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Theoretical study of novel dual-core microstructured photonic crystal fiber
Optik 127 (2016) 3427–3429
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Theoretical study of novel dual-core microstructured photonic crystal fiber Qiang Xu a,b,∗ , Miao Wang a , Shebao Lin a,b , Zhihuai Yang a , Yani Zhang a,b , Lei Zhang a a b
College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721016, PR China Baoji Key Laboratory of Ultrafast Spectroscopy, Baoji 721016, PR China
a r t i c l e
i n f o
Article history: Received 15 October 2015 Accepted 2 December 2015 Keywords: Dual-core photonic crystal fibers Birefringence Dispersion
a b s t r a c t We have theoretically investigated a novel dual-core microstructured photonic crystal fiber, which consist of two cores and a rectangular lattice cladding. The full-vector the plane wave expansion method is applied to analyze its high birefringence and dispersion. The simulation result shows that negative dispersion slope values in C band and high birefringence (10−2 ) are obtained. The new structure is compact in size and easy to fabricate, making it promising for miniaturized complex communication devices. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fibers (PCFs), a new class of optical cables, have revealed many interesting features successfully applied to the telecommunication as well as to the sensing industries because they can provide unprecedented degrees of freedom in tailoring their modal and coupling properties [1]. Birefringence is usually an undesirable property of fiber optics, but highly birefringence fibers are usually required. Highly birefringent PCFs can be obtained by distorting the shape of the air holes, or altering the air hole sizes near the core are [2,3]. Wang et al. reported a kind of highly birefringent elliptical-hole rectangular lattice PCFs with modified air-holes near the core [4]. Tan el al. proposed a novel scheme, a hole-assistant microstructured optical fiber with an elongated rectangle-like fiber core and much higher core-cladding index contrast. The numeric results show that in such a simple structure, ultrahigh modal birefringence and low confinement loss can be simultaneously obtained [5]. A kind of dual-core highly birefringence PCF is proposed. The model introduces the asymmetrical structure through replacing the innermost eight air holes with four elliptic air holes [6]. According to the symmetry theory, the rectangular lattice is potentially more anisotropic than the triangular and honeycomb lattices [7–10]. The dispersion properties of square lattice PCFs have been reported by Bouk et al. [11]. Various dispersion compensating fibers that were optimized to compensate for the
dispersion in a single band, e.g., the S band (1460–1530 nm), C band (1530–1565 nm), L band (1565–1625 nm), and U band (1625–1675 nm), have been reported [12]. The square lattice PCFs with small pitch and large air-hole diameter, whose dispersion slope is negative, can be used to compensate the positive dispersion and dispersion slope of the conventional single-mode fibers in the C band [13]. In this work, to analyze modal birefringence and dispersion of our proposed dual-core PCF, a full-vector plane wave expansion (PWE) method [14,15] which is highly suitable for the analysis of periodic structure with anisotropic perfectly matched layers (PMLs) [16,17] is applied. The PWE method is based on the electromagnetic field using Bloch’s theorem. By using PMLs as boundary condition, propagation characteristics of dispersion can be accurately evaluated. 2. Structure of the dual-core PCF Fig. 1 shows the schematic cross section structure of the dualcore microstructured PCF. The geometry of dual-core PCF looks like to a lattice PCF. It is characterized by the hole pitch , an air-filling fraction f = d/. The blue circle and green circle are air-holes. The yellow circle is dual-core. In this paper, the refractive index of silica background is set as n = 1.45. In addition, the refractive index of air-hole is set as n0 = 1. 3. The birefringence of the proposed dual-core PCF
∗ Corresponding author. Tel.: +86 15891470363. E-mail address: [email protected] (Q. Xu). http://dx.doi.org/10.1016/j.ijleo.2015.12.101 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Highly birefringence fibers are widely used for polarization control in fiber-optic sensors, high precision optical instruments and
3428
Q. Xu et al. / Optik 127 (2016) 3427–3429
Fig. 3. Waveguide dispersion (x-polarized odd mode) dependence of the wavelength (a) change hole pitch when air-filling fraction f = 0.4 (b) change air-filling fraction f when hole pitch = 2.0 m. Fig. 1. Schematic structure of the dual-core PCF.
