Modes Analysis in Step Index Fibers

Abstract

The modes are solutions of Maxwell's equations depending on boundary conditions of the waveguide (step-index fiber with 1 n = n2 for core and 2 n = n for cladding). In this paper, the general characteristic equation was deduced. This equation was used to determine modes TE, TM, and the hybrid modes EH and HE. Also, the linear polarization modes of the weakly guiding approximation 1 2 n = n were illustrated. The results proved that: the mode spot size, the propagation constants, the eigenvalues, and the nonlinearity depend on the mode order and the normalized frequency. 
Thereafter, the simulation proved that the number of modes is related to the normalized frequency in a quadratic function.