- Email: [email protected]
A polymer photonic crystal fiber with high and flattened birefringence
Optik 125 (2014) 1330–1332
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
A polymer photonic crystal fiber with high and flattened birefringence Peng Song School of Physics and Technology, University of Jinan, Jinan, 250022, China
a r t i c l e
i n f o
Article history: Received 3 April 2013 Accepted 5 August 2013
Keywords: Photonic crystal fiber Polymer Birefringence Squeezing ratio Elliptical ratio
a b s t r a c t A novel high birefringence polymer photonic crystal fiber (PCF) is proposed in this work. This PCF is composed of a polymer core and a cladding with elliptical air holes and squeezed triangular lattice. The high birefringence is introduced on the combined effect of elliptical air holes and the squeezed lattice. Our numerical results based on the supercell lattice method indicate that the birefringence can reach as high as 0.0018 at 650 nm wavelength with a properly designed cladding structure. We also analyze the dependence of the birefringence on structure parameters. And we design a PCF that has high and flattened birefringence. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction In recent years, photonic crystal fibers (PCFs) [1] have attracted significant attention. PCFs consist of a regular array of air-filled holes running along its length and a defect region in its center, so it has many unique properties which are not realized in traditional optical fibers, such as high birefringence and low or high nonlinearity, etc. [2,3]. By using PCFs, high birefringence fibers can be easily realized because of the sharp index contrast between air and silica. PCFs have exhibited their potential for a number of applications and high-performance polarization-relative components, such as photonic crystal fiber laser [4–6], optical communication systems [7], and polarization maintaining fibers (PMF) [8]. So far there are several high birefringence PCFs to be presented as PMFs, whose birefringence is one order of magnitude larger than that of conventional PMFs. A type of high birefringence PCF with squeezed hexagonal crystal lattice has been presented [9], in which all the air holes in its cladding are uniformly circular and the lattice constants in the xand y- directions are different. The squeezed lattice can break the multi-fold rotational symmetry of PCFs. Peng Song [10] has promoted a model to describe the squeezed degree of PCFs and studied the influence of the squeezing on those PCFs. This structure can lessen the chance of the air holes’ deformation and collapse in the fiber drawing process. Thus, the fabrication of such PCFs is feasible. In addition, studies show that elliptical air holes in the cladding also can break the multi-fold rotational symmetry of PCFs, and then
E-mail address: Song [email protected] 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.08.009
introduce birefringence [11]. The elliptical air holes are a kind of the squeezed circular air holes. The first such non-silica single-mode PCF reported was made using polymer, which was a microstructured polymer optical fiber [12] made of polymethylmethacrylate (PMMA). The change to polymers had significant potential given the range of polymers and processing methods available, and the low processing temperatures which would allow organic and inorganic dopants to be used that would not otherwise survive the higher processing temperatures of silica. In this paper, we propose a polymer high birefringence PCF with elliptical air holes and squeezed triangular lattice in the cladding. All the air holes in the cladding are uniformly elliptical. Meanwhile, the PCFs’ lattice constants in the x- and y- directions can be adjustable. We study the influence of structural parameters on the birefringence of PCFs based on the supercell lattice method [13]. Studies show that the birefringence on the order of 10−3 can be easily achieved. And we get the proper structural parameters to design a high birefringence polymer PCF with flattened birefringence, which decreases the difficulty of the fabrication process of PCFs. 2. Theoretical model Fig. 1 shows the cross section of the PCFs with squeezed lattice and uniform elliptical air holes. The lattice of PCFs is characterized by the lattice constants in x- and y-direction (i.e., Lx and Ly ). In order to describe the squeezed degree of the PCFs’ lattice, we introduce a concept of squeezing ratio (SR), which is defined as: SR =
2Ly , Lx
(1)
1331
10
10
5
5
y /µm
y /µm
P. Song / Optik 125 (2014) 1330–1332
0
−5
−10 −10
0
−5
−5
0
5
−10 −10
10
−5
0
x /µm
(a)
Fig. 1. The cross section of PCF.
