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Octagonal photonic crystal fiber dual core polarization splitter
Optik 126 (2015) 1415–1418
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Octagonal photonic crystal fiber dual core polarization splitter Hao Rui ∗ , Du Huijing College of Sciences, Yanshan University, Qinhuangdao 066004, PR China
a r t i c l e
i n f o
Article history: Received 24 February 2014 Accepted 31 March 2015 Keywords: Photonic crystal fiber Polarization splitter Finite element method
a b s t r a c t An octagonal dual core polarization splitter based on highly birefringent photonic crystal fiber (PCF) is proposed and the full vector finite element method (FEM) is employed to analyze the impacts of structural parameters on birefringence and the coupling length, and simulation results show that high birefringence on the order of 10−3 can be achieved at 1.55 m, moreover, the hole size and hole pitch both affect birefringence and the coupling length. Based on these results, the PCF’s structure is optimized to realize a polarization splitter of 314 m whose largest extinction ratio is around −50.5 dB at 1.55 m. Meanwhile, the bandwidth at the extinction ratio of −10 dB is about 170 nm, and around 60 nm at −20 dB. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fibers [1,2] have attracted great research interest in recent years due to their unique and excellent optical properties, such as a wide wavelength range of single-mode operation [3,4], controllable effective modal area [5–7], tailorable dispersion [8,9] and high birefringence [10,11]. With the development of PCFs, polarization splitters based on PCFs have attracted more attention and they are of great significance for many optical applications, such as coherent optical communication systems and fiber optical sensors. Novel PCF polarization splitters with various structures have been reported in recent years. Rosa [12] proposed a polarization splitter based on a square lattice PCF, which comprises three asymmetrical cores. Mao [13] reported a polarization splitter based on all solid dual core PCF and the full vector finite element method was employed to analyze characteristics of the splitter. Lu [14] presented a three core PCF polarization splitter with a bandwidth of 400 nm, and two fluorine-doped cores and an elliptical modulation core are introduced in this structure. Shuo [15] put forward a polarization splitter in dual core hybrid PCF and their structure is composed of elliptical holes and comprises different materials. In this paper, a novel dual core polarization splitter based on an octagonal PCF is proposed and the finite element method is used to calculate the effective indexes of the dual core octagonal PCF. Moreover, the impacts of structural parameters on birefringence and coupling length are numerically analyzed. By adjusting the
structural parameters, high birefringence, high extinction ratios, small coupling lengths and large bandwidths can be achieved. 2. The proposed splitter’s structure and theory Fig. 1 illustrates the structure of the octagonal dual core PCF splitter whose cladding is composed of circular air holes arranged in octagonal configuration. A and B are two symmetrical cores of the PCF and d is the diameter of air holes. x and y denote the hole pitches along the x- and y-direction, respectively. The effective index of the proposed PCF is calculated by FEM and birefringence can be expressed as [16] y
B = |Re(nxeff − neff )|
where B represents birefringence, Re stands for the real part of the y effective index, nxeff and neff denote effective refractive indices of the x- and y-polarized fundamental modes, respectively. According to the mode coupling theory, the total modes can be considered as a superposition of four modes, including the odd x,y x,y modes Eodd and the even modes Eeven . And their effective refracx,y x,y tive indexes are nodd and neven , respectively. The coupling length is defined as [17] Lx,y =
x,y
http://dx.doi.org/10.1016/j.ijleo.2015.03.035 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
(2)
x,y
2(neven − nodd )
where is the optical wavelength. x,y When the power inputted into one core is Pin , the output power x,y Pout can be calculated from the following equation [18]
∗ Tel.: +86 13722577675; fax: +86 3358057027. E-mail addresses: [email protected], [email protected] (H. Rui).
