Binary-optimization-based Multilayers and Their Practical Applications

Multilayers composed of two or more materials enable the regulation of transmission, reflection, and absorption spectra across one or multiple bands. While analytic formulas based on well-established interference conditions, such as those employed in single-, double-, and triple-layer antireflective coatings and distributed Bragg reflectors, have provided suitable solutions for traditional optical coatings, they are limited in achieving the intricate spectral characteristics required by multifunctional optical coatings. To overcome this limitation, a variety of machine learning-based design algorithms have been rigorously studied. Among these, binary optimization has proven particularly effective for designing multilayer optical coatings. This approach transforms a given multilayer into a binary vector with multiple bits, where each bit represents one of the constituent materials, and quickly identifies an optimal figureof-merit by analyzing the interactions among the elements of the binary vector. In this review article, we elucidate the principles of binary optimization and explore its applications in the design of multilayers for antireflective coatings for high-numerical-aperture lenses, transparent radiative coolers for energy-saving windows, and bandpass filters for thermophotovoltaics. Furthermore, we address the limitations, challenges, and perspectives of machine learning-based optical design to guide directions for future research in this field.