A compact and low-loss polarization splitter based on dual-core photonic crystal fiber

Abstract

The characteristics of a novel dual-core photonic crystal fiber are investigated. In the center of photonic crystal fiber, an energy transmission channel is introduced. The optimized photonic crystal fiber can be used for polarization splitter, which has a short length and low loss.

1 Introduction

When the light is transmitted in a single-mode fiber, there are two mutually perpendicular intrinsic polarization modes in the fiber. Due to the elliptical deformation of the core and the residual internal stress, the fiber always exhibits birefringence in practice. As a result, the two polarization states of the fundamental mode are no longer degenerate, and they propagate at different velocities. It may lead to the pulse broadening and signal distortion, which limits the transmission bandwidth of the system. A polarization device could be used to avoid the aforementioned problems. Although the polarization devices based on the traditional optical fiber have been applied in practical for a long time (Miliou et al. 1993; Wu et al. 1995; Peng et al. 1990), they have some defects such as long length and narrow working bandwidth. Since optical fiber communications evolve toward the large capacity and integration, more compacted polarization devices are desired.

In recent years, new photonic crystal fiber (PCF) has been used in the polarization devices, and many excellent products have sprung up. On one hand, the structure of PCF is flexible and adjustable, such as the diameters, pitch and arrangement of the air holes, the size and shape of the core area (Fan et al. 2014; Liu et al. 2015; Wu et al. 2013; Li and Zhou 2016; Yogalakshmi et al. 2016). By adjusting the diameter of dual-core tellurite glass photonic crystal fiber, Fan et al. (2014) obtained a polarization beam splitter with high extinction ratios at the wavelengths of 1.33 and 1.55 $\upmu \hbox {m}$. Liu et al. (2015) proposed a polarization splitter based on square-lattice ZnTe glass PCF, with the fiber length of 1.1452 mm. On the other hand, by selectively filling or coating metal in the holes of PCF, the plasma wave is only stimulated by a certain polarization state, which is an ideal attribute that can be used in the polarizing filters and splitters (Li and Zhao 2013; Nagasaki et al. 2011; Khaleque and Hattori 2015; Schmidt et al. 2008). Nagasaki et al. (2011) investigated the effect of the filling position of the metal wires on the polarization characteristics. Khaleque and Hattori (2015) proposed a polarizer based on a squeezed rectangular lattice PCF coating with the gold layer, of which the modal losses for the x-polarized mode and y-polarized mode are 1221 and 1.6 dB/cm. However, the output power and the loss of PCF polarizers are rarely reported.

In this paper, we present a novel polarization splitter based on dual-core photonic crystal fiber. The finite element method (FEM) is utilized to investigate the polarization-dependent coupling in dual-core PCF. By changing the diameters and pitch of the air holes, we get the optimum coupling lengths of x- and y-polarization state for the 1.55 $\upmu \hbox {m}$ polarization splitter. The performance of the polarization splitter is evaluated.

2 Basic theory and original structure

The cross section of the PCF we proposed is shown in Fig. 1. The background material of the fiber is pure silica, whose dispersion relationship is calculated by the Sellmeier equation (Geng et al. 2012). The air holes consist of two kinds of circular holes and two elliptic holes, which are arranged in a rectangular lattice. The diameter of the big circular holes is denoted by $d_{1}$, and the spacing between big circular holes is denoted by $\varLambda _{1}$. The diameter of the small circular holes is denoted by $d_{2}$, and the spacing between the adjacent big and small circular holes is denoted by $\varLambda _{2}$. The long axis of two elliptic holes is denoted by a, and the short axis is denoted by b. Two circular holes in x-direction are taken out to form core A and core B. The original parameters of PCF are: $d_{1}=2\,\upmu \hbox {m}$, $d_{2}=1\,\upmu \hbox {m}$, $\varLambda _{1}=2.5\,\upmu \hbox {m}$, $\varLambda _{2}=2\,\upmu \hbox {m}$, ${\varvec{{a}}}=2\,\upmu \hbox {m}$, ${\varvec{{b}}}=1\,\upmu \hbox {m}$.