(1)
x,y
x,y
Pout = Pin cos2
z 2 Lx,y
(3)
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H. Rui, H. Du / Optik 126 (2015) 1415–1418
Fig. 3. Birefringence as a function of y for different x /y . Fig. 1. Cross section of the octagonal dual core PCF polarization splitter. x,y
where z is the propagation length along the fiber. With the Pout obtained, the extinction ratio, ER, can be defined as follows [19] y
ER = 10 log10
Pout x Pout
(4)
3. Numerical results and discussions The finite element method is applied to calculate the effective refractive index and simulate the distribution of fundamental modes of the PCF splitter, and the distribution of even modes and odd modes are shown in Fig. 2. The coupling length is one of those important parameters for evaluating the performance of polarization splitters and birefringence has a big impact on the coupling length difference, so we calculate the coupling length and birefringence with altered structural parameters. Fig. 3 shows birefringence as a function of y with different values of x /y and d/y = 0.5 at the wavelength of 1.55 m, and we can see that with x /y fixed, birefringence decreases as y increases. This is because x increases along with y and the
large hole pitch may reduce the structure’s asymmetry, resulting in smaller birefringence. While y is fixed, the smaller x /y is, the higher birefringence becomes. This is because the smaller x can make the structure squeezed transversely, which enhances its asymmetry and leads to higher birefringence. Fig. 4 illustrates the coupling length as a function of y with different values of x /y and d/y = 0.5 at the wavelength of 1.55 m, and it is seen that with x /y fixed, the coupling length increases with y increasing, and the reason is while x and y both increase, the two cores can be further separated from each other and meanwhile modal fields are confined in the cores more intensely, so the coupling between two cores becomes more difficult, which results in the increased coupling length. While the ratio is fixed as x /y = 0.6, we analyze the variation of birefringence and the coupling length with d/y at 1.55 m, and in Fig. 5 we can see that with d/y fixed, birefringence decreases
Fig. 4. Coupling length as a function of y for different x /y .
Fig. 2. Distribution of even and odd components of fundamental modes. (a) and (b) Even and odd modes of the x polarized mode. (c) and (d) Even and odd modes of the y polarized mode.
Fig. 5. Birefringence as a function of y for different d/y .
H. Rui, H. Du / Optik 126 (2015) 1415–1418
1417
Fig. 8. Coupling length as a function of wavelength for the optimized splitter. Fig. 6. Coupling length as a function of y for different d/y .
while y increases because in this case x and y both increase and the structure’s symmetry can be enhanced, which leads to the decrease of birefringence. And when y is fixed, x is also fixed but birefringence increases as d/y increases because the increase of d/y means a larger size of air holes in the structure, and thus the two cores can be further squeezed, which enhances the asymmetry of the cores and results in higher birefringence. As for the coupling length, it is seen in Fig. 6 that as d/y is fixed, the coupling length increases with y increasing because in this case d, x and y are all increased and the two cores are further separated from each other, moreover, modal fields are confined in the cores more strongly, leading to the increase of the coupling length. But while y is fixed, and so is x , the increase of d/y can enhance the structure’s ability to confine modal fields, and the coupling between the two cores becomes more difficult, thus the coupling length also increases. From the results mentioned above, we see that in this structure birefringence on the order of 10−3 can be achieved and small coupling lengths of x- and y-polarized modes can be realized, but birefringence is not high enough to realize the large difference of coupling lengths, so we need to optimize this structure. In order to accomplish high birefringence and the large coupling length difference, we choose an elliptical hole in the center and proper structural parameters are as follows: x = 1.2 m, y = 1.7 m, d = 1.1 m, the long and short axes of the elliptical hole are a = 1.6 m and b = 1.1 m, respectively. The optimized structure is shown in Fig. 7. It is seen from Fig. 8 that as the wavelength increases, the coupling length decreases because modal fields expand and the coupling between the two cores becomes easier. At 1.55 m, the coupling lengths of x- and y-polarized modes are Lx = 157.1 m and
Fig. 7. Cross section of the optimized octagonal dual core PCF polarization splitter.
Fig. 9. Normalized power as a function of the propagation distance.
Ly = 314.1 m, respectively. The difference of coupling lengths is large and it makes the splitting of fundamental modes much easy. The core A is identical with the core B, so we simulate the normalized transmission power of fundamental modes in the core A along the propagation distance at 1.55 m, and results are illustrated in Fig. 9. It is seen in Fig. 9 that at the propagation distance of L = 2Lx = Ly = 314 m the x polarized mode still remains in the core A while the y polarized mode is completely coupled into the core B. Therefore, we can design a polarization splitter with the length of 314 m and at the end of the splitter x- and y-polarized modes can be separated into two cores, respectively. The bandwidth of polarization splitters is defined as the wavelength range within which the extinction ratio is better than −10 dB, and Fig. 10 shows the extinction ratio as a function of wavelength from 1.45 m to 1.65 m. We can see from Fig. 10 that at 1.55 m the largest extinction ratio can reach −50.5 dB, and the bandwidth at the extinction ratio of −10 dB
Fig. 10. Extinction ratio as a function of wavelength.
