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Analysis of a new circular photonic crystal fiber with large mode area
Accepted Manuscript Title: Analysis of a New Circular Photonic Crystal Fiber with Large Mode Area Author: Abdelkader Medjouri Lotfy Moktar Simohamed Omar Ziane Azzedine Boudrioua PII: DOI: Reference:
S0030-4026(15)01091-8 http://dx.doi.org/doi:10.1016/j.ijleo.2015.09.035 IJLEO 56240
To appear in: Received date: Accepted date:
3-10-2014 7-9-2015
Please cite this article as: A. Medjouri, L.M. Simohamed, O. Ziane, A. Boudrioua, Analysis of a New Circular Photonic Crystal Fiber with Large Mode Area, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.09.035 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of a New Circular Photonic Crystal Fiber with Large Mode Area Abdelkader MEDJOURI 1, 2, Lotfy Moktar SIMOHAMED 3, Omar ZIANE 2 and Azzedine BOUDRIOUA 4 : Laboratoire d’Exploitation et Valorisation des Ressources Sahariennes (LEVRES), Faculté
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1
des Sciences et Technologie, Université d’EL Oued, 39000, El Oued, Algeria.
: Laboratoire d’Electronique Quantique (LEQ), Faculté de Physique, USTHB, BP no. 32 ElAlia, Bab-Ezzouar, 16111 Algiers, Algeria. 3
: Laboratoire Des Systèmes Electroniques Et Optroniques (LSEO), Ecole Militaire
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Polytechnique, 16111 Algiers, Algeria. 4
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2
: Laboratoire de Physique des Lasers (LPL), Institut Galilée, UMR 7538 CNRS, Université Paris 13, 93430 Villetaneuse, France.
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E-mail: [email protected]
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Abstract
A new design of large mode area (LMA) Circular Lattice Photonic Crystal
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d
Fiber (CL-PCF) is proposed and numerically investigated. The cladding is formed by
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six rings of air holes arranged in circular configuration and the core is obtained by only omitting one air hole in the center. The transmission characteristics such as confinement loss, effective mode area, chromatic dispersion and bending loss are analyzed by using a Finite Difference in Time Domain (FDTD) method combined with Perfectly Matched Layer (PML) boundary condition. Results show that around 1.55 µm, the proposed CL-PCF exhibits an effective mode area larger then 1000 µm2 with a confinement loss as low as 7.64 10 3 dB/km for an air filling fraction
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of d
0.16 . Furthermore, the effect of bending is reported and two new variants of
CL-PCF are presented in the aim to mitigate its induced loss: CL-PCF with double air
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holes diameter in single side and CL-PCF with double cladding constant.
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Keywords: Circular lattice photonic crystal fiber; large mode area; FDTD method;
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confinement loss; bending loss.
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1. Introduction
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Photonic crystal fibers (PCFs) are optical fibers realized by a transverse two
d
dimensional photonic crystal with a micrometer-spaced array of air holes running
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down their length and a defect region in the center [1]. The unique and interesting
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optical properties that characterize PCFs, compared to conventional optical fibers, like single mode operation over a wide range of wavelengths [2], chromatic dispersion management [3-7], high birefringence [8-13], high nonlinearity [14,15] and so on, have lead to many potential applications such as: dispersion compensating fibers [1618], polarization maintaining fibers [19-21], highly nonlinear fibers [22-24], supercontinuum generation [25], fiber based lasers [26-28], sensors [29-31] and terahertz applications [32-34] .
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Among these features, the effective mode area (Aeff) is considered as a critical issue when a high power must be delivered with a reduced nonlinearity, as in fiber
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lasers [35], amplifiers [36], wavelength multiplexing division systems (WDM) [37]
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and fiber to the home (FTTH) networks [38]. In fact, large mode area (LMA) helps to
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mitigate the impairments that arise from different nonlinear effects, such as stimulated
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Raman scattering, stimulated Brillouin scattering and self-phase modulation, by reducing the power density over the fiber core area.
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PCFs with large effective mode area have been the subject of many recently
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published papers. In [39], H. Demir and S. Ozsoy presented a comparative study of
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large hexagonal lattice solid core PCFs. With a core formed by the omission of seven
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air holes. They found that Aeff increases when the air fraction decreases in the
cladding region. A maximum value of Aeff = 500 µm2 is obtained when an air fraction
of d
0.1 is used. Also, for a square lattice PCFs with a core formed by nine
omitted air holes [40], the same authors found that Aeff increases when the air fraction
decreases, but a value of Aeff = 630 µm2 is reached for an air fraction of 0.1 too. However, the effect of bending (radius and orientation) on Aeff and the confinement loss has not been reported.
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In [41], Xin Wang et al studied a kind of bend resistant large-mode-area PCF. Their structure is composed of a triangular-core with three missing air holes and the
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cladding is composed of two similar sizes of air holes. They found that at the
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wavelength of 1.064 μm, the mode field area of the fundamental mode reaches 930
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µm2 at the straight state and 815 µm2 at a bending radius of 30 cm. Considering the
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confinement loss, the authors have found that it is as low as 1.6 10 5 dB/m at the wavelength 1.064 µm when the fiber is straight. When the fiber is bent with a radius
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of 30 cm, the confinement loss decreases and reaches the value 0.0025 dB/m.
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Furthermore, the effect of bending orientation is considered. Over a range of bending
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orientation angle that varies from - 550 to 550 and for a bending radius of 30 cm, the
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authors found that, the authors found that the average bending losses of the fundamental mode is 0.0144 dB/m and the average mode area is 848 µm2. In another hand, in [42], Md. Asiful Islam and M. Shah have proposed a new
design of PCF with circular lattice and selectively enlarged air holes for both WDM and FTTH systems. The impact of bending radius and orientation on the effective mode area is considered. The authors have found that the proposed structure exhibits a
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low loss which lies in the range of 10-3 to 10-4 dB/turn and an effective area around 250 µm2 in the range [1300 nm, 1700 nm].
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Moreover, doping the core region with a high index material is also used in the
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aim of obtaining a large effective core. In this context, J. Li et al, proposed a kind of
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hexagonal lattice PCF where six air holes near the center are filled with high index
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material [43]. Results showed that Aeff can be tuned by adjusting the filled air holes radius, the filled material index and the radius of the central air hole.
