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Abstract
We reported on a polarization beam splitter based on a novel chalcogenide dual-core photonic crystal fiber. The glass matrix of the optical fiber is Ge10As22Se68. We used computerized numerical control precision drilling methods to manufacture preforms. Then the preform was drawn into an optical fiber with a regular hole structure. The maximum extinction ratio reached -32.76 dB with a 26.27 mm-long optical fiber. Numerical results show that the shortest working length of the designed polarization beam splitter is 636 µm. In addition, the modeling analysis based on the actual structure shows that the theoretical value is consistent with the measured value.
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1. Introduction
Polarization beam splitter can split the incident light into two orthogonally polarized lights. It has essential applications in coherent receivers and ultra-density chips [1] and is an important part of integrated photonics. The polarization beam splitter based on the fiber structure has received extensive attention due to its high integration and low-cost advantages. However, the polarization beam splitter designed with traditional optical fiber as the carrier has greater limitations. The major disadvantage is their long length. In [2] and [3], the working length of the beam splitter is 262 mm and 25 mm, respectively. They have difficulty meeting the requirements of integration and high capacity in modern communication systems. Photonic crystal fiber (PCF) is composed of periodic holes distributed along the axial direction, and its characteristics can be adjusted by changing the parameters of the holes. The flexible structure of PCF makes it have the advantages of high nonlinearity, endless single-mode transmission, controllable mode field area, high birefringence, etc. [4–10], so it can be used as an excellent carrier for polarization beam splitters.
In recent years, PCF polarization beam splitters based on different structures have been reported. Among them, polarization beam splitter designed based on silica glass material has been studied mostly. Mao et al. proposed an all-solid PCF with local asymmetry in the dual-core region. Based on the mode interference effect, a 6.8 mm-long polarization beam splitter was achieved [11]. Lu et al. proposed an improved three-core photonic crystal fiber with central microstructure cores. By adjusting the parameters of the central core, a wide-bandwidth polarization beam splitter with the extinction ratio reaching -30 dB at 1.55 µm was realized [12]. The polarization beam splitter designed by Zi et al. has a simple structure with only three layers of air holes. It has a short length of 249 µm, and the bandwidth as the extinction ratio better than 20 dB was about 17 nm [13]. Fan et al. placed Au/Ag nanowires in a PCF, and the resulting surface plasmon resonance effect enhanced the coupling between modes. Based on this structure, the working length of the polarization beam splitter at 1.55 µm is 809 µm, and the bandwidth with an extinction ratio greater than -20 dB is 104 nm [14].
Soft glass, especially chalcogenide glass, has excellent characteristics such as large nonlinearity and infrared transmission. However, the difficulty of preparing PCF limits the research on polarization beam splitters, and the current research is mainly focused on theoretical calculations. Liu et al. found that the performance of the three-core PCF based on ZnTe tellurite glass is better than that of the silica glass. Then, an 8.7983 mm-long beam splitter is realized with an extinction ratio better than -20 dB and a bandwidth of 20 nm [15]. In addition, they also reported a polarization beam splitter based on tellurite glass dual-core photonic crystal fiber. The splitter has a length of 0.36 mm and an extinction ratio of -31 dB [16].
Elliptical holes were usually selected in the above-mentioned polarization beam splitter to break the whole or part of the circular symmetry to improve the polarization performance. However, the coexistence of elliptical holes [17] and circular holes is challenging in PCF manufacturing. The stacking method is the most common method for preparing PCF preform, but it often has minor defects that affect the transmission of light [18]. The PCF preform prepared by traditional mechanical drilling methods [19,20] has the problem of inaccurate hole positioning. We combined the drilling method with computerized numerical control procedures to prepare PCF preforms with perfect hole positions and complex structures.
In matrix selection, the high refractive index [21] of chalcogenide glass enables it to achieve ultra-high nonlinearity with a relatively short length. In addition, chalcogenide glass has a lower glass transition temperature than other materials, which is beneficial to PCF manufacture. By optimizing structural parameters and careful experimentation, we successfully prepared the chalcogenide dual-core PCF with short length and high extinction ratio for the first time, which has potential application value in all-optical communications and other fields.