Fig. 1

Cross section of the designed polarization splitter

PCFs used for polarization splitter always have high birefringence, the coupling lengths of x- and y-polarized state are defined as (Florous et al. 2005)

$$\begin{aligned} {L_{x,y}} = \frac{\lambda }{2\left( n_{even}^{x,y} - n_{odd}^{x,y}\right) } \end{aligned}$$

(1)

where $\lambda$ is the wavelength in free space.

Assumed that the input power is pumped into core A, the output power of x- and y-polarized state in core A can be calculated as (Florous et al. 2005)

$$\begin{aligned} P_{out}^{x,y} = {P_{in}}{\cos ^2}\left( \frac{{\pi\,\cdot\,L}}{{2{L_{x,y}}}}\right) \end{aligned}$$

(2)

Similarly, the output power of x- and y-polarized state in core B can be calculated as (Florous et al. 2005)

$$\begin{aligned} P_{out}^{x,y} = {P_{in}}{\sin ^2}\left( \frac{{\pi \cdot L}}{{2{L_{x,y}}}}\right) \end{aligned}$$

(3)

L stands for the propagation distance.

When the values meet the condition of $L = m L_{x} = nL_y$, where m and n are positive integers and their parity are different, the two polarized states in the cores can be separated.

The crosstalk between different polarization states can be assessed by the extinction ratios (ER). $E{R_A}$ and $E{R_B}$ are defined as (Jiang et al. 2014)

$$\begin{aligned} E{R_A}= & {} 10{\log _{10}}\left( \frac{{P_A^y}}{{P_A^x}}\right) \end{aligned}$$

(4)

$$\begin{aligned} E{R_B}= & {} 10{\log _{10}}\left( \frac{{P_B^x}}{{P_B^y}}\right) \end{aligned}$$

(5)

where $P_A^x$ is the output power of x-polarized mode in core A, $P_A^y$ is the output power of y-polarized mode in core A; $P_B^x$ is the output power of x-polarized mode in core B, $P_B^y$ is the output power of y-polarized mode in core B.

When the extinction ratio is less than $-\,20$ dB, the output power ratio of two polarization modes is greater than 100, two polarization modes can be separated very well (Jiang et al. 2014).

3 Simulation process and numerical analysis

The simulation software is Comsol Multiphysics, and finite element method (FEM) is utilized to calculate the characteristics of PCF. Scattering boundary conditions are employed in the simulation process, and the thickness of perfect matched layer (PML) is set to be 3 $\upmu \hbox {m}$. Figure 2 shows the electrical field distribution of fundamental modes in x- and y-polarized direction, including two odd modes (Fig. 2a, c) and two even modes (Fig. 2b, d). Core A and core B are separated by two elliptical holes in the center of PCF. Due to the short axes of two elliptic holes are located in the y-direction, a channel is formed in the area between two elliptic holes for energy transmission. Compared to Fig. 2d, the energy in Fig. 2b is more easily transferred between two core areas.

Fig. 2

Electrical field distributions at the wavelength of 1.55 $\upmu \hbox {m}$ for a x-odd mode, b x-even mode, c y-odd mode, d y-even mode

Figure 3 shows the effective refractive indexes of four polarization modes, the descending order is x-even mode, y-even mode, y-odd mode and x-odd mode. Due to the structure asymmetry of the PCF, the refractive index difference between x-odd mode and x-even mode is significantly bigger than that between y-odd mode and y-even mode.

