Discrete-layer sawtooth thickness-modulated thin-film designs: stopband count and spacing by frequency

A modulation scheme was developed to determine optical thickness for discrete thin-film layers of alternating low and high refractive index that follows a sawtooth waveform. Design constraints were determined to ensure sawtooth waveform thickness patterns and to maximize stopband reflectance and bandwidth. The resulting analytically derived sawtooth thickness-modulated designs were investigated for the generation of stopbands between first- and third-order stopbands. Designs with integer values of modulation period two and higher produce an increasing number of stopbands that are equally spaced by frequency between first- and third-order stopbands for the designs evaluated.