# Structural Analysis of Nano Core PCF With Fused Cladding for Supercontinuum Generation in 6G Networks

Rajesh Anbazhagan, S. Chandru, Ravikumar Chinthaginjala, Kalapraveen

Bagadi, Mohammad Alibakhshikenari, Bal Virdee, Syed Mansoor Ali, Iyad

Dayoub, Patrizia Livreri, Sonia Aïssa

► To cite this version:

Rajesh Anbazhagan, S. Chandru, Ravikumar Chinthaginjala, Kalapraveen Bagadi, Mohammad Alibakhshikenari, et al.. Structural Analysis of Nano Core PCF With Fused Cladding for Supercontinuum Generation in 6G Networks. Radio Science, 2023, 58 (9), 10.1029/2023RS007690. http://dx.doi.org/10.1109/RS007690.2023RS007690

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Radio Science®

RESEARCH ARTICLE

10.1029/2023RS007690

**Key Points:**

* A Supercontinuum Generation through photonic crystal fiber (PCF) is proposed which provides excellent broadening of the optical spectrum

* PCF designed with silicon nanocrystal core and cladding microstructures is arranged in fusion approach to optimize the optical parameters

* The structural analysis of nano-core PCF with fused cladding provides a baseline for designing the 6G architecture

**Correspondence to:**

R. Chinthaginjala and

M. Alibakhshikenari,

cvrkvit@gmail.com;

mohammad.alibakhshikenari@uc3m.es

**Citation:**

Anbazhagan, R., Chandru, S., Chinthaginjala, R., Bagadi, K., Alibakhshikenari, M., Virdee, B. S., et al. (2023). Structural analysis of nano core PCF with fused cladding for supercontinuum generation in 6G networks. *Radio Science*, 58, e2023RS007690. https://doi.org/10.1029/2023RS007690

Received 27 FEB 2023

Accepted 9 AUG 2023

Corrected 3 OCT 2023

This article was corrected on 3 OCT 2023. See the end of the full text for details.

**Author Contributions:**

**Conceptualization:** Rajesh Anbazhagan, Bal S. Virdee

**Data curation:** Rajesh Anbazhagan, Kalapraveen Bagadi

**Formal analysis:** S. Chandru, Mohammad Alibakhshikenari, Sonia Aïssa

**Funding acquisition:** Mohammad Alibakhshikenari

© 2023. The Authors.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<figure><img src="image_2.png" /></figure>

# Structural Analysis of Nano Core PCF With Fused Cladding for Supercontinuum Generation in 6G Networks

Rajesh Anbazhagan¹, S. Chandru², Ravikumar Chinthaginjala³ ID,
Kalapraveen Bagadi³ ID, Mohammad Alibakhshikenari⁴ ID, Bal S. Virdee⁵, Syed Mansoor Ali⁶,
Iyad Dayoub⁷,⁸ ID, Patrizia Livreri⁹, and Sonia Aïssa¹⁰

¹School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, India, ²Department of ECE, Global Institute of Engineering and Technology, Vellore, India, ³School of Electronics Engineering, Vellore Institute of Technology, Vellore, India, ⁴Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés, Spain, ⁵Center for Communications Technology, School of Computing and Digital Media, London Metropolitan University, London, UK, ⁶Department of Physics and Astronomy, College of Science, King Saud University, Riyadh, Saudi Arabia, ⁷Université Polytechnique Hauts-de-France, Institut d'Électronique de Microélectronique et de Nanotechnologie (IEMN) CNRS UMR 8520, ISEN, Centrale Lille, University of Lille, Valenciennes, France, ⁸INSA Hauts-de-France, Valenciennes, France, ⁹Department of Engineering, University of Palermo, Palermo, Italy, ¹⁰Institut National de la Recherche Scientifique (INRS), Université du Quebec, Montreal, QC, Canada

**Abstract** The Sixth Generation (6G) networks have identified the use of frequency range between 95 GHz and 3 THz with a targeted data rate of 1 Terabytes/second at the access network for holographic video applications. As is demands broadening of spectrum at the core network, this paper proposes a Supercontinuum Generation (SCG) through photonic crystal fiber (PCF) as it provides excellent broadening of the optical spectrum. Discussed in the paper is supercontinuum generation at high pumping power as per the standards specified by the International Telecommunications Union. The proposed PCF is designed with silicon nanocrystal core and the cladding microstructures is arranged in a fusion approach to effectively optimize the optical parameters such as dispersion, nonlinearity, birefringence, group-velocity dispersion, and confinement loss. The fused cladding comprises of a flower-cladding assembly in which air-holes arrangement is inspired from petals in a pleated structure. Such arrangement is shown here to provide high nonlinearity and negative dispersion for high power supercontinuum generation. The novel nanocore assembly with improved structural constraints delivers a non-linearity of $6.37 \times 10^6 \text{ W}^{-1} \text{ km}^{-1}$ and a negative dispersion of $-142.1 (\text{ps/nm-km})$ at 1,550 nm. Moreover, a supercontinuum spectrum is generated using different pulse widths ranging from 350 to 650 ps with 25 kW pump power for PCF lengths of 10 and 15 mm.

## 1. Introduction

The broadening of the spectrum for Sixth Generation (6G) networks can be realized in two different ways, namely, levitating the pump power in pre-amplification stage or varying the wavelength of pump to zero-dispersion wavelength. In many cohesive applications of Supercontinuum Generation (SCG), the most feasible and economical material is Silicon (Si). But, the disadvantage of using this material is that it has a high impact on two-photon absorption that constraints the broadening of the spectrum. Hence, materials which do not have any impact on nonlinear absorption have raised interest. The micro-structured fiber commonly known as Photonic Crystal Fiber (PCF) comprises numerous air-holes distributed periodically over the longitudinal axis has attracted attention due to its extraordinary features such as high nonlinear properties, optimizable dispersion, well-behaved mode area, and endlessly single-mode guidance (M. Abdullah-Al-Shafi & Sen, 2021; M. S. Hossain, et al., 2021; A. K. Vyas, 2021). PCF is broadly classified into two types based on the mechanism of the guidance of light propagated as effective-index guidance and photonic bandgap PCF (Y. Guo, et al., 2021; M. A. Islam, et al., 2021; Y. L. She, et al., 2021; Y. Qu, et al., 2021).

