Abstract

A novel kind of highly birefringent large-mode-area optical fiber is proposed in this paper. Birefringence in the fiber is realized by the introduction of an anisotropic microstructured core. The microstuctured core is composed of down-doped silica rods embedded in the background of up-doped silica. Numerical investigations demonstrate that high birefringence on the order of 2×10-4 and hexagonal profile mode fields with mode areas larger than 300 µm2 can be achieved in the proposed fiber. The influence of doping levels on the properties of birefringence, confinement losses, and mode-areas of the fiber is also investigated. Based on the design, we also propose a novel kind of single-polarization single-mode optical fiber with a mode area of 725 µm2 and an operating wavelength range as large as 340 nm.

©2007 Optical Society of America

1. Introduction

Polarization-maintaining (PM) optical fibers have been widely used for polarization control in fiber-optic sensors, precision optical instruments, and optical communication systems. The invention of photonic crystal fibers (PCFs) or microstructured optical fibers (MOFs) present a novel and effective way of realizing highly birefringent optical fibers. Different approaches have been investigated to realize PM-PCFs [16], which generally are based on form birefringence. Birefringence on the order of 10-3 can be achieved, which is one order of magnitude larger than that of conventional PMFs. Generally, form birefringence is largest for wavelengthsλ close to Λ (center-to-center distance between the adjacent air holes), but for larger values of Λ the birefringence decreases rapidly [7]. Thus, form-induced birefringence has been considered a valid method for making PM fibers in the small core regime only.

Large-mode-area optical fibers with high birefringence are very interesting for fiber devices such as fiber lasers and fiber-based gyroscopes. To obtain a polarization-maintaining large-mode-area fiber, an anisotropic fiber core has to be introduced. The well-known technique of stress-applying parts (SAP) inside the fiber, where the elasto-optical effect introduces anisotropy and therefore birefringence, has been investigated [78]. The fibers proposed have mode field diameters from about 4 to 6.5 µm and exhibit a typical birefringence of 1.5×10-4. Recently, Belardi et al. introduced an elliptical hollow photonic crystal fiber with a group birefringence of 1×10-4 and an effective mode area of 167 µm2 at the same time, which is greater than in commercially available LMA-PM-PCFs based on the SAP technique [9].

A microstructured optical fiber is generally an optical fiber with microstructured air holes in the cladding, the optical properties of which can be modified by selecting appropriate parameters of the cladding such as air-hole sizes and lattice periods. Recently, a complex core design has been introduced to tailor the optical properties of optical fibers [1015]. A microstructured core composed of small air holes in the background of Polymethyl Methacrylate (PMMA) has been explored to enhance the evanescent field for gas/liquid sensing in Ref. [10]. Simulations and experimental results have demonstrated the feasibility of the proposed fiber for sensing. Very recently, a microstructured-core PCF with elliptical air holes in the fiber core was proposed to achieve both ultrahigh birefringence and ultralow confinement loss [11]. In Ref. [14], a polarization-maintaining fiber in which the birefringence is due to artificially introduced anisotropy in the core material is introduced. The core of this fiber is composed of two commercial glasses, which induces a phase-index birefringence of 6.4×10-3 at the wavelength of 543 nm.

In this paper, a novel kind of microstructured-core optical fiber (MCOF) is proposed and investigated, the core of which is composed of down-doped silica rods embedded in the background of up-doped silica. Numerical investigation demonstrated that birefringence of 2×10-4 and hexagonal profile mode fields with mode areas larger than 300 µm2 can be achieved in the fiber. Based on the design, we also propose a single-polarization single-mode MCOF with a mode area as large as 725 µm2.