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Also, in [44], Gautam Prabhakar et al, have studied the chromatic dispersion
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and the effective mode area of a microstructure based on a dual core dispersion
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compensating PCF. In their design, an inner core formed by Ge-doped glass is
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surrounded by an inner cladding that consists of pure silica with micro-structured air holes arranged in concentric circular rings. The outer core is also Ge-doped and is surrounded by outer cladding made of pure silica. By adjusting its opto-geometrical parameters, the proposed PCF exhibits an effective mode area of 67 µm2 and a
chromatic dispersion of – 42 000 ps/nm.km at the wavelength 1.544 µm. Accordingly, an extensive analysis of the large mode area property of a PCF with circular lattice has not been performed. In fact, and to the best of our knowledge,
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only in [42] and [44], a circular lattice based PCF was considered for analysis. However, the obtained mode area is not large enough (250 µm2 and 67 µm2,
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respectively). Furthermore, the solution provided by [42], to force the PCF to single
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mode operation by canceling the high order modes, is based on selectively enlarging
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air holes in one side. Yet, using double cladding constant in a single side, as an
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alternative, has not been considered to be compared with the first approach. In this article, a numerical investigation of a large mode area circular lattice
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photonic crystal fiber (CL-PCF) is presented. The propagation characteristics such as
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chromatic dispersion, confinement loss, effective mode area and bending loss are
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investigated. Also, the geometrical parameters of the structure are optimized by using
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a finite difference in time domain (FDTD) method combined with the perfectly matched layer (PML) as a boundary condition. The study is divided in two parts. Firstly, the optical properties of a large core CL-PCF are calculated when the waveguide is straight. The large mode area is demonstrated and its dependence to the geometrical parameters is shown too. Secondly, the effects of bending radius and orientation on the effective mode area and the confinement loss are considered. In addition to that, the first large core CL-PCF is also analyzed. Furthermore, two
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variants are proposed for the first time as a solution to mitigate the impairments induced by the bending: CL-PCF with double air holes diameter in single side and
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CL-PCF with double cladding constant.
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2. PCF parameters computation
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2.1 Numerical method
In order to accurately simulate the propagation of light within PCFs, a full vector
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FDTD (FV-FDTD) method is used. From Maxwell's equations, the following vector
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wave equation can be derived:
(1)
d
1 s E k02 n 2 s E 0
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Where k0 2 / 0 , is the wave number in the vacuum, 0 is the wavelength,
E denotes the electric field, n is the refractive index, s is the PML matrix and s
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1
is an inverse matrix of s . By applying the FV-FDTD method, the mode field profile
and the effective refractive index neff can be obtained from the eigenvalue equation
(1). neff satisfies the condition below:
nFSM neff nco
(2)
Where nco is the core refractive index and nFSM is the effective cladding refractive index corresponding to the fundamental space-filling mode.
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2.2 Confinement loss Theoretically, the light beam is totally confined into the PCF core due to the
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infinite periodic structure around the centre. Practically, only a few number of air holes rings form the cladding. Thereby, a fraction of the optical power leaks out of the
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structure. This kind of losses is called the confinement loss and its value can be
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calculated by using the formula [8]:
8.686k0 Imneff
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(3)
In decibel per meter, where Im neff is the imaginary part of the effective refractive
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index and k0 is the free space wave number.
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2.3 Chromatic dispersion
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The control of chromatic dispersion in PCFs is a very important issue for
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practical applications in dispersion compensation of optical communication systems and nonlinear optics. As for standard fibre, the chromatic dispersion of a PCF is the sum of the material dispersion and the waveguide dispersion: D Dm Dw
(4)
The material dispersion, Dm , is derived from the Sellmeier equation [45]: bk 2 2 2 k 1 k 3
2 ( ) 1 nsilica
(5)
Where b1 0.6961663 , b2 0.4079426 , b3 0.8974794 , 1 0.0684043 µm,
2 0.1162414 µm and 3 9.896161 µm. 8
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The waveguide dispersion is given by [46]: 2 d neff Dw c d2
(6)
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Where and c are the wavelength and the speed of light, respectively.
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2.4 Effective mode area
The effective mode area is a key factor in designing PCFs. It provides a
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quantitative measurement of how much the mode field is confined within the PCF
( E 2 dxdy ) 2
E
4
dxdy
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Aeff
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core. It can be calculated using [37]:
d
Where E denotes the amplitude of the transverse electric field propagating inside the
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PCF.
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3. Simulation results and discussions To fully analyze the proposed structure, we considered straight and bent
waveguides.
3.1 Straight CL-PCF
The cross section of the proposed CL-PCF is illustrated in Fig. 1. The cladding is formed by an array of air holes arranged in circular lattice of six rings and the core is obtained by omitting one air hole in the center. The radius of air holes is d and the
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hole-to-hole spacing is . R and indicates the radius and orientation angle of the bending, respectively. The background material is silica and its refractive index is
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given by the Sellmeier equation [45]. By applying the FV-FDTD method and by using
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the formulas mentioned above, a complete analysis of the proposed CL-PCF can be
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achieved. Numerical simulations of the proposed structure are performed for different
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values of the air-filling fraction d / , where the radius of the air holes is fixed to d 4 µm and the hole-to-hole spacing lies from 20 µm to 25 µm.
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Before studying the optical properties of the fundamental mode, the single
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mode regime must be verified. Fig. 2 depicts the variation of the confinement loss as
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function of the air filling factor ( d / ) around 1.55 µm, for the fundamental mode,
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the first, the second and the third high order modes (HOM). As it can be seen, the fundamental mode propagates with a very low confinement loss, however, the high order modes suffer of a high loss so they vanish quickly and the PCF operates in the single mode regime. In fact, for an air filling fraction of d / 0.16 , the fundamental
mode propagates with a confinement loss of 7.63 10 8 dB/cm where the three high order modes propagate with a confinement loss of 0.12 dB/cm, 0.16 dB/cm and 0.14 dB/cm respectively.
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Considering the fundamental mode, Fig.3 shows the variation of the real part of its effective refractive index as a function of the wavelength.