To exhibit high birefringent and non-linearity, a compressed PCF using hexagonal arrangement of circular holes has been discussed in (B. Yu & H. Rui, 2019). At a wavelength of 1,550 nm, the PCF structure display non-linearity of $42.58 \text{ W}^{-1} \text{ km}^{-1}$ and birefringence equal to 0.0159. Here, the core region of the PCF encompasses micro holes arranged in a definite pattern. The PCF is constructed using silica through perfectly matched layer (PML) setting. To improve the non-linearity, the holes have been coated using gold with silica background (A. Dixit, et al., 2017). Here, the construction of holes in outer cladding section is carried out as hexagonal
**Investigation:** Ravikumar Chinthaginjala,
Kalapraveen Bagadi, Mohammad
Alibakhshikenari, Bal S. Virdee

**Methodology:** S. Chandru, Syed Mansoor
Ali, Iyad Dayoub, Patrizia Livreri

**Project Administration:** Ravikumar
Chinthaginjala, Kalapraveen Bagadi,
Mohammad Alibakhshikenari

**Resources:** Rajesh Anbazhagan, S.
Chandru, Ravikumar Chinthaginjala,
Patrizia Livreri

**Software:** Rajesh Anbazhagan, S.
Chandru

**Supervision:** Ravikumar Chinthaginjala,
Kalapraveen Bagadi, Mohammad
Alibakhshikenari

**Validation:** Rajesh Anbazhagan, S.
Chandru, Ravikumar Chinthaginjala,
Kalapraveen Bagadi, Mohammad
Alibakhshikenari, Bal S. Virdee, Syed
Mansoor Ali, Patrizia Livreri, Sonia Aïssa

**Visualization:** Syed Mansoor Ali, Iyad
Dayoub, Sonia Aïssa

**Writing – original draft:** Rajesh
Anbazhagan, S. Chandru

**Writing – review & editing:** Ravikumar
Chinthaginjala, Kalapraveen Bagadi,
Mohammad Alibakhshikenari, Bal S.
Virdee, Syed Mansoor Ali, Iyad Dayoub,
Patrizia Livreri, Sonia Aïssa

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Positioning of proposed spiral flower cladding photonic crystal fiber in 6G networks.</figcaption></figure>

arrangement and finite elements are arranged in triangular lattice. The PCF display a persistent effective area and
a high negative dispersion for varying intensity and for the wavelength ranging between 200 and 500 nm.

The authors in (J. Liao, et al., 2017) have designed an ultra-high birefringent PCF by means of elliptical glass rod in core section and spiral arrangement by means of circular air gaps with silica in cladding section. Here, the refractive index of the elliptical rod is kept high as compared to the conventional elliptical structures to exhibit non-linearity of 817.5 W⁻¹ km⁻¹ with negative dispersion of −491.16 ps/(nm-km). The construction of PCF using arsenic triseLENide based chalcogenide material has been explored in (J. Li, et al., 2019). The air holes in the cladding region are made up of five layers of concentric rings with uniform air hole and the core region is made up of two layers with

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Geometric structure of spiral shaped flower pattern cladding photonic crystal fiber.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Dispersion performance of flower-cladding photonic crystal fiber for various magnitudes of pitch.</figcaption></figure>

asymmetric air holes and micro concentric rings. The choice of chalcogenide glass is due to its nonlinear refractive index property at the mid-infrared range. The structure generates a broadband supercontinuum at the mid-infrared range (3,887 nm) with a 4 mm PCF that is driven by 100 fs laser pulse with a peak power of 10 kW.

To control the pulse shaping in the process of supercontinuum generation, optimization rule by means of genetic algorithm has been discussed in (M. L. Michaeli & A. Bahabad, 2018). The main advantage with the pulse shaping is the tuning of the spectrum with Gaussian like characteristics. Here, the shaping of pulse prior to feeding the PCF enable the functionality of tunable supercontinuum generation. The tunable source finds its application in realizing broad optical bandwidth and four wave mixing applications with a single laser source (T. Eltaif, 2017). A hybrid PCF with circular and hexagonal planning of air holes in cladding section and elliptical hole with silicon nano rod in core region has been discussed in (Paul, Ahmed, et al., 2018; Paul, Khalek, et al., 2018; Paul, Rajesh, et al., 2018). The PCF exhibits a non-linearity of $1.28 \times 10^6 W^{-1} km^{-1}$ in 500 nm. The confinement loss with hybrid PCF is flattened for a wavelength between 500 and 1,800 nm. However, the confinement loss increases exponentially for a wavelength between 1900 and 2,500 nm. The hybrid structure is viable for shorter wavelengths due to reduced scattering loss.

