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This paper presents four rings square, circular, and hexagonal photonic crystal fiber (PCF) geometry for analyzing different optical properties in a wavelength ranging from 800 nm to 1600 nm. These three types of geometry have been used for analyzing Effective area, Propagation constant, Confinement loss and Waveguide dispersion. Silica glass is chosen as background material and the cladding region is made of four air hole layers. COMSOL Multiphysics (
*v*
*.*5) software is used to simulate these proposed PCF geometries. From the numerical analysis, it is found that the effective area is small for hexagonal PCF geometry and large for square PCF geometry (11.827
μm
^{2}, 10.588
μm
^{2} and 9.405
μm
^{2} for square, circular, and hexagonal PCF geometry respectively). From the analysis, the Confinement loss is approximately zero at wavelength ranges from 800 nm to 1250 nm and approximately zero waveguide dispersion is achieved from 900 nm to 1500 nm for all the three PCF structures. Again, negative dispersion approximately
−30.354 ps/(nm
⋅km) is achieved for circular PCF structure at the wavelength of 900 nm.

Photonic crystal fiber (PCF) is among the most special optical light guides. The core region always has high refractive index (silica glass) where the cladding region is usually provided by micro structured arrangement of air holes along the fiber [^{2} is offered [

The main goal of the work is to design four rings square, circular and hexagonal geometry as simple as possible for analyzing effective area, propagation constant, confinement loss, waveguide dispersion etc. in a wavelength ranges from 800 nm to 1600 nm. These structures ensure small effective mode area, low dispersion and low confinement loss in a wide wavelength range and the proposed structures are relatively simpler than the existing designs.

In this thesis, we have designed photonic crystal fiber of square, circular and hexagonal structure with four layers of air holes in COMSOL (version 5). The Silica glass (n = 1.46) material is used as a background material. We have taken four layers of air holes to guide the light in the core region.

The first (inner) layer is elliptical with diameter, d1 = 0.35 um in x axis and 0.7 um in y axis. The other three layers are circular shape with diameter d2 = d3 = d4 = 1.4 um and pitch, Ʌ = 2 um. A perfectly matched layer (PML) absorbing boundary condition is applied after the air hole layers.

Our proposed structures are simulated for same air hole diameter, pitch to evaluate the optical properties such as effective area, propagation constant, confinement loss, and waveguide dispersion under wavelength ranges from 800 nm to 1600 nm. Effective area is the fiber area that covers transverse dimension of the fiber. A low effective area provides high density of power in the core region required for non-linear effects to be significant. The effective area can also be related to spot-size, with the Gaussian width w, though. The effective area can be calculated directly from COMSOL Multiphysics. The effective mode area A_{eff} is established [

A e f f = ( ∫ ∫ | E 2 | d x d y ) 2 / ∬ | E 4 | d x d y (1)

Here, the effective mode area A_{eff} in μm^{2} and electric field amplitude is E in the medium.

The propagation constant of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction. The propagation constant β is given by [

β = n e f f 2 Π / λ (2)

where, n_{eff} is the effective refractive index and λ is the wavelength of the input light.

Confinement loss is one of the most important parameters in the fiber transmission. The loss in light confinement due to the periodic arrangement of cladding in PCF is called the confinement loss. Confinement loss is calculated from the following equation [

L = 8.686 K o I m ( n e f f ) (3)

where, K_{0} = 2π/λ and it is the propagation constant in free space and I_{m} (n_{eff}) is the imaginary part of effective refractive index.

When the fraction of light power propagating through the cladding region faster than the core region, then waveguide dispersion occurs. Waveguide dispersion is calculated from the following equation [

D = − λ / c ( d 2 n e f f / d λ 2 ) (4)

where, λ is the wavelength and c is the velocity of light in free space.

At the first step, we used COMSOL Multiphysics software for creating four rings square, circular, and hexagonal photonic crystal fiber structures. After defined all parameters, the simulation is run. After simulating, we got the structural view of the respective design, confinement of the electric field in the core region of those respective designs. COMSOL Multiphysics software simulation gives us the complex effective refractive index which has a real part and an imaginary part. In the second step, we used these values to calculate effective area, propagation constant, dispersion and confinement loss using Microsoft Office Excel, and MATLAB was used to plot the outcome.

COMSOL Multiphysics software simulation gives us the fundamental effective refractive index data for square, circular and hexagonal photonics crystal fiber structure at a wavelength ranges from 800 nm to 1600 nm. For each structure, the silica glass (n = 1.46) material is used as a background material and we have taken four layers of air holes.

The first (inner) layer is elliptical shape with diameter, d1 = 0.35 um in x axis and 0.7 um in y axis. The other three layers are circular shape with diameter, d2 = d3 = d4 = 1.4 um and pitch, Ʌ = 2 um. We tried to focus on the variation of effective area, confinement loss, waveguide dispersion, and propagation constant etc. due to change of structure of PCFs.

Figures 1-3 represent transverse geometry and fundamental mode field for the square, circular and hexagonal PCF geometry.

^{2}, 10.588 µm^{2}, 9.405 µm^{2} for square, circular, and hexagonal PCF geometry respectively at wavelength 1550 nm.

loss is approximately zero at wavelength ranges from 800 nm to 1250 nm and after that, it increases with the increases of wavelength for all the three structures. Large confinement loss is seen for hexagonal PCF geometry and low confinement loss is seen for circular PCF geometry. For the square PCF geometry

the Confinement loss is nearly 1.592 × 10^{−16} dB/km, for the circular PCF geometry the confinement loss is 6.88 × 10^{−16} dB/km, for the hexagonal PCF geometry, the confinement loss is 0.58 × 10^{−16} dB/km in wavelength 1550 nm.

Another very significant optical parameter is waveguide dispersion.

We have got only negative dispersion for circular PCF structure and it is −30.354 ps/(nm∙km) at the wavelength of 900 nm.

In this research work, four-layer square, circular and hexagonal photonic crystal fiber have been designed. The research is focused on the variation of optical properties like propagation constant, confinement loss, effective area, and waveguide dispersion by varying the structure of PCFs. The simulation results have shown that the effective area is small for hexagonal PCF geometry and large for square PCF geometry. From the analysis, the Confinement loss is approximately zero at wavelength ranging from 800 nm to 1250 nm and approximately zero waveguide dispersion is achieved from 900 nm to 1500 nm for all the three PCF structures. Besides, negative dispersion, approximately −30.354 ps/(nm∙km), is also achieved for circular PCF structure at the wavelength of 900 nm.

In this paper, simulation is carried out for square, circular, and hexagonal photonics crystal fiber geometry to analysis the effective area, confinement loss, waveguide dispersion, propagation constant etc. In the next work, relative sensitivity, coupling length and birefringence for different PCF geometries will be taken into account during simulation. Finally, the PCF fabrication process will be studied and the proposed PCF structures will be fabricated.

Hossain, M.B., Bulbul, A.A.-M., Mukit, M.A. and Podder, E. (2017) Analysis of Optical Properties for Square, Circular and Hexagonal Photonic Crystal Fiber. Optics and Photonics Journal, 7, 235-243. https://doi.org/10.4236/opj.2017.711021