Proceedings Article | 12 September 2021
KEYWORDS: Multilayers, Absorption, Optical coatings, Thermal modeling, Temperature metrology, Pulsed laser operation, Modeling, Thin films, Refractive index
Optical coatings have been extensively characterized these last decades, due to more and more severe requirements. These characterizations include optical properties, uniformity, hardness, adhesion and stress, damage threshold, absorption, scattering and others… Despite this state of the art, photo-induced thermal radiation [1]–[3] in optical coatings was rarely investigated in detail until now, while emissivity plays a key role in numerous sectors related to energy and defence, space optics and MIR imaging... This is the scope of this paper to provide an exact theory of thermal radiation in optical multilayers submitted to an arbitrary illumination (continuous, pulsed, modulated). The spectral range of thermal radiation (TR) is temperature (Tp) dependent. Hence it varies with incident power, and with the imaginary indices of the thin film materials. Index dispersion also plays a key role for short duration beams. As always with thin films, the TR waves follow Maxwell equations and their angular and spectral patterns are shaped by the coating design, which may open an opportunity to control these patterns [4], [5]. Relying on the fluctuation dissipation theorem [1], we introduce in Maxwell equations the adequate currents responsible for thermal radiation. These currents are temperature related, for which reason the depth and time distribution of temperature is also calculated for arbitrary illumination regimes. The Tp calculation relies on the analogy [6], [7] between thermal (diffusion equation) and optics (propagation equation) in metallic media. The resulting currents are bulk currents which vary within the depth of the stack, which creates a similarity with luminescent micro-cavities [8]. Eventually we calculate the waves emitted from these currents and this gives the angular, wavelength and temporal patterns of thermal radiation which merges in free space. The TR patterns are analysed for a series of coatings and a few ideas are presented to reduce, confine, or enhance the thermal waves.
