated THz-based sensing. Besides, numerous THz waveguides, for instance, the Bragg waveguide [9], metal wires [10], metallic tubes [11], etc., have been proposed recently. However, most of these waveguides fail to achieve higher relative sensitivity. To avoid this problem, several photonic crystal fibre (PCF)-based THz waveguides have been proposed in recent years.
Researchers have successfully modelled PCF-based chemical and biosensors functioning in the THz band. As a sensor, PCF is applied to sense multiple chemical and biological elements, for example, the detection of fuel adulteration [12], salinity [13], bane chemicals [14], blood components [5], and cholesterol [15]. is sensor resolves the snags of conventional fibres by maintaining higher diversity and standard values for optical parameters. Besides, this type of sensor is much faster than the existing detection systems. One of the splendid properties of this sensor is the tunability of the optical parameters through careful adjustment of the size, position, and structure of the core and cladding hole of the PCF. Also, this type of sensor offers a lot more advantageous features that includes higher relative sensitivity, lower material and confinement loss (CL), light weight, robustness, cheaper, etc. All these features have widened the potential application of PCF-based sensors in chemical and bio-sensing applications, which includes the study of RNA and DNA [16][17][18], detection of cancerous cells [19][20][21], classification and detection of alcohol [22][23][24][25][26], detection of formalin [27,28], and surface plasmon resonance-based biosensors [29][30][31].
Since the last decades, several refractive index (RI)based chemical and biosensors have been proposed. In [5], a PCF-based biosensor is proposed. e model is particularly aimed to sense blood components based on RI. e model maintains low CL, but it shows a high effective area (EA) of about 166000 μm 2 at 1.5 THz. Besides, the relative sensitivity attained for the sensor is only 79.9% and the dispersion is higher. In [32], a PCF-based chemical sensor is proposed where the cladding holes are heptagonally positioned. e sensing performance of the sensor has been evaluated while detecting benzene, ethanol, and water. e sensor exhibits lower CL, but the relative sensitivity attained for the sensor is only 63.24% at 1.0 THz. Several key optical parameters including numerical aperture and effective material loss (EML) have not been determined for the sensor. Another PCF-based chemical sensor is presented in [14]. e sensor is modelled to detect bane chemicals, namely sarin, soman, and tabun. e sensor exposes 0.009 cm −1 EML and 1.71 × 10 −14 cm −1 CL. e relative sensitivity attained for the sensor is 94.4% for tabun at 1.8 THz. However, the true sensing region and numerical aperture are ignored for the sensor. A PCF-based NaCl sensor is presented in [33], where the core of the sensor comprises tetra-rectangles. e sensor shows 91.5% relative sensitivity and 0.004 cm −1 EML, but it has a higher EA of 397340 μm 2 at 1.8 THz. Recently, a PCF-based chemical sensor is proposed in [34] to detect ethanol, benzene, and water. e sensor shows 3.02 × 10 −8 cm −1 CL, but the EML has not been estimated for this sensor. However, the sensor has achieved almost 78.1% relative sensitivity for benzene. In [35], a Ag-graphene-coated surface plasmon resonance (SPR) sensor is proposed to sense analytes with RI ranging from 1.33 to 1.41. is model shows 12.6 μm/RIU wavelength sensitivity and 79.4 × 10 −5 RIU resolution, but this model suffers from high CL of about 1.75 × 10 2 dB/cm at 625 nm for water. Besides, this sensor comprises complex H-shaped PCF. In [36], another H-shaped PCF-based SPR sensor is presented to enhance the sensing range. is sensor can detect analytes with 1.33 to 1.49 RI. is model exhibits only 1.2 × 10 3 nm/RIU sensitivity and a high peak loss of 14.34 dB/cm for water.
Most of the existing hollow and porous core PCF sensors are particularly modelled to detect any specific analyte or a group of correlated analytes. Also, most of the available sensor models fail to attain higher relative sensitivity and lower losses at the same time, whereas SPR sensors have a RI limit as most of the SPR sensors fail to effectively sense the analytes with RI greater than 1.41 [35,[37][38][39][40]. However, most of the existing sensors are modelled with a complex PCF structure that includes a compound arrangement of air holes. is complex structure will certainly increase fabrication constraints. Hence, there is still scope to model a biochemical sensor (BCS) based on fabrication-friendly PCF structure that will be capable to sense a wide variety of chemicals and biocomponents.
In this paper, a simple rectangle-based PCF (R-PCF) structure has been modelled as a BCS. e proposed R-PCF structure has been numerically explored in the THz band in the range of 1.5-4.0 THz. Optical parameters have been studied for the proposed BCS to examine the sensing performance. is study has been carried out for the analytes with the RI ranging from 1.33 to 1.48. In addition to getting the typical values for all the performance metrics, one of the key objectives of this study is to present a highly fabrication-friendly BCS, which is ensured by the presence of only rectangular holes in the PCF structure. R-PCF ensures heterodyne detection, and several sensors based on R-PCF have been proposed [41][42][43][44][45]. Besides, asymmetrical PCF structures comprising rectangles have already been implemented [46,47].