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H. Rui, H. Du / Optik 126 (2015) 1415–1418
is about 170 nm from 1.46 m to 1.63 m, and around 60 nm from 1.52 m to 1.58 m at −20 dB. 4. Conclusions In summary, we present a novel polarization splitter based on an octagonal PCF and high birefringence of 10−3 can be reached at 1.55 m. A polarization splitter of 314 m based on this PCF structure is designed and the largest extinction ratio at 1.55 m is −50.5 dB. The bandwidth at the extinction ratio of −10 dB is about 170 nm from 1.46 m to 1.63 m, and around 60 nm from 1.52 m to 1.58 m at −20 dB. Acknowledgements The author is grateful to Su Jiguo and Wu Yidong who have offered their support and helpful advices. This work has been supported in part by the Doctoral Project Foundation of Yanshan University (Grant No.: B844) and Natural Science Guidance Project of Hebei Province Higher Colleges (Grant No.: Z2013023). References [1] J. Broeng, D. Mogilevstev, S.E. Barkou, A. Bjarklev, Photonic crystal fibers: a new class of optical waveguides, Opt. Fiber Technol. 5 (1999) 305–330. [2] T.A. Birks, J.C. Knight, B.J. Mangan, P.S.J. Russell, Photonic crystal fibers: an endless variety, IEICE Trans. Electron. E84-C (2001) 585–592. [3] J.C. Knight, T.A. Birks, P.S.J. Russell, D.M. Atkin, All-silica single-mode optical fiber with photonic crystal cladding, Opt. Lett. 21 (1996) 1547–1549. [4] L. Dong, H.A. McKay, L. Fu, All glass endless single mode photonic crystal fibers, Opt. Lett. 33 (2008) 2440–2442.
[5] J. Li, J. Wang, Y. Cheng, et al., Novel large mode area photonic crystal fibers with selectively material filled structure, Opt. Laser Technol. 48 (2013) 375–380. [6] H. Ademgil, S. Haxha, Endlessly single mode photonic crystal fiber with improved effective mode area, Opt. Commun. 285 (2012) 1514–1518. [7] F. Begum, Y. Namihira, S.M. Abdur Razzak, et al., Design and analysis of novel highly nonlinear photonic crystal fibers with ultra flattened chromatic dispersion, Opt. Commun. 282 (2009) 1416–1421. [8] Y. Liu, J.Y. Wang, Y.Q. Li, R. Wang, J.H. Li, X.G. Xie, A novel hybrid photonic crystal dispersion compensating fiber with multiple windows, Opt. Laser Technol. 44 (2012) 2076–2079. [9] J.M. Hsu, G.S. Ye, Dispersion ultrastrong compensating fiber based on a liquid filled hybrid structure of dual concentric core and depressed clad photonic crystal fiber, J. Opt. Soc. Am. B 29 (8) (2012) 2021–2028. [10] S.E. Kim, B.H. Kim, et al., Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion, Opt. Express 20 (2) (2012) 1385–1391. [11] R. Bhattacharya, S. Konar, Extremely large birefringence and shifting of zero dispersion wavelength of photonic crystal fibers, Opt. Laser Technol. 44 (2012) 2210–2216. [12] L. Rosa, F. Poli, M. Foroni, et al., Polarization splitter based on a square lattice photonic crystal fiber, Opt. Lett. 31 (4) (2006) 441–443. [13] D. Mao, C. Guan, L. Yuan, Polarization splitter based in interference effects in all solid photonic crystal fibers, Appl. Opt. 49 (16) (2010) 3748–3752. [14] W. Lu, S. Lou, X. Wang, et al., Ultrabroadband polarization splitter based on three core photonic crystal fibers, Appl. Opt. 52 (3) (2013) 449–455. [15] S. Liu, S. Li, X. Zhu, A novel polarization splitter based on dual core elliptical holes hybrid photonic crystal fiber, Optik 123 (2012) 1858–1861. [16] J. Wang, J. Yao, H. Chen, et al., Ultrahigh birefringent polymer terahertz fiber based on a near tie unit, J. Opt. 13 (2011) 055402. [17] J. Li, J. Wang, R. Wang, et al., A novel polarization splitter based on dual core hybrid photonic crystal fibers, Opt. Laser Technol. 43 (2011) 795–800. [18] S. Zhang, W. Zhang, P. Geng, et al., Design of single polarization wavelength splitter based on photonic crystal fiber, Appl. Opt. 50 (36) (2011) 6576–6582. [19] L. Shuo, L.S. Guang, D. Ying, Analysis of the characteristics of the polarization splitter based on tellurite glass dual core photonic crystal fiber, Opt. Laser Technol. 44 (2012) 1813–1817.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Octagonal photonic crystal fiber dual core polarization splitter Hao Rui ∗ , Du Huijing College of Sciences, Yanshan University, Qinhuangdao 066004, PR China
