- Email: [email protected]
Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice
G Model IJLEO-52617; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice Wei Wang ∗ , Bo Yang, Hongru Song, Yue Fan College of Automation, Harbin Engineering University, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 20 April 2012 Accepted 23 August 2012 Keywords: Photonic crystal fiber Birefringence Negative dispersion Hybrid crystal lattice
a b s t r a c t Aiming at the requirements of high birefringence and negative dispersion in fiber-optic communication and sensing systems, a novel type of photonic crystal fiber (PCF) is proposed. In this structure, rectangular holes are arranged as hybrid lattice in the core and two bigger air holes symmetrical in the first cladding layer are added to gain high birefringence. Simulation results show that this kind of PCF exhibits high birefringence with a level of 10−2 , which will obtain better polarization. The negative dispersion is obtained over a wide wavelength range simultaneously, which has important applications in designing of dispersion compensation fibers. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fiber (PCF) has become a new hotspot because of its unique properties, such as flexible chromatic dispersion and high birefringence characteristics [1–4]. In recent years, significant research efforts have been devoted to the design and optimization of PCF or device based on PCF, for example, fibers, filters, splitters and couplers have been investigated thoroughly [5–9]. Investigations show that high birefringence and dispersion compensating play an important role in fiber-optic sensing systems and optical communication networks, which can further improve the performance of signal. For example, high birefringence make light propagate with better polarization for a long distance, and dispersion compensation fiber can improve the transmitting quality by reducing attenuation and broadening of signal. So it is a magnificent way to improve the quality of the system by designing PCF with high birefringence and negative dispersion. A great deal of work has been devoted to investigate high birefringence PCFs with different structures, and investigations show that birefringence can be improved by introducing dissymmetrical structure in cross-section of PCFs [10–12]. For example, Zhang et al. investigate high birefringence PCFs which has twofold symmetry by enlarging two of the central air holes, and simulation results show that the birefringence has reached 5 × 10−3 at 1550 nm [13]. And dispersion of the PCF designed by Yang et al. varies from −380 to −420 ps nm−1 km−1 [14], which has important applications in the field of dispersion compensation.
∗ Corresponding author. Tel.: +86 13159846192; fax: +86 82518741. E-mail address: [email protected] (W. Wang).
Although a great deal of efforts have been devoted to design and optimize PCFs, the birefringence can only achieve a level of 10−3 , which is still not sufficiently satisfied many applications. In this paper, a new kind of high birefringence PCF with hybrid lattice core is proposed, and the characteristics such as modal field, birefringence, and dispersion are analyzed by using Full-Vector Finite Element Method (FEM). Analyses show that birefringence can easily achieve a level of 10−2 , comparing with the value of the standard high birefringence hexagonal PCFs only 10−3 , which proves that the proposed PCF is highly polarized. In addition, negative dispersion also has been obtained over a wide wavelength range, which plays an important role in designing dispersion compensation fibers. 2. Numerical method In this paper, we explain the case for H field, which is same for the E field. After some simple derivation and use vector identity we have the vector wave equation for the H field which is given by
∇×
1 εr
− k2 r H =0 ∇ ×H 0
(1)
where r and εr are the permeability and permittivity of the material which used in the photonic crystal fiber, here we use SiO2 , = H(x, H y) exp(−jˇz) is the H field, k0 = 2/ is the wave number in the vacuum, is wavelength of light and ˇ is propagation constant. After derivation, we can get the propagation constant and other parameters, then the effective index will be obtained. With the effective index, the birefringence is given by B = |neffx − neffy |
(2)
0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.08.084
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084
G Model IJLEO-52617; No. of Pages 3
ARTICLE IN PRESS W. Wang et al. / Optik xxx (2012) xxx–xxx
2
Fig. 1. Cross-section of photonic crystal fiber with hybrid crystal lattice.
