Envelopes of optical interference spectra for duplex and triplex layered structures

Abstract

We have found analytical expressions for the envelopes of maxima and minima of interference reflection and transmission spectra for both transparent and absorbing two-and three-layer structures under the conditions of arbitrary light incidence and polarization state. General regularities for the shape of those spectral envelopes are established, depending on the optical thicknesses of constituent layers.

Application of spectral envelope functions of multilayer structures for analytical determination of antireflection conditions

“…In particular, the authors [8,9] have employed the envelope function for spectral reflection minima for finding of expressions for the incidence angles that provide zero p-or s-reflectance of one-layer structures. In spite of a common opinion that finding out the analytical functions for the spectral envelopes is hardly possible, even for relatively simple case of two transparent films [10], analytical expressions for the envelopes of both transparent and absorbing two-and three-layer structures have nevertheless been obtained [11].…”

Demonstration of optical beating in the reflectance and transmittance spectra of multilayer structures

“…It is worth noticing that the regularity explained by us has in fact been used by the authors [9] when finding the functions of spectral envelopes for the structures with two layers. Later on it has been generalised for the multilayer structures (see [10,15]).…”

“…These relations correspond to different possible ratios between the phase thicknesses of the layers. However, the studies [9,10] do not contain physical explanations of the phenomenon. In the present article we derive expressions for the envelopes in frame of analysis for the regularities of optical beating, which is demonstrated for the interference spectra of the structures with two (or more) layers.…”

“…A number of analytical relations for the envelopes of both the minimums and maximums of the interference spectra for the structures consisting of two and three layers have been derived in the work [9] using computer modelling of amplitude-and-phase Fabry-Perot spectra. These relations correspond to different possible ratios between the phase thicknesses of the layers.…”