2. Model and theory
The cross section of the proposed dual-core PCF is shown in Fig. 1. We propose a hole similar to “pea” to replace the elliptical air hole. This unique shape of holes is formed by overlapping three circular holes with radius r3. The cladding holes consist of two holes with radii r1 and r2 arranged in a hexagonal period. The distance between two adjacent cladding holes is Λ. Remove the two holes on the periodic structure to form core A and core B. The substrate material is Ge10As22Se68, and the refractive index is fit through the Sellmeier equation [22]:
High birefringence is an important indicator for evaluating the performance of a polarization beam splitter. Birefringence can be expressed as [23]:
where $n_{eff}^x$ and $n_{eff}^y$ represent the effective refractive index of the fundamental mode of X and Y polarization, respectively.According to the mode coupling theory, the mode field of dual-core PCF can be regarded as the superposition of even mode and odd mode [24]. When light enters from one core of the dual-core fiber, it will simultaneously excite two super modes. The coupling lengths (CL) of the x- and y-polarized state are expressed as Lx and Ly:
Generally, the complete power transfer of X and Y polarization occurs at different lengths. That is, Lx and Ly are not equal. The beam splitter length L approximately satisfies $L = m{L_x} = n{L_y}$ (m and n are positive integers, and the parity is opposite). In that case, it is considered that the two orthogonal polarization components are completely separated. The coupling length ratio (CLR) is defined as:
Another critical parameter to evaluate the performance of a polarization beam splitter is the extinction ratio (ER). The greater the absolute value of the extinction ratio, the better the performance of the polarization beam splitter.
If the input power is ${P_{in }}$, then the output power $P_{out }^i$ of the X and Y polarization states can be defined as [25]:
where L represents the fiber length.The normalized powers (NP) are expressed as:
When the absolute value of the extinction ratio is greater than 20 dB, the x- and y-polarized lights are considered to be separated so that the bandwidth of the polarization beam splitter can be determined. The extinction ratio can be expressed by the following formula [26]:
3. Experiments
3.1 Preparation of glass and preform
The Ge10As22Se68 glass rod was prepared by the conventional melt-quenching method. 150 g of high-purity elemental raw materials (Ge, As, and Se with a purity of 6 N) were weighed and placed in a quartz ampoule with a diameter of 26 mm. The ampoule was evacuated to 10−5 Pa and sealed. The rocking furnace was gradually increased from room temperature to 700°C at a heating rate of 1°C/min. The melt was rocked for 11 h at this temperature to be homogenized. Then the temperature was cooled to 500°C within 1 h and quenched quickly in water. The prepared glass rod was annealed at 20°C below the glass transition temperature for 6 h to remove internal stress. The dual-core PCF preform was prepared by a computerized numerical control (CNC) precision machine tool. The control accuracy of the equipment can reach 10 µm. Therefore, we can accurately locate the position of the hole, that is, control the hole pitch Λ.
3.2 Drawing and testing of the dual-core PCF
In the drawing process of the dual-core PCF, high-purity nitrogen (99.999%) was used to prevent oxidation of the preform and keep the holes from collapsing. A miniature gas flow meter (Vogtlin Instruments, Switzerland) was used to precisely control nitrogen pressure. The cross section of the optical fiber was observed by an optical microscope (Keyence, VHX-1000). The digital power meter (Thorlabs, PM100D) was used to measure the output energy of the dual-core PCF.
4. Results and discussion
4.1 Optimization of the fiber structure
The finite element method (FEM) [27,28] is adopted to optimize the parameters and performance of the dual-core PCF. The value of CLR needs to be 2 (Ly > Lx) or 1/2 (Lx > Ly) to obtain the optimum performance with the shortest length [28]. In this work, we optimized the structural parameters of the dual-core PCF to obtain the appropriate CL and CLR at the most commonly used communication wavelength of 1.55 µm. Due to the short length of the designed polarization beam splitter, the transmission loss can be neglected [29].
