2025/10/29 by Hannah Blasiyus, D. K. Sheena Christy, D. G. Thomas
Materials Science · Physics and Astronomy · #Quasicrystal Structures and Properties #Advanced Mathematical Theories and Applications #Metamaterials and Metasurfaces Applications
paper · doi:10.1080/00150517.2025.2490760
Fibonacci words are important in combinatorial theory because they have unique combinatorial features such as aperiodic behavior. Apostolico and Brimkov studied array repetitions by extending Fibonacci words to Fibonacci arrays. The study of formal languages, number theory, and the quasiperiodic nature of Fibonacci words and arrays is widely used in wave propagation, light transmission, signal processing, image processing, and so on. We want to take the idea of Fibonacci words and Fibonacci arrays and make them fuzzy Fibonacci words and fuzzy Fibonacci arrays. We will do this by adding membership grades and defining fuzzy Fibonacci one- and two-dimensional languages. We look at some operations on languages, like union, intersection, concatenation, Kleene closure, and complementation, and how they can be used to study how light moves through Fibonacci dielectric multilayers. Our goal is to get perfect transmission by messing up the thicknesses and refractive indices of the materials that make up the layers.