Mode Dispersion of Optical Waveguides with Complex Refractive Index Profile Using Equivalent TL Circuits

An analysis leading to an exact and efficient algorithm is presented for calculating directly and without numerical differentiation the mode dispersion characteristics of cylindrical dielectric waveguides of arbitrary complex refractive-index profile. The new algorithm is based on the equivalent transmission-line (T-L) technique. From Maxwell's equations, we derive an equivalent T-L circuit for a cylindrical dielectric waveguide. Based on the TL-circuit model we derive exact analytic formulas for a recursive algorithm which allows direct calculation of mode delay and dispersion. We demonstrate this technique by calculating the fundamental mode dispersion for step, triangular and W optical fiber refractive index profiles. The accuracy of the numerical results is also examined. The proposed algorithm computes dispersion directly from the propagation constant without the need for curve fitting and subsequent successive numerical differentiation. In the end, we "design" for first time a triangular refractive index profile fiber with flat complex refractive index which performs extremely low rms-value of dispersion, under 0.08 ps/(km nm), over the wavelength range [1.3 mu m, 1.55 mu m].