2. Numerical simulation

2.1 Configuration and mode-field distribution

The cross-section of the configuration we propose is illustrated in Fig. 1. The cladding of the fiber is composed of hexagonal-lattice air holes embedded in the background of pure silica, which is the same as that of a conventional PCF. The diameter of air holes in the cladding is defined as d, and we assume the background index of the microstructured cladding to be nb=1.45. In addition, the number of rings of air holes in the cladding is set as 4 in this paper, as shown in Fig. 1. The microstructured core is composed of rectangular-lattice down-doped rods embedded in the background of up-doped silica. The microstructured core can be fabricated by applying a stacking technique proposed in Ref. [4]. The up- and down-doped rods are stacked in order, and interstitial holes between the rods are filled with up-doped silica. All the rods are arranged in a circular section, and the diameter is defined as D, which is set as Λ in this paper. The microstructured core is characterized by the diameter of the down-doped rods as d , the length of the lattice is Λ′, the width of the lattice is b, and the ratio of the length and width of the lattice is defined as η=bΛ′. We set η=1/√3 so that the proposed core can be stacked as suggested in Ref. [4]. The refractive indexes of the down-doped and up-doped silica are defined as dn and nu, respectively. It should be noted that the pitch (Λ′) in the core equals 1/10 of the pitch (Λ) in the cladding. Furthermore, the relative index variations or doping levels of the down-doped and up-doped silica in the microstructured core are defined as Δd=(nb-nd)/nb and Δu=(nu-nb)/nb, respectively. In particular, the value of Δd is fixed at -0.015 in this paper. Therefore, the adjustable parameters in the fibers are the diameter of air holes d, the pitch of the air holes Λ, and the doping level of the up-doped rods Δu.

 figure: Fig. 1.

Fig. 1. (a) Cross-section of a microstructured-core optical fiber. The dark area denotes pure silica and the white areas represent air holes. (b) The enlarged core area. The darker area denotes pure silica, the lighter area represents up-doped silica, and the yellow area denotes down-doped silica.

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We solve the modes of the proposed fibers by a full vectorial finite-element method with perfectly matched layer boundary conditions [16]. In addition, a plane-wave expansion method [17] is applied to calculate the effective indexes of the microstructured core and cladding. Figure 2 shows the magnetic field of the x- and y- polarized states of the proposed fiber with Λ/λ=12, d/Λ=0.45, and Δu=0.011. The mode fields are similar to those of a conventional PCF except that the field distribution in the core is more complex. Owing to a lower core index, the profile of the x-polarized state extends further into the cladding. The birefringence in the fiber is 2.1×10-4 and the mode areas of the x- and y-polarized states at the wavelength of 1.55 µm are 492 and 379 µm2, respectively. The fiber shows polarization-dependent confinement losses of 0.71 and 0.001 dB/km for the x- and y-polarized states, respectively. The fiber should be very promising for fields where both high birefringence and large mode areas are required.

 figure: Fig. 2.

Fig. 2. Magnetic field profiles of the fundamental modes of a microstructured-core PCF: (a) x-polarized state, (b) y-polarized state.

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2.2 Birefringence

The effective indexes of the microstructured core (n eff,core) with Δu=0.010, 0.011, and 0.012 as functions of normalized frequency are illustrated in Fig. 3. Increased Δu leads to a higher effective core index, as expected. Also plotted in the figure are the effective indexes of the microstructured cladding (n eff,clad) with different air hole diameters. As the figure shows, for each Δu, different air hole diameters should be selected to meet the total internal reflection condition of n eff,clad<n eff,core. For example, for a core with Δu=0.012, the effective core indexes are larger than the effective cladding index, even if a small air hole diameter is selected. The disadvantage of this is that at high frequency, the index contrast between the core and the cladding would be too large, which would lead to the appearance of higher-order modes. For a core with Δu=0.011, the value of d/Λ could be as low as 0.30. For a core with a lower Δu, such as Δu=0.010, enlarged air holes (such as d/Λ=0.50) are required. If smaller air holes are introduced, the fiber would become an antiguide at a specified frequency region. Another thing we should note is that the effective core index increases with the increase of the frequency, which is quite different from a conventional solid core where the core index is only determined by the material dispersion. Therefore, the index contrast between the core and the cladding in the MCOF behaves quite differently from that of a conventional PCF. As we know, the index contrast in the latter is always decreasing as the frequency increases. In general, the index contrast in a MCOF decreases first as the frequency increases, then it increases after it reaches the minimum value.

The birefringence of the core is shown in Fig. 3(b). The birefringence of the core decreases with the increase of the normalized frequency, as the vectorial effect becomes weak at high frequency [3]. However, the birefringence is only slightly decreased as the frequency (or pitch) increases, which leads to the possibility of realizing both high birefringence and large mode area.

 figure: Fig. 3.

Fig. 3. (a) Effective indexes of the microstructured-core n eff,core for x-polarized state (dotted curves), and y-polarized state (solid curves). The thinner curves indicate the effective indexes of the microstructured-cladding n eff,clad with, from top to bottom, d/Λ=0.20, 0.30, 0.40, 0.50, and 0.60, respectively. (b) Birefringence of the microstructured core.

