Quasi-Periodic Photonic Structures: Fibonacci fractal-based optical filter design using ZnO/MgF2

This study investigates the optical properties of one-dimensional photonic crystals based on ZnO/MgF₂, designed using Fibonacci fractal sequences. The effects of structures based on standard Fibonacci (FFPC), inverted Fibonacci (IFFPC), and mirror symmetry Fibonacci (MSFFPC) sequences on photonic band gaps and light-matter interactions were theoretically analyzed. Calculations were performed using the Transfer Matrix Method (TMM). The analyses revealed that lower-order sequences offer broad and uniform transmission, while higher-order sequences exhibit complex optical resonances with narrower bandwidths. MSFFPC structures, characterized by their regular configurations and narrow bandwidths, are ideal candidates for applications requiring precise color selection, such as sensors and narrow-band optical filters. Conversely, IFFPC structures provide advantages for wide spectral applications due to their broad transmission bands. FFPC structures, offering a balanced performance, can be employed in both wide-band and narrow-band optical systems.