Coherent thermal infrared emission by two-dimensional silicon carbide gratings

The thermal emission of cross-slit silicon carbide grating is studied in the Restrahlen region over all emission angles. We show experimentally that the thermal excitation of surface-phonon polaritons on the surface of 2D grating allows us to get a high emissivity in both polarizations, which is collimated in $p$ polarization for a specific wavelength determined by the periodicity of the grating. We also show numerically that 2D gratings optimized to efficiently out-couple thermally excited surface-phonon polaritons of the flat part of the dispersion relation can have a high efficiency for all emission directions for both polarizations.

Figure 1

(a) Spherical coordinate system used in this paper. (b) Dispersion relation of the surface-phonon polaritons and its isofrequency projection on the $({\mathbf{k}}_{\mathbf{x}},{\mathbf{k}}_{\mathbf{y}})$ plane; the gray areas represent the propagating waves in air.

Figure 2

(a) Isofrequency contour of the SPP dispersion relation on the surface of a 2D shallow grating. (b) Scheme of the studied grating. The arrows represent the wave vectors of SPP which are coupled with the wave propagating perpendicularly to the surface.

Figure 3

Polar representation of the calculated emissivity at $\lambda =12.1$ $\mu$m in both $p$ (a) and $s$ polarizations (b) of a cross-slit SiC grating. The inset is the emissivity in $p$ polarization close to direction perpendicular to the surface. The parameters of this grating are ${\Lambda }_x={\Lambda }_y=11.5$ $\mu$m, $h=700$ nm, and $f_x=f_y=90\%$.

Figure 4

The two schemes represent the components parallel to the interface of the wave vectors of the electric and magnetic fields for the outgoing wave and for the coupled SPP in $p$ (a) and $s$ polarization (b). In this example, the outgoing wave and the SPP are coupled by the ($-$1,0) order of the grating, and their wave vectors follow the phase matching condition ${\mathbf{k}}_{//,\mathbf{out}}={\mathbf{k}}_{\mathrm{spp}}-{\mathbf{K}}_{\mathbf{g}}$, with $K_g=\frac{2\pi }{\Lambda }{\mathbf{e}}_{\mathbf{x}}$.

Figure 5

[(a)–(c)] Schemes of the fabrication steps of the grating. (a) Mask of nickel obtained by electronic lithography on a SiC substrate (200 $\mu$m thick). (b) Reactive ionic etching of the SiC. (c) Final grating after chemical etching of the nickel mask in a HNO${}_3$ solution. (d) Scanning electron microscope image of the sample.

Figure 6

Measurement (dots) and calculation (dashed line) of the emissivity spectrum in the direction normal to the surface. Parameters of the grating: ${\Lambda }_x={\Lambda }_y=11.5$ $\mu$m, $f_x=f_y=0.88$, and $h=700$ nm.

Figure 7

(a) Polar representation of the calculated emissivity at $\lambda =12.18$ $\mu$m in $p$ polarization. The blue and red lines represent the directions for which emissivity were measured. (b) Emissivity as a function of $\theta$ at $\lambda =12.18$ $\mu$m, for two azimuthal angles, $\phi =0\mathrm{deg}$ (blue) and $\phi =45\mathrm{deg}$ (red) in $p$ polarization. Cross and square markers represent the measurements and the lines the calculations.

Figure 8

(a) Polar representation of the calculated emissivity at $\lambda =12.18$ $\mu$m in $s$ polarizations. The blue and red lines represent the directions for which emissivity were measured. (b) Measured (markers) and calculated (line) emissivity at $\lambda =12.18$ $\mu$m as a function of $\theta$, with $\phi =0\mathrm{deg}$, in $s$ polarization. (c) Measurement (markers) and calculation (dashed line) of the emissivity as a function of the azimuthal angle $\phi$, with an incident angle $\theta =20\mathrm{deg}$, in $s$ polarization.

Figure 9

Calculated emissivity in $p$ (a) and $s$ (b) polarizations in the light cone at $\lambda =11.2$ $\mu$m.