optical communication. Birefringence is defined as a difference between the real part of effective refractive indices of x and y polarized fundamental modes and can be expressed as [18]
B() = Re(neff ()) − Re(nxeff ()) y
nx
(1)
ny
where eff and eff are effective refractive indices of two orthogonal polarization fundamental modes. First, the effects of hole pitch and fixing air-filling fraction f of the dual-core PCF are discussed. The calculation of birefringence for dual-core as a function of wavelength for different values of hole pitch are shown in Fig. 2(a). It can be seen from Fig. 2(a) that the birefringence increases as the hole pitch . In addition, as the wavelength increases, the birefringence increases as well. When = 1.6 m, and f = 0.4, the maximum of the birefringence can be up to 10−2 at 1.55 m. Fig. 2(b) shows the calculated birefringence by changing the air-filling fraction f from 0.2 to 0.45 in step size 0.05 with fixing = 1.6 m. From Fig. 2(b) we can see that birefringence value increases with the wavelength. When = 1.6 m, and f = 0.45, the maximum of the birefringence can be up to 10−2 at 1.55 m. 4. The dispersion of the proposed dual-core PCF Dispersion of the optical fibers a major factor causing optical pulse broadening. The waveguide dispersion parameter Dw () is obtained as [19,20] ∂ Dw () = − c
2
Re(neff ) ∂2
(2)
where is the wavelength and c is the velocity of the light in free space. Our design procedure is based on the possibility to approximate the real dispersion D() by a sum of the waveguide dispersion (or geometrical dispersion) Dw () and the material dispersion Dm () [21,22] D() = Dw () + Dm ()
(3)
The material dispersion can be obtained directly from the threeterm Sellmeier formula [23].
Fig. 2. Numerically calculated birefringence for different numbers of (a) hole pitch when f = 0.4 (b) fixing air-filling fraction f when = 1.6 m.
First, we investigate the influence of the geometric parameters hole pitch and air-filling fraction f on the waveguide dispersion of x-polarized odd mode for a dual-core PCF. We change the hole pitch of the proposed dual-core PCF, and we keep the following parameters fixed: f = 0.4. Fig. 3(a) shows the curves of Dw () as a function of wavelength for different hole pitch with = 1.6, 1.8, 2.0, 2.2, 2.4 m respectively. It can be seen from Fig. 3(a) that the proposed dual-core PCF has a negative dispersion parameter in the wavelength range around 1.55 m, which demonstrates an excellent dispersion compensating property. It is evident from Fig. 3(a) that the value of Dw () decreases gradually with wavelength in a shorter wavelength, and increases gradually in a longer wavelength range. Meanwhile, the minimum dispersion wavelength has a red-shift with an increase of hole pitch . Here, In order to obtain better dispersion compensating, we fixed = 2.0 m. Next, Fig. 3(b) shows the Dw () curves by changing air-filling fraction f from 0.2 to 0.45 in step size 0.05 with fixing = 2.0 m. Similarly, from Fig. 3(b), it follows the proposed dual-core PCF has a negative dispersion parameter in the wavelength range around 1.55 m, and the value of Dw () decreases gradually with wavelength in a shorter wavelength, and increases gradually in a longer wavelength range. Meanwhile, the minimum dispersion wavelength has a blue -shift with an increase of air-filling fraction f. According to the above numerical results, there exist an optimized set of design parameters that is hole pitch , and air-filling fraction f, which can lead to negative dispersion. These optimized values have been obtained through our numerical simulations to be = 2.0 m, and f = 0.4. The result shows similar dispersion characteristic as that of x-polarized odd and even mode for a dual-core PCF reported in this paper (e.g. Fig. 4). For convenience, the total dispersion is calculated using Eq. (3), but written in a slightly different form [22], D() = Dw () − (−Dm ())
(4)
In Fig. 5(a), the curves corresponding to the Dw (), the signchanged −Dm (), and D(), are represented in triangular sign, square sign and black circle sign, respectively. According to Eq. (4),
Fig. 4. Waveguide dispersion (x-polarized even mode) the dual-core PCF with (a) change hole pitch when air-filling fraction f = 0.4 (b) change air-filling fraction f when hole pitch = 2.0 m.
