1. Introduction

Polarization splitters are essential components in integrated photonics and have many applications. There are various types of optical polarization splitters reported in the literature [1–7]. van der Tol et al. fabricated polarization splitters based on asymmetric Y-branched semiconductor waveguides [1–3]. Wei and Wang demonstrated polarization splitters on lithium niobate by using titanium, nickel, and MgO diffusion waveguides [4]. Miliou et al. reported a glass waveguide polarization splitter based on stress-induced birefringence in ion-exchange waveguides [5]. Thyagarajan et al. proposed polarization splitters based on resonant tunneling in three-core couplers [6]. Lin et al. presented a directional coupler polarization splitter assisted by a nematic liquid crystal layer [7].

Recently photonic crystal fibers (PCFs) have attracted great research interest. PCFs consist of microscopic holes running parallel to the fiber axis and down the entire length of the fiber. Exploitation of new applications of such new fibers is the goal of many theoretical and experimental investigations [8–9]. Several groups have reported their studies on dual-core photonic crystal fibers. Fogli et al. analyzed dual-core photonic crystal fiber couplers with full vectorial beam propagation methods [10]. The properties of dual-core photonic crystal fibers were experimentally characterized by Mangan et al. [11]. Directional coupling in a twin core photonic crystal fiber were realized by Kakarantzas et al. by using heat treatment [12]. Blanchard et al. demonstrated a two-dimensional bend sensor with a single photonic crystal fiber [13]. The main advantage of photonic crystal fibers over their counterparts is that they are much easier to make into multiple cores and/or more complex structures [14].

In this letter we report a new directional-coupler polarization splitter based on highly birefringent dual-core photonic crystal fibers. High birefringence is realized by adjusting the size of the air holes around the two core regions, which gives rise to an enlarged difference in the coupling lengths for the two polarization modes. Capitalizing on the sharp contrast between indices of air and silica, we obtain a 1.7-mm-long splitter with the splitting ratio better than -11 dB and a bandwidth of 40 nm. The relationship between the length of the polarization splitter and the diameter of the air hole in the middle of the two cores is demonstrated.

2. Theory and numerical results

Many efficient models have already been developed to describe the propagation of lightwave guided in the photonic crystal fibers, such as modal field expansion method [15, 16], multipole method [17], beam propagation method [10, 18] and so on. Here we employ the full vectorial BPM proposed by Fogli et al. in Ref. [10] for modeling the light coupling propagation in the polarization splitters, and the coupling lengths of the devices can be intuitively displayed. The algorithm, in which the perfectly matched layers (PML) boundary conditions are adopted, is available for fibers of any transverse geometry. The accuracy and validation have been demonstrated in Ref. [10].

Figure 1 shows the transverse structure of the proposed polarization splitter. The centers of all air holes are anchored in a hexagonal lattice with the lattice spacing Λ of 2 µm. The two identical cores, A and B, are formed by combination of the large and small air holes. The diameters of large and small air holes in the central region are D_l=2.4 µm and D_s=0.6 µm respectively, and the diameter of others is 1 µm. Correspondingly, the relative sizes of these holes (D/Λ) are 1.2, 0.3, and 0.5. The cores are two-fold symmetry instead of the rotation symmetry in single core photonic crystal fibers, which makes the cores birefringent. The separation between the centers of A and B is 4 µm. A transverse window of 18 µm×18 µm is used in the simulations, in which a 1 µm thick PML boundary is set. The mesh with a spatial sampling step Δx=Δy=Δz=0.1 µm for the computation region is created.

 

Fig. 1. Structure of the photonic crystal fiber with high-birefringence cores.

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45-degree linearly polarized light with standard Gaussian distribution is launched into the A core. The input field is 45° linearly polarized with respect to the horizontal axis. The incident wavelength is 1.55 µm. Figure 2 shows the input field profile in the core A.

