A simple model for fibre optics: planar dielectric waveguides in rotation

Abstract

In planar dielectric waveguides, there is only one type of propagated ray: the one that crosses the waveguide axis after each total internal reflection. According to the model of geometrical optics, there are two types of guided ray in fibre optics: meridional and skew. Each one is formulated by a suitable mathematical treatment. In this work, we demonstrate that the complex mathematical treatment for the skew rays can be avoided by considering a planar waveguide (with the same refractive index profile as the fibre and thickness equal to its diameter) that rotates around the direction of the axis with angular velocity ω. A section of this fibre is inscribed in the hypothetical slab. This model has been successfully introduced to students of engineering and physics.

On the physics of propagating Bessel modes in cylindrical waveguides

“…The latter is possible by rotating the slab waveguide π radians, as it is shown in Ref. [18]. Since a plane wave in a polar coordinates can be represent by e ikρ(x cos ϕ+y sin ϕ)+ikzz the continuous interference of these counter-propagating plane waves in the π rotation can be represent by…”

Extension of the Rotating Planar Waveguide Model to Formation of Interference Patterns in Optical Fibers

“…As we demonstrated previously [1], the optical path followed by the rays S and S' in the trajectory   would be:…”

“…In previous works, we have developed a model that relates the propagation parameters of one given bounded ray in one optical fiber with the kinematic properties of a hypothetical planar waveguide containing the fiber [1,2]. This model, that provides a correspondence between each ray and one angular velocity, enables complex expressions of propagation to be determined in a simple way, in cases as sophisticated as gradient-index fibers [2].…”

Planar dielectric waveguides in rotation are optical fibers: comparison with the classical model

“…If the refractive index of the fiber is constant, these parameters remain constant [6] but, besides the trivial case of rays with 2 π θ φ = (meridional rays), an arbitrary guided ray (skew rays if 2 π θ φ ≠ ) will follow a complex path due to the cylindrical geometry of the fiber (see Fig. 1).…”

“…Due to the continuous refractions, the angles Z θ and φ θ are no longer constant and they change after each refraction according to the laws of the Geometrical Optics. This makes us use the eikonal equation, whose treatment is complex [6][7][8], and the parameters derived from its integration prove rather obscure, loosing a big part of their actual physical meaning. that decrease from the axis to the outer layers, a ray propagating within such fiber will suffer consecutive refractions until it meets a layer whose refractive index together with the angle of incidence of the ray cause total reflection and make it return [ Fig.…”