Q. Xu et al. / Optik 127 (2016) 3427–3429
Fig. 5. (a) shows the value of Dw (), Dm (), and D() for variation of wavelength (b) shows the dispersion slope vs. wavelength for the dual-core PCF when = 2.0 m and f = 0.4.
the black circle curve corresponding to D() is obtained by subtracting the values of the square curve from the triangular one. As you can see, the total dispersion is −38.6 ps km−1 nm−1 at wavelength of 1.55 m. The dispersion slope at 1.55 m is negative, −0.095 ps km−1 nm−2 as shown in Fig. 5(b). 5. Conclusions In summary, we proposed a novel dual-core PCF structure in which highly birefringence with negative dispersion is obtained. By using the full-vector-PWE with PMLs, the values of the properties are numerically simulated. When the parameters of the proposed dual-core PCF are optimized to be = 2.0 m, and f = 0.4, the optimized PCF has a negative dispersion slope of about −0.095 ps km−1 nm−1 at 1.55 m. Also, the birefringence is 10−2 at 1.55 m. This novel structure can be used in numerous practical application. Acknowledgements National Natural Science Foundation of China (grant 11547247), Key Science and Technology Program of Shaanxi Province (grant 2014K08-17, 2014KW07-01), Scientific Research Program Funded by Shaanxi Provincial Education Department (grant 15JK1043), Key Science and Technology Program of Baoji (grant 14GYGG5-2), Key Project of Baoji University of Arts and Sciences (grant ZK15009,ZK14011,ZK16028,YK1217). References [1] K. Saitoh, N.J. Florous, S.K. Varshney, M. Koshiba, Tunable photonic crystal fiber couplers with a thermo-responsive liquid crystal resonator, J. Lightwave Technol. 26 (2008) 663.
3429
[2] X. Zhang, J. Zhao, High birefringence photonic crystal fiber with low loss and a broad single-mode range, Nucl. Instrum. Methods Phys. Res., Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 637 (2011) S123. [3] Q. Xu, R.C. Miao, Y.N. Zhang, High birefringence low-dispersion of nonlinear photonic crystal fiber, Optik 124 (2013) 2269. [4] L. Wang, D. Yang, Highly birefringent elliptical-hole rectangular lattice photonic crystal fibers with modified air holes near the core, Opt. Express 1 (2007) 8892. [5] X. Tan, Y. Geng, J. Zhou, A novel ultrahigh birefringent hole-assistant microstructured optical fiber with low confinement loss, Opt. Laser Technol. 43 (2011) 1331. [6] D. Li, M. Liu, D. Jian, Z. Liao, D. He, Characteristics of highly birefringent dual-core photonic crystal fibers, Chin. J. Lasers 39 (2012) 0405005. [7] M.Y. Chen, R.J. Yu, A.P. Zhao, Highly birefringent rectangular lattice photonic crystal fibers, J. Opt. A: Pure Appl. Opt. 6 (2004) 997. [8] A. Ferrando, J.J. Miret, Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers, Appl. Phys. Lett. 78 (2001) 3184. [9] Q. Xu, Rectangular lattice on photonic crystal fibers with low dispersion and high birefringence, Chin. Opt. Lett. Suppl. (2014) S11302. [10] Q. Xu, Polarization properties rectangular lattice photonic crystal fiber, Optik 124 (2013) 4435. [11] A.H. Bouk, A. Cucinotta, F. Poli, S. Selleri, Dispersion properties of square-lattice photonic crystal fibers, Opt. Express 12 (2004) 941. [12] M. Aliramezani, Sh. Mohammad Nejad, Numerical analysis and optimization of a dual-concentric-core photonic crystal fiber for broadband dispersion compensation, Opt. Laser Technol. 42 (2010) 1209. [13] S. Kim, C. Kee, C.G. Lee, Modified rectangular lattice photonic crystal fibers with high birefringence and negative dispersion, Opt. Express 17 (2009) 7952. [14] Z. Zhu, T. Brown, Analysis of the space filling modes of photonic crystal fibers, Opt. Express 8 (2001) 547. [15] J. Arriaga, J.C. Knight, P.S.J. Russell, Modeling the propagation of light in photonic crystal fibers, Physica D: Nonlinear Phenom. 