To reduce the confinement loss and scattering loss with high non-linearity, a chalcogenide entrenched quasi PCF have been discussed in (Paul, Ahmed, et al., 2018; Paul, Khalek, et al., 2018; Paul, Rajesh, et al., 2018). The cladding section of PCF is fused with silica and the core region with elliptical holes is fused with chalcogenide. The choice of silica and chalcogenide is the optical transmittance and non-linearity, respectively of the chosen material. The PCF exhibits a non-linearity of $4.72 \times 10^4 W^{-1} km^{-1}$ at 1,000 nm for a numerical aperture of 0.85 and scattering loss of $1.92 \times 10^{-8}$ dB/km. To simplify the fabrication process, a hexagonal structured PCF

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Nonlinearity of the flower-cladding photonic crystal fiber for various magnitudes of pitch.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Group-velocity dispersion of flower-cladding photonic crystal fiber for various magnitudes of pitch.</figcaption></figure>

with circular air cavities has been reported (S. K. Biswas, et al., 2018). The PCH structure displays hexagonal symmetry with the introduction of isosceles triangular lattice with fused silica. The PCF exhibits a non-linearity of $96.51 \text{ W}^{-1} \text{ km}^{-1}$ with a negative dispersion of –753.20 ps/nm-km. Alternatively, a complex arrangement of circular and elliptical rings in cladding region with square lattice arrangement has been discussed in (M. I. Islam, et al., 2017). The complex structure provides a non-linearity of $131.91 \text{ W}^{-1} \text{ km}^{-1}$ and negative dispersion of –584.60 ps/nm-km.

Supercontinuum generation in PCF with novel guidance properties has made the spectrum broadening a practically feasible solution. From the results reported in literature (A. Rajesh et al., 2021), it is clear that PCF has made a remarkable development in both technical and essential studies of nonlinear optics. In concert, it also paved the way for developing novel and flexible instruments commercially and it also pursues to instigate the various technical fields. The range of the power of the pump is the most important challenge in solid-core PCF. Thus, the proposed PCF is designed with an optimized dispersion profile to provide the sources with high-power pulses. The profile of the dispersion is tuned by optimizing the design constraints, namely, core structure, diameter of the air-holes, distance among two successive air-holes, air-hole to air-hole gap ($\Lambda$) and normalized parameter or

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Impact of pitch on effective mode index and dispersion.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Effect of pitch on nonlinearity and birefringence.</figcaption></figure>

air-filling fraction (d/Λ). Moreover, distribution pattern of structural analysis of air-holes in cladding region has been investigated in detail to optimize the nonlinear properties of the proposed fiber.

It is evident from the above discussion that supercontinuum generation using PCF results in optical spectrum broadening. For effective broadening of the spectrum, the structure of PCF must be optimized to realize low dispersion (≤zero), high nonlinearity (in the order ≥10² W⁻¹ km⁻¹) with desired birefringence (polarization). The birefringence must be high as the linearly polarized light waves entering the core of an anisotropic fiber splits into two distinct polarized modes propagating with differing velocity orthogonally.

The remainder of the paper is detailed as follows: Section 2 discusses the requirement of the proposed structure in 6G networks with its structural analysis. Section 3 details the performance parameter of the proposed PCF. Section 4 tabulates the numerical comparison of the proposed structure and the works reported in literature. Finally, Section 5 concludes the important discoveries and applications of proposed structure.

## 2. Proposed Design of Fused Photonic Crystal Fiber

The research was carried out by employing anisotropic PML in finite element method to acquire the effective mode index, $n_{\text{eff}}$. This extends the dynamic features of the PCF comprises of dispersion factor, birefringence, and non-linear aspect (W. Wang, et al., 2020). Modifying the values of the design parameters, namely, the magnitude

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Effect of pitch on group-velocity dispersion and effective mode area.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 9. Impact of pitch on confinement loss.</figcaption></figure>

of air-holes and pitch display has an implausible effect on the properties. The refractive index as a function of the wavelength is given by Sellmeier's equation (A. A. Rifat, et al., 2019),

$$n^2(\lambda) = 1 + \frac{S_1}{1 - \left(\frac{T_1}{\lambda^2}\right)} + \frac{S_2}{1 - \left(\frac{T_2}{\lambda^2}\right)} + \frac{S_3}{1 - \left(\frac{T_3}{\lambda^2}\right)} \quad (1)$$

where the Sellmeier's constants, that is, $S_1$, $S_2$, $S_3$ and $T_1$, $T_2$, $T_3$ are quantified methodically, $\lambda$ denotes the wavelength, $n$ represents the refractive index of contextual material. The effective mode index of PCF can be determined from (Paul, Ahmed, et al., 2018; Paul, Khalek, et al., 2018; Paul, Rajesh, et al., 2018),

$$n_{\text{eff}} = \beta/k_0 \quad (2)$$

where $\beta$ refers to the propagation constant, and the free space wavenumber is $k_0$.

The components of the incident pulse propagate through the waveguide at different speeds that expand and distort the rectangular pulse shape referred to as dispersion or pulse broadening (M. M. Faruk, et al., 2019). Pulse propagation and the parameters of the waveguide alters the rate of the dispersion coefficient that varies between zero and a negative value. Dispersion can be restrained by altering the structural parameters, namely, pitch and air-hole

<figure><img src="image_12.png" /><figcaption>Figure 10. Dispersion properties of flower-cladding photonic crystal fiber for various air-filling fraction.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 11. Nonlinearity properties of flower-cladding photonic crystal fiber for various air-filling fraction.</figcaption></figure>

size (M. J. B. M. Leon, et al., 2021). The combination of material dispersion ($D_m$) with waveguide dispersion ($D_w$) provides the amount of dispersion $D(\lambda)$ defined by (T. Yang, et al., 2021),

$$D(\lambda) = D_m + D_w = \frac{-\lambda \partial^2 \text{Re}(n_{\text{eff}})}{c \partial \lambda^2} \quad (3)$$

where the real part of effective mode index is represented by Re($n_{\text{eff}}$).