Fig. 3. Effective refractive index curves as a function wavelength with different a/b (d1 = 1.8 m).
where neffx and neffy are effective index of x and y-polarization mode of the fiber, respectively. The dispersion is given by D() = −
∂2 |Re(neff )| c ∂2
(3)
where D() is the dispersion of PCF, c is the velocity of light in the vacuum and Re(neff ) is the real part of effective index. 3. Results and discussion The schematic of the proposed PCF is illustrated in Fig. 1, which consists of two major parts. One is the cladding formed by air holes arranged as triangle lattice in a silicon-based cross section, the other is the hybrid-core arranged with two parts in order to obtain higher birefringence. In the core, the upside is rectangular-holes arranged as triangle lattice, and the underside is rectangular-holes arranged as rectangular lattice. The diameter of air holes in cladding d = 1.6 m, the pitch of cladding hole = 2 m, and the pitch of rectangular hole 1 = 0.22 m. In addition, two bigger air holes with a diameter of d1 are added symmetrical in the first cladding layer to further improve the birefringence. In the core, we choose b = 1.414 m as constant to analyze properties of PCF by changing a or d1 . 3.1. The flow of power Fig. 2 illustrates the flow of power of x- and y-polarization mode with a/b = 0.5 and wavelength = 1.55 m. From Fig. 2, it is obviously observed that the power is commendably restricted in the core, and there is almost no diffuseness into the cladding both in the two modes. It can also be observed that the power of y-polarization mode exhibits more uniformity property than xpolarization, which will fulfill the requirements of high efficiency transmission.
Fig. 2. The flow of power of (a) x-polarization mode and (b) y-polarization mode of proposed PCF when d1 = 1.8 m, a/b = 0.5 and wavelength = 1.55 m.
3.2. Dispersion Fig. 3 illustrates the effective refractive index curves of xpolarization mode serve as a function of wavelength when a/b is 0.5, 0.6 and 0.7, respectively. From Fig. 3, it is clearly revealed that all the effective refractive index curves decrease monotonically with the increase of wavelength. It is also observed that the effective refractive index decreases with the increase of a/b at the same wavelength. In addition, analyses show that the effective refractive index of the proposed PCF is lower than solid-core PCF due to the adding of the hybrid crystal lattice arranged air holes in the core. Fig. 4 illustrates that the dispersion curves of the x-polarization mode serve as a function of wavelength when a/b is 0.5, 0.6 and 0.7, respectively. From Fig. 4, we find that the proposed PCF fulfils negative dispersion property, for example, the value of dispersion is −257 ps nm−1 km−1 when a/b is 0.7 and wavelength = 1.55 m. It is also observed that when wavelength < 1.8 m, dispersion increases monotonically with the increase of wavelength, and when ≥ 1.8 m, dispersion curves vary inconspicuously. This negative dispersion property will have important applications in dispersion compensating designing. In addition, simulation results show that the value of dispersion decreases with the increase of a/b due to the increase of symmetry of the PCF. 3.3. Birefringence Investigations show that light could transmit farther in a better polarization as long as the fiber has high birefringence. In this paper, the relationship between birefringence and wavelength under different a/b is illustrated in Fig. 5. The birefringence can reach a level of 10−2 , and all the birefringence curves increase monotonically
Fig. 4. Dispersion curves as a function of wavelength with different a/b (d1 = 1.8 m).
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084
G Model
ARTICLE IN PRESS
IJLEO-52617; No. of Pages 3
W. Wang et al. / Optik xxx (2012) xxx–xxx
4. Conclusions
0.02
0.018
In conclusion, a new type of hybrid-core photonic crystal fiber is proposed, in which air holes are arranged as hybrid crystal lattice in the core. The characteristics of effective index, birefringence and dispersion are simulated by FEM. Simulation results show that the birefringence of the proposed PCF can achieve a level of 10−2 , which fulfills high polarization requirements in many applications. Also the negative dispersion is obtained over a wide wavelength range with highly polarized, which may play an important role in designing dispersion compensation fibers.