189 (2004) 100. [16] J. Berenger, A perfectly matched layers for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185. [17] K. Saitoh, M. Koshiba, Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides, J. Lightwave Technol. 19 (2001) 405. [18] Y.N. Zhang, L.Y. Ren, Y.K. Gong, X.H. Li, L.R. Wang, C.D. Sun, Design and optimization of highly nonlinear low-dispersion crystal fiber with high birefringence for four-wave mixing, Appl. Opt. 49 (2010) 3208. [19] K. Saitoh, M. Koshiba, Empirical relations for simple design of photonic crystal fibers, Opt. Express 13 (2005) 267. [20] Q. Xu, R.C. Miao, Y.N. Zhang, Highly nonlinear low-dispersion photonic crystal fiber with high birefringence for four-wave mixing, Opt. Mater. 35 (2012) 217. [21] S. Haxha, H. Ademgil, Novel design of photonic crystal fibers with low confinement losses, nearly zero ultra-flatted chromatic dispersion, negative chromatic dispersion and improved effective mode area, Opt. Commun. 281 (2008) 278. [22] K.K. Chow, C. Shu, C. Lin, Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber, IEEE Photonics Technol. Lett. 17 (2005) 624. [23] Q. Xu, Highly nonlinear dispersion-flattened photonic crystal fiber with high birefringence, J. Nanoelectron. Optoelectron. 8 (2013) 306.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Theoretical study of novel dual-core microstructured photonic crystal fiber Qiang Xu a,b,∗ , Miao Wang a , Shebao Lin a,b , Zhihuai Yang a , Yani Zhang a,b , Lei Zhang a a b
College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721016, PR China Baoji Key Laboratory of Ultrafast Spectroscopy, Baoji 721016, PR China
a r t i c l e
i n f o
Article history: Received 15 October 2015 Accepted 2 December 2015 Keywords: Dual-core photonic crystal fibers Birefringence Dispersion
a b s t r a c t We have theoretically investigated a novel dual-core microstructured photonic crystal fiber, which consist of two cores and a rectangular lattice cladding. The full-vector the plane wave expansion method is applied to analyze its high birefringence and dispersion. The simulation result shows that negative dispersion slope values in C band and high birefringence (10−2 ) are obtained. The new structure is compact in size and easy to fabricate, making it promising for miniaturized complex communication devices. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fibers (PCFs), a new class of optical cables, have revealed many interesting features successfully applied to the telecommunication as well as to the sensing industries because they can provide unprecedented degrees of freedom in tailoring their modal and coupling properties [1]. Birefringence is usually an undesirable property of fiber optics, but highly birefringence fibers are usually required. Highly birefringent PCFs can be obtained by distorting the shape of the air holes, or altering the air hole sizes near the core are [2,3]. Wang et al. reported a kind of highly birefringent elliptical-hole rectangular lattice PCFs with modified air-holes near the core [4]. Tan el al. proposed a novel scheme, a hole-assistant microstructured optical fiber with an elongated rectangle-like fiber core and much higher core-cladding index contrast. The numeric results show that in such a simple structure, ultrahigh modal birefringence and low confinement loss can be simultaneously obtained [5]. A kind of dual-core highly birefringence PCF is proposed. The model introduces the asymmetrical structure through replacing the innermost eight air holes with four elliptic air holes [6]. According to the symmetry theory, the rectangular lattice is potentially more anisotropic than the triangular and honeycomb lattices [7–10]. The dispersion properties of square lattice PCFs have been reported by Bouk et al. [11]. Various dispersion compensating fibers that were optimized to compensate for the