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By using equations (4) and (6), the chromatic dispersion can be calculated. Its
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evolution with the wavelength is depicted in Fig. 4. The structure exhibits a chromatic
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dispersion which lies from -8 to 38 ps / nm.km over the wavelength domain, whatever
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is the value of d / . Also, and similarly to conventional optical fibers, the structure has two regimes of chromatic dispersion: positive and negative with zero dispersion
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wavelength around 1.25 µm.
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The confinement loss has been also studied. Its variation with wavelength is
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depicted in Fig. 5. From the calculated results, and besides the fact that the confinement loss increases with wavelength, it can be seen too that the confinement of the light beam is strongly related to the air-filling fraction d / . Around the
wavelength 1.55 µm, a very low confinement loss of about 1.41 10 5 dB/km is
obtained for d / 0.2 . When the air fraction decreases to d / 0.16 , the
confinement loss reaches a value of about 7.64 10 3 dB/km, which is very low too. This dependency can be interpreted by the fact that increasing of d / leads to the
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magnifying of the refractive index contrast between the core and the cladding, hence, forcing the light to be more confined within the core.
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Considering the effective mode area, numerical results indicates that
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large mode area is obtained over the entire wavelength interval (Fig. 6). Furthermore,
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it can be noticed that the mode area increases when d / decreases. In fact, around
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the wavelength 1.55 µm, the structure exhibits a large mode area of 538.85 µm2 for
d / 0.2 which increases to reach 1072.6 µm2 for d / 0.16 . These results can be
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explained by the fact that the core diameter increases when increases, hence, the
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distribution of the optical field will expand more over the core area. Despite the fact
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that the core of the proposed structure is formed by only one omitting one air hole, the
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obtained effective mode area is larger than that of the one obtained for a PCF with a hexagonal lattice and a core formed by omitting seven air holes [39,43].
3.2. Bending analysis
The resistance of the proposed structure against bending has been also
investigated. The bending radius and the orientation angle are set to be 50 cm and 00, respectively. Firstly, the effective mode area is calculated. Fig. 7 shows the evolution of the field mode area as a function of the wavelength for different values of d / . As 12
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it may be noticed, the effective mode area of the proposed structure reaches high values up to 1710.41 µm2 around 1.55 µm for d / 0.16 . However, this high value
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of field mode area is accompanied with a very high confinement loss. Fig. 8 gives the
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variation of the confinement loss as a function of the wavelength. Around 1.55 µm, an
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induced confinement loss of about 7.22 dB/km is occurred for the same air filling
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fraction. To overcome the impairment induced by the bending and simultaneously maintain the effective mode area as high as possible, two structures are proposed: CL-
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PCF with double air holes diameter in single side (structure a) and CL-PCF with
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double cladding (structure b). Fig. 9 and Fig. 10 show their cross sections. Hexagonal
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lattice PCF with increased air fraction in one side, either by increasing the air holes
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diameter or by doubling the lattice constant, has been studied and fabricated in the aim to increase the resistance of the PCF against bending [47]. When the PCF is bent, the region with large air fraction remains located at the outside and the fundamental mode stills well confined in the core which reduces the power losses.
For the two structures, the geometrical parameters are set as: d 4 µm, 1 25 µm, small pitch in structure (a), ' and big radius in structure (b), 2
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d ' 2d . The confinement loss is firstly calculated. Its variation as a function of wavelength for different values of bending radius is depicted in Fig. 11 for structure
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(a) and Fig. 12 for structure (b). As we can see, the two structures exhibit a very low
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bending loss even for small bending radius. Around 1.55 µm, a bending loss of about
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0.012 dB/km and 0.019 dB/km are obtained respectively for structure (a) and structure
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(b) for a bending radius R=10 cm. However, the situation is not the same for the effective mode area. Fig. 13 and Fig. 14 show the variation of the field mode area as a
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function of the wavelength for different values of the bending radius. For R=10 cm,
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an effective mode area of about 591.086 µm2 and 711.033 µm2 are obtained for
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structure (a) and structure (b), respectively for the same wavelength.
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Furthermore, the effect of bending orientation angle has been reported. The
confinement loss and the effective mode area have been calculated for a bending radius of 30, 40 and 50 cm with a bending orientation angle varying from 0 to 800. As
depicted in Fig. 15 and Fig. 16, the bending loss increases with the bending orientation. For the structure (a) and around 1.55 µm, a loss of about 0.008 dB/m is obtained for a bending radius and orientation angle of 40 cm and 00, respectively. It increases to reach 4.85 dB/m than 26 dB/m when the orientation angle increases to
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400 and 800, respectively. Considering the structure (b), the bending loss reaches the value 0.003 dB/m for a bending radius and orientation angle of 40 cm and 00,
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respectively. It increases to reach 0.77 dB/m then 9.86 dB/m when the orientation
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angle increases to 400 and 800, respectively.
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Similarly, the effect of bending orientation on the effective mode area is
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studied. Fig. 17 and Fig. 18 gives the variation of the effective field mode area as a function of the bending orientation for both the two structures. As it can be seen, the
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field mode area increases with bending orientation angle for both the two structures.
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Moreover, the structure (b) exhibits an effective mode area larger then the structure
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(a) whatever the value of the bending orientation angle. For a bending radius and
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orientation angle of 40 cm and 00, respectively, the structure (a) exhibits an effective mode area of Aeff = 659.638 µm2. It increases to reach 1351.49 µm2 then 1934.14 µm2 when the orientation angle increases to 400 and 800, respectively. Considering the
structure (b), the effective mode area reaches a value of Aeff = 842.9 µm2, for a
bending radius and orientation angle of 40 cm and 00, respectively. It increases to reach 936.13 µm2 then 2035.83 µm2 when the orientation angle increases to 400 and 800, respectively.
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4. Conclusion
In the present paper, a circular lattice photonic crystal fiber (CL-PCF) has
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been proposed and numerically investigated in the aim to obtain the large mode area
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(LMA) property. The CL-PCF is composed of six rings of air holes arranged in
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circular configuration acting as a cladding and a core formed by the omission of one
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air hole in the center. Moreover, the study has been performed taking into account the shape of the waveguide: straight ore bent.