Birefringence
0.016
0.014
0.012
0.01
0.008
3
a/b=0.5 a/b=0.6 a/b=0.7 1.3
1.4
1.5
1.6 1.7 Wavelength ( m)
1.8
1.9
2
Acknowledgements Fig. 5. Birefringence curves as a function of wavelength with different a/b (d1 = 1.8 m).
This work was supported by the New Century Excellent Talents Support Program (Grant No. NCET-11-0827) and the Fundamental Research Funds for the Central Universities (Grant No. HEUCFZ1110). References
Fig. 6. Relationship of birefringence and d1 with different wavelength (a/b = 0.5).
with the increase of wavelength when < 1.8 m, whereas the value varies slowly when ≥ 1.8 m. In addition, it is also observed that birefringence decreases with the increase of a/b due to the increase of symmetry. It is predictable that the birefringence will achieve lower when a/b = 1 because the rectangle holes in the core turn to square holes, which increases the symmetry of fiber evidently. Birefringence as a function of d1 is illustrated in Fig. 6 when wavelength is 1.35 m, 1.55 m and 1.75 m, respectively. From Fig. 6, it is revealed that birefringence increases with the increase of d1 at same wavelength. In addition, it is observed that the birefringence is almost of the same value between the wavelength 1.55 m and 1.75 m when the d1 varies from 1.4 m to 1.6 m, which accords with the slowly variety when > 1.55 m just as demonstrated in Fig. 5.
[1] L.P. Shen, W.P. Huang, S.S. Jian, Design of photonic crystal fibers for dispersionrelated applications, J. Lightwave Technol. 21 (2003) 1644–1651. [2] C.M. Jewart, S.M. Quintero, A.M.B. Braga, K.P. Chen, Design of a highlybirefringent microstructured photonic crystal fiber for pressure monitoring, Opt. Express 18 (2010) 25657–25664. [3] V. Pureur, J.M. Dudley, Nonlinear spectral broadening of femtosecond pulses in solid-core photonic bandgap fibers, Opt. Lett. 35 (2010) 2813–2815. [4] B. Sun, M.Y. Chen, Y.K. Zhang, J.C. Yang, J.Q. Yao, H.X. Cui, Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing, Opt. Express 19 (2011) 4091–4100. [5] K. Fasihi, S. Mohammadnejad, Highly efficient channel-drop filter with a coupled cavity-based wavelength-selective reflection feedback, Opt. Express 17 (2009) 8983–8997. [6] M.N. Petersen, L. Scolari, T. Tokle, T.T. Alkeskjold, S. Gauza, S.T. Wu, A. Bjarklev, Noise filtering in a multi-channel system using a tunable liquid crystal photonic crystal bandgap fiber, Opt. Express 24 (2008) 20067–20072. [7] J.B. Eom, J.H. Park, H.B. Lee, 2 × 2 photonic crystal fiber splitter based on silicabased planar lightwave circuits, Opt. Lett. 34 (2009) 3737–3739. [8] Z. Ma, K. Ogusu, Channel drop filters using photonic crystal Fabry-Perot resonators, Opt. Commun. 284 (2011) 1192–1196. [9] A. Yariv, Y. Xu, R.K. Lee, A. Scherer, Coupled-resonator optical waveguide: a proposal and analysis, Opt. Lett. 24 (1999) 711–713. [10] G.C. Zhang, The Principles and Technologies of Fiber-Optic Gyroscope, National Defense Industry Press, Beijing, 2008. [11] 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) 676–680. [12] Z.J. He, Highly birefringence photonic crystal fibers based on micro-holestructured fiber core, Acta Photon. Sin. 37 (2008) 2217–2221. [13] M.M. Zhang, X.R. Ma, Y. Cao, Y. Yue, L.W. Wang, Study on high birefringence photonic crystal fiber, Acta Photon. Sin. 37 (2008) 1126–1129. [14] S.G. Yang, Y.J. Zhang, L.N. He, S.Z. Xie, Broadband dispersion-compensating photonic crystal fiber, Opt. Lett. 31 (2006) 2830–2832.
