Photonic band gap atlas, formula extension, and design applications in 1D photonic crystals

The design and development of new photonic devices for technological applications require a deep understanding of the effects of structural properties on the resulting band gap size and its position. In this study, we perform a theoretical analysis of the behavior of photonic band gap sizes, positions, and percentages under variations of the parameters characterizing binary (two materials), ternary (three materials), and linear continuum dielectric function multilayer structures. The resulting band gap atlas shows that binary systems may suffice for most applications, but ternary systems can provide additional design flexibility if needed. Linear continuum dielectric function systems exhibit a regular pattern for all gaps studied, and this regularity is reproduced with only a few materials involved. The positions of the gaps demonstrate a very monotonous behavior across all calculations performed. Finally, we propose additional extensions of formulas commonly used in the design of Bragg mirrors/reflectors using binary materials, discussing their corresponding limitations. These results can be seen as a technological horizon for the development of photonic devices.