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 figure: Fig. 4.

Fig. 4. Birefringence of the MCOFs with (a) Δu=0.010 and (b) 0.011. The dotted curve indicates the birefringence of the microstructured core.

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Figure 4 shows the birefringence of the proposed fiber with Δu=0.010 and 0.011. At first, the birefringence generally decreases as the frequency increases. This is owing to the fact that the birefringence is induced by the two-fold symmetry of the microstructured core. Since the variation of the birefringence of the core is small for the frequency region investigated, the birefringence of the fiber is therefore determined mainly by the amount of energy contained in the core. As we have shown in Fig. 3(a), the index contrast at first decreases as the frequency increases, which leads to weaker confinement of the mode field; as a result, the power fraction in the core and the birefringence of the fiber reduce. As a demonstration, the fractional power in the core, which is defined as F=Pcore/Ptot, where Pcore, Ptot represent the power in the core and the total power in the fiber, respectively, is plotted in Fig. 5. It should be noted that the power fraction increases after it reaches the minimum value. This is because the index contrast increases after it reaches the minimum value, as shown in Fig. 3(a); therefore, the confinement ability becomes stronger, and as a result, the birefringence increases. Obviously, enlarging air holes could also lead to increased birefringence, owing to the increased index contrast and, accordingly, the increased fractional power in the core.

 figure: Fig. 5.

Fig. 5. The fractional power in the core as a function of the normalized frequency in the MCOFs with (a) Δu=0.010 and (b) 0.011.

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The appearance of high birefringence in the fiber with a large pitch makes the realization of high birefringence, large-mode-area optical fiber possible. However, owing to the fact that the index contrast between the core and the cladding does not decrease monotonously as the normalized frequency increases, the mode area of the fiber does not increase monotonously as in a conventional PCF. This phenomenon will be investigated further in the next section.

2.3 Mode area

The mode area of a conventional PCF is determined by the core area and the index contrast of the cladding and the core. Owing to the fact that an increased air-hole pitch leads to an enlarged core area and a reduced index contrast, the mode area increases with the increase of the pitch. However, the mode area in MCOF generally increases with the pitch at first, and decreases with the increase of the pitch after it reaches the maximum value. This is shown in Fig. 6, where the operating wavelength is fixed at 1.55 µm. It should be noted that the mode area is plotted as a function of normalized pitch Λ/λo, owing to the fact that the mode area is wavelength-dependent. The reduction of a mode area at a large pitch is due to the fact that although an increased pitch leads to an enlarged core area, the index contrast increases as the pitch increases, which leads to stronger field confinement and, as a result, a reduced mode area. At a low air-hole diameter, the difference between the mode areas of the x- and y-polarized states is very large. An interesting thing is that the mode area of the x-polarized state for the fiber with d/Λ=0.5 is very large in a wide-pitch range. This leads to the possibility of realizing a single-polarization optical fiber, which will be discussed further in Subsection 2.5.

 figure: Fig. 6.

Fig. 6. Mode areas of MCOFs with (a) Δu=0.010 and (b) 0.011 as a function of normalized pitch Λ/λo, where λo is set as 1.55 µm.

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2.4 Confinement loss

The confinement losses of the fundamental modes for MCOFs are shown in Fig. 7. The operating wavelength is assumed to be λo=1.55 µm. It should be noted that as the confinement losses are wavelength-dependent, they are also plotted as functions of normalized pitch Λ/λo. Owing to a lower index contrast between the core and the cladding, the confinement loss of the x-polarized state is larger than that of the y-polarized state. Enlarging the air holes in the cladding is found to be very effective in reducing the confinement losses. The confinement loss of the proposed fiber increases at first, especially for the x-polarized state, owing to the fact that the index contrast between the core and the cladding reduces. After the loss increases to the maximum value, it decreases rapidly, owing to the increased index contrast and enlarged core area.

The higher-order modes of the proposed fiber with Δu=0.010 appear at Λ/λo=17 and 13.8 for d/Λ=0.50 and 0.60, respectively. For the fiber with Δu=0.011, the higher-order modes appear at Λ/λo=15, 14.5, and 13.4 for d/Λ=0.40, 0.45, and 0.50, respectively. Therefore, the proposed fiber can be single-mode guided with a large pitch.

 figure: Fig. 7.

Fig. 7. Confinement loss of the proposed fiber with (a) Δu=0.010 and (b) 0.011 as a function of normalized pitch.

