The Application of Quasi-Periodic Sequence Models in Optical Waveguide
Optical Waveguides, Bragg Grid Fiber, Quasi Periodicals Sequences
In this work, waveguides based on directing light through media with sequentially refractive indices in the direction of propagation are proposed. The core guiding model of these structures is based on quasi-periodic sequencing of the refractive index that forms the signal propagation region. In this context, well-known optical fiber models are modified to adapt to the segmentation structures of optical signal guiding regions.
These modifications enable the development of new optical device models, such as lasers, filters, and optical sensors. One of the most traditional segmentation models applied in optical waveguides is the Bragg Grating, also known as Fiber Bragg Grating (FBG), where the sequencing in the propagation region follows a periodic pattern. More recently, some quasi-periodic sequence models have been applied in photonic crystals, primarily considering the cross-sectional area of the waveguide. In this context, a new segmentation strategy is proposed, based on quasi-periodic sequencing of the refractive index along the direction of propagation.
Structures of core fractionation in waveguides will be investigated by applying quasi-periodic models, such as Fibonacci sequences, Thue Morse, Period Doubling, and Octonacci, with the aim of comparing their performance with waveguides that use Bragg Grating as a segmentation strategy. For this study, a mathematical formulation based on the finite element method, in conjunction with the optical beam propagation method, will be used as a simulation tool. Parameters of transmission and reflection at the interfaces between the different media composing the applied sequences will be analyzed.