where ry , rx are the diameters on the y- and x- directions of elliptical air holes, respectively. In the case of ER = 1, the air holes are circular. The squeezed degree increases as ER value decreases when ER < 1, and as ER value increases when ER > 1. PCFs’ squeezed degree results from both the squeezed lattice and elliptical air holes. In the model of squeezing ratio, we usually set a fixed Lx and change the value of Ly to change the SR of PCFs. in four-fold rotational symWhen SR = 1, the lattice is a square one √ √ metry. Moreover, in the case of SR = 3 and SR = 3/3, both of which denote that the lattice is the triangular lattice. Each SR value except the above three SR values denotes a squeezed triangular lattice. To prevent the air holes from overlapping with each other, the air hole diameter ry must meet the following restriction:
ry < min
Lx cos[argtg(SR)] 2
(1 + SR2 ) 1 +
SR ER
2 + Lx SR + Lx
(3)
Studies show that there are two approximately linearly polarx and HE y , ization modes in the fundamental modes of PCFs, HE11 11 respectively. The effective indexes of the two polarization fundamental modes are denoted as neffx and neffy , which can be simulated by the supercell lattice method. The modal birefringence B is expressed as: B = neffy − neffx
(4)
The value of birefringence is determined by the complex effect of the squeezed lattice and elliptical air holes. The sign of birefringence expresses the directions of the fast axis and the slow axis.
(b)
which is disadvantage to the fabrication of PCFs. In our designed PCFs, We can choose proper SR value in the range from 0.65 to 0.80 to produce high birefringence PCFs. Such PCFs is not sensitive to the changed SR values, which birefringence is stable in the fiber drawing process. Fig. 4 shows that the influence of the elliptical ratio (ER) of the air holes in the cladding on the birefringence, when Lx = 2.4 m, ry = 1 m, SR = 0.7 and SR = 0.75. We can see that the birefringence is very small at ER = 1, because the air holes in cladding are circular in this case. It can be seen from Fig. 4 that the modulus of the birefringence increases with the decrease of ER, which means that the bigger squeezed degree of the air holes is, the bigger birefringence of PCFs is. The birefringence can be −0.0018 at ER = 0.5 and SR = 0.7. The birefringence curve with SR = 0.75 is very similar to the curve with SR = 0.7, which is consistent with the conclusion from Fig. 3. So we can get a conclusion that the elliptical ratio of the air holes makes a much influence on the birefringence of PCFs. However, it is north to note that the elliptical ratio value is properly set to assure that the air holes couldn’t overlap each other.
−3
−0.4
x 10
−0.6 −0.8 −1 −1.2 −1.4 −1.6 −1.8 −2 0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
SR
3. Simulation and discussion
Fig. 3. The birefringence versus SR.
−3
0
x 10
−0.5
Birefringence
In this section, we investigate the influence of SR and ER on the PCFs’ birefringence. We set Lx = 2.4 m, ry = 1 m. The refractive index of background polymer is set to be n = 1.49 and that of the air holes is set to be 1.The profiles of x- and y- polarized fundamental mode are given in Fig. 2, in which Lx = 2.4 m, SR = 0.7, ry = 1 m, ER = 0.5. The excitation wavelength is 650 nm. It can be observed in Fig. 2 that the x- and y- polarized fundamental modes are strongly confined in the core region. We further study the influence of the squeezing ratio (SR) on the birefringence of PCFs. Fig. 3 shows the birefringence as a function of SR ranging from 0.65 to 1.00, when Lx = 2.4 m, ry = 1 m, and ER = 0.7. It can be seen from Fig. 3 that the modulus of the birefringence decreases with the increase of SR when SR is bigger than 0.7. When SR varies from 0.65 to 0.80, we can find that the modulus of the birefringence can reach as high as 0.0016 at least, and varies slowly with the increase of SR. The birefringence values fluctuate when the SR values of PCFs changed in the fiber drawing process,
10
Fig. 2. The profiles of (a) x-polarized fundamental mode and (b) y-polarized fundamental mode.
Birefringence
We introduce a concept of elliptical ratio (ER) to describe the squeezed degree of the PCFs’ elliptical air holes, which is defined as: ry ER = (2) rx
5
x /µm
−1
−1.5
SR=0.7 SR=0.75 −2 0.5
0.6
0.7
0.8
0.9
ER Fig. 4. The birefringence versus EP.