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For the first case, results show that around 1.55 µm, high LMA and very low
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confinement loss of 1072.6 µm2 and 7.64 10 3 dB/km are achieved, respectively,
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when an air filling fraction of d / 0.16 is employed. For the second case, results
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indicate that around 1.55 µm, the effective mode area increases to reach 1710.41 µm2 for a bending radius of 50 cm. However, the bending weakens the guiding of the light beam which increases the confinement loss to reach 7.22 dB/km. To overcome this drawback, two variants are proposed: CL-PCF with double
air holes diameter in single side and CL-PCF with double cladding. Results show that for a very small bending radius of 10 cm, both the two structures exhibit a very low confinement loss of about 0.012 dB/km and 0.019 dB/km, respectively. However, the
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CL-PCF with double cladding has a larger LMA of 711.033 µm2 than the CL-PCF with double air holes diameter (591.086 µm2).
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The sensitivity to bending orientation has been also reported. Results have
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shown that CL-PCF with double cladding is preferable to resist bending effect. In this
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regard, numerical simulations indicate that CL-PCF with double cladding has a larger
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effective mode than the CL-PCF with double air holes diameter with a lower confinement loss. Considering the effective mode area, CL-PCF with double cladding
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exhibits a LMA of 842.9 µm2 with a bending radius and orientation angle of 40 cm
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and 00, respectively. It increases to reach 2035.83 µm2 when the bending orientation
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angle increases to 800. For the CL-PCF with double air holes diameter, an effective
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mode area of 659.638 µm2 with a bending radius and orientation angle of 40 cm and
00, respectively. It increases to reach 1934.14 µm2 when the bending orientation angle
increases to 800. Furthermore, the CL-PCF with double cladding exhibits a very low confinement loss of about 0.003 dB/m with a bending radius and orientation angle of 40 cm and 00, respectively. It then increases to reach 9.86 dB/m when the bending orientation angle increases to 800. However, the CL-PCF with double air holes diameter has a confinement loss of 0.008 dB/m are obtained with a bending radius
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and orientation angle of 40 cm and 00, respectively. Which increases to reach 26 dB/m when the bending orientation angle increases to 800.
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Finally, the obtained results show that our proposed structures are suitable for
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many applications such: laser, amplifiers, WDM systems and FTTH applications.
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Changming Li, A selectively coated photonic crystal fiber based surface plasmon resonance sensor, J. Opt. 12 (2010).
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[30] P. B. Bing, Z. Y. Li, A photonic crystal fiber based on surface plasmon resonance temperature sensor with liquid core, Modern Physics Letters B 26(13) (2012).
[31] Ying Lu, Cong-Jing Hao, Bao-Qun Wu, Mayilamu Musideke, Liang-Cheng Duan, Wu-Qi Wen, Jian-Quan Yao, Surface plasmon resonance sensor based on polymer photonic crystal fibers with metal nanolayers, Sensors 13 (2013) 956-965. [32] Jian Tang, Zhigang Zhang, Deng Luo, Ming Chen, Hui Chen, High birefringence terahertz photonic crystal fiber, Optical Engineering 52(1) (2013).
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[33] Arti Agrawal, N. Kejalakshmy, M. Uthman, B. M. A. Rahman, A .Kumar, K. T. V. Grattan, Ultra low bending loss equiangular spiral photonic crystal fibers in the terahertz regime, AIP Advances 2 (2012).
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[34] Yin Guo-Bing, Li Shu-Guang, Wang Xiao-Yan, Liu Shuo, High birefringence, low loss terahertz photonic crystal fibres with zero dispersion at 0.3 THz, Chin. Phys.
cr
B 20(9) (2011).
[35] Zhang Y, Zhang C, Hu M, Song S, Chai L, Wang C. High-energy subpicosecond
us
pulse generation from a mode-locked Yb-doped large-mode-area photonic crystal
an
fiber laser with fiber facet output. IEEE Photonics Technology Letters, ;22(5) 350–2 (2010).
M
[36] Varshney SK, Saitoh K, Koshiba M, Pal BP, Sinha RK. Design of S-band erbium- doped concentric dual-core photonic crystal fiber amplifiers with ASE
d
suppression. Journal of Lightwave Technology, 27(11) 1725–33 (2009).
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[37] T. Matsui et al. Single-mode photonic crystal fiber design with ultralarge effective area and low bending loss for ultra-high speed WDM transmission, J.
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Lightwave Technol. 29(4) 511–515 (2011). [38] Zhiqiang Wang, Chun-Liu Zhao and Shangzhong Jin, Design of a bendinginsensitive single-mode photonic crystal fiber, Optical Fiber Technology,19 213–218 (2013).
[39] H. Demir and S. Ozsoy, Comparative study of large-solid-core photonic crystal fibers: Dispersion and effective mode area, Optik 123 (2012) 739– 743. [40] H. Demir and S. Ozsoy, Large-solid-core square-lattice photonic crystal fibers, Optical Fiber Technology, 17 (2011) 594–600. [41] Xin Wang, Shuqin Lou, and Wenliang Lu, Bend-resistant large-mode-area photonic crystal fiber with a triangular-core, Applied Optics, 52 (18) 2013.
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[42] Md. Asiful Islam and M. Shah Alam, Bend-insensitive single-mode photonic crystal fiber with ultralarge effective area for dual applications, Optical Engineering letters, 52(5). 2013
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[43] Jianhua Li, Jingyuan Wanga, Yan Cheng, Rong Wang, Baofu Zhang and Huali Wanga, Novel large mode area photonic crystal fibers with selectively material-filled
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structure, Optics & Laser Technology 48 (2013) 375–380.
[44] Gautam Prabhakar, Akshit Peer, Vipul Rastogi and Ajeet Kumar, Largedispersion-compensating
fiber
based
on
dual-core
an
microstructure, Applied Optics, 52(19) 2013.
design
us
effective-area
[45] Govind P. Agrawal, Nonlinear Fiber Optics, Fifth edition, Elsevier, Great
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Britain, 2007.
[46] N. Nozhat, N. Granpayeh, Specialty fibers designed by photonic crystals,
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Progress In Electromagnetics Research, PIER 99 (2009) 225-244.
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[47] Marek Napierała, Elżbieta Bereś-Pawlik, Tomasz Nasilowski, Paweł Mergo, Francis Berghmans, Hugo Thienpont, Design of a low-bending-loss large-mode-area
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photonic crystal fiber, Proc. of SPIE, 8426 (2012).
