The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries

A novel numerical method called the Thermal Discrete Dipole Approximation (T-DDA) is proposed for modeling near-field radiative heat transfer in three-dimensional arbitrary geometries. The T-DDA is conceptually similar to the Discrete Dipole Approximation, except that the incident field originates from thermal oscillations of dipoles. The T-DDA is described in details in the paper, and the method is tested against exact results of radiative conductance between two spheres separated by a sub-wavelength vacuum gap. For all cases considered, the results calculated from the T-DDA are in good agreement with those from the analytical solution. When considering frequency-independent dielectric functions, it is observed that the number of sub-volumes required for convergence increases as the sphere permittivity increases. Additionally, simulations performed for two silica spheres of 0.5 micrometer-diameter show that the resonant modes are predicted accurately via the T-DDA. For separation gaps of 0.5 micrometer and 0.2 micrometer, the relative differences between the T-DDA and the exact results are 0.35% and 6.4%, respectively, when 552 sub-volumes are used to discretize a sphere. Finally, simulations are performed for two cubes of silica separated by a sub-wavelength gap. The results revealed that faster convergence is obtained when considering cubical objects rather than curved geometries. This work suggests that the T-DDA is a robust numerical approach that can be employed for solving a wide variety of near-field thermal radiation problems in three-dimensional geometries.

💡 Research Summary

The paper introduces the Thermal Discrete Dipole Approximation (T‑DDA), a novel numerical framework for simulating near‑field radiative heat transfer between arbitrarily shaped three‑dimensional objects. Building on the well‑established Discrete Dipole Approximation (DDA) used for electromagnetic scattering, the authors replace the external illumination with thermal fluctuations of electric dipoles that act as stochastic sources. Starting from the stochastic Maxwell equations, the thermal current density J(r) is modeled via the fluctuation‑dissipation theorem, which links its two‑point correlation to the local temperature and the imaginary part of the material permittivity. By separating the total electric field into an incident part (generated by the thermal currents in free space) and a scattered part (arising from material contrast), a volume‑integral equation involving the free‑space dyadic Green’s function G(r,r′) is derived.

The core of T‑DDA is the discretization of each object into N cubical sub‑volumes small compared with the wavelength. Within each sub‑volume the fields and material properties are assumed uniform, allowing the sub‑volume to be represented by an electric point dipole p_i. The dipole polarizability is expressed through the Clausius‑Mossotti relation, and a radiative correction term accounts for self‑interaction. Inter‑dipole coupling is captured by evaluating G(r_i,r_j) for all i ≠ j, leading to a deterministic 3N × 3N interaction matrix A. The stochastic dipole moments obey ⟨p_i⟩ = 0 but have a covariance ⟨p_i p_j*⟩ proportional to Θ(ω,T) Im