Novel liquid-crystal photonic crystal fiber with three-core and flattened dispersion

YANG Han-rui, YANG Yan, JIAO Sheng-xi, HUANG Wei-liang, XIA Lin-lin

(School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

Novel liquid-crystal photonic crystal fiber with three-core and flattened dispersion

YANG Han-rui, YANG Yan, JIAO Sheng-xi, HUANG Wei-liang, XIA Lin-lin

(School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

A new kind of multi-core photonic liquid crystal fiber (PLCF) is investigated to solve the problem of sharing one light source among three-axis fiber optic gyroscopes. This fiber has three liquid cores arrayed in equilateral triangle geometry. The characteristics of power distribution, modal field, effective index, and dispersion are analyzed by employing finite element method. Numerical analysis results show that the three-core PLCF can separate the transmitted light into three equal beams with flattened dispersion. The dispersion variation for 1.45-1.75 μm wavelength is less than 2 ps·km-1·nm-1. Additionally, it exhibits super flattened dispersion in ～150 nm wavelength range, and the wavelength range of super flattened dispersion can be adjusted by changing the diameter of the central air hole. The study results are of significance for the further development of the PLCF, the equal optical beam splitter (used in three-axis fiber optic gyroscope and three-phase optical fiber current transformers), 1×3 multi-core photonic crystal coupler, and flatteneddispersion optic fibers.

photonic crystal fibers; multi-core fibers; optical beam splitter; fiber coupler

Photonic crystal fiber (PCF) is a new type of fiber,whose wrap layer is composed of the ventage and silica arranging along the axial direction periodically[1-2]. It was emerged in the late 20th century. Its character of transmitting light can be controlled by changing the queuing discipline, size, distance of air holes, or filling the air holes with gas, liquid and so on. Due to its special optical properties, it has been attracting great interest in the research community and opening a bright future for the design and application of optical fibers[3-6]. With the development of PCF, the liquid crystal, as a filled stuff,has so many optical advantages, which recently attracts many of researchers[7-8].

Liquid crystal is a new kind of material, which has been found in 1888. It has both the fluidity of liquid and the crystal optical anisotropy. Its molecule is in the shape of long or other rules, and these molecules also have the anisotropy of physical properties. At the same time, these molecules are arranged according to certain rule in a certain temperature range, so we call this kind of material as‘liquid crystal’. Because of the high temperature and the voltage sensitivity of liquid crystal, it has been increasingly applied to the PCF sensing studies in recent years[9-11].

In this paper, we propose a photonic liquid crystal fiber (PLCF) with three liquid crystal cores and flattened dispersion. By using finite element method (FEM), its power distribution, modal field, effective index and the dispersion characteristics are numerically investigated.Numerical results indicate that the proposed fiber shows flattened dispersion. Dispersion is one of the intrinsic characteristics of optical fiber, and it is a necessary factor to be considered in the design of photo-electronic device.In optical fiber communication system and some optical devices, the dispersion of the fiber must be reasonably controlled. Both in some linear optics and nonlinear optics field, the fiber dispersion with reasonable size and flat nature is always expected in the application of wavelength window. Therefore, the proposed PLCF has admirable applications in the field of optical fiber communication and sensing that need flattened dispersion. Besides,it can be widely used in the field of 1×3 multi-core photonic crystal coupler and optical beam splitter of threeaxis fiber optic gyroscope and three-phase optical fiber current transformers because of power distribution[12-13].

1 Geometric modeling

Figure 1 presents our proposed design. Three liquid cores arrayed in equilateral triangle geometry. In this fiber,the air holes are arranged in the equal-lateral triangular lattice. There are six holes in the first ring surrounding each liquid crystal core. Due to the fact that the effective refractive index of liquid crystal is higher than that of pure silica, i.e., the effective refractive indices of the three fiber cores are greater than that of other sections in the fiber,the fiber still guides light by total internal reflection effect. In this paper, the power distribution, the modal field, the effective index and the dispersion characteristics are analyzed by using FEM.

Fig.1 Structure of the proposed PLCF

At present, the modal solution approach based on the FEM is more flexible than most approaches as it matches well to the complex structure of PCFs[14].Considering the Maxwell’s equation for a lossless optical guide and a two-dimensional wave equation for the FEM analysis is given as:

The various properties such as the modal field, the effective index, the waveguide dispersion are discussed by using FEM. Waveguide dispersionis one of the most important modal properties of an optical waveguide.It can be defined as[15-16]:

where c is the velocity of light,λ is the operating wavelength,is the effective index of the guided mode and can be calculated by using FEM. The refracttive index corresponding to the operating wavelength is given by Sellemier’s formula[17]:

2 Numerical results and analysis

2.1 The power distribution

The surface power flow and the longitudinal sections of power distribution of the three-core PLCF are shown in Figure 2. And its three-dimensional maps of power distribution are shown in Figure 3. It can be observed that the power can be divided into three equal beams, and is transmitted in the three liquid crystal cores.The results are of significance for the further development of the optical beam splitters.

Fig.2 Surface power flow and longitudinal section of power distribution

Fig.3 Three-dimensional map of power distribution

2.2 The modal field

Firstly, we analyzed the changing characteristic of the modal field influenced by wavelength. Figure 4 shows the modal field distributions of the proposed three-core PLCF with different wavelengths. The PLCF with the proposed structure is shown in Figure 4, whose design parameters are as follows: the hole spacingthe air hole diameterthe diameter of liquid crystal cores the diameter of central air holethe effective indexes of liquid crystal with the wavelength from left to right. Figure 4 confirms that the modal field of the proposed three-core PLCF can be well restricted. The fields can penetrate the lattice near each liquid crystal core of the fiber, but it dies out after a few holes. Obviously, it can be observed that the modal field increases monotonically with the increasing of the operating wavelength and there will be a coupling. Therefore, we can choose different wavelengths for different applications.

