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The process of designing a thin-film coating can be approached from an analytical or a scientific basis, a numerical or an actual experience, or—with the capability of present thin-film design software—perhaps with no basis (knowledge) at all. Over many decades, several design, analysis, and other related books and technical articles have been published on this subject. As more optical systems have become multispectral with performance requirements at several wavelengths or wavelength regions, the required coatings have become more complex. A particular subset or type of coating design is typically used to highly reflect at several wavelengths and may also have high transmittance at others. Classical designs, such as bandpass, cavity, notch, minus filters, rugate, etc., are routinely used for these applications. This chapter is a brief review of well-established thin-film theory as it relates specifically to the above subset of coating designs. The basic physics of optical thin films involves the interaction of one or more wavelengths of light and real media boundaries. Without these boundaries, Maxwell's equations describe properties of light waves that are typically modeled as planar or Gaussian. With boundary conditions, where different dielectric or conductive media are present, Maxwell's equations are solved accordingly to describe the reflected and transmitted waves. Specifically, the complex reflection coefficient is the amplitude ratio of the reflected to incident electric fields. From this coefficient, the reflectance (which is the ratio of the reflected wave's power to the incident wave's power) and the phase shift between the reflected and incident waves are determined. The rigorous mathematical development of the electromagnetic theory for propagating waves and interactions with boundaries for various materials is covered in other texts on electromagnetics and optics.
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