Figure 3 illustrates the normalized power transfer along the fiber length. It is found that the x- and y-polarized lights have different coupling lengths. The coupling lengths are 0.571 mm and 0.857 mm for the x- and y-polarized lights, respectively. The two polarizations are separated from each other at the propagation length of 1.715 mm. Simulation indicates that the splitting ratios are -12.32 dB and -11.31 dB for the x- and y-polarized lights, respectively. Due to the high birefringence, the polarization splitter based on photonic crystal fibers has a much shorter length than their counterparts. For instance, the polarization splitter with ion-exchanged glass waveguide has a length of 22.5 mm reported in Ref. [5]. We note that the curves of the power transfer versus the fiber length are not smooth, which was also observed by Miliou et al. [5].

 

Fig. 2. Input field with Gaussian distribution.

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Figure 4 shows the output field profiles. The length of the polarization splitter is 1.715 mm. The x- and y-polarization fields are decoupled from each other. The x-polarization field is in the core A, while the y-component goes into the core B.

 

Fig. 3. The normalized power transfers for x- and y-polarized light versus the length of fiber.

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Figure 5 presents the wavelength dependence of the normalized output power from port A at a fixed length of the polarization splitter. The power exchange between the two cores is periodic with input wavelength. The power exchange is similar to the case of the conversional identical directional coupler. The bandwidth of -10 dB splitting ratio is almost 40 nm, i.e., from 1525 nm to 1565 nm.

 

Fig. 4. The field distributions for x- and y-polarized lights after a propagation of 1.715 mm.

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3. Discussion

Figure 6 shows the splitting ratio and the length of the polarization splitter as functions of the size of the air hole in the middle of the two cores. When the central air-hole diameter decreases, the birefringence of each core and, hence, the difference between the coupling lengths for the x- and y-polarized lights decreases. This leads to a longer splitter length. On the other hand, decreasing the central air hole diameter enhances the light coupling between the two cores, which leads to shorter length of the splitter. The length of the polarization splitter can be optimized through adjusting the size of the central air hole.

 

Fig. 5 The normalized power transfers for x- and y-polarized light versus the light wavelength.

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We note that there are bumps on uneven curves of the power exchange in Fig. 3. These bumps might arise from the relatively strong coupling between the two cores. For the PCF structure shown in Fig. 1, it is observed that obvious streams of energy pass through the upper and lower silica bridges, joining the two cores in the process of energy coupling. On the contrary, while the light coupling is weakened and other parameters are retained, the power transfer curves could be smoother.

 

Fig. 6. The splitting ratio and the splitter length as a function of the relative size of the central air hole.

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In order to smooth the power transfer curves we intentionally increase the size of the upper and lower six holes. Meanwhile we decrease the size of the hole between the two cores. The diameter of the six air holes is increased to 1.4 µm and the diameter of the hole between the two cores is 2.2 µm. Other parameters are unchanged. 45-degree linearly polarized light with wavelength of 1.55 µm is launched into the A core. The normalized power transfer curves are plotted in Fig. 7. It is obvious that the curves of the power transfer are much smoother.

 

Fig. 7. The normalized power transfers for x- and y-polarized light versus the length of fiber.

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Moreover, higher splitting ratio can be obtained for the PCF. The splitting ratios are 16.75 dB and 16.44 dB for x- and y-polarized modes, respectively. The splitter length is enlarged to 3.28 mm. It is found that the outflow of light from the core regions, especially for y-polarized light, is diminished due to the smaller size of the hole between the two cores than that of the PCF structure in Fig. 1.

We note that the coupling efficiency is different for x- and y-polarized lights in Fig. 5, and the difference might result from fact that the narrow silica bridges have different effect on coupling intensity of two polarization modes.

4. Conclusion

We have proposed a new kind of polarization splitter based on dual-core photonic crystal fibers. The polarization splitter has a symmetric directional coupler configuration. Each core has only two-fold symmetry, making the structure highly birefringent. Significant difference of coupling lengths for the x- and y-polarized light ensures a split of the two orthogonal polarizations in a relatively short length of the splitter. The polarization splitter proposed has a splitting ratio better than -11 dB and a bandwidth of 40 nm. The length of this component is 1.715 mm. The splitting ratio can be improved by optimizing the parameters of the photonic crystal fibers. Two splitter structures are comparatively investigated to examine the coupling properties of the new kind of dual-core photonic crystal fibers.