The throughput and latency requirement of 6G communication systems and networks will enable the convergence of optical and wireless technologies for holistic approach of device connectivity (H. R. D. Filgueiras, et al., 2023). The evolution of higher wireless bands in 6G systems in THz bands will increase the channel capacity of core network. This motivates the inclusion of PCF in fronthaul, middle haul and backhaul of the radio access network. As compared to the conventional microwave circuits, the integrated microwave photonics meet

<figure><img src="image_14.png" /><figcaption>Figure 12. Group-velocity dispersion performance of flower-cladding photonic crystal fiber for various air-filling fraction ($d/\Lambda$).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure 13.** Impression of air-filling section on effective mode index and dispersion.</figcaption></figure>

the requirements of multi-wavelength transmission with PCF supercontinuum generation for 6G networks. This will enable baseband data transmission over the fronthaul 6G fiber network allowing data rates of better than 25 GB/s per channel. For terabit data rate considerations in 6G systems, photonics-based transceivers systems have been developed at middle haul networks (M. Sung, et al., 2021). It includes free running optical source at the transmitter, optical amplifier, supercontinuum PCF at the channel and envelope detection at the receiver. The design of multi-core fiber or PCF for backhaul network using transition technologies has been reported in (T. R. Raddo, et al., 2021) for 6G networks. The major variations in 6G network realization are the deployment of fiber to the antenna section using supercontinuum enabled PCF with high birefringence. Further, the key 6G enablers of optical technologies for mobile transport network include, reconfigurable Mach Zehnder Modulators, and optical dispersion compensator (P. Iovanna, et al., 2021). These devices enable the deployment of optical hub over optical distribution fibers for 100 Gb/s in the downstream. To support such data transmission, a wavelength separation of 2.4 nm with a chromatic dispersion of 170 ps/nm and polarization insensitivity is required (S. R. Moon, et al., 2021).

Various techniques have been reported to optimize generation of supercontinuum in 6G networks that includes the use of air-holes with nonuniform size and hybrid type arrangement of air-holes, as shown in Figure 2. In this paper, supercontinuum has been generated with the pumping power of 20 kW. Further, to generate supercontinuum with high pumping power, innovative structures of PCF have been designed and analyzed. The innovation in

<figure><img src="image_16.png" /><figcaption>**Figure 14.** Influence of air-filling segment on effective mode index and nonlinearity.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Influence of air-filling segment on group-velocity dispersion parameter and birefringence.</figcaption></figure>

the structure is that the cladding part is constructed with the inspiration from nature in the shape of flower petals. Apart from the optical characteristics that are discussed in conventional designs, the focus on confinement loss is investigated in this paper as the potential application of the proposed structure is to connect the mmWave Access Points, as illustrated in Figure 1. The loss is calculated by introducing the cladding part of the fiber which determines the imaginary part of $n_{\text{eff}}$. Here, the optical parameters are investigated by changing the design constraints, namely, air-filling fraction ($d/\Lambda$), pitch ($\Lambda$), and core diameter ($d_c$). The core material is the same as that used in the previous structures of the PCF.

Figure 2 illustrates the flower shaped cladding PCF in which air-holes are arranged in a petal shape. The cladding consists of 10 petals with air-holes of 1.35 µm diameter. Each petal consists of two spiral arms in which the angular displacement of air-holes in first arm can be calculated using $\theta_n = n180^{\circ}/N$, where N refers to number of petal rings. Whereas the angular displacement denoted as $\theta$ of the air-holes is 30°. The air-holes in the semi-circular part of each petal are displaced with respect to the last row of that petal. The diameter of core is represented by $d_c$ and ranges between 0.6 and 1.35 µm in steps of 0.15 µm. Here, distance between two successive air-holes namely pitch, $\Lambda$, is varied from 0.5 to 3 µm in a step of 0.5 µm. For the air-filling section to maintain the single-mode of propagation, its value must be such that $d/\Lambda \le 0.45$. We have altered the dimension of the air-filled hole to see how this parameter affects the performance of the PCF. We have used the same background and core materials,

<figure><img src="image_18.png" /><figcaption>**Figure 16.** Dispersion of flower-cladding photonic crystal fiber for various core diameters.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Figure 17. Nonlinearity of flower-cladding photonic crystal fiber for various core diameters.</figcaption></figure>

that is, silica and silicon nanocrystal, respectively, as in the previous works to maintain the stability in the performance characteristics of the fiber,

The coefficient of nonlinearity is the metric used to determine the various nonlinear effects that are responsible for the generation of supercontinuum (T. Baselt, et al., 2017). As discussed earlier, pulse broadening in upcoming 6G applications requires the non-linear coefficient (γ) to be as high as possible. Such requirement is obtained by using a source of high intensity at the core region of reduced effective mode area (A<sub>eff</sub>). The non-linear coefficient is given by (M. S. Rao & V. Singh, 2018),

$$ \gamma = \frac{2\pi n_2}{\lambda A_{\text{eff}}} \qquad (4) $$

where n<sub>2</sub> specifies non-linear refractive index. Effective mode area can be calculated using (M. Seifouri, & M. R. Alizadeh, 2018),

<figure><img src="image_20.png" /><figcaption>Figure 18. Group-velocity dispersion of flower-cladding photonic crystal fiber for various core diameters.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure 19. Impact of core diameter on effective mode index with dispersion.</figcaption></figure>

$$A_{\text{eff}} = \frac{\left[ \begin{array}{cc} \infty & \infty \\ \int \int |E(x, y)|^2 dx dy & \\ -\infty & -\infty \end{array} \right]^2}{\begin{array}{cc} \infty & \infty \\ \int \int |E(x, y)|^4 dx dy & \\ -\infty & -\infty \end{array}} \quad (5)$$

where $E(x,y)$ refers to electric field mode distribution of fundamental fiber mode. Birefringence introduces a difference in refractive index (M. A. Gandhi, et al., 2017; M. Kalantari, et al., 2018). The difference in the real part of $n_{\text{eff}}$ of two polarized modes, which is referred to as modal birefringence, can be determined from (H. Saghaei, 2017; G. M. Zheng, 2021),

