# A Modified Design of a Hexagonal Circular Photonic Crystal Fiber with Large Negative Dispersion Properties and Ultrahigh Birefringence for Optical Broadband Communication

^{1}

^{2}

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## Abstract

**:**

^{−2}at the operating wavelength of 1550 nm for the optimum geometrical parameters. Our proposed HC-PCF exhibited the desirable optical properties without non-circular air holes in the core and cladding region which facilitates the fabrication process. The large negative dispersion of the proposed microstructure over the wide spectral range, i.e., 1350 nm to 1600 nm, and high birefringence make it a suitable candidate for high-speed optical broadband communication and different sensing applications.

## 1. Introduction

## 2. Design Structure of the Proposed HC-PCF

## 3. Numerical Method

^{2}and $E$ is the electric field. The non-linearity $\gamma $ is inversely proportional to the effective mode area ${A}_{eff}$ [28] and can be defined as follows:

## 4. Simulation Result and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Electric field distribution of the fundamental mode at wavelength of $1550$ nm for $x$ polarization; (

**b**) electric field distribution of the fundamental mode at wavelength of $1550$ nm for $y$ polarization; (

**c**) convergence plot of the numerical simulation.

**Figure 3.**Wavelength-dependent dispersion coefficient of the proposed HC-PCF for both $x$ and $y$ polarization for optimum geometrical parameters: $\Lambda =0.76\text{}\mathsf{\mu}\mathrm{m},\text{}{d}_{1}/\Lambda =0.97,$ and ${d}_{2}/\Lambda =\mathrm{0.45.}$.

**Figure 4.**Dispersion properties due to (

**a**) ${d}_{1}/\Lambda $ = 0.97, ${d}_{2}/\Lambda $ = 0.45, and $\Lambda =\left(0.76\text{}\mathsf{\mu}\mathrm{m},\text{}0.78\text{}\mathsf{\mu}\mathrm{m},\text{}0.80\text{}\mathsf{\mu}\mathrm{m}\right)$; (

**b**) $\Lambda $ = 0.76 μm, ${d}_{2}/\Lambda $= 0.45, and ${d}_{1}/\Lambda $ = $\left(0.93\text{}0.95\text{}0.97\right)$; (

**c**) $\Lambda $= 0.76 μm, ${d}_{1}/\Lambda $ = 0.97, and ${d}_{2}/\Lambda $= $\left(0.40\text{}0.43\text{}0.45\right)$ of the proposed HC-PCF.

**Figure 5.**Birefringence properties of HC-PCF with (

**a**) Λ = (0.76 μm, 0.78 μm, 0.80 μm) and fixed ${d}_{1}/\Lambda $ = $0.97$, ${d}_{2}/\Lambda $ = $0.45$; (

**b**) ${d}_{1}/\Lambda $ = $\left(0.93\text{}0.95\text{}0.97\right)$ and fixed $\Lambda $ = $0.76$ μm, ${d}_{2}/\Lambda $ $=0.45$; (

**c**) $\Lambda $ = $0.76$ μm, ${d}_{1}/\Lambda $ = $0.97$, and ${d}_{2}/\Lambda $ = $\left(0.40\text{}0.43\text{}0.45\right)$.

**Figure 6.**Non-linear characteristics of the proposed HC-PCF for (

**a**) both $x$ and $y$ polarization modes; (

**b**) ${d}_{1}/\Lambda $ = $0.97$, ${d}_{2}/\Lambda $ = $0.45$, and $\Lambda $ = ($0.76$ μm, $0.78$ μm, $0.80$ μm); (

**c**) $\Lambda $ = $0.76$ μm, ${d}_{2}/\Lambda $ = $0.45$, and ${d}_{1}/\Lambda $ = ($0.93\text{}0.95$ $0.97$) (

**d**) $\Lambda $ = $0.76$ μm, ${d}_{1}/\Lambda $ = $0.97$, and ${d}_{2}/\Lambda $ = ($0.40\text{}0.43\text{}0.45$).

**Figure 7.**(

**a**) Numerical aperture for two orthogonal polarization modes and (

**b**) confinement loss of the proposed HC-PCF for optimum geometrical parameters.

**Figure 8.**Effect on the (

**a**) dispersion properties and (

**b**) birefringence for $\pm 1\%$ to $\pm 2\%$ variation in the pitch.

**Figure 9.**Effect on the (

**a**) dispersion properties and (

**b**) birefringence properties of the proposed HC-PCF for $\pm 1\%$ to $\pm 2\%$ variation in ${d}_{1}/\Lambda $.

**Figure 10.**Effect on the (

**a**) dispersion properties and (

**b**) birefringence properties of the proposed HC-PCF for $\pm 1\%$ to $\pm 2\%$ variation in ${d}_{2}/\Lambda $.

**Table 1.**A comparison table on the contemporary PCF structures with the proposed HC-PCF in terms of modal properties for corresponding air hole nature at $1550$ nm wavelength.

Prior Reference | Air Hole Shape | Dispersion $\mathit{D}\mathbf{\left(}\mathit{\lambda}\mathbf{\right)}$, ps/nm.km | Birefringence $\mathit{B}$ |
---|---|---|---|

[26] | Circular | $-753.20$ | $3.87\times {10}^{-2}$ |

[31] | Circular and elliptical | $-1694.80$ | - |

[35] | Circular | $-578.50$ | $2.640\times {10}^{-2}$ |

[36] | Circular and elliptical | $-544.70$ | $2.20\times {10}^{-2}$ |

[37] | Circular and elliptical | $-650.00$ | $2.10\times {10}^{-2}$ |

Proposed HC-PCF | Circular | $-1044$ | $4.321\times {10}^{-2}$ |

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**MDPI and ACS Style**

Biswas, S.K.; Arfin, R.; Habib, A.B.; Amir, S.B.; Zahir, Z.B.; Islam, M.R.; Hussain, M.S.
A Modified Design of a Hexagonal Circular Photonic Crystal Fiber with Large Negative Dispersion Properties and Ultrahigh Birefringence for Optical Broadband Communication. *Photonics* **2019**, *6*, 19.
https://doi.org/10.3390/photonics6010019

**AMA Style**

Biswas SK, Arfin R, Habib AB, Amir SB, Zahir ZB, Islam MR, Hussain MS.
A Modified Design of a Hexagonal Circular Photonic Crystal Fiber with Large Negative Dispersion Properties and Ultrahigh Birefringence for Optical Broadband Communication. *Photonics*. 2019; 6(1):19.
https://doi.org/10.3390/photonics6010019

**Chicago/Turabian Style**

Biswas, Shovasis Kumar, Rishad Arfin, Ashfia Binte Habib, Syed Bin Amir, Zunayeed Bin Zahir, Mohammad Rezaul Islam, and Md. Shahriar Hussain.
2019. "A Modified Design of a Hexagonal Circular Photonic Crystal Fiber with Large Negative Dispersion Properties and Ultrahigh Birefringence for Optical Broadband Communication" *Photonics* 6, no. 1: 19.
https://doi.org/10.3390/photonics6010019