A spiral index profile for high power optical fibers

A new optical fiber, based on a spiral-shaped refractive index profile, is proposed. This study shows that the assumption of the spiral index profile as a perturbation of the step index profile leads to an exact solution for the fiber modes. The classic Helmholtz equation for wave propagation is split into an azimuthal Hermite eigenvalue equation and a radial Bessel eigenvalue equation. The resulting TE and TM (transverse electric and magnetic) modes are products of Hermite and Bessel functions (Hermite-Bessel modes). This result is complementary to the theory of step index fibers, where unperturbed cylindrical geometry requires perturbation theory for its solutions. The spiral profile fibers have the unique property of focusing light azimuthally at fixed angles and therefore the polarization of the mode is maintained. In addition, spiral fibers are proven to be particularly efficient as they produce excellent confinement of the electromagnetic fields.