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Abstract. Photonic crystal fibers are very useful as nonlinear media with the combination of nonlinear coefficient and positively tailored zero and flattened dispersion wavelength. This type of flexibility is hard to achieve in any other of medium. We design a fiber containing five rings with two shapes of air holes (circular and elliptical). Our design is helpful to achieve both zero dispersion and flattened dispersion in a wide wavelength range. It is shown from numerical results that it is providing the zero dispersion and flattened dispersion of 0 + 0.96 ps/(nm-km) from a wavelength of 1.58 ''m to 1.9 ''m. In this paper we also define the effect on optimum dispersion by changing the diameter of inner ring of fiber. Generally, in PCF + 1% variation in diameter may be occurred during fabrication. Due this reason, we have analyzed the effect on dispersion by varying diameter + 2% to + 4%.There is insignificant effect on dispersion by varying global diameter of air holes in first ring.

Keywords: Photonic crystal fiber, zero dispersion, flattened dispersion, nonlinear coefficient.

1   Introduction

The idea to prepare photonic crystal fibers (PCF) as their name indicates by using photonic crystals. Photonic crystal structures are three dimensional, dielectric structures and periodic. The scheme of the photonic crystal fiber in 1996 [1], the first steps towards the greatest revolution within the field of fiber optics were taken. Within a relatively short period of time it became obvious that photonic crystal fibers could be realized with novel properties compared to those known from conventional solid fibers. In particular, In PCFs is having a hollow core in which light can be guided in air. PCFs are giving most important applications, such as transmission of high power, guidance on low loss without the uncertainty of fiber damage. Moreover, air-guiding type of PCFs is easy to bend, even having small values of diameter for bending and they exhibit highly dispersion properties, extremely influenced by the component of waveguide. Finally, filled hollow core PCFs by liquids and proper gases can be successfully used in nonlinear optics and sensor applications. The probability of changing the air-hole geometry in the fiber representation is restricted only by the technological expediency of the proposed PCFs. It is also define that how the properties of PCF can be influenced by the improvement in the geometry and 'how far' it is spreaded and demonstrated properties of excellent optical fibers. Photonic crystal fibers are very useful as nonlinear media with the combination of nonlinear coefficient and positively tailored zero and flattened dispersion wavelength. Photonic crystal fibers (PCF) have drawn increased attention nowadays because of their attractive properties [2,3], like very low or very high nonlinearity, wideband dispersion-flattened characteristics, high birefringence, single mode guiding etc. Its flexibility is due to the particular design flexibility, which allows them to fit a specific application by only varying its geometrical structure. The concept of effective refractive index [4] was proposed to intuitively analyze the index guiding PCF, which guides light along total internal reflection between a solid core and a cladding zone with structure of multiple air holes. Since the effective refractive index of the core area is higher than that of the cladding, light in the PCF is guided by modified total internal reflection.

In this paper, we propose a hexagonal structure is containing five rings with two shapes of air holes (circular and elliptical) that is suitable to achieve the zero dispersion and flattened dispersion in over a wide range of wavelengths. The main advantage of our proposed MOF is the design flexibility with zero and flattened dispersion of 0 + 0.96 ps/(nm-km) from a wavelength of 1.58 ''m to 1.9 ''m  which is very crucial in high bit rate transmission network and sensing applications. Another observation of proposed MOF shows the insignificant effect on dispersion by varying the global diameter of air holes during the fabrication process. Generally, in PCF + 1% variation in diameter may be occurred during fabrication. In our design we defined + 2% to + 4% variation in global diameter of air holes in first ring.

2 Design Methodology

Fig. 1 shows the air holes distribution of the proposed H-MOF which contains five air hole rings. Where '' is the pitch of the lattice, d3 is the air hole diameter of the 3rd ring and d is the air hole diameter of rest of the ring. The hot material in our proposed structure is silica and air holes are arranged in hexagonal structure symmetry. In order to achieve zero and flattened dispersion air holes in first ring make small and air hole in second ring is in elliptical shapes. The air holes diameter in the third ring is relatively smaller than rest rings.