Sensor Design
is paper focuses on modelling a novel, uniform, and simple BCS based on PCF.
e PCF-based sensor was modelled using FEM-based software. e x-y plane representation of the BCS is depicted in Figure 1. e core region of the sensor contains a single rectangle, which is denoted by Cr in the figure. e height of Cr is 400 μm, whereas the width of it is 410 μm.
e cladding area is modelled through the simple arrangement of eight rectangular air holes. ese eight rectangles can be grouped into two different classes based on their similarities in height and width. ese two types of cladding rectangles are denoted by Cl 1 and Cl 2 . e width and height of Cl 1 are 200 μm and 1000 μm individually. On the other hand, the width and height of Cl 2 are 200 μm and 400 μm exclusively. e radius of the sensor is 750 μm, including a 75 μm (10% of the radius) perfectly matched layer (PML) at the outer layer. e strut, the gap between two consecutive rectangles, is 10 μm for this PCF-based sensor. Multiple fibre materials are available that include silica, zeonex, topas, etc. [48][49][50]. Various splendid properties of zeonex and topas have influenced the researchers to select them as the fibre material. Both of them have a fixed RI of 1.53, lower dispersion, and lower material loss in the THz band. However, zeonex has some additional features; for instance, higher chemical resistance and glass transition temperature [49,50]. ese two features are highly desired in the successful fabrication of any PCF. Hence, zeonex is chosen to be the fibre substance for the proposed BCS. e light propagation profile in the x and y polarization mode (PoM) are pictured in Figures 2(a) and 2(b), respectively, while sensing the analyte with 1.44 RI. is figure reveals the fact that propagating wave is highly confined within the core region. e experimental setup of PCF-based models in sensing applications has been described in several papers [51][52][53][54]. e model represented in Figure 1 has resulted from the trial and error method. rough modelling different structures and comparing their optical parameters, this model has been chosen due to its dominant results. We have denoted this model as the optimum (OPT) model. Keeping the strut value constant, we have tuned the OPT model by ±10% to represent a comparison among their optical parameters and justify the selection of the OPT model as the proposed BCS in this paper. e design parameters for the two models resulted from the tuning along with the OPT model are represented in Table 1 that includes the respective width (W) and height (H) of each rectangle.

