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Optical and Radiative Properties of Solid Media: Analysis and Modeling with Nonlocal Differential Operators


Design objectives involving the radiant exchange of electromagnetic fields demand accurate, continuously defined knowledge of the optical and radiative properties of the interacting media. Attempts to improve the accuracy of the classical descriptions for these properties have often led to models that: do not adhere to important physical criteria, are overparameterized and possess superfluous components, are realized in terms of ad hoc components lacking physical provenance, or that suffer from any combination of these shortcomings. These issues can entirely preclude their use in standard simulation frameworks for design-driven applications. Further complications arise when pursuing thermophysical adaptations of these descriptions, since it is unclear how to properly accommodate the temperature dependence, much less how to do so while simultaneously addressing the noted deficiencies.

In this work, we develop and delineate a practical, high-fidelity thermophysical optical property modeling framework that more accurately reflects experimental observations while also remaining fully compliant with fundamental physical constraints. The macroscopic behaviors of even modestly sized spectroscopic systems are the average result of a very large number of constituent particles. Thus, to aid in our endeavor, we exploit the infinite dimensionality of temporally nonlocal differential operators in relevant model components. The modeling framework is accompanied by our recently developed generalized spectroscopic analysis framework, which derives from a variable order calculus formalism. The latter is used for the analysis and interpretation of spectroscopic systems in general, as well as for the nonlocal components of the model specifically.

Emphasis is placed on modeling the temperature-dependent intraband and interband dynamics of metals in the technically significant infrared regime. Results are given for several metals of engineering relevance. Validation obtained over several data sources demonstrates that---in addition to the desired modeling fidelity---the framework is capable of forming meaningful inverse extrapolatory estimates of the complex-valued optical properties at higher temperatures (i.e., phase information recovery), despite the fact that the model parameters are derived from real-valued radiative property measurements at those temperatures. Such estimates are desirable for use with more complex Fresnel frameworks, such as those used to model systematically or randomly roughened media.

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