a r t i c l e
i n f o
Article history: Received 24 February 2014 Accepted 31 March 2015 Keywords: Photonic crystal fiber Polarization splitter Finite element method
a b s t r a c t An octagonal dual core polarization splitter based on highly birefringent photonic crystal fiber (PCF) is proposed and the full vector finite element method (FEM) is employed to analyze the impacts of structural parameters on birefringence and the coupling length, and simulation results show that high birefringence on the order of 10−3 can be achieved at 1.55 m, moreover, the hole size and hole pitch both affect birefringence and the coupling length. Based on these results, the PCF’s structure is optimized to realize a polarization splitter of 314 m whose largest extinction ratio is around −50.5 dB at 1.55 m. Meanwhile, the bandwidth at the extinction ratio of −10 dB is about 170 nm, and around 60 nm at −20 dB. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fibers [1,2] have attracted great research interest in recent years due to their unique and excellent optical properties, such as a wide wavelength range of single-mode operation [3,4], controllable effective modal area [5–7], tailorable dispersion [8,9] and high birefringence [10,11]. With the development of PCFs, polarization splitters based on PCFs have attracted more attention and they are of great significance for many optical applications, such as coherent optical communication systems and fiber optical sensors. Novel PCF polarization splitters with various structures have been reported in recent years. Rosa [12] proposed a polarization splitter based on a square lattice PCF, which comprises three asymmetrical cores. Mao [13] reported a polarization splitter based on all solid dual core PCF and the full vector finite element method was employed to analyze characteristics of the splitter. Lu [14] presented a three core PCF polarization splitter with a bandwidth of 400 nm, and two fluorine-doped cores and an elliptical modulation core are introduced in this structure. Shuo [15] put forward a polarization splitter in dual core hybrid PCF and their structure is composed of elliptical holes and comprises different materials. In this paper, a novel dual core polarization splitter based on an octagonal PCF is proposed and the finite element method is used to calculate the effective indexes of the dual core octagonal PCF. Moreover, the impacts of structural parameters on birefringence and coupling length are numerically analyzed. By adjusting the
structural parameters, high birefringence, high extinction ratios, small coupling lengths and large bandwidths can be achieved. 2. The proposed splitter’s structure and theory Fig. 1 illustrates the structure of the octagonal dual core PCF splitter whose cladding is composed of circular air holes arranged in octagonal configuration. A and B are two symmetrical cores of the PCF and d is the diameter of air holes. x and y denote the hole pitches along the x- and y-direction, respectively. The effective index of the proposed PCF is calculated by FEM and birefringence can be expressed as [16] y
B = |Re(nxeff − neff )|
where B represents birefringence, Re stands for the real part of the y effective index, nxeff and neff denote effective refractive indices of the x- and y-polarized fundamental modes, respectively. According to the mode coupling theory, the total modes can be considered as a superposition of four modes, including the odd x,y x,y modes Eodd and the even modes Eeven . And their effective refracx,y x,y tive indexes are nodd and neven , respectively. The coupling length is defined as [17] Lx,y =
x,y
http://dx.doi.org/10.1016/j.ijleo.2015.03.035 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
(2)
x,y
2(neven − nodd )
where is the optical wavelength. x,y When the power inputted into one core is Pin , the output power x,y Pout can be calculated from the following equation [18]
∗ Tel.: +86 13722577675; fax: +86 3358057027. E-mail addresses: [email protected], [email protected] (H. Rui).