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International Journal of Optics

Fabrication Feasibilities
In earlier stages, PCF fabrication was considered to be implemented using the stack and draw method [55], but this method fails to satisfactorily fabricate the PCF models with a complex and asymmetrical arrangement of holes [56]. To resolve these issues, several more methods have been advanced, which include drilling [57], sol-gel [58], extrusion [59], 3D-printing [46], etc. ese methods are capable to fabricate complex PCF structures. e sol-gel method can potentially perform the fabrication of the PCF model with circular holes. On the other hand, both the 3D-printing and extrusion methods fabricate the asymmetrical PCF models, which include rectangular, square, and elliptical holes. e proposed BCS comprises a mono-rectangular core and a cladding with eight rectangular air holes. Hence, both 3Dprinting and extrusion will be a suitable choice to fabricate the proposed R-PCF-based BCS. Besides, the fibre with rectangular holes guarantees the heterodyne detection [41,42]. A few asymmetrical PCF models have been fabricated recently by the Max Planck Institute [46,47]. e institute has successfully fabricated different PCF models comprising the elliptic, rectangle, etc. is clearly ensures the feasible fabrication of the proposed PCF structure comprising a simple arrangement of rectangles using the existing fabrication strategies. e core of the BCS needs to be infiltrated with the target sample. ere are several available techniques for the selective filling of PCF; for instance, selective filling by collapsing air holes [60], by splicing single-mode fibre [61], by femtosecond laser micromachining [62], etc. Among these strategies, we prefer the selective filling by the femtosecond laser micromachining method. is method comprises three steps. First, the PCF is spliced with a normal single-mode fibre.
en, the single-mode fibre is cut near to spliced junction using FL. Finally, selective laser drilling is performed to make a path to the core or target holes using FL. rough these three steps, the fibre will be prepared to be infiltrated with the target sample. e method has proved its higher efficiency, preciseness, and flexibility, and thereby, it has become a dependable technique of SF [63].

Mathematical Methods for Sensing Performance Evaluation
To assess the potentiality of the presented BCS in this paper, several optical parameters need to be calculated. ese parameters are estimated separately for each analyte. Filling the core with the target analyte, light is injected into the core.
ough the light should be bound into the core, a portion of light spreads outside the core region. e true sensing area, also known as the EA, is the measure of light spreading. e EA is evaluated using the following equation, where E defines the transverse electric field [5,33].
e numerical aperture (NA) is a measure of the range of angles of the incident light that can enter and exit from a fibre. It is a unitless parameter, which is a function of the EA, the speed of light (c), and the operating frequency (f ). Higher NA is desirable for sensing applications, and this desired value results from lower EA. e value for this parameter is calculated using the folllowing equation [64]: (2) e EML is the loss of optical power due to the absorption of the fibre materials. Zeonex, the fibre material of the proposed BCS, is responsible for this loss. Appropriate designing of the PCF model and lessening the background region will keep the EML at a negligible level. Following the perturbation theory [33,65], equation (3) has been used to compute this key parameter for the proposed BCS.
e denominator of equation (3) represents the integral of the Poynting vector, where H stands for the magnetic field strength. ε 0 and μ 0 stand for the free space permittivity and permeability, respectively. η and α represent the RI and absorption coefficient, respectively. e use of zeonex as a fibre material may introduce a negligible amount of material dispersion [66]. Hence, this dispersion can be avoided, and the only dispersion that needs to be considered is the waveguide dispersion. A PCF with flat dispersion facilitates the examination of the capability of the fibre to inherit multichannel signals. erefore, the quality of signal propagation from the source to the sink can be evaluated through this parameter. e dispersion (D) for the proposed BCS is estimated using the following equation [67,68]: where ω and η eff represent the angular frequency and the effective RI, respectively.
Another key parameter that has an impact on the sensing performance is the CL. is loss results from improper PCF structure and the leaky nature of the mode. Hence, a proper PCF model can result in a reduced CL value. e amount of CL is quantified using the following equation: e most important optical parameter that directly computes the sensing performance of any PCF-based sensor is the relative sensitivity (RS).
is parameter is directly proportional to the power fraction (P f ), which quantifies the amount of light power present in the core compared with the entire injected power. e relative sensitivity for the proposed BCS is calculated using 4 International Journal of Optics where η a denotes the RI of the analyte.

Simulation Results
Different types of analytes or target samples are injected into the core region of the sensor separately and once at a time. en, the light propagation through the core region of the proposed BCS provides us with different values for the optical parameters for different types of analytes.