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List of figure captions
Figure 1: Cross section of the proposed CL-PCF.
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Figure 2: Variation of the confinement loss of the fundamental mode, the first, the
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second and the third high order modes for different values of the hole to hole spacing.
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Figure 3: Variation of the real part of the effective index as function of the wavelength for different values of the hole to hole spacing.
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different values of the hole to hole spacing.
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Figure 4: Variation of the chromatic dispersion as function of the wavelength for
Figure 5: Variation of the confinement loss as function of the wavelength for
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d
different values of the hole to hole spacing. Figure 6: Variation of the effective mode area as function of the wavelength for
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different values of the hole to hole spacing. Figure 7: Variation of the effective mode area as function of the wavelength for
different values of the hole to hole spacing. Figure 8: Variation of the confinement loss as a function of the wavelength for
different values of the hole to hole spacing. Figure 9: Cross section of the CL-PCF with double air holes diameter in single side. Figure 10: Cross section of the CL-PCF with double cladding.
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Figure 11: Variation of the confinement loss as function of the wavelength for structure (a) for different values of the bending radius.
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Figure 12: Variation of the confinement loss as function of the wavelength for structure (b) for different values of the bending radius.
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structure (a) for different values of the bending radius.
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Figure 13: Variation of the effective mode area as function of the wavelength for
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Figure 14: Variation of the effective mode area as function of the wavelength for structure (b) for different values of the bending radius.
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Figure 15: Variation of the confinement loss as function of the bending orientation
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angle for structure (a) for different values of the bending radius.
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Figure 16: Variation of the confinement loss as function of the bending orientation
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angle for structure (b) for different values of the bending radius. Figure 17: Variation of the effective mode area as function of the bending orientation
angle for structure (a) for different values of the bending radius. Figure 18: Variation of the effective mode area as function of the bending orientation
angle for structure (b) for different values of the bending radius.
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S0030-4026(15)01091-8 http://dx.doi.org/doi:10.1016/j.ijleo.2015.09.035 IJLEO 56240
To appear in: Received date: Accepted date:
3-10-2014 7-9-2015
Please cite this article as: A. Medjouri, L.M. Simohamed, O. Ziane, A. Boudrioua, Analysis of a New Circular Photonic Crystal Fiber with Large Mode Area, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.09.035 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of a New Circular Photonic Crystal Fiber with Large Mode Area Abdelkader MEDJOURI 1, 2, Lotfy Moktar SIMOHAMED 3, Omar ZIANE 2 and Azzedine BOUDRIOUA 4 : Laboratoire d’Exploitation et Valorisation des Ressources Sahariennes (LEVRES), Faculté
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1
des Sciences et Technologie, Université d’EL Oued, 39000, El Oued, Algeria.
: Laboratoire d’Electronique Quantique (LEQ), Faculté de Physique, USTHB, BP no. 32 ElAlia, Bab-Ezzouar, 16111 Algiers, Algeria. 3
: Laboratoire Des Systèmes Electroniques Et Optroniques (LSEO), Ecole Militaire
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Polytechnique, 16111 Algiers, Algeria. 4
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2
: Laboratoire de Physique des Lasers (LPL), Institut Galilée, UMR 7538 CNRS, Université Paris 13, 93430 Villetaneuse, France.
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E-mail: [email protected]
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Abstract
A new design of large mode area (LMA) Circular Lattice Photonic Crystal
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d
Fiber (CL-PCF) is proposed and numerically investigated. The cladding is formed by
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six rings of air holes arranged in circular configuration and the core is obtained by only omitting one air hole in the center. The transmission characteristics such as confinement loss, effective mode area, chromatic dispersion and bending loss are analyzed by using a Finite Difference in Time Domain (FDTD) method combined with Perfectly Matched Layer (PML) boundary condition. Results show that around 1.55 µm, the proposed CL-PCF exhibits an effective mode area larger then 1000 µm2 with a confinement loss as low as 7.64 10 3 dB/km for an air filling fraction
1
Page 1 of 43
of d
0.16 . Furthermore, the effect of bending is reported and two new variants of
CL-PCF are presented in the aim to mitigate its induced loss: CL-PCF with double air
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holes diameter in single side and CL-PCF with double cladding constant.
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Keywords: Circular lattice photonic crystal fiber; large mode area; FDTD method;
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confinement loss; bending loss.
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1. Introduction
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Photonic crystal fibers (PCFs) are optical fibers realized by a transverse two
d
dimensional photonic crystal with a micrometer-spaced array of air holes running
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down their length and a defect region in the center [1]. The unique and interesting
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optical properties that characterize PCFs, compared to conventional optical fibers, like single mode operation over a wide range of wavelengths [2], chromatic dispersion management [3-7], high birefringence [8-13], high nonlinearity [14,15] and so on, have lead to many potential applications such as: dispersion compensating fibers [1618], polarization maintaining fibers [19-21], highly nonlinear fibers [22-24], supercontinuum generation [25], fiber based lasers [26-28], sensors [29-31] and terahertz applications [32-34] .
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Page 2 of 43
Among these features, the effective mode area (Aeff) is considered as a critical issue when a high power must be delivered with a reduced nonlinearity, as in fiber
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lasers [35], amplifiers [36], wavelength multiplexing division systems (WDM) [37]
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and fiber to the home (FTTH) networks [38]. In fact, large mode area (LMA) helps to
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mitigate the impairments that arise from different nonlinear effects, such as stimulated
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Raman scattering, stimulated Brillouin scattering and self-phase modulation, by reducing the power density over the fiber core area.
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PCFs with large effective mode area have been the subject of many recently
d
published papers. In [39], H. Demir and S. Ozsoy presented a comparative study of
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large hexagonal lattice solid core PCFs. With a core formed by the omission of seven
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air holes. They found that Aeff increases when the air fraction decreases in the
cladding region. A maximum value of Aeff = 500 µm2 is obtained when an air fraction
of d
0.1 is used. Also, for a square lattice PCFs with a core formed by nine
omitted air holes [40], the same authors found that Aeff increases when the air fraction
decreases, but a value of Aeff = 630 µm2 is reached for an air fraction of 0.1 too. However, the effect of bending (radius and orientation) on Aeff and the confinement loss has not been reported.
