Authentification abonné
 Numéro J. Phys. Radium Volume 11, Numéro 7, juillet 1950 315 - 320 https://doi.org/10.1051/jphysrad:01950001107031500
J. Phys. Radium 11, 315-320 (1950)

## L'admittance optique des couches homogènes et hétérogènes

B.S. Blaisse

Abstract
By introducing the concept of impedance into Optics, the optical properties of thin films can be studied in a simple manner making use of the methods known in Electricity, The impedance Z has to be defined as the ratio of two quantities so that Z always varies continuously with the thickness of the film, even if the refractive index varies discontinuously. The ratio Et/Ht satisfies this condition, where Et and Ht are the components of the electric and magnetic vectors E and H parallel to the plane separating the two different média. If the impedance Z t is known, the coefficient of reflection Rt can be easily calculated. The values of E and H in a plane parallel to the surface of a film can be deduced from the two values Et' and Ht' in another plane by means of two linear équations ; the film between the two planes behaves like an optical quadrupole. By decreasing the thickness of this film indefinitely, one can dérive a differential equation of the first order for the impedance and four simultaneous differential equations for the four coefficients of the quadrupole. We consider the special case where the inverse of the refractive index varies linearly with the thickness of the transparent film. For the case of normal incidence it is found that the " reduced " impedance Z (defined as the product of the impédance and the refractive index) as a function of the thickness describes a circle in the complex plane Z. A different circle is found for each frequency. For any thickness of the film, one can construct the diagram of the impedance as function of the frequency of the incident light. The reflection coefficient R of such a transparent film placed between two transparent media of refractive indices n0 and n1, has minima of value zero, provided the refractive index of the film at the boundaries of those media is equal to n0 and n1 respectively.

PACS
7866 - Optical properties of specific thin films.

Key words
refractive index