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084
ARTICLE IN PRESS Optik xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice Wei Wang ∗ , Bo Yang, Hongru Song, Yue Fan College of Automation, Harbin Engineering University, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 20 April 2012 Accepted 23 August 2012 Keywords: Photonic crystal fiber Birefringence Negative dispersion Hybrid crystal lattice
a b s t r a c t Aiming at the requirements of high birefringence and negative dispersion in fiber-optic communication and sensing systems, a novel type of photonic crystal fiber (PCF) is proposed. In this structure, rectangular holes are arranged as hybrid lattice in the core and two bigger air holes symmetrical in the first cladding layer are added to gain high birefringence. Simulation results show that this kind of PCF exhibits high birefringence with a level of 10−2 , which will obtain better polarization. The negative dispersion is obtained over a wide wavelength range simultaneously, which has important applications in designing of dispersion compensation fibers. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fiber (PCF) has become a new hotspot because of its unique properties, such as flexible chromatic dispersion and high birefringence characteristics [1–4]. In recent years, significant research efforts have been devoted to the design and optimization of PCF or device based on PCF, for example, fibers, filters, splitters and couplers have been investigated thoroughly [5–9]. Investigations show that high birefringence and dispersion compensating play an important role in fiber-optic sensing systems and optical communication networks, which can further improve the performance of signal. For example, high birefringence make light propagate with better polarization for a long distance, and dispersion compensation fiber can improve the transmitting quality by reducing attenuation and broadening of signal. So it is a magnificent way to improve the quality of the system by designing PCF with high birefringence and negative dispersion. A great deal of work has been devoted to investigate high birefringence PCFs with different structures, and investigations show that birefringence can be improved by introducing dissymmetrical structure in cross-section of PCFs [10–12]. For example, Zhang et al. investigate high birefringence PCFs which has twofold symmetry by enlarging two of the central air holes, and simulation results show that the birefringence has reached 5 × 10−3 at 1550 nm [13]. And dispersion of the PCF designed by Yang et al. varies from −380 to −420 ps nm−1 km−1 [14], which has important applications in the field of dispersion compensation.
∗ Corresponding author. Tel.: +86 13159846192; fax: +86 82518741. E-mail address: [email protected] (W. Wang).
Although a great deal of efforts have been devoted to design and optimize PCFs, the birefringence can only achieve a level of 10−3 , which is still not sufficiently satisfied many applications. In this paper, a new kind of high birefringence PCF with hybrid lattice core is proposed, and the characteristics such as modal field, birefringence, and dispersion are analyzed by using Full-Vector Finite Element Method (FEM). Analyses show that birefringence can easily achieve a level of 10−2 , comparing with the value of the standard high birefringence hexagonal PCFs only 10−3 , which proves that the proposed PCF is highly polarized. In addition, negative dispersion also has been obtained over a wide wavelength range, which plays an important role in designing dispersion compensation fibers. 2. Numerical method In this paper, we explain the case for H field, which is same for the E field. After some simple derivation and use vector identity we have the vector wave equation for the H field which is given by
∇×
1 εr
− k2 r H =0 ∇ ×H 0
(1)
where r and εr are the permeability and permittivity of the material which used in the photonic crystal fiber, here we use SiO2 , = H(x, H y) exp(−jˇz) is the H field, k0 = 2/ is the wave number in the vacuum, is wavelength of light and ˇ is propagation constant. After derivation, we can get the propagation constant and other parameters, then the effective index will be obtained. With the effective index, the birefringence is given by B = |neffx − neffy |
(2)
0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.08.084
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084
G Model IJLEO-52617; No. of Pages 3
ARTICLE IN PRESS W. Wang et al. / Optik xxx (2012) xxx–xxx
2
Fig. 1. Cross-section of photonic crystal fiber with hybrid crystal lattice.
