Focused thermal emission from a nanostructured SiC surface

Incandescent sources that produce light from electrically heated filaments or films tend to feature low efficiencies and offer poor spectral and angular control. We demonstrate that a judicious nanostructuring of a SiC surface can focus thermal emission of a preselected spectral range to a well-defined height above the surface. SiC is known to support electromagnetic surface waves that afford the required thermal emission control. Here, we provide general design rules for this type of focusing element that can be extended to other material systems, such as metals supporting surface plasmon-polariton waves. These rules are verified using full-wave calculations of the spatial variation of thermal emission. The obtained results establish a foundation for developing more complex algorithms for the design of complex thermal lenses.

Figure 1

(a) Operation of a SiC thermal lens capable of focusing thermally generated surface waves (black) by decoupling them from appropriately positioned nanobeams to achieve constructive interference in a line focus above the surface (blue arrows). The proposed design will lead to the generation of diverging waves at the same time (red arrows). (b) Scattering of a surface phonon polariton propagating to the right (black) by a simplified version of a thermal lens made of only three subwavelength beams. The arrows depict various pathways by which the surface wave can be decoupled to the far field. Geometrical parameters are defined in this cross-sectional view of the structure.

Figure 2

Phase differences between the waves scattered by SiC beams at the focal point as a function of the beam spacing $d$, for a focal length of (a) $f=50$ and (b) $f=100\mu \text{m}$. In these figures, the red dotted lines show the variation of phase ${\theta }_1$, green solid lines show the variation of phase ${\theta }_2$, and blue dashed lines show the variation of the phase ${\theta }_3$. Shaded regions show ranges of distance $d$ for which the absolute values of all the phase differences are smaller than $\pi /2$.

Figure 3

Schematic of the geometry used to perform thermal emission calculations. The thermal emission from an arbitrarily shaped periodic structure can be calculated at a specific height by placing a hypothetical planar body with a small loss at the height of interest and by looking at the thermal transfer between the periodic structure and this planar body.

Figure 4

Thermal emission variation with the beam spacing $d$, at angular frequency $\omega =1.66\times {10}^{14}\text{rad}/\mathrm{s}$ for the structure shown in Fig. 1, at the focal height of (a) $f=50$ and (b) $f=100\mu \text{m}$. These calculations are performed for three different choices of the width and height of the scattering nanobeams.

Figure 5

(a) Thermal emission lateral variation at different heights at angular frequency $\omega =1.66\times {10}^{14}\text{rad}/\mathrm{s}$. (b) Thermal emission lateral variation at the focal height of $f=50\mu \text{m}$. This variation is plotted along with the corresponding variations if only three scatterers were used with different beam spacings $d$.

Figure 6

(a) Thermal emission lateral variation at different heights at angular frequency $\omega =1.66\times {10}^{14}\text{rad}/\mathrm{s}$. (b) Thermal emission lateral variation at the focal height of $f=100\mu \text{m}$. This variation is plotted along with the corresponding variations if only three scatterers were used with different beam spacings $d$.