(1)
x,y
x,y
Pout = Pin cos2
z 2 Lx,y
(3)
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H. Rui, H. Du / Optik 126 (2015) 1415–1418
Fig. 3. Birefringence as a function of y for different x /y . Fig. 1. Cross section of the octagonal dual core PCF polarization splitter. x,y
where z is the propagation length along the fiber. With the Pout obtained, the extinction ratio, ER, can be defined as follows [19] y
ER = 10 log10
Pout x Pout
(4)
3. Numerical results and discussions The finite element method is applied to calculate the effective refractive index and simulate the distribution of fundamental modes of the PCF splitter, and the distribution of even modes and odd modes are shown in Fig. 2. The coupling length is one of those important parameters for evaluating the performance of polarization splitters and birefringence has a big impact on the coupling length difference, so we calculate the coupling length and birefringence with altered structural parameters. Fig. 3 shows birefringence as a function of y with different values of x /y and d/y = 0.5 at the wavelength of 1.55 m, and we can see that with x /y fixed, birefringence decreases as y increases. This is because x increases along with y and the
large hole pitch may reduce the structure’s asymmetry, resulting in smaller birefringence. While y is fixed, the smaller x /y is, the higher birefringence becomes. This is because the smaller x can make the structure squeezed transversely, which enhances its asymmetry and leads to higher birefringence. Fig. 4 illustrates the coupling length as a function of y with different values of x /y and d/y = 0.5 at the wavelength of 1.55 m, and it is seen that with x /y fixed, the coupling length increases with y increasing, and the reason is while x and y both increase, the two cores can be further separated from each other and meanwhile modal fields are confined in the cores more intensely, so the coupling between two cores becomes more difficult, which results in the increased coupling length. While the ratio is fixed as x /y = 0.6, we analyze the variation of birefringence and the coupling length with d/y at 1.55 m, and in Fig. 5 we can see that with d/y fixed, birefringence decreases
Fig. 4. Coupling length as a function of y for different x /y .
Fig. 2. Distribution of even and odd components of fundamental modes. (a) and (b) Even and odd modes of the x polarized mode. (c) and (d) Even and odd modes of the y polarized mode.
Fig. 5. Birefringence as a function of y for different d/y .
H. Rui, H. Du / Optik 126 (2015) 1415–1418
1417
Fig. 8. Coupling length as a function of wavelength for the optimized splitter. Fig. 6. Coupling length as a function of y for different d/y .
while y increases because in this case x and y both increase and the structure’s symmetry can be enhanced, which leads to the decrease of birefringence. And when y is fixed, x is also fixed but birefringence increases as d/y increases because the increase of d/y means a larger size of air holes in the structure, and thus the two cores can be further squeezed, which enhances the asymmetry of the cores and results in higher birefringence. As for the coupling length, it is seen in Fig. 6 that as d/y is fixed, the coupling length increases with y increasing because in this case d, x and y are all increased and the two cores are further separated from each other, moreover, modal fields are confined in the cores more strongly, leading to the increase of the coupling length. But while y is fixed, and so is x , the increase of d/y can enhance the structure’s ability to confine modal fields, and the coupling between the two cores becomes more difficult, thus the coupling length also increases. From the results mentioned above, we see that in this structure birefringence on the order of 10−3 can be achieved and small coupling lengths of x- and y-polarized modes can be realized, but birefringence is not high enough to realize the large difference of coupling lengths, so we need to optimize this structure. In order to accomplish high birefringence and the large coupling length difference, we choose an elliptical hole in the center and proper structural parameters are as follows: x = 1.2 m, y = 1.7 m, d = 1.1 m, the long and short axes of the elliptical hole are a = 1.6 m and b = 1.1 m, respectively. The optimized structure is shown in Fig. 7. It is seen from Fig. 8 that as the wavelength increases, the coupling length decreases because modal fields expand and the coupling between the two cores becomes easier. At 1.55 m, the coupling lengths of x- and y-polarized modes are Lx = 157.1 m and
Fig. 7. Cross section of the optimized octagonal dual core PCF polarization splitter.
Fig. 9. Normalized power as a function of the propagation distance.
Ly = 314.1 m, respectively. The difference of coupling lengths is large and it makes the splitting of fundamental modes much easy. The core A is identical with the core B, so we simulate the normalized transmission power of fundamental modes in the core A along the propagation distance at 1.55 m, and results are illustrated in Fig. 9. It is seen in Fig. 9 that at the propagation distance of L = 2Lx = Ly = 314 m the x polarized mode still remains in the core A while the y polarized mode is completely coupled into the core B. Therefore, we can design a polarization splitter with the length of 314 m and at the end of the splitter x- and y-polarized modes can be separated into two cores, respectively. The bandwidth of polarization splitters is defined as the wavelength range within which the extinction ratio is better than −10 dB, and Fig. 10 shows the extinction ratio as a function of wavelength from 1.45 m to 1.65 m. We can see from Fig. 10 that at 1.55 m the largest extinction ratio can reach −50.5 dB, and the bandwidth at the extinction ratio of −10 dB
Fig. 10. Extinction ratio as a function of wavelength.
