Asymptotic expansion for the temporal coherence functions of a finite blackbody

Abstract

Planckian thermal radiation of temperature $T$ shows a broad continuous spectrum and poor, monotonically decreasing, temporal coherence. We study the effects due to the discreteness of the exact resonances in a finite, cube-shaped cavity (volume $L^3$) bounded by perfectly reflecting walls. Using the Poisson summation technique, we calculate the almost periodic spatially averaged temporal ($t$) correlation tensors in terms of the simultaneous asymptotic series in powers of both $\frac{1}{\mathrm{LT}}$ and $\frac{t}{L}$ with Riemann and Epstein zeta-function coefficients. The according cross-spectral tensors yield all orders of the expansion of the spectral mode density including the oscillatory terms.