The designed dual-core PCF is composed of three different sizes of air holes. The effects of small air hole radius r1, big air hole radius r2, and central air hole radius r3 on the coupling length and the coupling ratio are shown in Figs. 2(a) – 2(c). In this part, the air hole pitch is set as 1.2 µm. The coupling length increases as the r1 and r3 values become larger. The energy transfer is achieved through the glass bridge between core A and B during the coupling process [30]. The increase of r1 and r3 will narrow the two channels. Transmission of the same energy requires a longer coupling length, which will weaken the coupling capability between the two cores. However, the increase of r2 will make the outer region of the core in the X direction more squeezed, and the mode field will be constrained toward the center of the fiber. In contrast, the glass bridge transmits more energy and shortens the coupling length. As a result, the values of r1, r2, and r3 are optimized to 0.25 µm, 0.5 µm, and 0.25 µm, respectively. Moreover, the CLR is very close to the desired optimum value of 2.
Fig. 2. At the wavelength of 1.55 µm. (a) The effect of r1 on CL and CLR with the parameters of Λ = 1.2 µm, r2 = 0.5 µm, and r3 = 0.25 µm. (b) The effect of r2 on CL and CLR with the parameters of Λ = 1.2 µm, r1 = 0.25 µm, and r3 = 0.25 µm. (c) The effect of r3 on CL and CLR with the parameters of Λ = 1.2 µm, r1 = 0.25 µm, and r2 = 0.5 µm. (d) The effect of Λ on CL and CLR with the parameters of r1 = 0.25 µm, r2 = 0.5 µm, and r3 = 0.25 µm.
As shown in Fig. 2(d), increasing Λ can increase Lx and the decrease of Ly. When Λ is 1.2 µm, the CLR is very close to 2. When the hole spacing becomes larger, the duty ratio in the x-polarized direction will become smaller, and the coupling distance between core A and core B will increase. Ultimately, this situation will lead to the reduction of CLR.
By adjusting the structural parameters of the dual-core PCF, a short-length polarization beam splitter is obtained. In Fig. 3, the mode field distribution diagram at a wavelength of 1550 nm is plotted. The electric field directions of the two cores are the same in the even mode and opposite in the odd mode. Odd mode and even mode in the x- and y-polarized directions are both well limited to cores.
Fig. 3. The fundamental mode field distribution diagram of the proposed dual-core PCF. (a) Even mode of y-polarized mode. (b) Even mode of x-polarized mode. (c) Odd mode of x-polarized mode. (d) Odd mode of y-polarized mode.
Figure 4 shows the effect of wavelength on the coupling length of the x- and y-polarized states. As the wavelength increases, the value of Lx and Ly decreases. At 1.55 µm, the coupling lengths of the two polarization modes are Lx = 319.1 µm and Ly = 636.3 µm. In addition, birefringence increases with wavelength. High birefringence can increase the difference in coupling length between two orthogonal polarized states [31]. That is, it is easier to distinguish different polarization states. At 1550 nm, we obtained a high birefringence value of 1.6×10−3.
Fig. 4. Under the optimized structure parameter Λ = 1.2 µm, r1 = 0.25 µm, r2 = 0.5 µm, and r3 = 0.25 µm, coupling length and birefringence of the polarization splitter as function of wavelength.
4.2 Characteristics of the polarization splitter
Figure 5 shows the relationship between the normalized power changes of the x- and y-polarized modes and the propagation distance. The normalized power difference between X and Y polarization changes periodically with the propagation length. According to Eq. (4), when the propagation distance L = 636 µm = 2Lx = Ly, the two polarization modes are almost completely separated. L = 636 µm is the shortest length that satisfies the separation condition. Then the two polarization modes will be periodically separated. The period length is consistent with the minimum working length of the designed polarization beam splitter.
Fig. 5. The relationship between the normalized power of X and Y polarization with the propagation distance under the optimized structure parameter. The dashed line shows the minimum working length of 636 µm.