1
1332
P. Song / Optik 125 (2014) 1330–1332
sensitive to the changed SR values in the fiber drawing process, which provides a significant reference to design the high birefringence PCFs.
Birefringence
0
−0.005
Acknowledgment −0.01
The author (Peng Song) acknowledge support from the Scientific Research Fund for the Excellent Middle-Aged and Youth Scientists of Shandong Province of China under Grant Nos. BS2010DX003 and BS2012DX003.
−0.015
−0.02 0.6
0.8
1
1.2
1.4
1.6
1.8
2
Wavelength /µm Fig. 5. The birefringence versus the wavelength.
Fig. 5 plots the calculated birefringence as a function of the wavelength ranging from 600 nm to 2000 nm. The Simulation results show that the birefringence is sensitive to the varying wavelength. The modulus of birefringence increases with the excitation wavelength. The x- polarized fundamental mode has a larger neff because the long axis of elliptical holes is in the x-direction. So the birefringence is negative always. 4. Conclusion To summarize, a high birefringence polymer photonic crystal fiber with squeezed lattice and elliptical air holes is proposed and analyzed by the supercell lattice method. The high birefringence is introduced on the combined effect of the squeezed lattice and elliptical air holes in cladding. Our numerical results indicate that the birefringence can reach as high as −0.0018 at 650 nm wavelength with a properly designed cladding structure. We also analyze the dependence of birefringence on structure parameters. Based on our studies, when SR varies from 0.65 to 0.80, we can find that the modulus of the birefringence can reach as high as 0.0016 at least, and varies slowly with SR. In order to avoid the birefringence values fluctuate when the SR values of PCF changed in the fiber drawing process, we can set Lx = 2.4 m, SR = 0.7, ry = 1 m, and ER = 0.5 to produce high birefringence in our designed PCFs. Such PCFs is not
References [1] J.C. Knight, P.S.J. Russell, Photonic crystal fibers: new ways to guide light, Science 296 (2002) 276–277. [2] A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, P.S.J. Russell, Highly birefringent photonic crystal fibers, Opt. Lett. 25 (2000) 1325–1327. [3] S.M.A. Razzak, Y. Namihira, Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers, IEEE Photon. Technol. Lett. 20 (2008) 249–251. [4] J.H. Li, J.Y. Wang, R. Wang, Y. Liu, A novel polarizaton splitter based on dualcore hybrid photonic crystal fibers, Opt. Laser Technol 43 (2011) 795–800. [5] H. Wang, M.K. Al-Qaisi, T. Akkin, Polarization-maintaining fiber based polarization-sensitive optical coherence tomography in spectral domain, Opt. Lett. 35 (2010) 154–156. [6] A.M. Jones, A.V. Nampoothiri, et al., Mid-infrared gas filled photonic crystal fiber laser based on population inversion, Opt. Express 19 (2011) 2309–2316. [7] R. Buczynski, et al., Dispersion management in nonlinear photonic crystal fibres with nanostructured core, J. Eur. Opt. Soc. Rapid 6 (2011) 11038. [8] K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, M. Fujita, Optical properties of a low-loss polarization-maintaining photonic crystal fiber, Opt. Express 9 (2001) 670–676. [9] Z. Lin, Y. Changxi, Photonic crystal fibers with squeezed hexagonal lattice, Opt. Express 12 (2004) 2371–2376. [10] S. Peng, Z. Lu, H. Qianggao, Z. Shengzhi, J. Shan, Birefringence characteristics of squeezed lattice photonic crystal fibers, J. Lightwave Technol. 25 (2007) 1771–1776. [11] Y. Yue, G. Kai, Z. Wang, T. Sun, L. Jin, Y. Lu, C. Zhang, J. Liu, Y. Li, Y. Liu, S. Yuan, X. Dong, Highly birefringent elliptical-hole photonic crystal fiber with squeezed hexagonal lattice, Opt. Lett. 32 (2007) 469–471. [12] Y.N. Zhang, K. Li, L. Wang, et al., Casting preforms for mierostructured polymer optical fibre fabrication, Opt. Express 14 (2006) 5541–5547. [13] W. Zhi, R. Guobin, L. Shouqin, J. Shuisheng, Supercell lattice method for photonic crystal fibers, Opt. Express 11 (2003) 980–991.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
A polymer photonic crystal fiber with high and flattened birefringence Peng Song School of Physics and Technology, University of Jinan, Jinan, 250022, China
a r t i c l e
i n f o
Article history: Received 3 April 2013 Accepted 5 August 2013