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H. Rui, H. Du / Optik 126 (2015) 1415–1418
is about 170 nm from 1.46 m to 1.63 m, and around 60 nm from 1.52 m to 1.58 m at −20 dB. 4. Conclusions In summary, we present a novel polarization splitter based on an octagonal PCF and high birefringence of 10−3 can be reached at 1.55 m. A polarization splitter of 314 m based on this PCF structure is designed and the largest extinction ratio at 1.55 m is −50.5 dB. The bandwidth at the extinction ratio of −10 dB is about 170 nm from 1.46 m to 1.63 m, and around 60 nm from 1.52 m to 1.58 m at −20 dB. Acknowledgements The author is grateful to Su Jiguo and Wu Yidong who have offered their support and helpful advices. This work has been supported in part by the Doctoral Project Foundation of Yanshan University (Grant No.: B844) and Natural Science Guidance Project of Hebei Province Higher Colleges (Grant No.: Z2013023). References [1] J. Broeng, D. Mogilevstev, S.E. Barkou, A. Bjarklev, Photonic crystal fibers: a new class of optical waveguides, Opt. Fiber Technol. 5 (1999) 305–330. [2] T.A. Birks, J.C. Knight, B.J. Mangan, P.S.J. Russell, Photonic crystal fibers: an endless variety, IEICE Trans. Electron. E84-C (2001) 585–592. [3] J.C. Knight, T.A. Birks, P.S.J. Russell, D.M. Atkin, All-silica single-mode optical fiber with photonic crystal cladding, Opt. Lett. 21 (1996) 1547–1549. [4] L. Dong, H.A. McKay, L. Fu, All glass endless single mode photonic crystal fibers, Opt. Lett. 33 (2008) 2440–2442.
[5] J. Li, J. Wang, Y. Cheng, et al., Novel large mode area photonic crystal fibers with selectively material filled structure, Opt. Laser Technol. 48 (2013) 375–380. [6] H. Ademgil, S. Haxha, Endlessly single mode photonic crystal fiber with improved effective mode area, Opt. Commun. 285 (2012) 1514–1518. [7] F. Begum, Y. Namihira, S.M. Abdur Razzak, et al., Design and analysis of novel highly nonlinear photonic crystal fibers with ultra flattened chromatic dispersion, Opt. Commun. 282 (2009) 1416–1421. [8] Y. Liu, J.Y. Wang, Y.Q. Li, R. Wang, J.H. Li, X.G. Xie, A novel hybrid photonic crystal dispersion compensating fiber with multiple windows, Opt. Laser Technol. 44 (2012) 2076–2079. [9] J.M. Hsu, G.S. Ye, Dispersion ultrastrong compensating fiber based on a liquid filled hybrid structure of dual concentric core and depressed clad photonic crystal fiber, J. Opt. Soc. Am. B 29 (8) (2012) 2021–2028. [10] S.E. Kim, B.H. Kim, et al., Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion, Opt. Express 20 (2) (2012) 1385–1391. [11] R. Bhattacharya, S. Konar, Extremely large birefringence and shifting of zero dispersion wavelength of photonic crystal fibers, Opt. Laser Technol. 44 (2012) 2210–2216. [12] L. Rosa, F. Poli, M. Foroni, et al., Polarization splitter based on a square lattice photonic crystal fiber, Opt. Lett. 31 (4) (2006) 441–443. [13] D. Mao, C. Guan, L. Yuan, Polarization splitter based in interference effects in all solid photonic crystal fibers, Appl. Opt. 49 (16) (2010) 3748–3752. [14] W. Lu, S. Lou, X. Wang, et al., Ultrabroadband polarization splitter based on three core photonic crystal fibers, Appl. Opt. 52 (3) (2013) 449–455. [15] S. Liu, S. Li, X. Zhu, A novel polarization splitter based on dual core elliptical holes hybrid photonic crystal fiber, Optik 123 (2012) 1858–1861. [16] J. Wang, J. Yao, H. Chen, et al., Ultrahigh birefringent polymer terahertz fiber based on a near tie unit, J. Opt. 13 (2011) 055402. [17] J. Li, J. Wang, R. Wang, et al., A novel polarization splitter based on dual core hybrid photonic crystal fibers, Opt. Laser Technol. 43 (2011) 795–800. [18] S. Zhang, W. Zhang, P. Geng, et al., Design of single polarization wavelength splitter based on photonic crystal fiber, Appl. Opt. 50 (36) (2011) 6576–6582. [19] L. Shuo, L.S. Guang, D. Ying, Analysis of the characteristics of the polarization splitter based on tellurite glass dual core photonic crystal fiber, Opt. Laser Technol. 44 (2012) 1813–1817.