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2.5 Single-mode single-polarization operation

Single-polarization single-mode (SPSM) fibers are optical fibers that guide only one polarization state in a specific wavelength range. SPSM fibers can eliminate both polarization mode coupling and polarization mode dispersion, which will improve the stability of optical devices and transmission systems. SPSM fibers find applications in gyroscopes, fiber polarizers, and fiber lasers and amplifiers to ensure linearly polarized output. It has been shown that highly birefringent PCFs have possibilities of realizing better SPSM fibers than conventional SPSM fibers [18]. In addition, polarization-dependent losses have been investigated in rectangular lattice PCFs [5]. Furthermore, a large-mode-area SPSM fiber has been demonstrated in Ref. [19], where the stress-induced birefringence introduced in the fiber caused one of the polarized states to become antiguiding in a broad wavelength range.

SPSM guiding can also be realized in MCOFs, as we proposed. For example, the confinement losses of the x-polarized state for a fiber with d/Λ=0.5 and Δu=0.010 is larger than 20 dB/m for the normalized pitch in the range of 11.5–14.5. Therefore, if we choose the pitch of the fiber to be 19 µm, single-polarization operation can be realized over the wavelength range of 1.31–1.65 µm. The maximal confinement loss of the y-polarized state in the operating wavelength range is 95 dB/km. Although it is slightly high for long-haul communication, it has been low enough for fiber-based device application. The mode area of the y-polarized state is very large, which is 725 µm2 at the wavelength of 1.55 µm. Certainly the confinement losses can be reduced by increasing the air-hole rings in the cladding, although this would also lower the losses of the x-polarized state, and it therefore reduces the operating wavelength range of the single polarization.

3. Discussion

An important issue about the fabrication is that the interfaces of the rods in the core will introduce scattering loss; therefore, analyzing the amount of the loss and investigation on the technique of reducing it will be a major task of future work. At present, we think one feasible solution is the replacement of the rods in the core with plates, as were applied in Ref. [14]; the method can reduce greatly the number of interfaces in the core. Another solution is reducing the number of rods in the core; that is, increasing the ratio of ΛΛ. Certainly when the number of rods is reduced, the effective core index will have stronger dependence on the normalized frequency, which will lead to the reduced operating wavelength range. Another issue about the fabrication is the effect of diffusion during the fiber-drawing process, which decreases the index contrast between the up- and down-doped rods. The main effect of this is the reduction of birefringence. We think one possible solution is to increase the index contrast between the up- and down-doped rods while preserving the value of the effective core index. It should be noted that the effect of diffusion has been discussed in Ref. [14]. Owing to larger rod sizes and a low-index difference between the up- and down-doped rods, the effects of diffusion actually should be weak in the proposed fiber.

4. Conclusion

In conclusion, we have demonstrated numerically that both high birefringence and a large mode area can be achieved in the microstructured-core optical fiber we propose. Owing to the fact that birefringence in the fiber is introduced by the anisotropic microstructured core, whereas the mode area and single-mode operating is mainly determined by the index difference between the core and the cladding, high birefringence, large mode area, and low confinement losses can be achieved simultaneously in the fiber. In other words, the birefringence is mainly determined by the microstructured core, whereas the other optical properties of the fiber, such as mode area, single-mode regime, and confinement loss can be adjusted by selecting the appropriated cladding parameters. In addition, single-polarization single-mode operation with a large mode area can also be realized in the fiber by selecting appropriate parameters.

Acknowledgments

This work is supported by the Senior Talent Foundation of Jiangsu University, China, under project grant 06JDG062.

References and links

1. A. Oritigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. S. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]  

2. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001). [CrossRef]  

3. M. J. Steel and R. M. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001). [CrossRef]  

4. M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004). [CrossRef]  

5. M. Y. Chen, R. J. Yu, and A. P Zhao, “Confinement losses and optimization in rectangular-lattice photonic crystal fibers,” J. Lightwave Technol. 23, 2707–2712 (2005). [CrossRef]  

6. L. Zhang and C. Yang, “Photonic crystal fibers with squeezed hexagonal lattice,” Opt. Express 12, 2371–2376 (2004). [CrossRef]   [PubMed]  

7. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004). [CrossRef]   [PubMed]  

8. T. Schreiber, H. Schultz, O. Schmidt, F. Röser, J. Limpert, and A. Tünnermann, “Stress-induced birefringence in large-mode-area microstructured optical fibers,” Opt. Express 13, 3637–3646 (2005). [CrossRef]   [PubMed]  