Fig. 3. Effective refractive index curves as a function wavelength with different a/b (d1 = 1.8 m).
where neffx and neffy are effective index of x and y-polarization mode of the fiber, respectively. The dispersion is given by D() = −
∂2 |Re(neff )| c ∂2
(3)
where D() is the dispersion of PCF, c is the velocity of light in the vacuum and Re(neff ) is the real part of effective index. 3. Results and discussion The schematic of the proposed PCF is illustrated in Fig. 1, which consists of two major parts. One is the cladding formed by air holes arranged as triangle lattice in a silicon-based cross section, the other is the hybrid-core arranged with two parts in order to obtain higher birefringence. In the core, the upside is rectangular-holes arranged as triangle lattice, and the underside is rectangular-holes arranged as rectangular lattice. The diameter of air holes in cladding d = 1.6 m, the pitch of cladding hole = 2 m, and the pitch of rectangular hole 1 = 0.22 m. In addition, two bigger air holes with a diameter of d1 are added symmetrical in the first cladding layer to further improve the birefringence. In the core, we choose b = 1.414 m as constant to analyze properties of PCF by changing a or d1 . 3.1. The flow of power Fig. 2 illustrates the flow of power of x- and y-polarization mode with a/b = 0.5 and wavelength = 1.55 m. From Fig. 2, it is obviously observed that the power is commendably restricted in the core, and there is almost no diffuseness into the cladding both in the two modes. It can also be observed that the power of y-polarization mode exhibits more uniformity property than xpolarization, which will fulfill the requirements of high efficiency transmission.
Fig. 2. The flow of power of (a) x-polarization mode and (b) y-polarization mode of proposed PCF when d1 = 1.8 m, a/b = 0.5 and wavelength = 1.55 m.
3.2. Dispersion Fig. 3 illustrates the effective refractive index curves of xpolarization mode serve as a function of wavelength when a/b is 0.5, 0.6 and 0.7, respectively. From Fig. 3, it is clearly revealed that all the effective refractive index curves decrease monotonically with the increase of wavelength. It is also observed that the effective refractive index decreases with the increase of a/b at the same wavelength. In addition, analyses show that the effective refractive index of the proposed PCF is lower than solid-core PCF due to the adding of the hybrid crystal lattice arranged air holes in the core. Fig. 4 illustrates that the dispersion curves of the x-polarization mode serve as a function of wavelength when a/b is 0.5, 0.6 and 0.7, respectively. From Fig. 4, we find that the proposed PCF fulfils negative dispersion property, for example, the value of dispersion is −257 ps nm−1 km−1 when a/b is 0.7 and wavelength = 1.55 m. It is also observed that when wavelength < 1.8 m, dispersion increases monotonically with the increase of wavelength, and when ≥ 1.8 m, dispersion curves vary inconspicuously. This negative dispersion property will have important applications in dispersion compensating designing. In addition, simulation results show that the value of dispersion decreases with the increase of a/b due to the increase of symmetry of the PCF. 3.3. Birefringence Investigations show that light could transmit farther in a better polarization as long as the fiber has high birefringence. In this paper, the relationship between birefringence and wavelength under different a/b is illustrated in Fig. 5. The birefringence can reach a level of 10−2 , and all the birefringence curves increase monotonically
Fig. 4. Dispersion curves as a function of wavelength with different a/b (d1 = 1.8 m).
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084
G Model
ARTICLE IN PRESS
IJLEO-52617; No. of Pages 3
W. Wang et al. / Optik xxx (2012) xxx–xxx
4. Conclusions
0.02
0.018
In conclusion, a new type of hybrid-core photonic crystal fiber is proposed, in which air holes are arranged as hybrid crystal lattice in the core. The characteristics of effective index, birefringence and dispersion are simulated by FEM. Simulation results show that the birefringence of the proposed PCF can achieve a level of 10−2 , which fulfills high polarization requirements in many applications. Also the negative dispersion is obtained over a wide wavelength range with highly polarized, which may play an important role in designing dispersion compensation fibers.