$$B = |\text{Re}(n_{\text{eff}}^x) - \text{Re}(n_{\text{eff}}^y)| \quad (6)$$

<figure><img src="image_22.png" /><figcaption>Figure 20. Impact of core diameter on effective mode index with nonlinearity.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure 21. Impact of core diameter on group-velocity dispersion parameter and birefringence.</figcaption></figure>

where Re($n_{eff}^x$) and Re($n_{eff}^y$) are the real parts of $n_{eff}$ in the x and y directions, respectively. Ideally, the light waves would be totally confined in the core of proposed PCF if the cladding has infinite periodic rings of microstructures. However, in reality the PCF cladding will consist of a limited number of rings of microstructures. As a result, a fraction of the optical pulse power will escape from the structure. Such leakage is characterized by confinement loss, which can be deduced from (A. M. I. Aaidi, et al., 2021; A. Habib, et al., 2021),

$$L_c = 8.686k \operatorname{Im}(n_{\text{eff}}) \qquad (7)$$

where $k = 2\pi/\lambda$ is a free space wave number, and $\operatorname{Im}(n_{eff})$ refer to imaginary part of $n_{eff}$. The surface of an optical pulse propagates at the group velocity ($v_g$) that depends on the frequency or wavelength whereas the parameter $\beta_2$ indicates the dispersion of the group velocity and it is highly involved in the broadening of an optical pulse (T. L. Courtney, et al., 2021; Dhara & Singh, 2021). This process is generally known as group-velocity dispersion (GVD) and $\beta_2$ is termed as GVD parameter. Its value may be either positive or negative and it depends on the position of wavelength with respect to the zero-dispersion wavelength. Group-velocity dispersion can be calculated using (R. Salgueiro, & A. Ferrando, 2018; D. Xiong, et al., 2021),

$$GVD = \frac{-2\pi c}{\omega^2} \times D(\lambda) \qquad (8)$$

where c is the speed of light, $\omega$ is the angular frequency, and D signifies the dispersion coefficient.

### 3. Results and Discussion

The variation of dispersion in proposed PCF for various values of pitch and a function of wavelength is shown in Figure 3. It is evident from the figure that the dispersive property of the PCF for lower pitch values ranging from 0.5 to 2 µm oscillates between a positive and a negative value. In this range of pitch, the fiber exhibits a negative dispersion value of -417.2 ps/(nm.km) at pitch value of 1 µm. Further, a reduced negative dispersion value corresponding to -194.7 ps/(nm.km) the pitch value obtained is 1.5 µm at a wavelength of about 1.55 µm. But for higher pitch values of about 2.5 and 3 µm, the dispersive property of the fiber reduces from positive to a negative value. In this range of pitch, at a wavelength of about 1.55 µm the fiber provides a degraded dispersion value of -285.8 ps/(nm.km) at pitch value of 2.5 µm, and dispersion of -142.1 ps/(nm.km) at pitch value of 3 µm. Here, the zero-dispersion wavelength of the proposed PCF is about 1.2 µm.

Nonlinear properties of the proposed PCF reduces with increasing pitch, as shown in Figure 4. At $\lambda = 1.55$ µm, it offers a very high nonlinearity of about $1.70 \times 10^8$ W$^{-1}$ km$^{-1}$ for a low pitch value of 0.5 µm. For the higher pitch value ranging from 1 to 2 µm, the nonlinearity is almost constant and is in the order of $10^7$ W$^{-1}$ km$^{-1}$. The nonlinearity is $4.8 \times 10^7$ W$^{-1}$ km$^{-1}$ for a pitch 1 µm at $\lambda = 1.55$ µm. Whereas, for the pitch values of about 2.5 and 3 µm, the proposed structure provides nonlinearity in the order of $10^6$ W$^{-1}$ km$^{-1}$. For a pitch of 2.5 µm, the nonlinearity is
<figure><img src="image_24.png" /><figcaption>**Figure 22.** Spectral and time evolution of supercontinuum generation for 10 mm photonic crystal fiber.</figcaption></figure>

about $8.69 \times 10^6$ W$^{-1}$ km$^{-1}$, and for a pitch of 3 µm it is about $1.7 \times 10^6$ W$^{-1}$ km$^{-1}$ at $\lambda = 1.55$ µm. Figure 5 shows how the GVD parameter ($\beta_2$) value changes from a positive to a negative value for the low pitch values ranging from 0.5 to 2 µm. The GVD has a very low value of about $-6.11 \times 10^{-5}$ ps$^2$/km for a pitch of 0.5 µm, and a comparatively high value of about $2.48 \times 10^{-4}$ ps$^2$/km at $\lambda = 1.55$ µm. But for the high pitch values of about 2.5 and 3 µm, the GVD value increases from a low value to high value. For a pitch 1 µm, the GVD of the fiber is about $3.64 \times 10^{-4}$ ps$^2$/km and a comparatively low value of about $1.811 \times 10^{-4}$ ps$^2$/km for a pitch of 3 µm at a wavelength of 1.55 µm.

