Approximate solutions of the eigenvalue equation near cutoff for TE0mand TM0m modes for a step index fiber optic: new forms and considerations

Abstract

In this work the authors intend to present a new approximate technique of solving the characteristic (eigenvalue) equation for a step index fiber optic near cut-off. To illustrate this new method, there are presented (and demonstrated) two particular forms, corresponding to the case v equals 0 (TE0m and TM0m modes). Solutions of these equations are compared with other solutions suggested by Marcuse and--also--it is analyzed the accuracy of our results compared with the general solution of the characteristic equation.