Fig. 1. Structure of proposed H-MOF, d/ ''= d4/ '' = d5/'' = 0.95, d3 /'' = 0.59, d2 = (a= 0.4 ''m, b=0.2 ''m), d1= 0.3 and pitch ''=0.90 ''m

3 Numerical Method

Finite Difference Time Domain method (FDTD) with perfectly matched layers (PML) boundary condition is used to calculate the dispersion of the proposed structure. Once the modal effective index neff is acquired by solving an eigen value issue using FEM, the Chromatic dispersion D ('') can be calculated by the following equations [5].

                  D ('') = -''/c (d2Re[neff]/ d''2)                                                      (1)

Where Re[neff] and Im[neff] is the real part and imaginary of effective refractive index neff respectively , '' is the wavelength in vacuum, c is the velocity of light in vacuum and k0 is the free space number.

                                                                                                                                                                                     

For the total dispersion coefficient and dispersion slope of the SMF, the requirements of a material dispersion and waveguide dispersion.

                                                        

                            D(T) = D(m) + D('')                                                       (2)

Where D(T), D('') and D(m) are the total dispersion, waveguide dispersion and material dispersion coefficient of the mode fiber.

3 Simulation results and discussion

Fig. 2 shows the dispersion characteristics of both x and y polarization for optimum design parameters with d/'' =0.95, d3/'' = 0.59 and pitch '' =0.90 ''m. Global diameter of the air holes in 1st ring 0.3. From curve it is seen that, the proposed fiber exhibits zero dispersion  and flattened dispersion coefficient about 0 + 0.96 ps/(nm-km) along the from 1.58 ''m to 1.9 ''m. Due to having zero dispersion  and flattened dispersion coefficient our proposed fiber could be suitable in sensing application.

In PCF '' 1% variation in global diameters may be occurred during fabrication [6]. Due to this reason, we have analyzed the effect on dispersion by varying diameter '' 2% to '' 4%, which is discussed in the following section.

    Fig. 3 reveals the effect by varying global diameter of first ring '' 2% to '' 4%, while other parameters are kept constant. . Red and blue line depicts due to increment in parameters respectively whereas green and pink line for decrement. When d1 is varied as '' 2% to ''4%, their corresponding dispersion value becomes -1.7, 1.2, -2.3 and 1.33 ps/(nm-km) respectively. But there is insignificant effect in dispersion by varying global diameter of air holes in first ring. According to this output, we observe if there is '' 2% to '' 4% variation is in diameter during fabrication process so it is shown insignificant effect on dispersion property of photonic crystal fiber.

                       

Fig. 2. Graph between Total dispersion and wavelength

Fig. 3. Effect on dispersion by changing d1of air holes in first ring

4 Conclusion

In summary, we have reported a relatively simple zero dispersion and flattened dispersion for particular waveguide window. It has been shown through simulation results, using this proposed PCF design in industrial level may lead to many benefits such as miniaturization, high degree of integration and remote sensing application. It is shown from numerical results that it is providing the zero dispersion and flattened dispersion of 0 + 0.96 ps/(nm-km) from a wavelength of 1.58 ''m to 1.9 ''m. Fig 3 shows the effect on dispersion by varying diameter + 2% to + 4. According to this output, we observe if there is '' 2% to '' 4% variation is in diameter during fabrication process so it is shown insignificant effect on dispersion property of photonic crystal fiber.

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Appendix:

FDTD: - OptiFDTD is user-friendly, powerful, highly integrated, software that allows simulation and CAD of photonic components or advance technology. The OptiFDTD tool is depends on the finite-difference time-domain (FDTD) method. The FDTD tool has been established as a powerful engineering tool for simulations of optics device. This is because of its special combination of properties, such as the capability to model light travelling, reflection, diffraction, scattering, and effects of polarization. It can also model material dispersion and anisotropy without any prediction of field behavior such as the slowly vibrating amplitude approximation. The FDTD used for the powerful and effective analysis simulation of sub-micron devices with quality structural details.

Boundary Conditions:  The basic algorithm of FDTD must be improved computational window at the boundaries where boundary conditions (ABC) are used for suitable numerical absorbing. Boundary conditions are one of the most challenging features of FDTD simulations. There is various options for the type of boundary conditions. The best performance in FDTD of Perfectly Matched Layer (PML) boundary conditions. The FDTD tool uses the Anisotropic PML, or it is called as Un-split PML (UPML) version.

Refractive index:   In optical medium Refractive index n is a dimensionless quantity that is use to describe how radiation and light, travel throughout the medium.

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