Design and analysis of heptagonal cladding with rotated-hexa elliptical core based PCF for the applications of communication sectors in the THz region

Photonic crystal fiber-based heptagonal cladding with the elliptical rotated-Hexa core is reported in the terahertz waveguide for the applications of communication area in this paper. By utilizing the photonic crystal fiber concept, all numerical results have been obtained by the finite element method with perfectly matched layers based on the COMSOL Multiphysics computer software tool. This H-PCF fiber shows a low effective material loss of 0.0076 cm−1, with a larger effective area of 5.95 × 10–8 m2, power flows within the core area of 90%, confinement loss of 3.35 × 10–16 cm−1, and scattering loss of 1.24 × 10–10 cm−1 at 1 THz. Besides, other optical properties like confinement loss, scattering loss, power fraction, V-parameter, and effective area have also been considered briefly. So, it is expected that the mentioned H-PCF structure-based waveguide will significantly improve many kinds of communication fields of the THz technology.

In 2012, Bao et al. (2012) proposed porous-core honeycomb bandgap THz fibers, which show higher EML and coupling loss of 0.35 cm − 1 and 5 dB, respectively. Their proposed structure EML is very high. Later, Islam et al. (2015a) introduced a spiral shape PCF which achieved efficient area, and EML is 1.82 × 10-7 m2 and 0.10 cm − 1 accordingly at 1 THz frequency range. Through obtained EML is high and did not show two essential factors as V-parameter and power fraction. Moreover, Hasanuzzaman et al. (2015) proposed kagome lattice structure PCF and decreased the EML to 0.035 cm − 1 with a dispersion difference of 0.13955 ps/THz /cm. But their proposed structure is nearly challenging to fabricate. In that context, Islam et al. (2016b) proposed a system built in a circular lattice with a hexagonal core and achieved an EML of 0.047 cm − 1 with a dispersion variance of 0.15 ps/THz/ cm. Sultana et al. (2019) proposed a Zeonex based kagome structured cladding and hexagonal shaped core PCF with an EML of 0.04 cm-1 and dispersion of ± 0.09 ps/THz/cm at 1 THz. Very recently, in 2020, another micro-structure PCF structure named THz wave propagation quasi-pattern was introduced by Paul and Ahmed (2020a); their oriented model obtains EML of 0.038 cm-1 with an optimum frequency of 1 THz. Bulbul et al. (2021) proposed a rectangular PCF and showed a high EML and dispersion of 0.1176 ± 0.0112 ps/ THz/cm at 1 THz. After comparing the previous suggested articles (Bao et al. 2012;Islam et al. 2015aIslam et al. ,2016bHasanuzzaman et al. 2015;Sultana et al. 2019;Paul and Ahmed 2020a;Bulbul et al. 2021), there is an enormous scope to design and modifying PCF sensors in the THz frequency region to achieve the best optical guidance properties.
This article introduced H-PCF for THz wave propagation, and TOPAS is used as the background material for our proposed model. The proposed H-PCF exhibits outstanding optical properties as well. The presented model displays lower effective material loss of 0.0076 cm −1 and gained maximum core power fraction of 90% with a larger effective area of 5.95 × 10 -8 m 2 , lower confinement loss of 3.35 × 10 -16 cm-1, and lower scattering loss of 1.24 × 10 -10 cm −1 at the frequency of 1 THz.

Design methodology
The cross-view of PCF is uncovered in Fig. 1 where P1 and m1 are characterized by the pitch and diameter of our plan concept. The parameters d1/A1 are called the air filling proportion, and this proportion tries to watch against collapse between two air holes in the cladding area. A c , d a , and d b parameters are called the pitch and diameters of the elliptical air hole in the core area. At the elliptical rotated-Hexa core territory, the first layer of 6 circular air holes contains a 20°, 80°, 140°, 200°, 260°, 320° angles and the second layer of 12 circular air holes contain a 20°, 50°, 80°, 110°, 140°, 170°, 200°, 230°, 260°, 290°, 320°, 350°. Here, we discover the numerical properties such as confinement loss, scattering loss, power fraction, effective area, effective material loss, V-parameter of the fiber within the THz wave pulse with the COMSOL Multiphysics software. The ideal parameters are cladding distance across d 1 = d 2 = d 3 = d 4 = d 5 = 299 μm, cladding pitch A 1 = A 2 = A 3 = A 4 = A 5 = 355 μm, core distance across d a = 54 μm, d b = 56 μm and core pitch A c = 60 μm.
In Fig. 1c, we visualize that the full lights pass through the core areas strongly for modes of x, y polarization. Consequently, we get the low effective material loss for both polarizations of modes at the operating region of 1 THz.