Fig. 3

Effective refractive indexes of four polarization modes vary with wavelength

3.1 Structure optimization

Figure 4 depicts the effect of hole spacing on the coupling lengths. $L_{x}$ and $L_{y}$ are the coupling lengths of x- and y-polarization mode at the wavelength of 1.55 $\upmu \hbox {m}$. When the spacing (denoted by $\varLambda _{1}$) between large circular holes changes to 2.2, 2.3, 2.4, 2.5 $\upmu \hbox {m}$, the spacing (denoted by $\varLambda _{2}$) between the adjacent large and small circular holes changes to 1.7, 1.8, 1.9, 2.0 $\upmu \hbox {m}$, correspondingly. As increasing $\varLambda _{1}$ and $\varLambda _{2}$, the mode fields of core A and core B expand and the energy becomes divergent. This change increases the difficulty of the mode coupling and leads to the increase of $L_{x}$ and $L_{y}$. In order to obtain smaller coupling lengths, we reduce the values of $\varLambda _{1}$ and $\varLambda _{2}$: $\varLambda _{1}=2.2\,\upmu \hbox {m}$ and $\varLambda _{2}= 1.7\,\upmu \hbox {m}$.

Fig. 4

Coupling lengths vary with the spacing between big circular holes

Fig. 5

Coupling lengths vary with the diameter of small circular holes

For the purpose of improving the birefringence of PCF, we introduce two columns of small circular holes on both sides of the elliptical holes. The diameter of small circular holes (denoted by $d_{2}$) is changed to 0.4, 0.6, 0.8, 1.0, 1.2, 1.4 $\upmu \hbox {m}$, in turn. Figure 5 shows when $d_{2}$ is 0.4 $\upmu \hbox {m}$, $L_{x}$ is 50 $\upmu \hbox {m}$ and $L_{y}$ is 99 $\upmu \hbox {m}$; when $d_{2}$ is 1.4 $\upmu \hbox {m}$, $L_{x}$ is 332 $\upmu \hbox {m}$ and $L_{y}$ is 627 $\upmu \hbox {m}$. $L_{x}$ and $L_{y}$ obviously increase as $d_{2}$ increasing. This is because the mode field is enlarged in the x-direction, which increases the difficulty of energy transmission between core A and B. So we optimize the value of $d_{2}$ to 0.4 $\upmu \hbox {m}$.

Fig. 6

Coupling length varies with the short axis length of the elliptic holes

Figure 6 shows the coupling lengths vary with the short axis length of the elliptic holes (denoted by b). When b increase, the channel between core A and B becomes narrow. It increases the difficulty of the energy transfer between two cores. Thus $L_{x}$ and $L_{y}$ increase as b increasing. However, we can not blindly reduce b. The ratio of the coupling lengths should be taken into account at the same time. When b is 1.02 $\upmu \hbox {m}$, $L_{x}$ is 51.6 $\upmu \hbox {m}$ and $L_{y}$ is 103.1 $\upmu \hbox {m}$, the ratio is 1.998. The ratio is very close to the integer value of 2. So the optimized value of b is 1.02 $\upmu \hbox {m}$.

In summary, the optimized parameters of PCF are as follows: $d_{1}=2\,\upmu \hbox {m}$, $d_{2}=0.4\,\upmu \hbox {m}$, $\varLambda _{1} = 2.2\,\upmu \hbox {m}$, $\varLambda _{2} = 1.4\,\upmu \hbox {m}$, ${\varvec{{a}}}=2\,\upmu \hbox {m}$, ${\varvec{{b}}}=1.02\,\upmu \hbox {m}$.

3.2 Splitting distance and extinction ratio

Assumed that the normalized power pumped into core A is 1, while the normalized power pumped into core B is 0. The length of the polarization splitter is set to 103 $\upmu \hbox {m}$ ($L = {L_y} = 2{L_x}$), which is an important parameter of polarization splitter. Figure 7a shows that the normalized power in core A depends on the propagation distance, and the curves follow the law of cosine function. When the propagation distance is 103 $\upmu \hbox {m}$, $P_{x}$ is 0.99991 and $P_{y}$ is 0.00006. $P_{x}$ and $P_{y}$ differ by four orders of magnitude. $P_{y}$ is so small that it is negligible. In core A, the output light has only x-polarized mode. Figure 7b shows that the normalized power in core B depends on the propagation distance, and the curves follow the law of sine function. When the propagation distance is 103 $\upmu \hbox {m}$, $P_{x}$ is 0.00009 and $P_{y}$ is 0.99994. In core B, the output light has only y-polarized mode. By the polarization splitter, the output light is separated into x-polarized light in core A and y-polarized light in core B.

