Numerical Simulation and Analysis on Mode Property of Photonic Crystal Fiber with High Birefringence by Fast Multipole Method

Abstract

In this paper the mode property of a photonic crystal flber with triangle-lattice array in a silica matrix has been simulated by fast multipole method. The PCFs studied in this paper have a silica core, obtained by introducing a defect, that is by removing three holes in the center of the flber transverse section. The model flelds, efiective index and conflnement loss about the fundamental mode in the flbre are analysed and compared. It is demonstrated that lower conflnement loss and higher birefringence can be realized in the condition of fewer rings of air holes. At the wavelength of 1.55m the conflnement loss is 7:3£10 i6 dB/m and the birefringence is 1:65£10 i3 in this flber. The simulation results show that birefringence of this triangle-lattice PCF is dominated by inner-ring air holes in the flbre efiectively. The simulation results in this paper have important meaning for instructing the fabrication of birefringent photonic crystal flber. 1. INTRODUCTION In recent year, great interest has been focused on the study of photonic crystal flber (PCF). By using the structure adjustability of the PCF, zero dispersive wavelength moving towards short- wave spectroscopy, chromatic dispersion compensating, dispersion truncating, high nonlinearity and birefringence can be realized (1{15). The mode birefringence of PCF mainly comes from the geometer structure of flber and the usual method to cause birefringence is employing double-core or multi-core structure, changing the flber core or the shape of the air holes and altering the distri- bution of the air holes. High birefringence PCF can be used in optical flber sensor, interferometer and polarizer, etc. In addition, by designing the high birefringence and intensive nonlineality PCF required, we can make a flber not only high birefringence, but also intensive nonlineality. We can also make the large mode property polarization maintaining PCF (15). This can make the prop- erty of PCF integrate, so it can be used in the Raman magniflcation, ex-continous spectum of the polarization, four-wave frequency mixing and the crossing phase modulation. The development of the birefringence PCF will promote the study and appliance of the new photoelectric device. In the progress of making the PCF flber, we flnd that maintaining the ideal structure of the flber and the number of air holes layers of the PCF cladding is a contradiction (2,4,17). Generally speaking, the more layers the PCF cladding have, the smaller the conflnement loss will be, but at the same time increasing the layers will make the distortion of the air holes a big problem when the flbers are produced. On the fundament of the traditional triangular arrayed air holes, this article proposes a birefringence structure PCF which has C2v symmetry. And by using the fast multipole method, its modal property is numerically simulated. It is found that in this PCF, there will be several conductive modes, and its fundamental mode has very low conflnement loss and high birefringence. 2. BASIC THEORY The ordinary solution about multipole theory at the complex boundary electrostatic fleld has been deduced and developed by Zheng Qinhong. Nie Zaiping (22) analyzed the three dimensional vector scattering of complicated object by using the fast multipole method. These examples show that the multipole method is an efiective way to analyze electromagnetic fleld theory. Using the multipole method to simulate the dispersion and the loss property of microstructured flber is originally proposed by T. P. White and B. T. Kuhlmey (23{25) in Sydney University. Zhao Mingzhu (26) also simulated the PCF by using multipole method. This method is adopted when the air holes of microstructured flber is cylindrical. By using this method, we can get real part and imaginary part of the efiective refractive index of the flber and the mode propagation constant. And then by using the real part, we can analyze the dispersion, or using the imaginary part to analyze the conflnement loss of limited cladding air holes. We can also use this method to get its propagation constant corresponding to the input wavelength (or frequency). Accordingly, we can consider the material dispersion in the progress of simulation by using the Sellmeier formula. In this paper, the theory of T. P. White (23,24) is used for reference