Numerical analysis
TOPAS is a background material that has been utilized in this PCF fiber to diminish the effective material loss. Here, EML α eff is premeditated through (Hossain and Sen 2020): where, α mat is the bulk material absorption loss and n mat is the RI of the material. 0 is the relative permittivity and the permeability of free space is 0 . S z = 1 2 (E × H * ). z is the pointing vector, where, z is component of S z , E and H * are electric field apparatuses and the complex couple of the magnetic field.
Scattering loss of this PCF fiber is thought-out by the subsequent equation (Mou et al. 2019): where, f is the frequency, c is the speed of photon and C R is called the scattering coefficient.
The low confinement loss-based PCF fiber is highly used for different types of communication sectors. Here, the confinement loss L c is calculted the equation (Raonaqul Islam et al. 2015): where, K 0 = f c is the free wave number, f is the frequency and c is the speed of photon. Im n eff is the imaginary part of effective refractive index.
In this PCF fiber, the principal part is formed by the effective area. Here, the effective area is figured by Pennetta et al. (2019): where, A effective is the EMA and I(rr) =|E rt | 2 is the cross-sectional electric field intensity.
Power fraction is resulted by the total power through this PCF fiber. So, the power fraction η is intended by Nagel et al. (2002): V-parameter describes the mode propagation of this PCF structure. So, V-parameter is presented by the following equation  where, the core radius is r, n co and n cl are signed by the effective mode index of the core and cladding area.
The ERI of the PCF directly influences the dispersion profile. The β is the modal propagation constant. It can be acquired from the second order of Taylor expansion that is shown in Paul and Ahmed (2019): where, N eff = Re (β)ω/c and ω = 2πf; For propagation mode, there are found two polarizations (x and y polarizations).

