Thermal emission and absorption of radiation in finite inverted-opal photonic crystals

We study theoretically the optical properties of a finite inverted-opal photonic crystal. The light-matter interaction is strongly affected by the presence of the three-dimensional photonic crystal and the alterations of the light emission and absorption processes can be used to suppress or enhance the thermal emissivity and absorptivity of the dielectric structure. We investigate the influence of the absorption present in the system on the relevant band edge frequencies that control the optical response of the photonic crystal. Our study reveals that the absorption processes cause spectral broadening and shifting of the band edge optical resonances, and determine a strong reduction of the photonic band gap spectral range. Using the angular and spectral dependence of the band edge frequencies for stop bands along different directions, we argue that by matching the blackbody emission spectrum peak with a prescribed maximum of the absorption coefficient, it is possible to achieve an angle-sensitive enhancement of the thermal emission/absorption of radiation. This result opens a way to realize a frequency-sensitive and angle-sensitive photonic crystal absorbers/emitters.

Figure 1

(Color online) Band structure and corresponding density of states (DOS) for a close-packed fcc lattice of air spheres in silicon $({ϵ}_{\mathrm{Si}}=11.9)$ (see also Ref. 18).

Figure 2

(Color online) A close-packed opal structure $(r∕a=\sqrt{(}2)∕4)$ viewed as a sequence of … ABCABC … planes grown along the [111] direction. In each plane, the high-dielectric constant spheres are embedded in a low-dielectric constant host medium (here, for simplicity, the dielectric background is assumed to be air) and are sitting on a triangular lattice of lattice constant $a_{xy}=a∕\sqrt{2}$. In the numerical simulations, the structure is assumed to extend to infinity in the $xy$ plane, but to have a finite size along the growth direction.

Figure 3

(Color online) A close-packed inverted opal structure $[r∕a=\sqrt{(}2)∕4]$ viewed as a sequence of … ABCABC … planes grown along the [111] direction. In each plane, the low-dielectric constant spheres (here, for simplicity, we assume air spheres) are embedded in a high-dielectric constant host medium and are sitting on a triangular lattice of lattice constant $a_{xy}=a∕\sqrt{2}$.

Figure 4

Band structure and transmission coefficient for a close-packed inverted structure of air spheres in a silicon $(ϵ=11.9)$ background along the $\Gamma \text{−}L$ direction. In the evaluation of the transmission coefficient, the photonic crystal is assumed to extend to infinity in the $xy$ plane but to have a finite thickness (16 unit cells) along the $z$ direction and we consider $s$-polarized incident light. The photonic crystal consists of close-packed air spheres (${ϵ}_{\text{air}}=1$) in a silicon dielectric background $({ϵ}_{\mathrm{Si}}=11.9)$.

Figure 5

Transmission spectrum for a 16 unit cell inverted opal structure for $s$-polarized incident light along the [111] direction of the underlying fcc lattice.

Figure 6

(Color online) Transmission spectra for a 16 unit cell inverted opal structure on a spectral range centered around the low-frequency edge of the first stop gap, for $s$-polarized incident light with increasing angles of incidence with respect to the [111] direction ($\Gamma \text{−}L$ direction in the reciprocal space, which is denoted by $\theta =0$ in the figure).

Figure 7

(Color online) Transmission spectra for a 16 unit cell inverted opal structure on a spectral range centered around the full photonic band gap of the underlying lattice, for $s$-polarized incident light with increasing angles of incidence with respect to the [111] direction.

Figure 8

Absorption spectrum for $s$-polarized incident light on a 16 unit cell inverted opal structure in the case of normal incidence.

Figure 9

(Color online) Absorption spectra for $s$-polarized incident light on a 16 unit cell inverted opal structure for different angles of incidence for a spectral region centered around the low frequency fundamental stop gap.

Figure 10

(Color online) Absorption spectra for $s$-polarized incident light on a 16 unit cell inverted opal structure for different angles of incidence for a spectral region centered around the full photonic band gap of the underlying lattice.

Figure 11

Absorption spectra for $s$-polarized incident light on a 16 unit cell inverted opal structure stacked on highly absorptive $(ϵ=11.9+i)$ and very thick $(t=160a)$ substrate for normal incidence along the [111] direction.

Figure 12

(Color online) Absorption spectrum for $s$-polarized incident light on a 16 unit cell inverted opal structure stacked on highly absorptive $(ϵ=11.9+i)$ and very thick $(t=160a)$ substrate for a frequency interval centered around the full photonic band gap of underlying periodic lattice for different angles of incidence.

Figure 13

(Color online) The absolute thermal power spectra for $p$-polarized incident light on a 16 unit cell inverted opal structure stacked on highly absorptive $(ϵ=11.9+i)$ and very thick $(t=160a)$ substrate for different angles of incidence at $T=1873.5\mathrm{K}$. The temperature is chosen such that the blackbody peak aligns with the low-frequency band edge and the spectrum is normalized to the blackbody spectrum in free space.

Figure 14

(Color online) The absolute thermal power spectra for $s$-polarized incident light on a 16 unit cell inverted opal structure for different angles of incidence at $T=309\mathrm{K}$. The temperature is chosen such that the blackbody peak aligns with a spectral feature located in the low-frequency part of the spectrum $(\omega \approx 0.121{\omega }_0)$ and the spectrum is normalized to the blackbody spectrum in free space. The figure illustrates the possibility to achieve angular selectivity for the thermal response of the photonic crystal system and the interplay between the choice of temperature, which determines the maximum of the thermal power at $\omega \approx 0.12{\omega }_0$, and the absorption coefficient of the photonic crystal, which give rise to the local maxima located around $\omega \approx 0.45{\omega }_0$. The magnitude of the blackbody thermal power spectrum has been scaled down to fit on the same plot.