Electromagnetic modes in optical fiber waveguides using Nikifarov-Uvarov method

Optical fiber is a cylindrical dielectric medium that transmits electromagnetic waves at optical frequency range, guiding them through the fiber core via constructive phase-shifted total internal reflection. Wave propagation in optical fibers can be modeled and described using Maxwell’s equations. This paper employs the parametric Nikiforov-Uvarov (NU) method, commonly used in quantum mechanics, to solve the Helmholtz equation derived by combining Maxwell’s equations. The NU method is less computationally cumbersome than traditional techniques such as Bessel functions or finite element methods. We derive the equation that describes the characteristics of the propagating electromagnetic wave with refractive index as an unnormalized radial wave function. We show that NU energy equation can be used to obtain the exact phase propagation constant condition for wave propagation in optical fibre. Additionally, we investigate the effects of wavelength, core radius, refractive index, and azimuthal index on wave propagation. Our results show that the phase propagation constant decreases as the wavelength increases. The radial function is found to be proportional to the degree of the Laguerre polynomial and the azimuthal index. We also report the effects of the azimuthal index, core radius, and refractive index on the radial function.