Keywords: Photonic crystal fiber Polymer Birefringence Squeezing ratio Elliptical ratio
a b s t r a c t A novel high birefringence polymer photonic crystal fiber (PCF) is proposed in this work. This PCF is composed of a polymer core and a cladding with elliptical air holes and squeezed triangular lattice. The high birefringence is introduced on the combined effect of elliptical air holes and the squeezed lattice. Our numerical results based on the supercell lattice method indicate that the birefringence can reach as high as 0.0018 at 650 nm wavelength with a properly designed cladding structure. We also analyze the dependence of the birefringence on structure parameters. And we design a PCF that has high and flattened birefringence. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction In recent years, photonic crystal fibers (PCFs) [1] have attracted significant attention. PCFs consist of a regular array of air-filled holes running along its length and a defect region in its center, so it has many unique properties which are not realized in traditional optical fibers, such as high birefringence and low or high nonlinearity, etc. [2,3]. By using PCFs, high birefringence fibers can be easily realized because of the sharp index contrast between air and silica. PCFs have exhibited their potential for a number of applications and high-performance polarization-relative components, such as photonic crystal fiber laser [4–6], optical communication systems [7], and polarization maintaining fibers (PMF) [8]. So far there are several high birefringence PCFs to be presented as PMFs, whose birefringence is one order of magnitude larger than that of conventional PMFs. A type of high birefringence PCF with squeezed hexagonal crystal lattice has been presented [9], in which all the air holes in its cladding are uniformly circular and the lattice constants in the xand y- directions are different. The squeezed lattice can break the multi-fold rotational symmetry of PCFs. Peng Song [10] has promoted a model to describe the squeezed degree of PCFs and studied the influence of the squeezing on those PCFs. This structure can lessen the chance of the air holes’ deformation and collapse in the fiber drawing process. Thus, the fabrication of such PCFs is feasible. In addition, studies show that elliptical air holes in the cladding also can break the multi-fold rotational symmetry of PCFs, and then
E-mail address: Song [email protected] 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.08.009
introduce birefringence [11]. The elliptical air holes are a kind of the squeezed circular air holes. The first such non-silica single-mode PCF reported was made using polymer, which was a microstructured polymer optical fiber [12] made of polymethylmethacrylate (PMMA). The change to polymers had significant potential given the range of polymers and processing methods available, and the low processing temperatures which would allow organic and inorganic dopants to be used that would not otherwise survive the higher processing temperatures of silica. In this paper, we propose a polymer high birefringence PCF with elliptical air holes and squeezed triangular lattice in the cladding. All the air holes in the cladding are uniformly elliptical. Meanwhile, the PCFs’ lattice constants in the x- and y- directions can be adjustable. We study the influence of structural parameters on the birefringence of PCFs based on the supercell lattice method [13]. Studies show that the birefringence on the order of 10−3 can be easily achieved. And we get the proper structural parameters to design a high birefringence polymer PCF with flattened birefringence, which decreases the difficulty of the fabrication process of PCFs. 2. Theoretical model Fig. 1 shows the cross section of the PCFs with squeezed lattice and uniform elliptical air holes. The lattice of PCFs is characterized by the lattice constants in x- and y-direction (i.e., Lx and Ly ). In order to describe the squeezed degree of the PCFs’ lattice, we introduce a concept of squeezing ratio (SR), which is defined as: SR =
2Ly , Lx
(1)
1331
10
10
5
5
y /µm
y /µm
P. Song / Optik 125 (2014) 1330–1332
0
−5
−10 −10
0
−5
−5
0
5
−10 −10
10
−5
0
x /µm
(a)
Fig. 1. The cross section of PCF.
