A novel derivation for number of modes in step-index fiber

This paper introduces a novel derivation of the number of modes for a step-index fiber using a mixed ray/wave approach. The number of modes is a useful tool in defining the core size of a single-mode or a few-mode optical fiber. In deriving the number of modes, the conventional method uses the wave theory of modes propagating in a step-index fiber. Here a ray approach is used for the maximum allowable angle of the ray entering the fiber, namely the numerical aperture of the fiber. The minimum allowable angle is derived using the two plane waves interference. Thus the number of modes is formulated by taking the ratio of the maximum value over the minimum value. The result is identical to that of the complete wave approach. This novel derivation is much simpler than that of the wave technique and pointing to more subtleties in the mode characteristics of the fiber.