In this paper, we analyze the optical power transmission in structures that include a low-index intermediate layer and sources with a wide angular distribution. Special attention is paid to the angular average of the transmission coefficient, which can be cast in a universal form for two practically relevant classes of source layers. Due to the so-called frustrated total internal reflection, the structure transparency is highly sensitive to the intermediate layer thickness and index contrast. We show that the transmission coefficient for isotropic radiation may remain low even for optically thin low-index intermediate layers, so that the usual comparison between the optical thickness and the wavelength is no longer a reliable criterion. Calculations are presented for exemplary structures, such as a semiconductor scintillator bonded to a photodiode. The angular dependence of the transmission coefficient is shown to satisfy a simple and universal sum rule.
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