Birefringence
0.016
0.014
0.012
0.01
0.008
3
a/b=0.5 a/b=0.6 a/b=0.7 1.3
1.4
1.5
1.6 1.7 Wavelength ( m)
1.8
1.9
2
Acknowledgements Fig. 5. Birefringence curves as a function of wavelength with different a/b (d1 = 1.8 m).
This work was supported by the New Century Excellent Talents Support Program (Grant No. NCET-11-0827) and the Fundamental Research Funds for the Central Universities (Grant No. HEUCFZ1110). References
Fig. 6. Relationship of birefringence and d1 with different wavelength (a/b = 0.5).
with the increase of wavelength when < 1.8 m, whereas the value varies slowly when ≥ 1.8 m. In addition, it is also observed that birefringence decreases with the increase of a/b due to the increase of symmetry. It is predictable that the birefringence will achieve lower when a/b = 1 because the rectangle holes in the core turn to square holes, which increases the symmetry of fiber evidently. Birefringence as a function of d1 is illustrated in Fig. 6 when wavelength is 1.35 m, 1.55 m and 1.75 m, respectively. From Fig. 6, it is revealed that birefringence increases with the increase of d1 at same wavelength. In addition, it is observed that the birefringence is almost of the same value between the wavelength 1.55 m and 1.75 m when the d1 varies from 1.4 m to 1.6 m, which accords with the slowly variety when > 1.55 m just as demonstrated in Fig. 5.
[1] L.P. Shen, W.P. Huang, S.S. Jian, Design of photonic crystal fibers for dispersionrelated applications, J. Lightwave Technol. 21 (2003) 1644–1651. [2] C.M. Jewart, S.M. Quintero, A.M.B. Braga, K.P. Chen, Design of a highlybirefringent microstructured photonic crystal fiber for pressure monitoring, Opt. Express 18 (2010) 25657–25664. [3] V. Pureur, J.M. Dudley, Nonlinear spectral broadening of femtosecond pulses in solid-core photonic bandgap fibers, Opt. Lett. 35 (2010) 2813–2815. [4] B. Sun, M.Y. Chen, Y.K. Zhang, J.C. Yang, J.Q. Yao, H.X. Cui, Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing, Opt. Express 19 (2011) 4091–4100. [5] K. Fasihi, S. Mohammadnejad, Highly efficient channel-drop filter with a coupled cavity-based wavelength-selective reflection feedback, Opt. Express 17 (2009) 8983–8997. [6] M.N. Petersen, L. Scolari, T. Tokle, T.T. Alkeskjold, S. Gauza, S.T. Wu, A. Bjarklev, Noise filtering in a multi-channel system using a tunable liquid crystal photonic crystal bandgap fiber, Opt. Express 24 (2008) 20067–20072. [7] J.B. Eom, J.H. Park, H.B. Lee, 2 × 2 photonic crystal fiber splitter based on silicabased planar lightwave circuits, Opt. Lett. 34 (2009) 3737–3739. [8] Z. Ma, K. Ogusu, Channel drop filters using photonic crystal Fabry-Perot resonators, Opt. Commun. 284 (2011) 1192–1196. [9] A. Yariv, Y. Xu, R.K. Lee, A. Scherer, Coupled-resonator optical waveguide: a proposal and analysis, Opt. Lett. 24 (1999) 711–713. [10] G.C. Zhang, The Principles and Technologies of Fiber-Optic Gyroscope, National Defense Industry Press, Beijing, 2008. [11] 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) 676–680. [12] Z.J. He, Highly birefringence photonic crystal fibers based on micro-holestructured fiber core, Acta Photon. Sin. 37 (2008) 2217–2221. [13] M.M. Zhang, X.R. Ma, Y. Cao, Y. Yue, L.W. Wang, Study on high birefringence photonic crystal fiber, Acta Photon. Sin. 37 (2008) 1126–1129. [14] S.G. Yang, Y.J. Zhang, L.N. He, S.Z. Xie, Broadband dispersion-compensating photonic crystal fiber, Opt. Lett. 31 (2006) 2830–2832.
Please cite this article in press as: W. Wang, et al., Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.084