dispersion in a single band, e.g., the S band (1460–1530 nm), C band (1530–1565 nm), L band (1565–1625 nm), and U band (1625–1675 nm), have been reported [12]. The square lattice PCFs with small pitch and large air-hole diameter, whose dispersion slope is negative, can be used to compensate the positive dispersion and dispersion slope of the conventional single-mode fibers in the C band [13]. In this work, to analyze modal birefringence and dispersion of our proposed dual-core PCF, a full-vector plane wave expansion (PWE) method [14,15] which is highly suitable for the analysis of periodic structure with anisotropic perfectly matched layers (PMLs) [16,17] is applied. The PWE method is based on the electromagnetic field using Bloch’s theorem. By using PMLs as boundary condition, propagation characteristics of dispersion can be accurately evaluated. 2. Structure of the dual-core PCF Fig. 1 shows the schematic cross section structure of the dualcore microstructured PCF. The geometry of dual-core PCF looks like to a lattice PCF. It is characterized by the hole pitch , an air-filling fraction f = d/. The blue circle and green circle are air-holes. The yellow circle is dual-core. In this paper, the refractive index of silica background is set as n = 1.45. In addition, the refractive index of air-hole is set as n0 = 1. 3. The birefringence of the proposed dual-core PCF
∗ Corresponding author. Tel.: +86 15891470363. E-mail address: [email protected] (Q. Xu). http://dx.doi.org/10.1016/j.ijleo.2015.12.101 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Highly birefringence fibers are widely used for polarization control in fiber-optic sensors, high precision optical instruments and
3428
Q. Xu et al. / Optik 127 (2016) 3427–3429
Fig. 3. Waveguide dispersion (x-polarized odd mode) dependence of the wavelength (a) change hole pitch when air-filling fraction f = 0.4 (b) change air-filling fraction f when hole pitch = 2.0 m. Fig. 1. Schematic structure of the dual-core PCF.
optical communication. Birefringence is defined as a difference between the real part of effective refractive indices of x and y polarized fundamental modes and can be expressed as [18]
B() = Re(neff ()) − Re(nxeff ()) y
nx
(1)
ny
where eff and eff are effective refractive indices of two orthogonal polarization fundamental modes. First, the effects of hole pitch and fixing air-filling fraction f of the dual-core PCF are discussed. The calculation of birefringence for dual-core as a function of wavelength for different values of hole pitch are shown in Fig. 2(a). It can be seen from Fig. 2(a) that the birefringence increases as the hole pitch . In addition, as the wavelength increases, the birefringence increases as well. When = 1.6 m, and f = 0.4, the maximum of the birefringence can be up to 10−2 at 1.55 m. Fig. 2(b) shows the calculated birefringence by changing the air-filling fraction f from 0.2 to 0.45 in step size 0.05 with fixing = 1.6 m. From Fig. 2(b) we can see that birefringence value increases with the wavelength. When = 1.6 m, and f = 0.45, the maximum of the birefringence can be up to 10−2 at 1.55 m. 4. The dispersion of the proposed dual-core PCF Dispersion of the optical fibers a major factor causing optical pulse broadening. The waveguide dispersion parameter Dw () is obtained as [19,20] ∂ Dw () = − c
2
Re(neff ) ∂2
(2)
where is the wavelength and c is the velocity of the light in free space. Our design procedure is based on the possibility to approximate the real dispersion D() by a sum of the waveguide dispersion (or geometrical dispersion) Dw () and the material dispersion Dm () [21,22] D() = Dw () + Dm ()
(3)
The material dispersion can be obtained directly from the threeterm Sellmeier formula [23].
Fig. 2. Numerically calculated birefringence for different numbers of (a) hole pitch when f = 0.4 (b) fixing air-filling fraction f when = 1.6 m.
