Calculation of Effective Refractive Index for Fiber Core Fundamental Mode Using Bisection Method

This document presents a computationally efficient program that calculates the effective refractive index of the fundamental mode in optical fiber cores through bisection method implementation. The effective refractive index serves as a critical design parameter for optical fiber performance characterization. The algorithm operates by iteratively narrowing the search interval between the fiber core refractive index (upper bound) and cladding refractive index (lower bound), evaluating characteristic equations at each midpoint until the solution converges within specified tolerance. Key implementation features include boundary condition validation, convergence threshold configuration, and modal equation root-finding through successive interval halving. This robust numerical approach ensures reliable determination of waveguide dispersion properties, providing essential data for fiber optic system optimization and transmission analysis. The program architecture supports customizable precision settings and modular function design for seamless integration with broader photonic simulation frameworks.