Unified Model Combining the Boundary Conditions Encountered at the Input, the Carrier Optical Fiber and the Output in Spatially Multiplexed Optical Communication Channels
Abstract
Spatial domain multiplexing allows for expansion of optical fiber data rates by
utilizing the spatial dimensions within the fiber. One form of this multiplexing
method utilizes oblique input angles to generate ring-like spatial modes within the
optical fiber core. This radial based spatial multiplexing (rSDM) is compatible
with single core fibers and conventional optical fiber systems. As rSDM has been
shown to be independent of wavelength, rSDM channels allow for adaption of wavelength
division multiplexing, and has been experimentally shown to be capable of
improving optical fiber data rates by at least an order of magnitude.
Current research into rSDM system have been largely experimental in nature;
however, the full capabilities of rSDM are unknown as the technology currently
lacks a rigorous theoretical model. Conventional models have been shown to be
incompatible with the characteristics shown by experimental rSDM systems. For
example, the most prevalent model utilizes Laguerre-Gaussian beams to generate
similar radial ring patterns to that of rSDM; however, this is a free-space solution
and fails to fully describe the optical fiber characteristics used to generate and propagate the rSDM rings. Hence, an end-to-end mathematical model compatible
with rSDM is desired.
This dissertation explores current optical vortex models and their theories by
comparing them to six unique rSDM characteristics derived from experimental
results. The explored models consist of phase vortices, Laguerre-Gaussian beams,
Modified Laguerre-Gaussian beams, linear polarized modes, and Bessel-Gaussian
beams; however, each model lacks the capability of fully describing rSDM. Bessel-
Gaussian beams provide the closest match, but lacks explanation on continuity for
the optical fiber system that generates rSDM.
In order to achieve an applicable model, Fresnels diffraction equations are applied
at the input and output of the optical fiber system. The input conditions show a
clear input angle to azimuthal angle relationship; whereas, the output conditions
give a higher order Bessel-Gaussian form. These two combine to provide a full
end-to-end mathematical model. This model is compared to experimental rSDM
results by comparing the central radial location of generated rings from a 200 um
radius optical fiber and shows good correlation to the model.