Thermal radiation in photonic crystals

We analyze the properties of thermal radiation in photonic crystals and show that the spectral energy density, the spectral intensity, and the spectral hemispherical power are only limited by the total number of available photonic states and their propagation characteristics. In addition, we show that the central quantity that determines these thermal radiation characteristics is the area of the isofrequency surfaces and not the photonic density of states as it is generally assumed. Through the presence of partial or complete photonic band gaps and the associated spectral and angular redistribution of photonic states, it is possible to have spectral regions over which the thermal radiation intensity is enhanced relative to the free space blackbody limit and propagation directions along which thermal photon focusing effects appear.

Figure 1

(Color online) Frequency dependence of the spectral energy density (left-hand panel, upper figure) and spectral hemispherical emissive power (left-hand panel, lower figure) for free space (continous line), a homogeneous dielectric with dielectric constant equal to $ϵ=1.52$ (dotted-dashed line) and the model photonic crystal (see text; with a long wavelength effective dielectric constant ${ϵ}_{\mathrm{av}}=1.52$) (dashed line). The temperature is chosen such that the conventional blackbody exhibits a maximum at the frequency of the first van Hove singularity of the model system’s DOS, ${\omega }_{\max }\approx 0.327{\omega }_0$, and frequencies are measured in units of ${\omega }_0=2\pi c∕a$. On the right-hand panel, we show the ratios of the respective quantities relative to their free space values.

Figure 2

(Color online) Band structure for a 2D square lattice of dielectric cylinders ($ϵ=8.41$, $r∕a=0.15$) in air. In the $\omega =0$ plane we show the $\mathbf{k}$-space domain used (first three Brillouin zones) and the isofrequency contours for $\omega ∕{\omega }_0=0.25$ (dotted-dashed line), 0.327 (line), 0.345 (continuous line).

Figure 3

Dependence of the directional spectral emissive power within the 2D model photonic crystal on the emission angle for ${\omega }_1∕{\omega }_0=0.25$ (continous line), ${\omega }_2∕{\omega }_0=0.31$ (dashed line), ${\omega }_3∕{\omega }_0=0.327$ (dotted-dashed line), and ${\omega }_5∕{\omega }_0=0.34$ (double dotted-dashed line). For visualization purposes the first three quantities are multiplied by a factor of 3.