First, we investigate the influence of the geometric parameters hole pitch and air-filling fraction f on the waveguide dispersion of x-polarized odd mode for a dual-core PCF. We change the hole pitch of the proposed dual-core PCF, and we keep the following parameters fixed: f = 0.4. Fig. 3(a) shows the curves of Dw () as a function of wavelength for different hole pitch with = 1.6, 1.8, 2.0, 2.2, 2.4 m respectively. It can be seen from Fig. 3(a) that the proposed dual-core PCF has a negative dispersion parameter in the wavelength range around 1.55 m, which demonstrates an excellent dispersion compensating property. It is evident from Fig. 3(a) that the value of Dw () decreases gradually with wavelength in a shorter wavelength, and increases gradually in a longer wavelength range. Meanwhile, the minimum dispersion wavelength has a red-shift with an increase of hole pitch . Here, In order to obtain better dispersion compensating, we fixed = 2.0 m. Next, Fig. 3(b) shows the Dw () curves by changing air-filling fraction f from 0.2 to 0.45 in step size 0.05 with fixing = 2.0 m. Similarly, from Fig. 3(b), it follows the proposed dual-core PCF has a negative dispersion parameter in the wavelength range around 1.55 m, and the value of Dw () decreases gradually with wavelength in a shorter wavelength, and increases gradually in a longer wavelength range. Meanwhile, the minimum dispersion wavelength has a blue -shift with an increase of air-filling fraction f. According to the above numerical results, there exist an optimized set of design parameters that is hole pitch , and air-filling fraction f, which can lead to negative dispersion. These optimized values have been obtained through our numerical simulations to be = 2.0 m, and f = 0.4. The result shows similar dispersion characteristic as that of x-polarized odd and even mode for a dual-core PCF reported in this paper (e.g. Fig. 4). For convenience, the total dispersion is calculated using Eq. (3), but written in a slightly different form [22], D() = Dw () − (−Dm ())
(4)
In Fig. 5(a), the curves corresponding to the Dw (), the signchanged −Dm (), and D(), are represented in triangular sign, square sign and black circle sign, respectively. According to Eq. (4),
Fig. 4. Waveguide dispersion (x-polarized even mode) the dual-core PCF with (a) change hole pitch when air-filling fraction f = 0.4 (b) change air-filling fraction f when hole pitch = 2.0 m.
Q. Xu et al. / Optik 127 (2016) 3427–3429
Fig. 5. (a) shows the value of Dw (), Dm (), and D() for variation of wavelength (b) shows the dispersion slope vs. wavelength for the dual-core PCF when = 2.0 m and f = 0.4.
the black circle curve corresponding to D() is obtained by subtracting the values of the square curve from the triangular one. As you can see, the total dispersion is −38.6 ps km−1 nm−1 at wavelength of 1.55 m. The dispersion slope at 1.55 m is negative, −0.095 ps km−1 nm−2 as shown in Fig. 5(b). 5. Conclusions In summary, we proposed a novel dual-core PCF structure in which highly birefringence with negative dispersion is obtained. By using the full-vector-PWE with PMLs, the values of the properties are numerically simulated. When the parameters of the proposed dual-core PCF are optimized to be = 2.0 m, and f = 0.4, the optimized PCF has a negative dispersion slope of about −0.095 ps km−1 nm−1 at 1.55 m. Also, the birefringence is 10−2 at 1.55 m. This novel structure can be used in numerous practical application. Acknowledgements National Natural Science Foundation of China (grant 11547247), Key Science and Technology Program of Shaanxi Province (grant 2014K08-17, 2014KW07-01), Scientific Research Program Funded by Shaanxi Provincial Education Department (grant 15JK1043), Key Science and Technology Program of Baoji (grant 14GYGG5-2), Key Project of Baoji University of Arts and Sciences (grant ZK15009,ZK14011,ZK16028,YK1217). References [1] K. Saitoh, N.J. Florous, S.K. Varshney, M. Koshiba, Tunable photonic crystal fiber couplers with a thermo-responsive liquid crystal resonator, J. Lightwave Technol. 26 (2008) 663.