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Page 3 of 43
In [41], Xin Wang et al studied a kind of bend resistant large-mode-area PCF. Their structure is composed of a triangular-core with three missing air holes and the
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cladding is composed of two similar sizes of air holes. They found that at the
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wavelength of 1.064 μm, the mode field area of the fundamental mode reaches 930
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µm2 at the straight state and 815 µm2 at a bending radius of 30 cm. Considering the
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confinement loss, the authors have found that it is as low as 1.6 10 5 dB/m at the wavelength 1.064 µm when the fiber is straight. When the fiber is bent with a radius
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of 30 cm, the confinement loss decreases and reaches the value 0.0025 dB/m.
d
Furthermore, the effect of bending orientation is considered. Over a range of bending
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orientation angle that varies from - 550 to 550 and for a bending radius of 30 cm, the
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authors found that, the authors found that the average bending losses of the fundamental mode is 0.0144 dB/m and the average mode area is 848 µm2. In another hand, in [42], Md. Asiful Islam and M. Shah have proposed a new
design of PCF with circular lattice and selectively enlarged air holes for both WDM and FTTH systems. The impact of bending radius and orientation on the effective mode area is considered. The authors have found that the proposed structure exhibits a
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Page 4 of 43
low loss which lies in the range of 10-3 to 10-4 dB/turn and an effective area around 250 µm2 in the range [1300 nm, 1700 nm].
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Moreover, doping the core region with a high index material is also used in the
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aim of obtaining a large effective core. In this context, J. Li et al, proposed a kind of
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hexagonal lattice PCF where six air holes near the center are filled with high index
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material [43]. Results showed that Aeff can be tuned by adjusting the filled air holes radius, the filled material index and the radius of the central air hole.
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Also, in [44], Gautam Prabhakar et al, have studied the chromatic dispersion
d
and the effective mode area of a microstructure based on a dual core dispersion
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compensating PCF. In their design, an inner core formed by Ge-doped glass is
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surrounded by an inner cladding that consists of pure silica with micro-structured air holes arranged in concentric circular rings. The outer core is also Ge-doped and is surrounded by outer cladding made of pure silica. By adjusting its opto-geometrical parameters, the proposed PCF exhibits an effective mode area of 67 µm2 and a
chromatic dispersion of – 42 000 ps/nm.km at the wavelength 1.544 µm. Accordingly, an extensive analysis of the large mode area property of a PCF with circular lattice has not been performed. In fact, and to the best of our knowledge,
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Page 5 of 43
only in [42] and [44], a circular lattice based PCF was considered for analysis. However, the obtained mode area is not large enough (250 µm2 and 67 µm2,
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respectively). Furthermore, the solution provided by [42], to force the PCF to single
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mode operation by canceling the high order modes, is based on selectively enlarging
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air holes in one side. Yet, using double cladding constant in a single side, as an
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alternative, has not been considered to be compared with the first approach. In this article, a numerical investigation of a large mode area circular lattice
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photonic crystal fiber (CL-PCF) is presented. The propagation characteristics such as
d
chromatic dispersion, confinement loss, effective mode area and bending loss are
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investigated. Also, the geometrical parameters of the structure are optimized by using
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a finite difference in time domain (FDTD) method combined with the perfectly matched layer (PML) as a boundary condition. The study is divided in two parts. Firstly, the optical properties of a large core CL-PCF are calculated when the waveguide is straight. The large mode area is demonstrated and its dependence to the geometrical parameters is shown too. Secondly, the effects of bending radius and orientation on the effective mode area and the confinement loss are considered. In addition to that, the first large core CL-PCF is also analyzed. Furthermore, two
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variants are proposed for the first time as a solution to mitigate the impairments induced by the bending: CL-PCF with double air holes diameter in single side and
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CL-PCF with double cladding constant.
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2. PCF parameters computation
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2.1 Numerical method
In order to accurately simulate the propagation of light within PCFs, a full vector
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FDTD (FV-FDTD) method is used. From Maxwell's equations, the following vector
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wave equation can be derived:
(1)
d
1 s E k02 n 2 s E 0
te
Where k0 2 / 0 , is the wave number in the vacuum, 0 is the wavelength,
E denotes the electric field, n is the refractive index, s is the PML matrix and s
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1
is an inverse matrix of s . By applying the FV-FDTD method, the mode field profile
and the effective refractive index neff can be obtained from the eigenvalue equation
(1). neff satisfies the condition below:
nFSM neff nco
(2)
Where nco is the core refractive index and nFSM is the effective cladding refractive index corresponding to the fundamental space-filling mode.
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2.2 Confinement loss Theoretically, the light beam is totally confined into the PCF core due to the
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infinite periodic structure around the centre. Practically, only a few number of air holes rings form the cladding. Thereby, a fraction of the optical power leaks out of the
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structure. This kind of losses is called the confinement loss and its value can be
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calculated by using the formula [8]:
8.686k0 Imneff
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(3)
In decibel per meter, where Im neff is the imaginary part of the effective refractive
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index and k0 is the free space wave number.
d
2.3 Chromatic dispersion
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The control of chromatic dispersion in PCFs is a very important issue for
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practical applications in dispersion compensation of optical communication systems and nonlinear optics. As for standard fibre, the chromatic dispersion of a PCF is the sum of the material dispersion and the waveguide dispersion: D Dm Dw
(4)
The material dispersion, Dm , is derived from the Sellmeier equation [45]: bk 2 2 2 k 1 k 3
2 ( ) 1 nsilica
(5)
Where b1 0.6961663 , b2 0.4079426 , b3 0.8974794 , 1 0.0684043 µm,
2 0.1162414 µm and 3 9.896161 µm. 8
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The waveguide dispersion is given by [46]: 2 d neff Dw c d2
(6)
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Where and c are the wavelength and the speed of light, respectively.
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2.4 Effective mode area
The effective mode area is a key factor in designing PCFs. It provides a
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quantitative measurement of how much the mode field is confined within the PCF
( E 2 dxdy ) 2
E
4
dxdy
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Aeff
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core. It can be calculated using [37]:
d
Where E denotes the amplitude of the transverse electric field propagating inside the
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PCF.