9. W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005). [CrossRef]  

10. C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fiber for evanescent sensing applications,” Opt. Express 14, 13056–13066 (2006). [CrossRef]   [PubMed]  

11. D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007). [CrossRef]  

12. S. Kim, Y. Jung, K. Oh, J. Kobelke, K. Schuster, and J. Kirchhof, “Defect and lattice structure for air-silica index-guiding holey fibers,” Opt. Lett. 31, 164–166 (2006). [CrossRef]   [PubMed]  

13. M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005). [CrossRef]  

14. A. Wang, A. George, J. Liu, and J. Knight, “Highly birefringent lamellar core fiber,” Opt. Express 13, 5988–5993 (2005). [CrossRef]   [PubMed]  

15. M. Y. Chen, “Polarization maintaining large mode area photonic crystal fibers with solid microstructured cores,” J. Opt. A: Pure Appl. Opt. , 9, 868–871 (2007). [CrossRef]  

16. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001). [CrossRef]  

17. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef]   [PubMed]  

18. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004). [CrossRef]  

19. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005). [CrossRef]   [PubMed]  

References

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  1. A. Oritigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. S. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000).
    [Crossref]
  2. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
    [Crossref]
  3. M. J. Steel and R. M. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001).
    [Crossref]
  4. M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
    [Crossref]
  5. M. Y. Chen, R. J. Yu, and A. P Zhao, “Confinement losses and optimization in rectangular-lattice photonic crystal fibers,” J. Lightwave Technol. 23, 2707–2712 (2005).
    [Crossref]
  6. L. Zhang and C. Yang, “Photonic crystal fibers with squeezed hexagonal lattice,” Opt. Express 12, 2371–2376 (2004).
    [Crossref] [PubMed]
  7. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004).
    [Crossref] [PubMed]
  8. T. Schreiber, H. Schultz, O. Schmidt, F. Röser, J. Limpert, and A. Tünnermann, “Stress-induced birefringence in large-mode-area microstructured optical fibers,” Opt. Express 13, 3637–3646 (2005).
    [Crossref] [PubMed]
  9. W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
    [Crossref]
  10. C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fiber for evanescent sensing applications,” Opt. Express 14, 13056–13066 (2006).
    [Crossref] [PubMed]
  11. D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007).
    [Crossref]
  12. S. Kim, Y. Jung, K. Oh, J. Kobelke, K. Schuster, and J. Kirchhof, “Defect and lattice structure for air-silica index-guiding holey fibers,” Opt. Lett. 31, 164–166 (2006).
    [Crossref] [PubMed]
  13. M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005).
    [Crossref]
  14. A. Wang, A. George, J. Liu, and J. Knight, “Highly birefringent lamellar core fiber,” Opt. Express 13, 5988–5993 (2005).
    [Crossref] [PubMed]
  15. M. Y. Chen, “Polarization maintaining large mode area photonic crystal fibers with solid microstructured cores,” J. Opt. A: Pure Appl. Opt.,  9, 868–871 (2007).
    [Crossref]
  16. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
    [Crossref]
  17. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  18. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
    [Crossref]
  19. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005).
    [Crossref] [PubMed]

2007 (2)

D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007).
[Crossref]

M. Y. Chen, “Polarization maintaining large mode area photonic crystal fibers with solid microstructured cores,” J. Opt. A: Pure Appl. Opt.,  9, 868–871 (2007).
[Crossref]

2006 (2)

2005 (6)

2004 (4)

L. Zhang and C. Yang, “Photonic crystal fibers with squeezed hexagonal lattice,” Opt. Express 12, 2371–2376 (2004).
[Crossref] [PubMed]

J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004).
[Crossref] [PubMed]

M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
[Crossref]

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

2001 (4)

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

M. J. Steel and R. M. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001).
[Crossref]

2000 (1)

Arriaga, J.

Barretto, E. C. S.

Belardi, W.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[Crossref]

Birks, T. A.

Bjarklev, A.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Bouwmans, G.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[Crossref]

Broeng, J.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Chen, D. R.

D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007).
[Crossref]

Chen, M. Y.