3429
[2] X. Zhang, J. Zhao, High birefringence photonic crystal fiber with low loss and a broad single-mode range, Nucl. Instrum. Methods Phys. Res., Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 637 (2011) S123. [3] Q. Xu, R.C. Miao, Y.N. Zhang, High birefringence low-dispersion of nonlinear photonic crystal fiber, Optik 124 (2013) 2269. [4] L. Wang, D. Yang, Highly birefringent elliptical-hole rectangular lattice photonic crystal fibers with modified air holes near the core, Opt. Express 1 (2007) 8892. [5] X. Tan, Y. Geng, J. Zhou, A novel ultrahigh birefringent hole-assistant microstructured optical fiber with low confinement loss, Opt. Laser Technol. 43 (2011) 1331. [6] D. Li, M. Liu, D. Jian, Z. Liao, D. He, Characteristics of highly birefringent dual-core photonic crystal fibers, Chin. J. Lasers 39 (2012) 0405005. [7] M.Y. Chen, R.J. Yu, A.P. Zhao, Highly birefringent rectangular lattice photonic crystal fibers, J. Opt. A: Pure Appl. Opt. 6 (2004) 997. [8] A. Ferrando, J.J. Miret, Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers, Appl. Phys. Lett. 78 (2001) 3184. [9] Q. Xu, Rectangular lattice on photonic crystal fibers with low dispersion and high birefringence, Chin. Opt. Lett. Suppl. (2014) S11302. [10] Q. Xu, Polarization properties rectangular lattice photonic crystal fiber, Optik 124 (2013) 4435. [11] A.H. Bouk, A. Cucinotta, F. Poli, S. Selleri, Dispersion properties of square-lattice photonic crystal fibers, Opt. Express 12 (2004) 941. [12] M. Aliramezani, Sh. Mohammad Nejad, Numerical analysis and optimization of a dual-concentric-core photonic crystal fiber for broadband dispersion compensation, Opt. Laser Technol. 42 (2010) 1209. [13] S. Kim, C. Kee, C.G. Lee, Modified rectangular lattice photonic crystal fibers with high birefringence and negative dispersion, Opt. Express 17 (2009) 7952. [14] Z. Zhu, T. Brown, Analysis of the space filling modes of photonic crystal fibers, Opt. Express 8 (2001) 547. [15] J. Arriaga, J.C. Knight, P.S.J. Russell, Modeling the propagation of light in photonic crystal fibers, Physica D: Nonlinear Phenom. 189 (2004) 100. [16] J. Berenger, A perfectly matched layers for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185. [17] K. Saitoh, M. Koshiba, Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides, J. Lightwave Technol. 19 (2001) 405. [18] Y.N. Zhang, L.Y. Ren, Y.K. Gong, X.H. Li, L.R. Wang, C.D. Sun, Design and optimization of highly nonlinear low-dispersion crystal fiber with high birefringence for four-wave mixing, Appl. Opt. 49 (2010) 3208. [19] K. Saitoh, M. Koshiba, Empirical relations for simple design of photonic crystal fibers, Opt. Express 13 (2005) 267. [20] Q. Xu, R.C. Miao, Y.N. Zhang, Highly nonlinear low-dispersion photonic crystal fiber with high birefringence for four-wave mixing, Opt. Mater. 35 (2012) 217. [21] S. Haxha, H. Ademgil, Novel design of photonic crystal fibers with low confinement losses, nearly zero ultra-flatted chromatic dispersion, negative chromatic dispersion and improved effective mode area, Opt. Commun. 281 (2008) 278. [22] K.K. Chow, C. Shu, C. Lin, Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber, IEEE Photonics Technol. Lett. 17 (2005) 624. [23] Q. Xu, Highly nonlinear dispersion-flattened photonic crystal fiber with high birefringence, J. Nanoelectron. Optoelectron. 8 (2013) 306.