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3. Simulation results and discussions To fully analyze the proposed structure, we considered straight and bent
waveguides.
3.1 Straight CL-PCF
The cross section of the proposed CL-PCF is illustrated in Fig. 1. The cladding is formed by an array of air holes arranged in circular lattice of six rings and the core is obtained by omitting one air hole in the center. The radius of air holes is d and the
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Page 9 of 43
hole-to-hole spacing is . R and indicates the radius and orientation angle of the bending, respectively. The background material is silica and its refractive index is
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given by the Sellmeier equation [45]. By applying the FV-FDTD method and by using
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the formulas mentioned above, a complete analysis of the proposed CL-PCF can be
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achieved. Numerical simulations of the proposed structure are performed for different
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values of the air-filling fraction d / , where the radius of the air holes is fixed to d 4 µm and the hole-to-hole spacing lies from 20 µm to 25 µm.
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Before studying the optical properties of the fundamental mode, the single
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mode regime must be verified. Fig. 2 depicts the variation of the confinement loss as
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function of the air filling factor ( d / ) around 1.55 µm, for the fundamental mode,
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the first, the second and the third high order modes (HOM). As it can be seen, the fundamental mode propagates with a very low confinement loss, however, the high order modes suffer of a high loss so they vanish quickly and the PCF operates in the single mode regime. In fact, for an air filling fraction of d / 0.16 , the fundamental
mode propagates with a confinement loss of 7.63 10 8 dB/cm where the three high order modes propagate with a confinement loss of 0.12 dB/cm, 0.16 dB/cm and 0.14 dB/cm respectively.
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Page 10 of 43
Considering the fundamental mode, Fig.3 shows the variation of the real part of its effective refractive index as a function of the wavelength.
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By using equations (4) and (6), the chromatic dispersion can be calculated. Its
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evolution with the wavelength is depicted in Fig. 4. The structure exhibits a chromatic
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dispersion which lies from -8 to 38 ps / nm.km over the wavelength domain, whatever
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is the value of d / . Also, and similarly to conventional optical fibers, the structure has two regimes of chromatic dispersion: positive and negative with zero dispersion
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wavelength around 1.25 µm.
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d
The confinement loss has been also studied. Its variation with wavelength is
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depicted in Fig. 5. From the calculated results, and besides the fact that the confinement loss increases with wavelength, it can be seen too that the confinement of the light beam is strongly related to the air-filling fraction d / . Around the
wavelength 1.55 µm, a very low confinement loss of about 1.41 10 5 dB/km is
obtained for d / 0.2 . When the air fraction decreases to d / 0.16 , the
confinement loss reaches a value of about 7.64 10 3 dB/km, which is very low too. This dependency can be interpreted by the fact that increasing of d / leads to the
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Page 11 of 43
magnifying of the refractive index contrast between the core and the cladding, hence, forcing the light to be more confined within the core.
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Considering the effective mode area, numerical results indicates that
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large mode area is obtained over the entire wavelength interval (Fig. 6). Furthermore,
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it can be noticed that the mode area increases when d / decreases. In fact, around
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the wavelength 1.55 µm, the structure exhibits a large mode area of 538.85 µm2 for
d / 0.2 which increases to reach 1072.6 µm2 for d / 0.16 . These results can be
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explained by the fact that the core diameter increases when increases, hence, the
d
distribution of the optical field will expand more over the core area. Despite the fact
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that the core of the proposed structure is formed by only one omitting one air hole, the
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obtained effective mode area is larger than that of the one obtained for a PCF with a hexagonal lattice and a core formed by omitting seven air holes [39,43].
3.2. Bending analysis
The resistance of the proposed structure against bending has been also
investigated. The bending radius and the orientation angle are set to be 50 cm and 00, respectively. Firstly, the effective mode area is calculated. Fig. 7 shows the evolution of the field mode area as a function of the wavelength for different values of d / . As 12
Page 12 of 43
it may be noticed, the effective mode area of the proposed structure reaches high values up to 1710.41 µm2 around 1.55 µm for d / 0.16 . However, this high value
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of field mode area is accompanied with a very high confinement loss. Fig. 8 gives the
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variation of the confinement loss as a function of the wavelength. Around 1.55 µm, an
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induced confinement loss of about 7.22 dB/km is occurred for the same air filling
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fraction. To overcome the impairment induced by the bending and simultaneously maintain the effective mode area as high as possible, two structures are proposed: CL-
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PCF with double air holes diameter in single side (structure a) and CL-PCF with
d
double cladding (structure b). Fig. 9 and Fig. 10 show their cross sections. Hexagonal
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lattice PCF with increased air fraction in one side, either by increasing the air holes
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diameter or by doubling the lattice constant, has been studied and fabricated in the aim to increase the resistance of the PCF against bending [47]. When the PCF is bent, the region with large air fraction remains located at the outside and the fundamental mode stills well confined in the core which reduces the power losses.
For the two structures, the geometrical parameters are set as: d 4 µm, 1 25 µm, small pitch in structure (a), ' and big radius in structure (b), 2
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Page 13 of 43
d ' 2d . The confinement loss is firstly calculated. Its variation as a function of wavelength for different values of bending radius is depicted in Fig. 11 for structure
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(a) and Fig. 12 for structure (b). As we can see, the two structures exhibit a very low
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bending loss even for small bending radius. Around 1.55 µm, a bending loss of about
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0.012 dB/km and 0.019 dB/km are obtained respectively for structure (a) and structure
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(b) for a bending radius R=10 cm. However, the situation is not the same for the effective mode area. Fig. 13 and Fig. 14 show the variation of the field mode area as a
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function of the wavelength for different values of the bending radius. For R=10 cm,
d
an effective mode area of about 591.086 µm2 and 711.033 µm2 are obtained for
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structure (a) and structure (b), respectively for the same wavelength.
