In previous work, we have introduced an analytical approach that utilizes the dispersion relation for an infinite periodic multilayer structure to predict the performance of finite multilayer structures. We have validated the accuracy of our predictions by demonstrating numerical agreement with other established simulation methods, such as the transfer matrix method, and through experimental confirmation. In this work, we employ dispersion relations to first illustrate that metallo-dielectric structures, as opposed to multilayer dielectric-dielectric structures, can efficiently yield a sharp-edge transmittance spectrum profile, with control over both sides of the bandpass cutoff edges. Our approach also enables the calculation of effective permittivity without relying on traditional homogenization techniques. Next, utilizing the concept of effective permittivity, we illustrate that increasing the thickness of specific dielectric layers within MD structures leads to narrower passbands without significant loss in transmission, demonstrating the potential of this approach for engineering the transmittance spectrum of bandpass filters in the visible and near-IR regions. The capability to achieve a sharp-edge filter with a limited number of layers further underscores the cost-effectiveness of such bandpass filters.
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