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We propose a novel design of photonic crystal fiber (PCF) using an elliptical air hole in the core as a defected core in order to enhance the performance of modal birefringence and to control the properties of chromatic dispersion at the same time. From the simulation results, it is shown that the proposed fiber has high birefringence up to the order of 10−2, negative flattened chromatic dispersion in a broad range of wavelengths, and low confinement loss less than that of the single mode fiber. The outstanding advantage of the proposed PCF is that high birefringence, negative flattened dispersion, and low confinement loss can be achieved just by adding a small sized elliptical air hole in the core to the elliptical air hole PCF, especially at the same time.
©2012 Optical Society of America
1. Introduction
Photonic crystal fibers with the flexibility for the cross section design have been intensively studied due to their unique properties which would be difficult to realize in conventional optical fibers [1–5]. Especially, due to the large index contrast of a PCF compared to the conventional fiber, several designs based on the asymmetric microstructure in either cladding or the core region of PCFs have been reported to achieve high birefringence up to the order of 10−3 [5–7]. Furthermore, in order to enhance the birefringence up to the order of 10−2, elliptical air hole PCF (EPCF) was reported by M. J. Steel in 2001 for the first time [8,9]. After that, several designs using elliptical air holes have been investigated theoretically [10,11] and realized experimentally [12,13]. However, PCFs with elliptical air holes in the cladding have a weakness in mode confinement in the core since the bulk of the mode energy is in the fiber cladding. To overcome the weakness of poor mode confinement, novel designs of EPCF have been reported by adding the asymmetry in the fiber core using sub-wavelength elliptical air hole array [14,15]. However, in this structure, it is impossible to realize two different kinds of air holes (circular and elliptical) in PCFs using present fabrication techniques.
In fiber optic communication system, control of chromatic dispersion is no less important than control of polarization. To achieve ultra-flattened chromatic dispersion, several intriguing designs have been proposed [16–19]. Among them, the most simple and effective design to achieve ultra-flattened chromatic dispersion is reported by K. Saitoh using a single small sized air hole in the fiber core [19]. The basic idea relies on introducing a defected air hole in the core of PCF structure, which can enhance the waveguide dispersion in conjunction to the material dispersion in purpose to succeed the mutual cancellation between them and thus to obtain nearly zero dispersion characteristics over a wide wavelength range.
In this paper, in order to achieve high birefringence and flattened chromatic dispersion at the same time, a smaller sized elliptical air hole in the core is introduced as a defected core for the EPCF. The present design has the asymmetry in both fiber core and the cladding region by one kind of air holes (elliptical). The role of an elliptical defected core in the proposed fiber is not only to control the chromatic dispersion to be flattened but also to increase the value of birefringence up to the order of 10−2. Furthermore, the proposed EPCF exhibits low confinement loss less than that of the single mode fiber. In our simulation, the plane wave expansion method and full-vector finite element method (FEM) with the perfectly matched layer (PML) boundary condition are applied, which have been most popular and accurate methods to investigate the eigen-mode problems of guided modes in PCFs.
2. Design, simulation results and discussion
The schematic cross section of the proposed EPCF is shown in Fig. 1 . It is composed of elliptical air holes in the cladding arranged in a triangular array and an elliptical defected core, where Λ is the center-to-center spacing between the air holes, Dx ( = D) and Dy are the air hole diameters of the x and y axes in the cladding, respectively, and the ellipticity ratio η = Dy/Dx = dcy/dcx, where dcx ( = dc) and dcy are the air hole diameters of the x- and y-axes in the core.
Fig. 1 (a) Cross-section of the proposed EPCF with an elliptical air hole in the core with N = 6, and (b) Illustration of the structure parameters.
Figure 2 shows that the electric field distributions of the x- and y-polarized fundamental modes for the conventional and the proposed EPCF with the parameter of Λ = 1.6μm, D / Λ = 0.6, dc = D / 2, and η = 2. The excitation wavelength is 1.55μm. It can be observed in Fig. 2 that the x- and y- polarized modes of the conventional EPCF in Fig. 2(a) and (b) are more strongly confined in the core region than those of the proposed EPCF in Fig. 3(c) and 3(d) .
Fig. 2 Electric field distribution of (a), (c) y- and (b),(d) x-polarized mode for the conventional and proposed EPCF, respectively.
Fig. 3 Modal birefringence of the fundamental modes for the conventional and proposed EPCF with Λ = 1.6μm, D / Λ = 0.6, dc = D / 2, and η = 2.