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Furthermore, the effect of bending orientation angle has been reported. The
confinement loss and the effective mode area have been calculated for a bending radius of 30, 40 and 50 cm with a bending orientation angle varying from 0 to 800. As
depicted in Fig. 15 and Fig. 16, the bending loss increases with the bending orientation. For the structure (a) and around 1.55 µm, a loss of about 0.008 dB/m is obtained for a bending radius and orientation angle of 40 cm and 00, respectively. It increases to reach 4.85 dB/m than 26 dB/m when the orientation angle increases to
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Page 14 of 43
400 and 800, respectively. Considering the structure (b), the bending loss reaches the value 0.003 dB/m for a bending radius and orientation angle of 40 cm and 00,
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respectively. It increases to reach 0.77 dB/m then 9.86 dB/m when the orientation
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angle increases to 400 and 800, respectively.
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Similarly, the effect of bending orientation on the effective mode area is
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studied. Fig. 17 and Fig. 18 gives the variation of the effective field mode area as a function of the bending orientation for both the two structures. As it can be seen, the
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field mode area increases with bending orientation angle for both the two structures.
d
Moreover, the structure (b) exhibits an effective mode area larger then the structure
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(a) whatever the value of the bending orientation angle. For a bending radius and
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orientation angle of 40 cm and 00, respectively, the structure (a) exhibits an effective mode area of Aeff = 659.638 µm2. It increases to reach 1351.49 µm2 then 1934.14 µm2 when the orientation angle increases to 400 and 800, respectively. Considering the
structure (b), the effective mode area reaches a value of Aeff = 842.9 µm2, for a
bending radius and orientation angle of 40 cm and 00, respectively. It increases to reach 936.13 µm2 then 2035.83 µm2 when the orientation angle increases to 400 and 800, respectively.
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Page 15 of 43
4. Conclusion
In the present paper, a circular lattice photonic crystal fiber (CL-PCF) has
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been proposed and numerically investigated in the aim to obtain the large mode area
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(LMA) property. The CL-PCF is composed of six rings of air holes arranged in
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circular configuration acting as a cladding and a core formed by the omission of one
an
air hole in the center. Moreover, the study has been performed taking into account the shape of the waveguide: straight ore bent.
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For the first case, results show that around 1.55 µm, high LMA and very low
d
confinement loss of 1072.6 µm2 and 7.64 10 3 dB/km are achieved, respectively,
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when an air filling fraction of d / 0.16 is employed. For the second case, results
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indicate that around 1.55 µm, the effective mode area increases to reach 1710.41 µm2 for a bending radius of 50 cm. However, the bending weakens the guiding of the light beam which increases the confinement loss to reach 7.22 dB/km. To overcome this drawback, two variants are proposed: CL-PCF with double
air holes diameter in single side and CL-PCF with double cladding. Results show that for a very small bending radius of 10 cm, both the two structures exhibit a very low confinement loss of about 0.012 dB/km and 0.019 dB/km, respectively. However, the
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CL-PCF with double cladding has a larger LMA of 711.033 µm2 than the CL-PCF with double air holes diameter (591.086 µm2).
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The sensitivity to bending orientation has been also reported. Results have
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shown that CL-PCF with double cladding is preferable to resist bending effect. In this
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regard, numerical simulations indicate that CL-PCF with double cladding has a larger
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effective mode than the CL-PCF with double air holes diameter with a lower confinement loss. Considering the effective mode area, CL-PCF with double cladding
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exhibits a LMA of 842.9 µm2 with a bending radius and orientation angle of 40 cm
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and 00, respectively. It increases to reach 2035.83 µm2 when the bending orientation
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angle increases to 800. For the CL-PCF with double air holes diameter, an effective
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mode area of 659.638 µm2 with a bending radius and orientation angle of 40 cm and
00, respectively. It increases to reach 1934.14 µm2 when the bending orientation angle
increases to 800. Furthermore, the CL-PCF with double cladding exhibits a very low confinement loss of about 0.003 dB/m with a bending radius and orientation angle of 40 cm and 00, respectively. It then increases to reach 9.86 dB/m when the bending orientation angle increases to 800. However, the CL-PCF with double air holes diameter has a confinement loss of 0.008 dB/m are obtained with a bending radius
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and orientation angle of 40 cm and 00, respectively. Which increases to reach 26 dB/m when the bending orientation angle increases to 800.
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Finally, the obtained results show that our proposed structures are suitable for
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many applications such: laser, amplifiers, WDM systems and FTTH applications.
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5. References
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[33] Arti Agrawal, N. Kejalakshmy, M. Uthman, B. M. A. Rahman, A .Kumar, K. T. V. Grattan, Ultra low bending loss equiangular spiral photonic crystal fibers in the terahertz regime, AIP Advances 2 (2012).
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List of figure captions
Figure 1: Cross section of the proposed CL-PCF.
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Figure 2: Variation of the confinement loss of the fundamental mode, the first, the
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second and the third high order modes for different values of the hole to hole spacing.
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Figure 3: Variation of the real part of the effective index as function of the wavelength for different values of the hole to hole spacing.
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different values of the hole to hole spacing.
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Figure 4: Variation of the chromatic dispersion as function of the wavelength for
Figure 5: Variation of the confinement loss as function of the wavelength for
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different values of the hole to hole spacing. Figure 6: Variation of the effective mode area as function of the wavelength for
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different values of the hole to hole spacing. Figure 7: Variation of the effective mode area as function of the wavelength for
different values of the hole to hole spacing. Figure 8: Variation of the confinement loss as a function of the wavelength for
different values of the hole to hole spacing. Figure 9: Cross section of the CL-PCF with double air holes diameter in single side. Figure 10: Cross section of the CL-PCF with double cladding.
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Figure 11: Variation of the confinement loss as function of the wavelength for structure (a) for different values of the bending radius.
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Figure 12: Variation of the confinement loss as function of the wavelength for structure (b) for different values of the bending radius.
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structure (a) for different values of the bending radius.
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Figure 13: Variation of the effective mode area as function of the wavelength for
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Figure 14: Variation of the effective mode area as function of the wavelength for structure (b) for different values of the bending radius.
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Figure 15: Variation of the confinement loss as function of the bending orientation
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angle for structure (a) for different values of the bending radius.
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Figure 16: Variation of the confinement loss as function of the bending orientation
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angle for structure (b) for different values of the bending radius. Figure 17: Variation of the effective mode area as function of the bending orientation
angle for structure (a) for different values of the bending radius. Figure 18: Variation of the effective mode area as function of the bending orientation
angle for structure (b) for different values of the bending radius.
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