Abstract
A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently by three of the present authors. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then, the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar microcavities, diffraction gratings and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.
Highlights
Optics and heat conduction have often been associated, because optical devices and systems generally have to face thermal effects
When the electromagnetic field interacts with dense matter, optical losses are converted into heat, which generates conductive, convective and radiative transfer
To achieve this correspondence between admittance diagrams in heat conduction and light propagation, we considered a thermal multilayer with conduction number k = k + jk, and plotted the admittance diagrams at Ω = 5 Hz for decreasing values of k
Summary
Optics and heat conduction have often been associated, because optical devices and systems generally have to face thermal effects. An analogy can be unveiled in time harmonic regime when metallic media are considered in optics Under these conditions, electromagnetic fields decay exponentially fast away from a metal–dielectric interface, so that their behaviour is somewhat reminiscent of a temperature field undergoing a fast decay away from a heat source. With k the wavenumber (or conduction number by analogy with optics), u the scalar electric field or temperature and u its Fourier transform defined as u (ρ, f ) = u(ρ, t) exp(j2π ft)dt t (2.8a) and u(ρ, t) = u (ρ, f ) exp(−j2π ft)df f (2.8b). The k value is necessarily complex in conduction for reasons following (2.7)–(2.10), so that heat diffusion can be considered to be analogous to optical propagation (more exactly, electric field attenuation) in artificial metallic media. The original (real) field is reconstructed with a double inverse Fourier transform over temporal (f ) and spatial (ν) frequency
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