Fig. 7

Normalized output power varies with the propagation distance, a in core A, b in core B

Fig. 8

Normalized output power varies with wavelength a in core A, b in core B

Figures 4, 5, 6 and 7 show the simulation results when the wavelength of incident light is 1.55 $\upmu \hbox {m}$. When the incident wavelength changes, $L_{x}$ and $L_{y}$ vary with the wavelength, resulting in the variations of $P_{x}$ and $P_{y}$. Figure 8 shows the changes in $P_{x}$ and $P_{y}$ with wavelength.

Fig. 9

Extinction ratio varies with wavelength a in core A, b in core B

The performance of the polarization splitter can be assessed by the extinction ratio (ER). The extinction ratio in core A is denoted by $E{R_A}$ and the extinction ratio in core B is denoted by $E{R_B}$. Figure 9 shows $E{R_A}$ and $E{R_B}$ vary with wavelength. $E{R_A}$ is less than $-\,20$ dB within the range of 1.458–1.635 $\upmu \hbox {m}$. The minimum value of $E{R_A}$ is $-\,73$ dB, which appears at 1.55 $\upmu \hbox {m}$. $E{R_B}$ is less than $-\,20$ dB within the range of 1.508–1.587 $\upmu \hbox {m}$. The minimum value of $E{R_B}$ appears at 1.53 $\upmu \hbox {m}$. At the wavelength of 1.55 $\upmu \hbox {m}$, $E{R_B}$ is $-\,45$ dB.

3.3 Insertion loss

When designing an optical communication device, the insertion loss (IL) is also a parameter must be considered. IL is defined as (Khaleque and Hattori 2015)

$$\begin{aligned} IL = -10{\log _{10}}\left( \frac{{{P_{out}}}}{{{P_{\mathrm{{in}}}}}}\right) \end{aligned}$$

(6)

Fig. 10

Insertion loss varies with wavelength

Figure 10 shows that the insertion loss of x-polarized mode in core A (denoted by $IL_{x}$) is larger than the insertion loss of y-polarized mode in core B (denoted by $IL_{y}$). In the working bandwidth (1.508–1.587 $\upmu \hbox {m}$), the maximum value of $IL_{x}$ is 0.043 dB, the maximum value of $IL_{y}$ is 0.009 dB. At 1.55 $\upmu \hbox {m}$, $IL_{x}$ is 0.00013 dB, $IL_{y}$ is $2 \times 10^{-7}$ dB.

The parameters comparing with other polarization splitters are shown in Table 1. In Refs. Fan et al. (2015), Khaleque et al. (2015), the addition of gold in PCF excites surface plasmon resonance (SPR). Adding gold to the PCF can reduce the coupling length of the two polarization modes and shorten the split distance, but at the same time it also increase the insertion loss of the polarization beam splitter. The reason is part of the light field energy transfers to the metal surface, and dissipates through the heat generation. Compared to Fan et al. (2015), Khaleque et al. (2015), not only does our splitter have a short length, but also ultra-low insertion loss. In Ref. Liu et al. (2017), Younis et al. (2018), PCFs are selectively filled by tellurite glass and NLC material. Compared to Liu et al. (2017), Younis et al. (2018), our splitter has a shorter length, better extinction ratio and smaller insertion loss.

Table 1 Comparison of the parameters of DC-PCF polarization splitters.

4 Conclusions

In this paper, a novel polarization splitter based on dual-core photonic crystal fiber is investigated. By introducing a channel for energy transmission, the polarization splitter has a short length of only 103 $\upmu \hbox {m}$. At the wavelength of 1.55 $\upmu \hbox {m}$, the extinction ratios of core A and core B reach 73 and 45 dB, and the bandwidth with extinction ratio less than $-\,20$ dB are 177 and 79 nm. Moreover, the insertion loss of x-polarization mode is 0.00013 dB and the insertion loss of y-polarization mode is $2 \times 10^{-7}$ dB.