A polarization splitter based on a new type of dual-core photonic crystal fiber (DC-PCF) is proposed. The effects of geometrical parameters of the DC-PCF on performances of the polarization splitter are investigated by finite element method (FEM). The numerical results demonstrate that the polarization splitter possesses ultra-short length of 119.1 μm and high extinction ratio of 118.7 dB at the wavelength of 1.55 μm. Moreover, an extinction ratio greater than 20 dB is achieved over a broad bandwidth of 249 nm, i.e., from 1417 nm to 1666 nm, covering the S, C and L communication bands.
© 2014 Optical Society of America
Polarization splitter, a device that can split one light beam into two orthogonal polarization states, is widely used in optical communication systems, and it has been fabricated by conventional fibers [1–3]. However, one major disadvantage of polarization splitters based on conventional fibers is their long length. For example, the length of polarization splitters reported in Refs.  and  is 262 mm and 25 mm, respectively. With the development of modern optical communication systems toward large capacity and integration, more compacted polarization splitters are desired.
In recent years, photonic crystal fibers (PCFs) have attracted great research attentions due to their unique advantages of controlling light, such as endlessly single-mode [4,5], high nonlinearity , large birefringence [7–10] and anomalous dispersion [11–14], etc. Therefore, they provide a new way to design polarization splitters. Compared to conventional fiber-based splitters, the PCFs-based polarization splitters can achieve high extinction ratio, short length and broad bandwidth. In order to reduce the length of polarization splitters, several polarization splitters based on PCFs have been reported in literatures. Florous  proposed a 15.4 mm-long polarization splitter based on a DC-PCF with elliptic air holes that distribute uniformly in the cladding. Saitoh  obtained a 1.9 mm-long polarization splitter with a extinction ratio better than −20 dB and a bandwidth of 37 nm. Zhang [17,18] proved that polarization dependent coupling can be enhanced by introducing high birefringence, and designed a 1.7 mm-long DC-PCF polarization splitter with a bandwidth of 40 nm. Liu  designed a 0.36 mm-long polarization splitter based on a tellurite glass DC-PCF, but its bandwidth is just 20 nm. Although these splitters possess short lengths, their operating band is narrow. Broadband polarization splitters are also studied at the same time. Zhang [20, 21] proposed a 0.63 mm-long polarization splitter based on a coupled elliptical-hole core circular-hole holey fibers, and its bandwidth is 160nm. Rosa  obtained a 20 mm-long polarization splitter with a 90 nm-bandwidth by using a square-lattice photonic crystal fiber, and Chen  proposed a 5.9 mm-long polarization splitter which has a bandwidth of 101 nm. Li  proposed a 4.72 mm-long splitter with a bandwidth of 190 nm, and Lu  designed a 72 mm-long splitter with a bandwidth of 400 nm. As we can see above, to some extent, short length and broad bandwidth have not been realized simultaneously. An ultra-short length, high extinction ratio and broad-bandwidth polarization splitter based on a new type of DC-PCF is proposed in this work. It has great potential applications in the development of large-capacity and integrated optical communication systems.
2. Model and theory
The cross section of proposed DC-PCF is shown in Fig. 1. Air holes located in the three middle horizontal rows are arrayed in rectangular lattice with horizontal pitch Λ1 and vertical pitch Λ2, and the other circular air holes arrange in a hexagonal array with lattice constant Λ1. The diameter d of the circular air holes is 1 μm. The elliptic air hole E1 is located in the geometric center. The ellipticties of E1 and E2 are defined as η1 = d1/d and η2 = d2/d, respectively, and the pitch between E1 and E2 is 2Λ1. Besides, the core A and core B are formed by E1, E2 and the circular air holes around them. The background refractive index can be obtained from the Sellmeier formula .
According to the coupled-mode theory, the mode field of a DC-PCF can be regarded as the superimposition of an even mode and an odd mode. The coupling length (CL) , which is defined as length of the fiber over that a complete power transfer between core A and core B occurs, is given by28]Eq. (1). Further, the normalized powers (NP) are as follows:
3. Results and discussions
In order to obtain a short-length and high-performance polarization splitter at some wavelength of interest, the optimal CLR value should be found by adjusting the parameters of the DC-PCF. Through the analysis above, there are four geometrical parameters, i.e., η1, η2, Λ1 and Λ2. In this research, the values of CL and CLR are calculated accurately by finite element method, and a DC-PCF with optimal geometrical parameters is obtained. Finally, a polarization splitter based on the DC-PCF is proposed.