where ry , rx are the diameters on the y- and x- directions of elliptical air holes, respectively. In the case of ER = 1, the air holes are circular. The squeezed degree increases as ER value decreases when ER < 1, and as ER value increases when ER > 1. PCFs’ squeezed degree results from both the squeezed lattice and elliptical air holes. In the model of squeezing ratio, we usually set a fixed Lx and change the value of Ly to change the SR of PCFs. in four-fold rotational symWhen SR = 1, the lattice is a square one √ √ metry. Moreover, in the case of SR = 3 and SR = 3/3, both of which denote that the lattice is the triangular lattice. Each SR value except the above three SR values denotes a squeezed triangular lattice. To prevent the air holes from overlapping with each other, the air hole diameter ry must meet the following restriction:
ry < min
Lx cos[argtg(SR)] 2
(1 + SR2 ) 1 +
SR ER
2 + Lx SR + Lx
(3)
Studies show that there are two approximately linearly polarx and HE y , ization modes in the fundamental modes of PCFs, HE11 11 respectively. The effective indexes of the two polarization fundamental modes are denoted as neffx and neffy , which can be simulated by the supercell lattice method. The modal birefringence B is expressed as: B = neffy − neffx
(4)
The value of birefringence is determined by the complex effect of the squeezed lattice and elliptical air holes. The sign of birefringence expresses the directions of the fast axis and the slow axis.
(b)
which is disadvantage to the fabrication of PCFs. In our designed PCFs, We can choose proper SR value in the range from 0.65 to 0.80 to produce high birefringence PCFs. Such PCFs is not sensitive to the changed SR values, which birefringence is stable in the fiber drawing process. Fig. 4 shows that the influence of the elliptical ratio (ER) of the air holes in the cladding on the birefringence, when Lx = 2.4 m, ry = 1 m, SR = 0.7 and SR = 0.75. We can see that the birefringence is very small at ER = 1, because the air holes in cladding are circular in this case. It can be seen from Fig. 4 that the modulus of the birefringence increases with the decrease of ER, which means that the bigger squeezed degree of the air holes is, the bigger birefringence of PCFs is. The birefringence can be −0.0018 at ER = 0.5 and SR = 0.7. The birefringence curve with SR = 0.75 is very similar to the curve with SR = 0.7, which is consistent with the conclusion from Fig. 3. So we can get a conclusion that the elliptical ratio of the air holes makes a much influence on the birefringence of PCFs. However, it is north to note that the elliptical ratio value is properly set to assure that the air holes couldn’t overlap each other.
−3
−0.4
x 10
−0.6 −0.8 −1 −1.2 −1.4 −1.6 −1.8 −2 0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
SR
3. Simulation and discussion
Fig. 3. The birefringence versus SR.
−3
0
x 10
−0.5
Birefringence
In this section, we investigate the influence of SR and ER on the PCFs’ birefringence. We set Lx = 2.4 m, ry = 1 m. The refractive index of background polymer is set to be n = 1.49 and that of the air holes is set to be 1.The profiles of x- and y- polarized fundamental mode are given in Fig. 2, in which Lx = 2.4 m, SR = 0.7, ry = 1 m, ER = 0.5. The excitation wavelength is 650 nm. It can be observed in Fig. 2 that the x- and y- polarized fundamental modes are strongly confined in the core region. We further study the influence of the squeezing ratio (SR) on the birefringence of PCFs. Fig. 3 shows the birefringence as a function of SR ranging from 0.65 to 1.00, when Lx = 2.4 m, ry = 1 m, and ER = 0.7. It can be seen from Fig. 3 that the modulus of the birefringence decreases with the increase of SR when SR is bigger than 0.7. When SR varies from 0.65 to 0.80, we can find that the modulus of the birefringence can reach as high as 0.0016 at least, and varies slowly with the increase of SR. The birefringence values fluctuate when the SR values of PCFs changed in the fiber drawing process,
10
Fig. 2. The profiles of (a) x-polarized fundamental mode and (b) y-polarized fundamental mode.
Birefringence
We introduce a concept of elliptical ratio (ER) to describe the squeezed degree of the PCFs’ elliptical air holes, which is defined as: ry ER = (2) rx
5
x /µm
−1
−1.5
SR=0.7 SR=0.75 −2 0.5
0.6
0.7
0.8
0.9
ER Fig. 4. The birefringence versus EP.