The characteristics of proposed PCF for various pitch values is shown in Figures 6–9. It is evident that the fiber provides a very high birefringence of about $3 \times 10^{-6}$ for a pitch value of 0.5 µm. The birefringence is $1 \times 10^{-6}$ at $\lambda = 1.55$ µm for a pitch of 3 µm. For a pitch of 3 µm, the fiber behaves as a lossless fiber, that is, the confine-
<figure><img src="image_25.png" /><figcaption>**Figure 23.** Spectral and time evolution of supercontinuum generation for 15 mm photonic crystal fiber.</figcaption></figure>

<caption>**Table 1**</caption>

*Performance Parameters of Flower-Cladding Photonic Crystal Fiber for Various Pitch*

<table><thead><tr><th>Λ (μm)</th><th>n<sub>eff</sub></th><th>D(λ) (ps/nm.km)</th><th>A<sub>eff</sub> (μm<sup>2</sup>)</th><th>γ (W<sup>-1</sup> km<sup>-1</sup>)</th><th>B</th><th>Lc (dB/m)</th><th>β<sub>2</sub> (ps<sup>2</sup>/km)</th></tr></thead><tbody><tr><td>0.5</td><td>1.309213</td><td>-331.9</td><td>0.0443E<sup>-12</sup></td><td>1.70E<sup>8</sup></td><td>6.95E<sup>-6</sup></td><td>1.77E<sup>-2</sup></td><td>-6.109E<sup>-5</sup></td></tr><tr><td>1</td><td>1.377086</td><td>-417.2</td><td>0.1572E<sup>-12</sup></td><td>4.796E<sup>7</sup></td><td>0</td><td>2.03E<sup>-7</sup></td><td>5.318E<sup>-4</sup></td></tr><tr><td>1.5</td><td>1.443845</td><td>-194.7</td><td>0.3447E<sup>-12</sup></td><td>2.19E<sup>7</sup></td><td>0</td><td>0</td><td>2.482E<sup>-4</sup></td></tr><tr><td>2</td><td>1.486772</td><td>-366.6</td><td>0.5843E<sup>-12</sup></td><td>1.19E<sup>7</sup></td><td>0</td><td>0</td><td>4.672E<sup>-4</sup></td></tr><tr><td>2.5</td><td>1.520189</td><td>-285.8</td><td>0.8675 E<sup>-12</sup></td><td>8.69E<sup>6</sup></td><td>0</td><td>0</td><td>3.642E<sup>-4</sup></td></tr><tr><td>3</td><td>1.546877</td><td>-142.1</td><td>1.1833 E<sup>-12</sup></td><td>1.70E<sup>6</sup></td><td>0</td><td>0</td><td>1.811E<sup>-4</sup></td></tr></tbody></table>
<table><caption>**Table 2**
Performance Parameters of Flower-Cladding Photonic Crystal Fiber for Various Air-Filling Fraction</caption><thead><tr><th>d/Λ</th><th>n<sub>eff</sub></th><th>D(λ) (ps/nm.km)</th><th>A<sub>eff</sub> (μm<sup>2</sup>)</th><th>γ (W<sup>-1</sup> km<sup>-1</sup>)</th><th>B</th><th>Lc (dB/m)</th><th>β<sub>2</sub> (ps<sup>2</sup>/km)</th></tr></thead><tbody><tr><td>0.2</td><td>1.45295</td><td>-372.8</td><td>0.2769E<sup>-12</sup></td><td>2.723E<sup>7</sup></td><td>0</td><td>0</td><td>4.752E<sup>-4</sup></td></tr><tr><td>0.25</td><td>1.46837</td><td>-631.3</td><td>0.4218E<sup>-12</sup></td><td>1.788E<sup>7</sup></td><td>0</td><td>0</td><td>8.047E<sup>-4</sup></td></tr><tr><td>0.3</td><td>1.488933</td><td>-571.2</td><td>0.5874E<sup>-12</sup></td><td>1.284E<sup>7</sup></td><td>0</td><td>0</td><td>7.28E<sup>-4</sup></td></tr><tr><td>0.35</td><td>1.510283</td><td>-406</td><td>0.7703E<sup>-12</sup></td><td>9.788E<sup>7</sup></td><td>0</td><td>0</td><td>5.174E<sup>-4</sup></td></tr><tr><td>0.4</td><td>1.529877</td><td>-254.2</td><td>0.9691E<sup>-12</sup></td><td>7.780E<sup>6</sup></td><td>0</td><td>0</td><td>3.24E<sup>-4</sup></td></tr><tr><td>0.45</td><td>1.546877</td><td>-142.1</td><td>1.1833E<sup>-12</sup></td><td>6.37E<sup>6</sup></td><td>1E<sup>-6</sup></td><td>0</td><td>1.811E<sup>-4</sup></td></tr></tbody></table>

ment loss of the propagation is zero. From this analysis, it is concluded that for an efficient generation of SC, the pitch value of about 3 µm is suitable because it provides a fiber with low and negative dispersion, high non-linearity, low birefringence, and a zero confinement loss. It is found that the behavior of optical constraints in flower-cladding PCF varies with air-filling fraction (d/Λ). The variation of dispersion with reference to different values of d/Λ is shown in Figure 10. Here, the dispersive property of the fiber changes between the low and high value with an increase in d/Λ from 0.2 to 0.45. For lower wavelengths, the dispersion is near to zero and for longer wavelengths, it exhibits a high positive dispersion. At λ = 1.55 µm, the proposed structure exhibits a negative dispersion of -631.3 ps/(nm-km) for d/Λ = 0.25 and negative dispersion equivalent to -142.1 ps/(nm-km) for d/Λ = 0.45.

Nonlinear characteristics of the proposed PCF reduces with an increase in d/Λ, as shown in Figure 11. At λ = 1.55 µm, the d/Λ ranging from 0.2 to 0.35 the nonlinearity is in the order of 10⁷ W⁻¹ km⁻¹. More specifically, the nonlinearity is about 9.79 × 10⁷ W⁻¹ km⁻¹ for d/Λ = 0.35 at a wavelength of 1.55 µm. Whereas, for the values of d/Λ in the range of 0.4 & 0.45, the proposed structure provides nonlinearity in the order of 10⁶ W⁻¹ km⁻¹. For d/Λ = 0.4, the proposed PCF has a nonlinearity value of about 7.78 × 10⁶ W⁻¹ km⁻¹, and for d/Λ = 0.45, the nonlinearity is about 6.37 × 10⁶ W⁻¹ km⁻¹ at λ = 1.55 µm. Figure 12 shows the GVD parameter (β₂) value changes between a low and the high value with an increase in d/Λ from 0.2 to 0.45. Here, the β₂ values are positive as the dispersion for all d/Λ values is negative. It provides a low GVD value of about 1.81 × 10⁻⁴ ps²/km for d/Λ = 0.45, and a comparatively high GVD value of about 8.05 × 10⁻⁴ ps²/km at λ = 1.55 µm for d/Λ = 0.25.