The values of CL and CLR can be calculated from Eqs. (1) and (2). At λ = 1.55μm, the influences of geometrical parameters on CL and CLR are depicted in Fig. 2. Figure 2(a) demonstrates that Ly increases with η1, while Lx stays almost unchanged, that is, η1 has a relatively bigger influence on Ly than on Lx. On the other hand Ly and Lx decrease slowly as η2 increases, as illustrated in Fig. 2(b), i.e., the coupling strength is enhanced. Besides, Fig. 2(a) and Fig. 2(b) also depict that CLR increases with η1 and η2. The increasing rate caused by η1 is larger than that caused by η2. Because Ly and Lx increase with Λ1, as shown in Fig. 2(c), the coupling strength is weakened as Λ1 increases, but it is strengthened as Λ2 increases, as shown in Fig. 2(d). It is clearly seen from Fig. 2(c) and Fig. 2(d) that the CLR has a similar tendency.
The proposed structure enhances the birefringence of the DC-PCF, and results in a high difference between Ly and Lx. Most importantly, it can be seen from the four figures that Lx is always less than Ly in the proposed DC-PCF, and the value of CLR is very close to 2, so it is feasible to design a high-performance polarization splitter by use of the proposed DC-PCF.
Based on the above discussions, Lx is always less than Ly, and the value of CLR is very close to 2 under the geometrical parameters discussed above, therefore, we can get the optimal CLR value by appropriately setting the geometrical parameters of DC-PCF. Through an accurate analysis of Fig. 2, the optimal geometrical parameters are η1 = 1.4, η2 = 1.7, Λ1 = 1.1 μm and Λ2 = 1.7 μm. Figure 3(a) shows the variation of coupling lengths and the confinement losses of different polarizations under the conditions of optimal geometrical parameters. It is obvious that the coupling length decreases as wavelength increases. Numerical results demonstrate that Ly = 118.89 μm, Lx = 59.59 μm and CLR = Ly/Lx = 1.9949 at the wavelength of 1.55 μm. Because the proposed DC-PCF has a leaky core structure in the horizontal direction, the confinement loss of horizontal direction is larger than that of vertical direction. However, the confinement losses can be neglected due to the short coupling lengths. Figure 3(b) shows the field profiles of the first odd mode and the first even mode of two different polarizations. When light of a given polarization is incident upon one of the core (core A, for example), it excites both the odd and the even modes of that polarization. The two modes adds up in core A and cancels out completely in the other core, so that produces a confinement of energy in core A. Because propagation constants of the odd mode and the even mode are different, the relative phase between the two modes changes in propagation. This results in an incomplete cancellation of modal field in core B, corresponds to energy switch between the two cores. The alternative but equivalent view of this is that the incident wave upon core A excites the fundamental mode of this individual core, which is mainly confined in the core area for its modal field. Because of the coupling between the two cores, power transfers between core A and core B.
The propagation constants of odd and even mode for different polarization states are different, that is Lx ≠Ly, so the periodic output power which can be obtained from Eq. (3) is different. Assuming that the incident light port is core A at λ = 1.55 μm, the variations of normalized power with propagation distance can be obtained from Eq. (4), as shown in Fig. 4(a). Obviously, after a propagation distance of 119.1μm, the output power of X-polarization reach its peak but the Y-polarization power is almost zero, that is, they are separated from each other at the length of 119.1 μm.
As a function of wavelength, extinction ratio (ER) is an important technical parameter for polarization splitter. The two orthogonal polarization states of the incident light are regarded to be separated when the extinction ratio is greater than 20 dB, so ER determines the available bandwidth of a polarization splitter. Assuming that the incident light port is core A, the ER in core A is defined as 
Figure 4(b) illustrates the variation of ER with the wavelength when the propagation length is 119.1 μm. The polarization splitter possesses extremely high extinction ratio of 118.7dB at the wavelength of 1.55μm. Besides, for extinction ratio of greater than 20 dB, bandwidth of the splitter is 249 nm, i.e., from 1417nm to 1666nm, covering all the S, C and L bands.
Finally, in order to obtain the proposed high-performance polarization splitter, it is very important to be able to fabricate the DC-PCF proposed in this work. By now, PCFs with different structures have been fabricated by stack-and-draw technique [29, 30], die-cast process , performs drilling method , and sol-gel casting method , etc. Therefore, with the development of relevant techniques, it is feasible to fabricate the proposed DC-PCF.
To summarize, a novel high-performance polarization splitter based on a dual-core photonic crystal fiber is proposed, and its performance is numerically investigated by finite element method. Under the optimal condition of η1 = 1.4, η2 = 1.7, Λ1 = 1.1μm and Λ2 = 1.7μm, an ultra-short length, high extinction ratio and broad bandwidth is achieved for the polarization splitter. Because of its excellent performance, we believe that this type of polarization splitter could be widely useful in the development of large-capacity, broad-bandwidth and integrated optical communication systems.
This work was supported by the National Natural Science Foundation of China (Grant No. 60607005, 60877033 and 60588502).
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