A comparison of approximate and exact modes in few-mode micro-optical fibers

An analysis of different cases of few-mode micro-optical fibers from 10 to 1 microns in diameter is performed based on solving the eigenvalue equation using both the weak guidance approximation (scalar LP modes) when the refractive index difference is small, and the exact full eigenvalue equation (vector TE, TM, HE and EH modes), when the refractive index difference is large, for example having air or a gas as the surrounding medium. One of the objectives of this analysis is to show at what point the propagation constant and optical field intensity of the fundamental modes LP₀₁ and HE₁₁ differ significantly depending of the refractive index difference, the other objective is to find out the evolution of the other modes along the final tapered section in a few mode fiber taper. The graphical behavior of the solutions of the eigenvalue equation is presented and the optical intensity distributions are calculated for different sizes, as for example in adiabatic tapers to evaluate the extent of the evanescent field. In general, the propagation constant and effective refractive index depends on the size of the core waveguide diameter, the refractive index difference and the wavelength. This analysis is useful to calculate the extension of the evanescent field in liquids or gases for optical fiber sensors that can be used to model, for example, fluorescent optical fiber sensors for biological or industrial applications. Additionally, the propagation characteristics of the few-mode micro optical fiber could be controlled or tuned by changing the refractive index of the surrounding media by changing, for example, its temperature.