Figure 6 shows the relationship between the extinction ratio and the wavelength when the length of the polarization beam splitter is 636 µm. The result shows that at the wavelength of 1550 nm, the extinction ratio reaches -53.1 dB. When |ER| > 20 dB, the bandwidth reaches 60 nm from 1.52 µm to 1.58 µm.
Fig. 6. The extinction ratio of 636 µm-long polarization beam splitter with the optimized structure parameter near 1.55 µm wavelength.
The experimental device used to evaluate the capability of the splitter is shown in Fig. 7. The 1550 nm fiber laser passes through a collimator to form parallel light and then focuses the laser into one core of the two cores. Due to the coupling effect of the dual-core PCF, the output energy of x- and y-polarized light from one core of the fiber is changed with different fiber lengths. The minimum working length of designed dual-core PCF is 636 µm which exceeds our test capability. Therefore, the longer period length L = 26100 µm = 82Lx = 41Ly was chosen to measure the performance of the designed dual-core PCF. One core of the dual-core fiber that has been cut to a certain length was covered with opaque colloid under the microscope. The colloid does not transmit a 1550 nm laser. The cross section of the processed fiber is shown in the inset of Fig. 7. The optical fiber was tested by rotating the analyzer to record the maximum and minimum optical power on the experimental platform. Then the corresponding extinction ratio was calculated. Each fiber of different lengths was measured three times to reduce errors.
Fig. 7. Diagram of dual-core PCF polarization power measurement device. Insert: schematic diagram of the cross section of the optical fiber treated with opaque colloid so that light can only enter and exit from one core.
The cross section of the drawn fiber is shown in the insert of Fig. 8. By adjusting the amount of inflation, the best structure was obtained when the gas pressure was 15 mbar. Due to the uneven distribution of stress in the fiber structure during drawing, the circular hole in the cladding area has a slight deformation. The central hole is deformed due to the lack of adequate support between the overlapping circular holes and becomes an oval-like overlapping hole after being squeezed from both sides. From the previous theoretical results, this deformation is beneficial to improve the performance of the optical fiber. To be precise, the compression of the fiber structure in the x-polarized direction enhances the birefringence.
Fig. 8. The extinction ratio changes with the propagation distance. Black line: the theoretical value of the optimized structure; blue line: the theoretical value modeled according to the actual fiber structure. Insert: the cross section image of the fiber.
The cross section image of the fiber was established as a model, and the performance was calculated and then compared with the experimental data. The result of theoretical value and the actual extinction ratio is shown in Fig. 8. The maximum extinction ratio calculated according to the actual structure reaches -60.4 dB, larger than the optimized structure. We consider that this is related to the deformation of the circle hole during the fiber drawing process. In terms of the relationship between the extinction ratio and the propagation distance, the experimental data closely matches the theoretical results. When the propagation distance is 26.27 mm, the measured maximum extinction ratio is -32.76 dB. As shown in Fig. 8, the extinction ratio is greater than 20 dB in the fiber length range of 26.2 mm to 26.3 mm, and it provides wide fault tolerance for the interception of fiber length.
5. Conclusion
In summary, we presented a detailed study of a novel high-performance polarization beam splitter based on a chalcogenide dual-core PCF. The structure of PCF was designed and optimized by using the FEM, and the effects of structural parameters on the performance of dual-core coupling and beam splitter are analyzed. The dual-core PCF was successfully prepared by the CNC drilling and precision drawing process, and the measured maximum extinction ratio was -32.76 dB. In addition, the theoretical performance of the prepared optical fiber was analyzed by using the SEM image of the optical fiber. The theoretical results are consistent with the experimental results. Therefore, this polarization beam splitter and its preparation method have great potential in integrated optical system.
Funding
Natural Science Foundation of Zhejiang Province (LY19F050004); National Natural Science Foundation of China (61605095, 61975086); Key Research and Development Program of Zhejiang Province (2021C01025); K. C. Wong Magna Fund at Ningbo University.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
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