The performance characteristics of d/Λ is shown in Figures 13–15. The behavior of dispersion, nonlinearity, and GVD parameter were discussed earlier. It is evident that the fiber provides a very high Birefringence of about 1 × 10⁻⁶ at λ = 1.55 µm for d/Λ = 0.45. The change in the value of d/Λ doesn't create any loss in the propagation of an incident pulse. That is, the proposed PCF is a lossless fiber. From this analysis, it can be concluded that for an efficient generation of supercontinuum, the d/Λ value of about 0.45 is highly suitable because it provides a fiber with low negative value dispersion and high nonlinearity.

Examined now is the optical constraints of the proposed PCF as a function of core diameter (d_c). Variation of dispersion in the proposed PCF for various d_c is shown in Figure 16. The variation is analogous to the performance features of fiber corresponding to d/Λ. But, the values of the optical parameters obtained above λ = 1.55 µm

<table><caption>**Table 3**
Performance Parameters of the Flower-Cladding Photonic Crystal Fiber for Various Core Diameter</caption><thead><tr><th>d<sub>c</sub> (μm)</th><th>n<sub>eff</sub></th><th>D(λ) (ps/nm.km)</th><th>A<sub>eff</sub> (μm<sup>2</sup>)</th><th>γ (W<sup>-1</sup> km<sup>-1</sup>)</th><th>B</th><th>Lc (dB/m)</th><th>β<sub>2</sub> (ps<sup>2</sup>/km)</th></tr></thead><tbody><tr><td>0.6</td><td>1.45295</td><td>-348.8</td><td>0.2769E<sup>-12</sup></td><td>2.71E<sup>7</sup></td><td>1E<sup>-6</sup></td><td>0</td><td>4.445E<sup>-4</sup></td></tr><tr><td>0.75</td><td>1.46837</td><td>-566.2</td><td>0.4218E<sup>-12</sup></td><td>1.79E<sup>7</sup></td><td>0</td><td>0</td><td>7.217E<sup>-4</sup></td></tr><tr><td>0.9</td><td>1.488933</td><td>-541.1</td><td>0.5874E<sup>-12</sup></td><td>1.28E<sup>7</sup></td><td>0</td><td>0</td><td>6.897E<sup>-4</sup></td></tr><tr><td>1.05</td><td>1.510283</td><td>-394.8</td><td>0.7703E<sup>-12</sup></td><td>9.79E<sup>7</sup></td><td>0</td><td>0</td><td>5.031E<sup>-4</sup></td></tr><tr><td>1.2</td><td>1.529877</td><td>-250.8</td><td>0.9691E<sup>-12</sup></td><td>7.74E<sup>6</sup></td><td>0</td><td>0</td><td>3.197E<sup>-4</sup></td></tr><tr><td>1.35</td><td>1.546877</td><td>-142.1</td><td>1.1833E<sup>-12</sup></td><td>6.37E<sup>6</sup></td><td>1E<sup>-6</sup></td><td>0</td><td>1.811E<sup>-4</sup></td></tr></tbody></table>
<table><caption>**Table 4**
Comparison of Flower-Cladding Structure With Works in Literature</caption><thead><tr><th>Parameters</th><th>A. Medjouri, et al. (2019)</th><th>A. Aparna Nair, et al. (2019)</th><th>P. Chauhan, et al. (2018)</th><th>P. Chauhan, et al. (2019)</th><th>M. Sharma and Konar (2016)</th><th>T. Singh Saini et al. (2015)</th><th>Proposed work</th></tr></thead><tbody><tr><td>λ (μm)</td><td>4.5</td><td>0.850</td><td>1.35</td><td>4</td><td>1.55</td><td>4.1</td><td>1.55</td></tr><tr><td>D(λ) (ps/nm.km)</td><td>Zero</td><td>Zero</td><td>-92.08</td><td>-19.52 to -11.78</td><td>40</td><td>-</td><td>-142.1</td></tr><tr><td>γ (W<sup>-1</sup> km<sup>-1</sup>)</td><td>970</td><td>220</td><td>884</td><td>853</td><td>923</td><td>1.944</td><td>6.37E<sup>6</sup></td></tr><tr><td>Pulse width T<sub>0</sub> (ps)</td><td>0.48</td><td>0.49</td><td>NA</td><td>0.89</td><td>0.499</td><td>0.499</td><td>0.350-0.650</td></tr><tr><td>Initial peak power P<sub>0</sub> (kW)</td><td>20</td><td>1.8</td><td>0.00050</td><td>8.19</td><td>0.00100</td><td>3.5</td><td>25</td></tr></tbody></table>

exhibit negative dispersion. The dispersion is -566.2 ps/(nm.km) for $d_c = 0.75$ µm and it decreases to -142.1 ps/(nm.km) at $d_c = 1.35$ µm.

