TABLE OF CONTENTS In the preceding sections, rigorous analyses for the TE, TM and hybrid modes in a step-index fibers have been described. The refractive-index difference ? of practical fiber is of the order of 1%. Moreover index differences of the most important single-mode fibers for optical communication are about ? 
0 .3 0 .8%. Then we can approximate as n 1 /n 0 1. This approximation allows us to simplify the analysis of optical fibers drastically and enables us to obtain quite clear results. The analysis of fibers based on the approximation with n 1 /n 0 1 was first presented by Snyder [6]. Afterwards such mode groups with the approximation n 1 /n 0 1 were designated LP (linearly polarized) modes by Gloge [7]. Since an LP mode is derived by the approximation of n 1 /n 0 1, it means that the light confinement in the core is not so tight. Therefore this approximation is called weakly guiding approximation. We will study LP modes in detail in the following sections.
The strict solution [Eq. (3.19)] for the TE modes is adopted as it is. For the TM modes the weakly guiding approximation n 1 /n 0 1 is applied to the rigorous dispersion Eq. (3.28) to obtain the approximate form
This equation is known to be the same as the dispersion equation for TE modes (3.19). For the hybrid modes,...
