Calculation of Modes Dispersion in Anisotropic Optical Fiber Transmission Lines MOHAMMED YOUSEF AL-GAWAGZEH MOHAMMED RASOUL AL-HADIDI RAMI AL-RZOOQ Department Of Computer Engineering Faculty of Engineering, AL-Balqa Applied University, AL-Salt JORDAN E-mail: gogazeh@bau.edu.jo ,mohammed_gogazeh@yahoo.com Mohammad_hadidi@bau.edu.jo ; dr_hadidi@yahoo.com Abstract:-This paper shows how to obtain approximate analytic expressions which can be used to calculate with sufficient accuracy for practical applications the waveguide and polarization dispersion of the dominant orthogonally polarized modes in anisotropic optical fiber waveguides. It is shown that the anisotropy of a dielectric in the transverse cross section and the elliptical of the shape of this cross section alter the waveguide dispersion of modes in such waveguides compared with an isotropic waveguide. In the case of waveguides which conserve the state of polarization of the transmitted signal the changes in the waveguide dispersion due to the transverse anisotropy of the refractive index are considerably greater than the changes due to the elliptical of the shape of the transverse cross section of the waveguide. In a waveguide with a transverse anisotropy of the refractive index the maximum waveguide dispersion of two mutually orthogonal modes occurs at different frequencies. Key-Words: - Dispession, Anisotropy, Optical fiber, polarization, Transverse cross section. 1 Introduction Anisotropic optical fiber waveguides capable of conserving the polarization of the transmitted signal are currently the subject of intensive investigations. This property is very important for various fiber- optic devices and for long distance optical communication systems [1]. Anisotropic waveguides are understood to be those with a departure of the transverse cross section from the circular symmetry (which is known as the shape anisotropy) and with an anisotropy of the permittivity (refractive index) induced by mechanical stresses. In practice, the parameters of anisotropic waveguides can be calculated conveniently by approximate methods which are sufficiently accurate for the purpose [2-4]. One of these methods, which belong to the class of perturbation theory techniques, is the method of shift formulas [2]. This method was described in [5-8] to calculate the propagation constants and critical wavelengths of all the modes in anisotropic dielectric waveguides. We shall use this method to calculate the dispersion of modes in such waveguides. The chromatic dispersion is the most important factor that determines the width of a pass band of single-mode waveguides. It can be separated into the material dispersion and the waveguide (mode) dispersion [9]. We shall consider the waveguide dispersion associated with the guiding properties of waveguides. 2 Procedures The waveguide dispersion of any mode in a dielectric waveguide is defined as the produce the propagation constant of this mode and its frequency. The propagation constant of a mode in an anisotropic waveguide obtained by the method of shift formulas can be written as follows[2,7,8]: s l t h h h h h Δ + Δ + Δ + = ~ , (1) where h ~ and h are the propagation constants of a mode in the investigated anisotropic waveguide and of the corresponding mode in a circular isotropic comparison waveguide; ,and , are the correction describing the influence of the transverse and longitudinal (axial) anisotropies of the refractive index, respectively; t h Δ l h Δ s h Δ is the influence of the shape Proceedings of the 7th WSEAS International Conference on INFORMATION SECURITY and PRIVACY (ISP '08) ISSN: 1790-5117 39 ISBN: 978-960-474-048-2