Abstract

Successive interfacial reflectances or admittances for light incident normally upon a multilayer of N layers obey nonlinear recurrence formulas. Linear polynomials in the nth interfacial reflectance of admittance are defined. The partial products Q_ν of these polynomials from n=ν to n=N+1 are shown to obey linear recurrence formulas relating three successive partial products. Explicit formulas are given for computing the energy reflected or transmitted by the N layers. Methods for calculating the phase retardations produced by reflection from or passage through the N layers are stated. The application of the products Q_ν to the optical admittances is included.

© 1953 Optical Society of America

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