However, under the configurations of an elliptical air hole in the core as a defected core, the field distributions of the proposed EPCF are obviously more different between the x- and y-polarized modes than those of the conventional EPCF, which result in high birefringence. From the simulation results, there are two interesting points: 1) it is true that the value of confinement loss for the proposed EPCF is larger than that of the conventional EPCF because the fundamental modes of the conventional EPCF are more strongly bounded in the core region. However, the value of the confinement loss for the proposed EPCF is 0.1 dB/km at 1.55μm when the number of air hole rings N = 6, which value is comparable to that of the single mode fiber, 0.2 dB/km at 1.55μm. When N = 7, the confinement loss reduces down to 0.01 dB/km in our simulation results. In this study, N is set to be 6. 2) A significant difference in field distribution between x- and y-polarized modes is observed in the proposed EPCF as shown in Fig. 2(c) and 2(d). Field distribution is directly related to the effective refractive index of the mode such that the x-polarized mode with more bounded around the hole as shown in Fig. 2(d) will result in a lower effective index. For the proposed EPCF, high birefringence is induced by magnifying the polarization dependent disparity in the field distributions.
A comparison of the difference on the modal birefringence and the chromatic dispersion between the conventional and the proposed EPCF has been performed, taking into account in the wavelength range between 1μm to 2μm in Fig. 3 and Fig. 4 , in which Λ = 1.6μm, D / Λ = 0.6, dc = D / 2, and η = 2. The modal birefringence and the chromatic dispersion can be determined according to the following formulation;
where βy (λ) () and βx (λ) () are the propagation constants (the effective index) of the y- and x-polarized fundamental modes, respectively, λ is the wavelength of the light, Re (neff) is the real part of the effective refractive index of y-polarized fundamental mode, and c is the velocity of light in free space. As expected from electric field distributions of the proposed EPCF, the modal birefringence is enhanced by introducing an elliptical air hole in the core to the value of 1.94 × 10−2 at 1.55μm, which is one order of magnitude higher than that of the conventional EPCF of 4.91 × 10−3, which result is shown in Fig. 3.Fig. 4 Chromatic dispersion of the fundamental modes for the conventional and proposed EPCF with Λ = 1.6μm, D / Λ = 0.6, dc = D / 2, and η = 2.The inset picture shows that the waveguide dispersion for the conventional and proposed EPCF and the dashed line (red) shows the negative material dispersion for the proposed EPCF.
For the effect of an elliptical air hole in the core on the chromatic dispersion, the simulation results are shown in Fig. 4. The total dispersion in a fiber structure can be well approximated using the following relation [19]: D (λ) ≈Dw (λ) + Dm (λ), where D (λ) is the total dispersion of the fiber, Dw (λ) is the waveguide dispersion, and Dm (λ) is the material dispersion which can be obtained using the Sellmeier’s equation. According to the previous research using a defected air hole core [19], it is proved that the existence of the central air hole in the core affect the waveguide dispersion properties. The enlarged inset picture in Fig. 4 shows that the waveguide dispersion for the conventional and the proposed EPCF. The waveguide dispersion shifts down to negative value by introducing an elliptical air hole in the core and the dashed line (red) shows the negative value of material dispersion (-Dm (λ)) for the proposed EPCF. In the enlarged picture in Fig. 4, the slopes of Dw(λ) and -Dm (λ) are almost same. Therefore, the total dispersion (D (λ) ≈Dw (λ) – (-Dm (λ)) for the proposed EPCF becomes to be flattened with negative value. From the results in Fig. 4, we can clearly see that the proposed EPCF have negative flattened dispersion parameter in a broad range of wavelengths from 1 to 2μm. In particular, In the C and L band, the value of total dispersion, D is −156 ± 0.5 ps/nm/km and the slope of dispersion, S is 1.96 × 10−3 ps/nm2/km at 1.55μm.