Result analysis and discussions
Here, we have selected the optimum porosity among 66%, 70%, and 74% because from Figs. 2,3,4,5,6,7,8,9,10,11 and 12, it is clearly seen that the total amount of lights transmits within the core area. As a result, this H-PCF fiber shows better graphical results about of optical properties like as low effective material loss, low scattering loss, larger effective area, high core power fraction, better V-parameter, low confinement loss with the frequency ranges from 0.08 to 3 terahertz. COMSOL Multiphysics program is used to determine completely graphical results from Figs. 2, 3, 4, 5, 6, 7, 8 and 9 of the proposed H-PCF structure from 0.8 to 3 THz. The    effective area is decreased with the increase of frequency from 0.8 to 3 THz for 74%, 70%, and 66% porosities. The EA is measured as 5.95 × 10 -8 m 2 , 6.17 × 10 -8 m 2 , and 6.10 × 10 -8 m 2 for 74%, 70%, and 66% porosities individually. Figure 3 shows the effective area in agreement with core diameter (D core ) for 74%, 70%, and 66% porosities at 1 THz. Here, the effective area is decreased according to the increasing of the core diameter (D core ). For optimum core diameter D core = 400 μm, effective area is presented as 8.12 × 10 -8 m 2 , as 8.34 × 10 -8 m 2 and as 8.64 × 10 -8 m 2 for 74%, 70%, and 66% porosities for 1 THz frequency. Figure 4 shows the effective material loss with the frequency. Here, it is seen that the effective material loss decreases with the increase of frequency wave ranges from 0.8 THz to 3 THz. For optimum design parameters, the effective material losses (EML) are 0.0076 cm −1 , 0.0069 cm −1 , and 0.0136 cm −1 for 74%, 70% and 66% porosities correspondingly at 1 terahertz frequency. Figure 5 indicates the effective material loss with the core diameters for 66%, 70%, and 74% porosities. Here, the effective material loss is decreased according to the increase of core diameters. On the other hand, for D core = 400 μm, the effective material loss is approximately 0.0076 cm −1 for 74% core porosity and the frequency f = 1 THz at optimum design parameters.  Figure 6 shows the core, cladding, and material power fraction in agreement with the frequency ranges from 0.8 to 3 terahertz. Here, it is also seen that the highest amount of power (lights) passes in the core regions. So, the power fractions of core, cladding, and materials are 90%, 1%, and 17%, correspondingly according to the frequency of 1 terahertz at the optimum design parameters. Figure 7 demonstrates the scattering loss examination for the varieties in frequencies in the proposed structure. Here, the scattering loss is slightly increased with the increases of frequency from 0.08 THz to 3 THz. The scattering loss is achieved for 74% porosity of 1.24 × 10-10 cm −1 at an optical wavelength of 1 terahertz frequency. Figure 8 outlines the conduct of confinement loss concurring to recurrence at ideal plan parameters. Confinement loss is being diminished due to the rising of operating frequencies from 0.8 to 3 THz at the optimum core diameter value of D core = 400 μm. The confinement loss of expected development at optimum plan parameters for 1 THz of 3.35 × 10 -16 cm −1 .
V-parameter is explored as the function of frequency for optimal enterprise constraint at Dcore = 400 um, as shown in Fig. 9. Here, it is seen that the V-parameter is increased according to the frequency. Moreover, it is also seen that the value of the V-parameter throughout the entire operating frequency range remains 1.02 at an operating frequency of 3 terahertz (THz). Thus, the proposed H-PCF shows in single-mode communication applications (SMF ≤ 2.405). On the other hand, from Fig. 6, 7, 8 and Fig. 9, the optimum parameters are cladding distance across d 1 = d 2 = d 3 = d 4 = d 5 = 299 μm, cladding pitch A 1 = A 2 = A 3 = A 4 = A 5 = 355 μm, core distance across d a = 54 μm, d b = 56 μm and core pitch A c = 60 μm.
The suggested PCF's significant birefringence is one of its intriguing features. The modal birefringence may be demonstrated in Fig. 10, which calculates the effective refractive indices using FEM. Detailed research is carried out into the birefringence properties of the proposed PCF and the influence of structural factors. It is noticed that with the rise in the value, the modal birefringence is higher, and the birefringence value is 1.7 × 10 -6 . With additional optimizing settings, the suggested PCF can tune the birefringence up to a one magnitude order.
The numerical aperture controls how much fiber core optical light is captured. This is why the number opening is also known as the zone for the gathering of light. It's a parameter without units. Optical light is supported by the numerical aperture at the receiver portion. The high numerical aperture is enormously demanded in the communication and sensing field via optical fiber and may be achieved if the resultant difference is excellent between the core area and the recessed region. The following equations can find the NA of the proposed PCF. Figure 11 depicts the numerical aperture with a frequency profile spanning from 0.20 THz to 0.55 THz. It also demonstrates that as the frequency increases, the numerical aperture decreases. Because all of NA's curves pass through a small region, a zoom view part is also presented. Figure 12 illustrates well that both polarization curves exert themselves to the left and the right with close-fitting behavior. A flat dispersion of 0.97 THz to 1.09 THz near zero has been observed in a larger frequency spectrum.
In some cases, multiple optical signals with almost the same pulse spread can be transmitted simultaneously. The lower dispersion value also allows the transmitted optical signal to have a greater bandwidth. There is also a flatted dispersion near zero over a larger frequency spectrum from 0.97 to 1.09 THz. In some cases, multiple optical signals with almost the same pulse spread can be transmitted simultaneously. The lower dispersion value also allows the transmitted optical signal to have a greater bandwidth. This type of behavior with optical parameters gives the proposed fiber a positive degree.
The designed PCF shows effective material loss, confinement loss, core power fraction, and effective area belongings than other designed PCFs at 1 THz functional frequency as providing in Table 1.
It has been found in Table 1, which shows better outputs compared to the former research work. We have found effective material loss of 0.0076 cm −1 , power fraction of 90%, confinement loss of 3.35 × 10 -16 cm −1 , and an effective area of 5.95 × 10 -8 m 2 at monitoring region of 1 THz.

Conclusion
A great plan of heptagonal cladding range with curved turned elliptical rotated-Hexa based core areas is presented for communication areas, reducing different types of losses such as effective material loss, confinement loss, and scattering loss. Using the heptagonal PCF concept, all graphical results have been accomplished with the FEM and PML boundary conditions based on the COMSOL Multiphysics test system. This designed PCF fiber uncovers a low effective material loss (EML) of 0.0076 cm −1 , with a larger effective area of 5.95 × 10 -8 m 2 and a core power fraction of 90% at 1 THz. In addition, the proposed H-PCF moreover has other user profiles like standard control due to EML (< 0.0076 cm −1 ), low confinement loss (~ 3.35 × 10 −16 cm −1 ), and high core power fraction (~ 90%). Thus, this anticipated H-PCF would be a favorable candidate within the telecommunication, IoTbased wireless sensor network, and other communication that is now under investigation.