In the case of nonlinearity, as shown in Figure 17, it begins to reduce above $\lambda = 1.55$ µm and is in the order of $10^7$ W<sup>-1</sup> km<sup>-1</sup> for lower $d_c$ values between 0.6 and 1.35 µm. The nonlinearity is about $9.79 \times 10^7$ W<sup>-1</sup> km<sup>-1</sup> for $d_c = 1.05$ µm at a wavelength of 1.55 µm. Whereas, for the $d_c$ values of 1.2 µm & 1.35 µm, the proposed structure provides nonlinearity in the order of $10^6$ W<sup>-1</sup> km<sup>-1</sup>. For $d_c = 1.2$ µm, the nonlinearity is about $7.74 \times 10^6$ W<sup>-1</sup> km<sup>-1</sup> and for $d_c = 1.35$ µm, it is about $6.37 \times 10^6$ W<sup>-1</sup> km<sup>-1</sup> at $\lambda = 1.55$ µm. The GVD parameter ($\beta_2$) is shown in Figure 18. GVD parameter values are positive up $\lambda = 1.7$ µm since the dispersion for all values of $d_c$ is negative. The GVD parameter value is about $1.81 \times 10^{-4}$ ps<sup>2</sup>/km for $d_c = 1.35$ µm and increases to $7.22 \times 10^{-4}$ ps<sup>2</sup>/km at $\lambda = 1.55$ µm for $d_c = 1.35$ µm. The performance of PCF as a function of $d_c$ is shown in Figures 19–21. It is evident that the fiber provides a very high Birefringence of about $1 \times 10^{-6}$ at $\lambda = 1.55$ µm for two core diameters $d_c = 0.75$ µm & 1.35 µm. The change in the value of core diameter doesn't create any loss in the propagation of an incident pulse. That is, the proposed PCF is a lossless fiber. From Figure 20, can be concluded that for an efficient generation of SC, the $d_c$ value of about 1.35 µm is suitable because it provides a fiber with low negative value dispersion, high nonlinearity, high birefringence, and a zero confinement loss. Finally, can be concluded that for the generation of SC using PCF with $\Lambda = 3$ µm, $d/\Lambda = 0.45$ & $d_c = 1.35$ µm is preferable.

Spectral and temporal evolution of supercontinuum functionality for 10 mm fiber with preliminary maximum power of 25 kW for tetrad pulse dimensions are shown in Figure 22. The spectral and temporal evolution of supercontinuum for the extended 15 mm fiber for various pulse durations are shown in Figure 23. The dispersion distance is calculated using the expression $L_D = T_0^2 / |\beta_2|$. The dispersion distance is calculated to vary between 0.68 and 2.33 µm for pulse durations between 350 and 600 ps. Moreover, the nonlinear length can be found using the expression $L_{NL} = 1/\gamma P_0$ and calculated to be 0.0063 µm. Further, soliton numeral $N$ is calculated using $N^2 = L_D/L_{NL}$ and it lies between 10 and 19 for tetrad pulse dimensions.

By transmitting an intense pulse in an abnormal dispersion region, the spectrum is broadened. This spectrum broadening essentially balances the temporal compression due to anomalous dispersion. Here, spectrum broadening is achieved by means of self-phase modulation. The sidebands generated depend on pumping power. The flower-cladding PCF results in spectrum broadening for rapid pulses of duration between 350 and 450 ps, however the expansion is relatively small for stretched pulses corresponding to 550 and 650 ps duration.

## 4. Numerical Results

The measured optical parameters of the proposed structure are tabulated in Tables 1–3. The dispersive property of the proposed PCF oscillates between a positive and a negative value. Nevertheless, change in core diameter and the change in the air-filling fraction has an almost similar effect on the all-optical parameters. In all variations, the novel PCF exhibits a negative dispersion and its nonlinear properties are achieved in the order of $10^{-7}$ W<sup>-1</sup> km<sup>-1</sup> and $10^{-6}$ W<sup>-1</sup> km<sup>-1</sup>. Here, the novel PCF is highly birefringent, and it is maintained as a lossless fiber throughout its propagation at $\lambda = 1.55$ µm.

Finally, based on the observations, it is concluded that PCF with $\Lambda = 3$ µm, $d/\Lambda = 0.45$ & $d_c = 1.35$ µm is highly suitable for the generation of supercontinuum. This is because the proposed PCF, which is designed with these parameters, exhibits a reduced negative dispersion, an increased nonlinearity, high birefringence, and a zero confinement loss. The optical constraints of the proposed flower-cladding PCF are compared with several other PCF structures in Table 4. Compared to other structures the nonlinearity of the proposed bio-inspired innovative PCF structure is extremely high. But in contrast it has the highest dispersion, which is negative. The supercontinuum generated at 25 kW is relatively higher than that reported in literature. The proposed PCF is designed for application in 6G telecommunication band of 1.55 µm.

## 5. Conclusion

The design of an innovative structure of PCF has been discussed for supercontinuum generation with high pumping power. Analysis is presented on how the parameters of the photonic crystal structure such as pitch, air-filling fraction, and core diameter influences the performance metrics of the PCF. It is shown that the PCF exhibits a very high birefringence and the confinement loss obtained is zero. The optical pulse has been broadened with
high pumping power of 25 kW that is applicable for next generation 6G networks. The structural analysis of nano-core PCF with fused cladding will provide a baseline for designing the 6G architecture.

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

Data were not used, nor created for this research. All of the figures, materials, and data within the manuscript are original and owned by authors.

## Acknowledgments

Dr. Mohammad Alibakhshikenari acknowledges support from the CONEXPlus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 801538. The authors also sincerely appreciate funding from Researchers Supporting Project number (RSPD2023R699), King Saud University, Riyadh, Saudi Arabia. Besides above, the Article Processing Charge (APC) was afforded by Universidad Carlos III de Madrid (Agreement CRUE-Madrono 2023).

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Erratum

In the originally published version of this article, the third author's affiliation should have been "School of Electronics Engineering, Vellore Institute of Technology, Vellore, India" rather than "VIT-AP University, Amarvati, India." The affiliation has been corrected, and this may be considered the authoritative version of record.