To further investigate the impact of the design parameters, Λ, D and dc on the modal birefringence of the proposed fiber, we analyze the relationship between the modal birefringence and Λ, D and dc at 1.55μm as shown in Fig. 5 . As expected from the previous research [10], the modal birefringence decreases with the increase of Λ. In Fig. 5(a), for the proposed EPCF, when Λ increases to 2.6 μm, the order of magnitude for the modal birefringence maintains 10−2, which value is larger than that of the previous design for the high birefringent PCF with same Λ. For the design parameters, D and dc, in Fig. 5(b) and 5(c), the birefringence increases as the size of D and dc increases. This results show that: 1) the modal birefringence is affected more significantly by changing dc when the diameter of air holes in the cladding, D is set to be large due to the high index contrast resulting in more confinement mode in the core. The possible maximum value of D is set to be 0.6 from the geometrical structure. 2) The modal birefringence becomes larger as dc increases up to D / 2 due to the enhancement of asymmetry in the fiber core. However, if dc becomes larger than D / 2, the confinement loss of the fundamental mode increases rapidly. Therefore in this paper, the optimized dc is set to be D / 2, where D / Λ = 0.6 and η = 2.
Fig. 5 Influences of structure parameters for the proposed EPCF, (a) Λ (b) D and (c) dc on the birefringence.
Next, we investigate the impact of the design parameters, Λ, D and dc on the chromatic dispersion of the proposed fiber. Figure 6(a) shows the impact of varying Λ to the total dispersion of the proposed EPCF with D /Λ = 0.6, dc = D / 2, and η = 2. The simulation results show that the optimized value of Λ with most flattened dispersion from 1.0 to 2.0 μm in the wavelength region is 1.6μm. Figure 6 (b) shows the impact of varying D in the cladding to the total dispersion of the proposed EPCF with Λ = 1.6μm, dc = D / 2, and η = 2. For D / Λ = 0. 4 in the proposed EPCF, the slope of dispersion is negative and as D increases to possible maximum value, 0.6Λ, the slope of total dispersion becomes to be flattened. Finally, Fig. 6(c) shows the impact of variation of an elliptical air hole diameter in the core, dc, to the total dispersion of the proposed EPCF with Λ = 1.6 μm, D / Λ = 0.6, and η = 2. In the case of dc = 0, the fiber is the conventional EPCF and have positive value of total dispersion with negative slope. As dc increases to D / 2, the value of dispersion becomes negative and its slope to be flattened.
Fig. 6 Influences of structure parameters for the proposed EPCF, (a) Λ (b) D and (c) dc on the chromatic dispersion
So far, the influences of an elliptical defected core of dc on the modal birefringence and the chromatic dispersion are studied. The results are summarized that by introducing an elliptical defected core to the conventional EPCF, the modal birefringence increases an order of magnitude higher to 10−2 and the chromatic dispersion becomes to be negative flattened. In comparison to the previous study for EPCF with air holes in the core [14,15], the design of the proposed fiber is simpler and the enhancement of birefringence is more significantly. In addition, the outstanding advantage of the proposed EPCF is to control the polarization and dispersion properties of PCF at the same time by an elliptical defected core.
Finally, we briefly consider the possibility of fabrication for the proposed EPCF. In the fabrication process, the elliptical holes may be susceptible to collapse and to change into circular one due to the surface tension. To overcome these problems, the new fabrication method of the new multi-step process of forming perform was suggested by Falkenstein, P et al in 2004 and EPCF were experimentally realized in Ref [12]. In addition, by introducing new methods for fabrication PCFs such as performs drilling, sol-gel casting, and tapering [20,21], the possibility of drawing the proposed EPCF is enhanced.
3. Conclusions
In this paper, we have proposed the high birefringent photonic crystal fiber with negative flattened dispersion in a broad range of wavelengths using an elliptical air hole as a defected core. And we have analyzed in detail the effects of structure parameters on the modal birefringence and the chromatic dispersion. With the design, the high birefringence to the order of 10−2 was reached by optimizing structure parameters, Λ, D and dc. Even with the large Λ = 2.6μm, the birefringence at 1.55μm is up to the value of 1.94 × 10−2 at 1.55μm. In addition, the proposed EPCF has a negative flattened dispersion of −156 ± 0.5 ps/nm/km in a broad range of wavelengths including C and L bands. The confinement loss of the proposed fiber is 0.1dB/km, which value is less than that of the single mode fiber. The most interesting point of the proposed fiber is that high birefringence, negative flattened dispersion and low confinement loss can be achieved at the same time just by adding an elliptical air hole in the core to the conventional EPCF. The proposed EPCF may be useful as high birefringent and dispersion flattened photonic crystal fiber with low confinement loss in practical applications in fiber optic systems.
Acknowledgment
This research was supported by Basic Science Research and the Happy tech. program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-004180, 2010-0001858, and 2010-0020794).
References and links
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