1
1332
P. Song / Optik 125 (2014) 1330–1332
sensitive to the changed SR values in the fiber drawing process, which provides a significant reference to design the high birefringence PCFs.
Birefringence
0
−0.005
Acknowledgment −0.01
The author (Peng Song) acknowledge support from the Scientific Research Fund for the Excellent Middle-Aged and Youth Scientists of Shandong Province of China under Grant Nos. BS2010DX003 and BS2012DX003.
−0.015
−0.02 0.6
0.8
1
1.2
1.4
1.6
1.8
2
Wavelength /µm Fig. 5. The birefringence versus the wavelength.
Fig. 5 plots the calculated birefringence as a function of the wavelength ranging from 600 nm to 2000 nm. The Simulation results show that the birefringence is sensitive to the varying wavelength. The modulus of birefringence increases with the excitation wavelength. The x- polarized fundamental mode has a larger neff because the long axis of elliptical holes is in the x-direction. So the birefringence is negative always. 4. Conclusion To summarize, a high birefringence polymer photonic crystal fiber with squeezed lattice and elliptical air holes is proposed and analyzed by the supercell lattice method. The high birefringence is introduced on the combined effect of the squeezed lattice and elliptical air holes in cladding. Our numerical results indicate that the birefringence can reach as high as −0.0018 at 650 nm wavelength with a properly designed cladding structure. We also analyze the dependence of birefringence on structure parameters. Based on our studies, when SR varies from 0.65 to 0.80, we can find that the modulus of the birefringence can reach as high as 0.0016 at least, and varies slowly with SR. In order to avoid the birefringence values fluctuate when the SR values of PCF changed in the fiber drawing process, we can set Lx = 2.4 m, SR = 0.7, ry = 1 m, and ER = 0.5 to produce high birefringence in our designed PCFs. Such PCFs is not
References [1] J.C. Knight, P.S.J. Russell, Photonic crystal fibers: new ways to guide light, Science 296 (2002) 276–277. [2] A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, P.S.J. Russell, Highly birefringent photonic crystal fibers, Opt. Lett. 25 (2000) 1325–1327. [3] S.M.A. Razzak, Y. Namihira, Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers, IEEE Photon. Technol. Lett. 20 (2008) 249–251. [4] J.H. Li, J.Y. Wang, R. Wang, Y. Liu, A novel polarizaton splitter based on dualcore hybrid photonic crystal fibers, Opt. Laser Technol 43 (2011) 795–800. [5] H. Wang, M.K. Al-Qaisi, T. Akkin, Polarization-maintaining fiber based polarization-sensitive optical coherence tomography in spectral domain, Opt. Lett. 35 (2010) 154–156. [6] A.M. Jones, A.V. Nampoothiri, et al., Mid-infrared gas filled photonic crystal fiber laser based on population inversion, Opt. Express 19 (2011) 2309–2316. [7] R. Buczynski, et al., Dispersion management in nonlinear photonic crystal fibres with nanostructured core, J. Eur. Opt. Soc. Rapid 6 (2011) 11038. [8] K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, M. Fujita, Optical properties of a low-loss polarization-maintaining photonic crystal fiber, Opt. Express 9 (2001) 670–676. [9] Z. Lin, Y. Changxi, Photonic crystal fibers with squeezed hexagonal lattice, Opt. Express 12 (2004) 2371–2376. [10] S. Peng, Z. Lu, H. Qianggao, Z. Shengzhi, J. Shan, Birefringence characteristics of squeezed lattice photonic crystal fibers, J. Lightwave Technol. 25 (2007) 1771–1776. [11] Y. Yue, G. Kai, Z. Wang, T. Sun, L. Jin, Y. Lu, C. Zhang, J. Liu, Y. Li, Y. Liu, S. Yuan, X. Dong, Highly birefringent elliptical-hole photonic crystal fiber with squeezed hexagonal lattice, Opt. Lett. 32 (2007) 469–471. [12] Y.N. Zhang, K. Li, L. Wang, et al., Casting preforms for mierostructured polymer optical fibre fabrication, Opt. Express 14 (2006) 5541–5547. [13] W. Zhi, R. Guobin, L. Shouqin, J. Shuisheng, Supercell lattice method for photonic crystal fibers, Opt. Express 11 (2003) 980–991.