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In this study, Octagonal Photonic Crystal Fiber (O-PCF) structures are designed for different air filling fractions with fixed pitch length of 2.2 μm. The light propagating characteristics of PCF structures such as effective refractive index, confinement loss, chromatic dispersion mode effective area and nonlinear coefficient are numerically analyzed. The simulation results show that the fibers have dispersion flattened, ultra-low loss highly nonlinear nature in the wavelength region 1.3 μm to 1.7 μm.

Photonic Crystal Fibers (PCFs) are a new class of optical waveguides which offer exceptional light guiding mechanism and deliver significantly improved performance compared to conventional optical fibers [

Russel et al., in 1992 proposed this special type of fibers that consisted of intentionally made micro-structures in the form of periodic array of air-holes in either circular or in elliptical shape which might be in the form of hexagonal pattern. This will result in the periodic variation in refractive index around the fiber-core running down its length and the first PCF proto-type was reported in 1996 [

In the present work, we have proposed a new class of index guided photonic crystal fibers with octagonal arrangement of air holes in the SiO_{2} (refractive index 1.45) host material. The significant parameters for the PCF design are the diameter of the holes and the distance between adjacent holes called pitch (Λ). In the octagonal structure the basic unit is an isosceles triangle with vertex angle 450. The length of the identical legs is taken as the pitch. The length of the side opposite to the vertex angle, calculated from the formula_{hole}/A_{cell}, where A_{hole} is the area of the air-hole inside the unit triangle and A_{cell} is the area of the unit triangle. In the present work O-PCF structures are designed for six different d/Λ values (d/Λ= 0.2, 0.3, 0.4, 0.5, 0.6, 0.7). In each structure the pitch length is fixed and its value is taken to be 2.2 µm. As the pitch remains constant, different air filling fraction is calculated by varying the size of the air hole and the calculated values are 0.088813, 0.199828, 0.355250, 0.555079, 0.799314 and 1.087954, respectively. It is found that for all the structure the fractional area of the three air holes occupied in the unit isosceles triangles is same and is equal to the 50% of the area of a single air hole. For the easiness of the simulation work only four ring PCF structures are considered.

The propagation of electromagnetic radiations through the photonic crystal fiber is studied by the numerical technique full vectorial Finite Elemental Method (FEM). The studies are carried out over a radiation spectrum of wavelengths ranging from 800 nm to 2000 nm. The FEM technique is one of the advanced vectorial methods to study the light propagation characteristics in PCFs. In the present study we calculate the propagation of the electric vector through the fiber over the given wavelength range with the help of the software COMSOL Multiphysics 4.3. The full vector analysis of the fiber structure is done by calculating the propagation of electric vector through the fiber by solving an eigenvalue problem drawn from the Maxwell’s equations using FEM [_{eff}) of the PCF is obtained from the simulation result. The modified total internal reflection mechanism guide the radiation through the proposed PCFs. To lock the back reflection of the leaky modes into the core of the fiber structure a scattering boundary condition is applied around the cladding region of the PCF. Effective mode area (A_{eff}), confinement loss (Lc), Chromatic dispersion (D), Nonlinear coefficient (γ) and Numerical aperture (NA) can be obtained by using values of n_{eff} to the following equations.

As the electromagnetic radiation propagating through the designed PCFs, a part of the incident energy is leaking out of the core through the air holes and between the air holes. This may referred to as the confinement loss in the PCFs. It is given by [

where _{0} = 2π/ʎ, the free space wave number. Lc can be controlled by the proper selection of the dimension of air hole, pitch and the number of rings around the core. The confinement loss can also be reduced by simply increasing the index contrast between the core and cladding. With the increase in air filling fraction the modes are become more confined inside the core and hence the confinement loss decreases. But as the wavelength increase the modes are more and more spreading out of the center core, so the loss increases with the wavelength.

Dispersion means the broadening of light pulses as they pass through the light pipe. The large refractive index contrast between the core and cladding introduces a number of dispersion properties in photonic crystal fibers. The chromatic dispersion in PCFs can easily be controlled by changing the hole diameter, pitch and air holes arrangement i.e. cladding pattern. The total dispersion or chromatic dispersion of the PCF is the sum of the two components material dispersion and wave guide dispersion and is given by [

where Re(n_{eff}) is the real part of effective refractive index, ʎ is the wavelength and c is the velocity of electromagnetic waves in vacuum. The material dispersion of the silica that calculated from the Sellmeier’s formula is directly included in the FEM calculation.