Fig.4 Modal field distributions of the proposed PLCF with different wavelengths

Then, we analyzed the changing characteristic of modal field influenced by central air hole. Figure 5 shows the modal field distributions of the proposed three-core PLCF with different central air hole diameters.The PLCF with the proposed structure is shown in Figure 5,whose design parameters are as follows: the hole spacingthe air hole diameterthe diameter of liquid crystal coresthe effective index of liquid crystal with the wavelengthand the diameter of central air holecentral air hole is a solid rather than a hollow stem,is the effective index of central air hole,n is the effective index of air hole). It can be observed that the modal field can better spread to the central area with the decreasing of the diameter of the central air hole

Fig.5 Modal field distributions of the proposed PLCF with different central air hole diameters

In addition, we analyzed the changing characteristic of the modal field influenced by the diameter of liquid crystal cores. Figure 6 shows the modal field distributions of the proposed three-core PLCF with different diameters of liquid crystal cores. The PLCF with the proposed structure is shown in Figure 6, whose design parameters are as follows: the hole spacingthe air hole diameterthe diameter of central air holethe effective index of liquid crystal with the wavelengthand the diameters of liquid crystal coresfrom left to right. It can be observed that the modal field increases monotonically with the increasing ofMoreover, it can be observed obviously that the power can be better restricted with the increasing of the diameter of liquid crystal core.

Fig.6 Modal field distributions of the proposed PLCF with different central air holes

2.3 The effective index

Figure 7 shows the variation of the effective index of the proposed three-core PLCF. The PLCF with the proposed structure is shown in Figure 8, whose design parameters are as follows:It can be observed that the effective index of the threecore PLCF reduces monotonically with the increasing of the operating wavelength. At a constant temperature, due to the liquid crystal refractive index is not affected by temperature, the effective index’s variation with the wavelength of the optical fiber is not significant, and it can be observed that the variation value is less than 0.015.

Fig.7 The variation of effective index with the operating wavelength

Fig.8 Variation of waveguide dispersion with operating wavelength and diameter of the central air hole

2.4 The waveguide dispersion

The variation of waveguide dispersion with the operating wavelength and the diameter of the central air hole for the proposed three-core PLCF is shown in Figure 8. It can be observed that the waveguide dispersion of the PLCF is flat, and the variation of dispersion is less than 2 ps·km-1·nm-1in the wavelength range of 1.45-1.75 μm. Additionally, it can achieve super flattened dispersion in the wavelength range of about 150 nm, and the wavelength range of super flattened dispersion can be adjusted by changing the diameter of the central air hole.

3 Conclusions

A new kind of PLCF structure with three-core and flattened dispersion is proposed. By using the numerical analysis method based on the finite element, we simulate the power distribution, modal field, effective index and the dispersion characteristics of the PLCF. We also obtain the relationships between the modal field distribution and wavelength, the modal field distribution and central air hole, the modal field distribution and liquid crystal cores, the effective index and wavelength, the dispersion and wavelength, the dispersion and central air hole. Simulation results show that power in this type of PLCF can be divided into three equal beams transmitting in the three liquid crystal cores, and the modal field of the proposed three-core PLCF can be well restricted. It can be used for optical beam splitting of three-axis fiber optic gyroscope, three-phase optical fiber current transformers and other optical systems, and for the production of 1×3 multi-core photonic crystal coupler. Additionally,super flattened dispersion can be obtained in this PLCF,and the variation of dispersion is less than 2ps·km-1·nm-1for 1.45-1.75 μm wavelength.

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1005-6734(2017)04-0510-04

10.13695/j.cnki.12-1222/o3.2017.04.015

2017- 04-17；

2017-07-22

國家自然科學基金項目（61503073）；吉林省科技發(fā)展計劃項目（20160101249JC）；吉林市科技發(fā)展計劃資助項目（20156404）

楊漢瑞（1986—），女，講師，工學博士，從事光纖傳感及光電檢測技術研究。E-mail: yanghanrui1208@163.com

一種三芯液晶光子晶體光纖的特性

楊漢瑞，楊 燕，焦圣喜，黃蔚梁，夏琳琳
（東北電力大學 自動化工程學院，吉林市 132012）

針對三軸光纖陀螺共用光源問題，提出了一種新型的多芯液晶光子晶體光纖，該光纖具有三個呈等邊三角形幾何形狀排列的液晶纖芯。利用有限元法對其功率分布、模場、有效折射率和色散特性進行了數值分析，結果表明，這種三芯液晶光子晶體光纖可將傳輸光完全等分為三束光，且具有平坦色散特性，在波長為 1.45 μm～1.75 μm之間的色散變化小于 2 ps·km-1·nm-1。此外，該光纖在大約 150 nm的波長范圍內顯示出超平坦的色散，并且可以通過改變中心空氣孔的直徑來調整超平坦色散的波長范圍。研究成果對液晶光子晶體光纖、三軸光纖陀螺和三相光纖電流互感器的等光分束器、1×3多芯光子晶體耦合器和平坦色散光纖的進一步發(fā)展具有重要意義。

光子晶體光纖；多芯光纖；光分束器；光纖耦合器

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