Transient Behavior of Thermal Radiation in Photonic Systems

We investigate the transient behavior of thermal radiation in photonic systems. Specifically, we examine a photonic system that begins at absolute zero (0 Kelvin) and is placed next to a heat source. Using the finite-difference time-domain (FDTD) method and the ensemble average method, we simulate the energy density of photons as a function of time. The heat source, maintained at a well-defined temperature T, emits black-body radiation. Our findings indicate that the energy density of photons behaves similarly to that of an under-damped oscillator. The dynamics can be analyzed through circuit theory, where the photonic system is treated as being injected with photons rather than being charged. Initially, the photon injection process is linear, but it subsequently exhibits under-damped decay. We define photonic resistance, capacitance, and inductance based on the photon injection processes. We also discuss how these quantities depend on both one-dimensional and two-dimensional photonic systems.