Effective mode area is an important functional parameter that determines optical performance of PCF, which is strongly depends on the core area and the core cladding index contrast and is given by [

where E is the transverse component of the electric field propagating inside the fiber.

The nonlinear coefficient of PCF is calculated from the formula [

where n_{2} is the nonlinear part of the refractive index. From the relation it is clear that the non linear coefficient of the PCF is inversely related to the effective area. So the effective area is an important parameter in determining the nonlinearity in PCF.

The Numerical aperture (NA) of a PCF is related to the effective area through the relation [

Light propagation through the proposed solid core O-PCF for d/Λ-0.7 is shown in _{eff} is converging towards the refractive index of silica and the modes are tend to be

more confined in the core part due to its waveguide structure, but as the wavelength increases the n_{eff} diverge. At higher wavelengths and d/Λ values the slope of the curves increases negatively. The value of n_{eff} decreases with increase in d/Λ values.

^{−2} dB/km, 7.7043 × 10^{−6} dB/km and 6.90186 × 10^{−7} dB/km respectively.

chromatic dispersion increases with increase in d/Λ values. Also the zero dispersion wavelength can be shifted with the proper selection of air hole diameter and it can be shifted to visible region by increasing the hole size. The proposed O-PCFs with anomalous dispersion can be used as dispersion compensation fiber in the telecommunication lines. The Zero dispersion wavelength (ZDW) and dispersion at the operating wavelength 1.55 µm for all the structures are given in the

_{eff} increases linearly with the wavelength and decreases with the d/Λ values. This is due to the fact that when the wavelength increases the modes are leaking through the air holes and in between them. This will enhance the effective area of the guiding modes. For our particular structures we are keeping the pitch value constant throughout the entire designed fibers. Hence increasing the air filling fraction results in increase of the air hole size. This will in turn increase the confinement of the guiding modes through the core; as a result the mode effective area decreases with the increase in air filling fraction. The value of A_{eff} depends largely on the core radius and the core cladding refractive index contrast. The value of A_{eff} of different structures at the operating wavelength 1.55 µm is shown in _{eff} considerably affect the nonlinear property and the light gathering capacity of the PCFs.

Zero and Chromatic Dispersion wavelengths | ||
---|---|---|

d/Λ | ZDW (µm) | D at 1.55 µm (ps/nm・km) |

0.2 | 1.7089 | −8.9754 |

0.3 | 1.0604 | 9.9590 |

0.4 | 0.9666 | 56.4344 |

0.5 | 0.9401 | 87.9098 |

0.6 | 0.8888 | 110.7787 |

0.7 | 0.8505 | 131.3114 |

area using the relation (5) and it is clear that γ is inversely related to A_{eff}. For the calculation of γ the nonlinear refractive index coefficient for silica is taken as n_{2} = 3.09 × 10^{−20} m^{2}/W.

_{eff}) is a parameter obtained from the effective mode area of the PCFs from the relation_{eff} increases with the wavelength and decreases with the air

filling fraction. At the operating wavelength 1.55 µm structure with d/Λ-0.7 has a spot size of 1.15165 µm.

In this paper, Octagonal Photonic Crystal Fibers are designed and simulated for seven different air filling fractions with the help of the software COMSOL Multiphysics 4.3 by finite elemental method (FEM). All the structures

deliver Gaussian output. The wavelength response of fiber parameters such as confinement loss, effective mode area, chromatic dispersion, non-linearity coefficient and numerical aperture of the proposed fibers are thoroughly investigated. From the studies it is established that the proposed O-PCFs with higher air filling fractions have shown high nonlinearity, large numerical aperture, low confinement loss and dispersion flattened nature over the wavelength range 1.3 µm to 1.7 µm.

G. DhanuKrishna,G.Prasannan,S. K.Sudheer,V.P. MahadevanPillai, (2015) Design of Ultra-Low Loss Highly Nonlinear Dispersion Flattened Octagonal Photonic Crystal Fibers. Optics and Photonics Journal,05,335-343. doi: 10.4236/opj.2015.512032