Transmission properties of optical adhesives and bonding layers

We analyze the transparency of a thin film of low refractive index (an optical glue or a bonding layer) placed between higher-index media and forming an opto-pair. Examples include a semiconductor light-emitting diode with attached lens or a semiconductor scintillator bonded to a photodiode. The transparency of an opto-pair is highly sensitive to the film thickness due to the so-called frustrated total internal reflection. We show that high transparency in a wide range of the incidence angle can be achieved only with very thin layers, more than an order of magnitude thinner than the wavelength. The angular dependence of the transmission coefficient is shown to satisfy a simple and universal sum rule. Special attention is paid to the angular average of the optical power transmission, which can be cast in a universal form for two practically relevant classes of source layers.