Abstract
The design optimization for n-graded optic coatings based on variational calculus is discussed. In order to exemplify the approach, the Lagrange problem for minimizing refraction is stated and solved. The refraction law is generalized for alteration of the continuous refraction index. To solve problems of reflection minimization, an integro-differential equation of retarding potentials is proposed to use as a condition to the nonholonomic Lagrange problem.
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