Optimum Model Selection.
To validate the selection of the OPT model as the BCS in this paper, we have first carried out the values of the optical parameters for the OPT − 10%, OPT, and OPT + 10% models. We have performed this simulation for the analyte with 1.44 RI. e values of EffA in x-and y-PoM for the three models in the THz band are shown in Figures 3(a) and 3(b), respectively. Since EffA is a measure of how light is spread inside the PCF, the lower values for it is desirable. e lowest value of it is attained for the OPT − 10% model, whereas the highest value is found for the OPT + 10% model. e curve for the EffA for the OPT model lies between the other two models. e OPT model exhibits 98975 μm 2 and 99121 μm 2 in x-and y-PoM, respectively, at 2.5 THz.
e NA indicates the efficiency of a PCF in collecting light. A higher value of NA is expected for every PCF-based chemical sensor. Figure 4 Figure 6 represents the dispersion for the three models in the THz band. All three models show low dispersion, but the OPT and OPT + 10% model show lower dispersion compared with the OPT −10% model. However, all three models exhibit nearly flat dispersion in the frequency band ranging  Table 2 represents the numerical values of the optical parameters for the three models. e optimum values are marked in italics. is italic marking shows that none of the three models is dominant for all the parameters. Considering a trade-off among the optical parameters, the OPTmodel has been chosen as the BCS in this paper. e OPT model maintains a balance between the losses and relative sensitivities. To attain higher power fraction, relative sensitivity, and NA as well as lower EML, EA, dispersion, and CL are the key objectives for any type of PCF-based sensors. As no particular model among the OPT −10%, OPT, and OPT + 10% model has attained standard values for all the parameters at the same time, we have to select a model that has nearly attained typical values for the parameters. Hence, we have selected the OPT model as the BCS in this study.

Optimum Strut Selection.
To evaluate the optimum value of strut for our BCS, we have varied the values of it and evaluated the optical parameters for each time. We have simulated the OPT model for three values of strut, i.e., 7.5 μm, 10 μm, and 12.5 μm. We have performed this simulation for the analyte with 1.44 RI.    e values of the NA in the THz band for the 7.5 μm, 10 μm, and 12.5 μm strut models are shown in Figure 10 Table 3. e standard values attained for each optical parameter are marked in italics. e table reflects that the 7.5 μm strut model has typical values for the optical parameters except for the EML and dispersion. On the other hand, the 10 μm strut model has attained nearly typical values for all the optical parameters maintaining lower losses and higher relative sensitivity. Accounting for this scenario, we have selected the 10 μm strut model in this paper as it balances among the optical parameters through maintaining comparatively lower loss along with higher relative sensitivity.

RI-Based Analyte Sensing.
e optimum PCF structure and the optimum value for the strut have together modelled the proposed BCS of this paper. is sensor is then used to sense different chemicals with different RI. Injecting any particular chemical into the core region of the sensor, the optical parameters have been evaluated for that chemical using the finer mesh analysis.
is strategy is repeated several times to evaluate the optical parameters for the chemicals with different RI values ranging from 1.33 to 1.48.

Conclusions
is paper presents a simple rectangular-based BCS operating in the THz regime. is BCS can effectively be applied for both biocomponents and chemicals detection purposes. e sensing performance of this sensor is evaluated for the frequency band that ranges from 1.5 to 3.0 THz. Besides, the proposed BCS comprises a simple arrangement of rectangles, which will ensure the feasible fabrication of this sensor. e sensor attains a maximum of 95.82% relative sensitivity at 2.5 THz. Also, this sensor suffers from a negligible amount of EML and CL. Due to its ultra-lower losses and ultrahigher relative sensitivities, this BCS model can effectively and efficiently be applied in biochemical sensing applications for different samples with dissimilar RI ranging from 1.33 to 1.48.

Data Availability
is is a simulation-based study, and no external data have been used.

Conflicts of Interest
e authors declare no conflicts of interest.