M. Y. Chen, “Polarization maintaining large mode area photonic crystal fibers with solid microstructured cores,” J. Opt. A: Pure Appl. Opt.,  9, 868–871 (2007).
[Crossref]

M. Y. Chen, R. J. Yu, and A. P Zhao, “Confinement losses and optimization in rectangular-lattice photonic crystal fibers,” J. Lightwave Technol. 23, 2707–2712 (2005).
[Crossref]

M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
[Crossref]

Chesini, G.

Cordeiro, C. M. B.

Cruz, C. H. Brito

Cucinotta, A.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

Douay, M.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[Crossref]

Folkenberg, J.

Folkenberg, J. R.

Franco, M. A. R.

George, A.

Hansen, T. P.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Jakobsen, C.

Jensen, J. R.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Joannopoulos, J.

Johnson, S.

Jung, Y.

Kawanishi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Kim, S.

Kirchhof, J.

Knight, J.

Knight, J. C.

Knudsen, E.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Kobelke, J.

Koyanagi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Kubota, H.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Large, M. C. J.

Libori, S. E. B.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Limpert, J.

Liu, J.

Lwin, R.

Mangan, B. J.

Mortensen, N.

Nielsen, M.

Nielsen, M. D.

Oh, K.

Oritigosa-Blanch, A.

Osgood, R. M.

Provino, L.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[Crossref]

Röser, F.

Russell, P. S. J.

Schmidt, O.

Schreiber, T.

Schultz, H.

Schuster, K.

Selleri, S.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

Shen, L. F.

D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007).
[Crossref]

Shum, P.

M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005).
[Crossref]

Simonsen, H.

J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004).
[Crossref] [PubMed]

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

Steel, M. J.

Tanaka, M.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Tünnermann, A.

Vincetti, L.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

Wadsworth, W. J.

Wang, A.

Yamaguchi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Yan, M.

M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005).
[Crossref]

Yang, C.

Yu, R. J.

M. Y. Chen, R. J. Yu, and A. P Zhao, “Confinement losses and optimization in rectangular-lattice photonic crystal fibers,” J. Lightwave Technol. 23, 2707–2712 (2005).
[Crossref]

M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
[Crossref]

Yu, X.

M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005).
[Crossref]

Zhang, L.

Zhao, A. P

Zhao, A. P.

M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
[Crossref]

Zoboli, M.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (4)

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–560 (2001).
[Crossref]

D. R. Chen and L. F. Shen, “Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss,” IEEE Photon. Technol. Lett. 19, 185–187 (2007).
[Crossref]

M. Yan, P. Shum, and X. Yu, “Heterostructured photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1438–1440 (2005).
[Crossref]

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. A: Pure Appl. Opt. (2)

M. Y. Chen, R. J. Yu, and A. P. Zhao, “Highly birefringence rectangular lattice photonic crystal fibers,” J. Opt. A: Pure Appl. Opt. 6, 997–1000 (2004).
[Crossref]

M. Y. Chen, “Polarization maintaining large mode area photonic crystal fibers with solid microstructured cores,” J. Opt. A: Pure Appl. Opt.,  9, 868–871 (2007).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Cross-section of a microstructured-core optical fiber. The dark area denotes pure silica and the white areas represent air holes. (b) The enlarged core area. The darker area denotes pure silica, the lighter area represents up-doped silica, and the yellow area denotes down-doped silica.
Fig. 2.
Fig. 2. Magnetic field profiles of the fundamental modes of a microstructured-core PCF: (a) x-polarized state, (b) y-polarized state.
Fig. 3.
Fig. 3. (a) Effective indexes of the microstructured-core n eff,core for x-polarized state (dotted curves), and y-polarized state (solid curves). The thinner curves indicate the effective indexes of the microstructured-cladding n eff,clad with, from top to bottom, d/Λ=0.20, 0.30, 0.40, 0.50, and 0.60, respectively. (b) Birefringence of the microstructured core.
Fig. 4.
Fig. 4. Birefringence of the MCOFs with (a) Δ u =0.010 and (b) 0.011. The dotted curve indicates the birefringence of the microstructured core.
Fig. 5.
Fig. 5. The fractional power in the core as a function of the normalized frequency in the MCOFs with (a) Δ u =0.010 and (b) 0.011.
Fig. 6.
Fig. 6. Mode areas of MCOFs with (a) Δ u =0.010 and (b) 0.011 as a function of normalized pitch Λ/λo , where λo is set as 1.55 µm.
Fig. 7.
Fig. 7. Confinement loss of the proposed fiber with (a) Δ u =0.010 and (b) 0.011 as a function of normalized pitch.

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