Optical wave filtering by using some mixture of the rectangular, sinusoidal, sawtooth and triangular basic building blocks

In this work, we investigate novel one-dimensional photonic crystals theoretically constructed from primitive building blocks of rectangular, sinusoidal, sawtooth and triangular shapes. The central idea is to combine the filtering properties of these structures so that if one structure fails to filter a wave within a given frequency interval, subsequent layers with different shapes will filter it. As expected, this approach proves effective in some cases, while in others, we encounter specific conditions, as described in the text. Our results are obtained using the transfer matrix method. We study the effects of various parameters – such as the number of layers, their dielectric constant and the total system length – on the transmission coefficient. The core novelty of this work lies in the systematic investigation of hybrid refractive index profiles (e.g. rectangular-sinusoidal, sawtooth-triangular) that combine basic geometric shapes. A key finding is that these hybrid structures exhibit distinct and tunable photonic band gap (PBG) properties, such as the complete absence of a band gap in the Rec-Saw profile at lower frequencies.