Study and Simulation of Nonlinear effects in Bire-Fringent Fibers Using Efficient Numerical Algorithm Muddassir Iqbal, Z.Zheng, Tian Yu School of electronic information engineering, Beihang University, Beijing, CHINA Contact email: scholar547@gmail.com Abstract: Pulse propagation in a birefringent medium carries due weightage and importance in passive modelocking of fiber lasers. We have carried out study of nonlinear effects in birefringent medium by simulating pulse propagation using adaptive step size method, which is globally an efficient algorithm for solving Schrodinger type equations using split step Fourier method. Nonlinear optical loop mirror was realized and it was revealed that the results can be used in forming a figure of eight fiber laser using NOLM, where NOLM behaves like a fast saturable absorber. Novelty lies in producing accurate results using adaptive step size method. Index Terms: Non-linear Schrödinger equation (NLSE), Self Phase modulation (SPM), cross phase modulation (XPM), kerr non-linearity, Symmetrized split step Fourier method (SSSFM), Nonlinear Optical Loop Mirror (NOLM). 1. Introduction Linear birefringence causes the components of light travel with different group velocities [1,5]. Even a single mode fiber supports two orthogonally polarized modes with the same spatial distribution. In an idea fiber the effective refractive indices x n and y n of both the modes are identical [1]. It is pertinent to mention here that all fibers exhibit some modal birefringence ( ) x y n n ≠ ; this is due to unintentional variations in the core shape and anisotropic stresses along the fiber length. However the degree of modal birefringence, m x y B n n = − and the orientation of x and y axes changes randomly over a length scale 10m ≈ unless it is catered for [1,2]. A variety of linear and nonlinear fiber properties enable new applications in photonic devices as elements of a fiber laser cavity. One of the most interesting fiber element is the loop interferometer, also termed as Sangnac interferometer; it has transmission characteristics that can be controlled by outside influences, such as strain birefringence, current birefringence and temperature variations [3]. The nonlinear optical loop mirror (NOLM) [4] which is an example of Sangnac interferometer, has been used in a number of applications such as optical switching, passive modelocking of fiber lasers, logic gates, fiber sensors and all optical demultiplexing of data streams [5, 6, 7, 8, 9]. The basic concept of the conventional NOLM is based on the differential nonlinear phase phase shift between the counter propagating, linearly polarized light beams in the loop interferometer. Such a NOLM has high/low power reflection coefficient and provides nonlinear switching by an assymetrical coupler at the loop’s input, i.e. one in which coupling coefficient differs from 50/50. The transmission properties of the NOLM can be modified by using birefringent fiber and different polarization orientations between the counter propagating beams. The difference in mode propagation constant for different polarizations is defined as the modal birefringence [1] or phase birefringence B. 0 0 2 x y x y x y B n n k β β β β πλ − − = − = = ----- (1) , , x y x n n β and y β are the effective mode indices and mode propagation constants of the two orthogonal principle axes respectively. Since the effective mode index of the two polarizations are not the same, by injecting a linearly polarized light at 45 o to one principle axis, the polarization will evolve periodically from linear to elliptical, elliptical to circular and vice versa along the length of the fibre. The length of fibre for the light to exit with the exact same polarization as at the input is called the beat length LB. 2 B x y L B π λ β β = = − ---- (2) Figure 1 shows a schematic diagram of how the polarization varies along a birefringent fibre. Proceedings of the 7th WSEAS International Conference on Simulation, Modelling and Optimization, Beijing, China, September 15-17, 2007 357