# Important phenomena and applications thermal radiation in periodic gratings

The underlying mechanisms of several phenomena associated with periodic gratings are described below. Whenever possible, the applications for tailoring the radiative properties in energy systems and optoelectronics are discussed.

## Contents

#### Surface plasmon polaritons (SPPs) and surface phonon polaritons (SPhPs) in gratings

Plasmons are quasiparticles associated with oscillations of plasma, which is a collection of charged particles such as electrons in a metal or semiconductor [1,2]. Plasmons are longitudinal excitations that can occur either in the bulk or at the interface. The field associated with a plasmon is confined near the surface, while the amplitude decays away from the interface. Such a wave propagates along the surface, and it is called a surface electromagnetic wave. Surface plasmon polaritons (SPPs) can be excited by electromagnetic waves and are important for the study of optical properties of metallic materials, especially near the plasma frequency, which usually lies in the ultraviolet. The associated surface electromagnetic wave in polar materials due to the vibration of ions is called a surface phonon polariton (SPhP). The requirement of evanescent waves on both sides of the interface prohibits the coupling of propagating waves in air to the surface plasmons. Prisms and gratings are commonly used to couple propagating waves in air with surface plasmons.

When the plane of incidence is perpendicular to grooves, SPPs or SPhPs can be excited in metallic or polar dielectric gratings due to the evanescent wave nature of some diffraction orders. The Bloch-Floquet condition becomes

kx,j = kx + 2πj / Λ

(1)

where j is the diffraction order. For this reason, the SPP/SPhP dispersion relation can be folded into the region for   $k_{x} \le {\pi / \Lambda}$   so that surface polaritons can be excited on a grating surface with propagating waves in air.

#### Wood’s anomaly

Wood’s anomaly affects radiative properties and causes abrupt changes in the reflectance, transmittance, and absorptance spectra [1,3]. Wood’s anomaly occurs when a diffraction order emerges or disappears at the grazing angle. The transmittance through a 1D slit array can be either enhanced or suppressed due to Wood’s anomaly. Since Wood’s anomaly occurs as a result of diffraction, both polarizations may exhibit such an anomaly. For shallow gratings when the plane of incidence is perpendicular to the grooves, however, Wood’s anomaly is not obvious for TE waves, and thus, initial studies only dealt with the anomaly for TM waves.

#### Cavity resonance

When cavity resonance occurs, standing waves exist in cavities formed by the grating. At the resonance condition, a strong electromagnetic field exists inside the cavity or slit – the confined and enhanced fields subsequently enhance transmission through the gratings. Therefore, several peaks can be observed from the far-field transmittance shown in Fig. 1 [4]. The cavity resonance in gratings is not the same as a Fabry-Perot resonance, whose resonance condition is given by $n_{{\rm c}} d_{{\rm c}} =m\lambda \, {\rm /}\, {\rm 2}$, where nc and dc are the refractive index and thickness of the medium and m is an integer. Notice that each cavity formed by the grating has two open ends at z = 0 and z = d. However, the boundary condition requires that tangential field components be continuous, enabling electromagnetic waves to be confined inside the cavity. As a matter of fact, the resonance condition strongly depends on the grating’s geometric parameters as well as the boundary conditions [1]. The standing wave in the slit is a combination of all diffracted waves including evanescent waves, and it is not necessary for a single diffraction component to contribute to the cavity resonance. The interferences of all diffracted evanescent waves must be fully considered in order to predict the transmittance peak position. Also, large transmission enhancement and strong field localization can be achieved with nanoscale metallic slit arrays for mid-IR radiation [5].

Figure 1. Transmittance and absorptance of a free-standing Ag grating at normal incidence for (a) TE waves and (b) TM waves [4].

## References

[1] Zhang, Z. M., 2007, Nano/Microscale Heat Transfer, McGraw-Hill, New York.

[2] Raether, H., 1988, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer, Berlin.

[3] Chen, Y.-B., Zhang, Z. M., and Timans, P. J., 2007, “Radiative Properties of Pattered Wafers with Nanoscale Linewidth,” Journal of Heat Transfer, 129, pp. 79-90.

[4] Lee, B. J., Chen, Y.-B., and Zhang, Z. M., 2008, “Transmission Enhancement through Nanoscale Metallic Slit Arrays from the Visible to Mid-Infrared,” Journal of Computational and Theoretical Nanoscience, 5, pp. 201-213.

[5] Lee, B. J., Chen, Y.-B., and Zhang, Z. M., 2008, “Confinement of Infrared Radiation to Nanometer Scales through Metallic Slit Arrays,” Journal of Quantitative Spectroscopy and Radiative Transfer, 109, pp. 608-619.