This page provides a set of example files that demonstrate how thermal emission can be simulated with FDTD
Thermal emission simulation based on Kirchhoff's law
The simulation methodology is based on Kirchhoff’s law which states that the absorptivity and emissivity are equal when a system is at equilibrium. We calculate the absorption of the system with the FDTD simulation, then calculate the thermal emission as a post-processing step by using Kirchoff's law.
Here, we calculate the thermal emission of a periodic structure consisting of a tungsten slab and a dielectric slab with a periodic array of holes. The emission is calculated for hole periods of 2um and 3um. The thickness of the tungsten slab is chosen as 1.0a while the thickness of the dielectric is chosen as 0.2a with holes of radius 0.4a where a is the period of the array. In this simulation, we use a linearly polarized plane wave as an incident wave, although in the actual situation the thermally emitted light is unpolarized. For information about how to simulate unpolarized light, please see the Unpolarized beam. We study the thermal emission which is radiated into the perpendicular direction to the periodic structure.
The multi-coefficient material model gives an accurate material fit over a large wavelength range, allowing us to collect very broadband results from a single simulation.
Emissivity and thermal emission spectrum
To calculate absorptivity, i.e. emissivity, we put 2 power monitors located above and below the structure and calculate the power absorbed in the region between the monitors. The left figure below shows the emissivity for periods a=2μm and 3μm. The thermal emission spectrum can be obtained by multiplying the emissivity by the black body emission spectrum. They are shown in the right figure below together with the blackbody spectrum.
To reproduce these results, run the script file thermal_emission.lsf. It will run 2 simulations (one for a=2 μm and the other for a=3 μm) and create figures of the above results. Details of the thermal emission calculation can be found in the "thermal emission" analysis group.
- David L. C. Chan, Marin Soljaˇci´c and J. D. Joannopoulos, "Thermal emission and design in 2D-periodic metallic photonic crystal slabs," Optics Express, Vol 14, 8785-8796 (2006). http://dx.doi.org/10.1364/OE.14.008785