Ever since the first simple applications of thin film coatings in optics emerged, films with a gradually varying refractive index in the direction of the normal to the film surfaces have appeared particularly intriguing to scientists and engineers. The almost total absence of reflections from a gradual transition between two media with different indices, inspired early interest and hope for other unusual properties that could not be realized by stacks of homogeneous films. This paper will try to explore to what extent such hopes have come true so far, and as a basis for subsequent presentations during this conference, give a general overview of the analytical and computational as well as technical complexities particular to inhomogeneous films.
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