Skew ray tracing in a step-index optical fiber using geometric algebra

Abstract

We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the law of refraction, and the juxtaposed vector product form for the law of reflection. In particular, the exponential forms of the vector rotations enables us to take advantage of the addition or subtraction of exponential arguments of two rotated vectors in the derivation of the ray tracing invariants in cylindrical and spherical coordinates. We showed that the light rays inside the optical fiber trace a polygonal helical path characterized by three invariants that relate successive reflections inside the fiber: the ray path distance, the difference in axial distances, and the difference in the azimuthal angles. We also rederived the known generalized formula for the numerical aperture for skew rays, which simplifies to the standard form for meridional rays.

Helical plasma filaments from the self-channeling of intense femtosecond laser pulses in optical fibers

“…Eventually, in the asymptotic case of ϑ = 0 • , the projection becomes a straight segment, i.e., the beam behaves as a meridional ray. However, in the case of SIFs, beams injected with progressively larger input angles experience a stronger twisting than beams injected with smaller input angles, in agreement with the skew-ray description of optical fiber propagation [16]. Therefore, when the projection writes a full circle at ϑ = 5 • , only a semicircle is written at ϑ = 2 • .…”

“…1(b), we report an image of a helical PF in a 50/125 SIF for two different values of ϑ. The helical pitch varies according to the input angle ϑ, as it occurs for conventional skew rays [16]. Furthermore, the total length of the PF is shorter for wider input angles (ϑ = 5 • ), because the guiding effects of the corecladding interface are weaker.…”

“…Therefore, when a PF is generated, it inherits the same helical shape. The propagation of helical beams [14], which are usually referred as skew rays in fiber optics [15,16], has been considered in many studies. Recently, the propagation of skew rays in optical fibers was exploited to generate the emission of multicolor spiral beams in the output far-field intensity [13].…”

Annular Cavity Design for Photoluminescent Polymer Optical Fiber Sensors

“…During propagation in the fiber and reflections at the core-cladding interface, the polar angle and the propagation distance between reflections, , remain unchanged [ 46 ]. As the ray propagates, its position can be projected to the cross-section of the core.…”

Fiber-Optic Skew Ray Sensors

“…Ray tracing is undoubtedly a growing and important field for numerous applications in photography, solar concentrators and realistic simulations (e.g., games). Achenbach et al [39] and Ang et al [40] carried out extensive simulations with ray racing. Achenbach et al, established the groundwork for a numerical approach (e.g., Monte Carlo) to calculate trapping efficiencies for different types of rays in active fibers, which also applies to bent fibers.…”