One-dimensional photonic crystals

From Thermal-FluidsPedia

Jump to: navigation, search

A photonic crystal (PC) is a periodic structure that in analogy with real crystals can have optical properties similar to the electronic band structures of crystalline solids [1]. 1D PC is a periodic structure consisting of alternating dielectric layers. Like real crystalline materials, PCs show band structures composed of pass bands and stop bands in the photon energy versus momentum, i.e., ω–kx plane. When a PC is placed adjacent to a metallic layer, a surface wave can occur since an effective evanescent wave can exist in the PC [2]. The metallic layer can be replaced by a polar dielectric which can also strongly reflect the incident radiation in its phonon absorption band. A surface wave for either polarization can therefore be excited, even at normal incidence from air, resulting in strong absorption or emission in a narrow band.

Theory and dispersion relations

Like real crystalline materials, PCs show band structures composed of pass bands and stop bands in the ω–kx plane. Note that the period (i.e., lattice constant) of a PC is Λ = d1 + d2, where d1 and d2 are the thickness of the two dielectric materials of different refractive indices. It is not appropriate to treat a PC structure as a homogeneous medium with equivalent ε and μ. The surface-wave dispersion relation for 1D PCs is rather complicated. A technique to obtain the dispersion between a PC and a metal is called the supercell method [3]. The dispersion relation of surface waves at the PC-Ag interface for both TE and TM waves is shown in Fig. 1, where the PC materials are SiO2 (n1 1.45) and Si3N4 (n2 = 2.0). The shaded regions correspond to the pass band, and the unshaded regions represent the stop band. The light line in air is denoted by a dash-dotted line. The dispersion curves (dashed lines) of the surface wave are located in the stop band of the PC. In the calculation, the thicknesses of the dielectric layers are set to be d1 = d2 = 153 nm, and the surface termination layer is dt = 100 nm. The PC-on-Ag structure was fabricated and shown in Fig. 2 [4]. The excitation of surface waves results in coherent thermal emission as discussed in the subsequent section.

Figure 1. Surface wave dispersion relations: (a) TE waves; (b) TM waves. The shaded regions represent pass bands of the PC, and the unshaded regions correspond to stop bands. The resonance conditions obtained from the spectrometer measurements and from the scatterometer measurements are denoted by the circular and triangular marks, respectively [3].


Figure 2. (a) Cross-sectional view by FIB image of the PC-on-Ag structure; (b) Polar plot of the directional emissivity demonstrates spatial coherence [3,4].


Coherent thermal emission measurements

A PC-on-Ag structure was designed and fabricated on a silicon substrate, and its cross-sectional image obtained by using a focused ion beam (FIB) workstation is shown in Fig. 2(a). A Ti adhesive layer was first deposited on a Si substrate, followed by a Ag film, which is thick enough to be opaque (semi-infinite). The truncated PC with six unit cells was formed on the Ag film using plasma enhanced chemical vapor deposition of SiO2 and Si3N4 layers. The thicknesses were obtained from fitting the reflectance dip wavelengths. The measured root-mean-square (rms) surface roughness is approximately 10 nm. A Fourier-transform infrared spectrometer (FTIR) was used to measure the spectral reflectance at incidence angles of 10°, 30°, and 45°. The period of the PC is about 300 nm with a surface termination layer of 100 nm thick, which were obtained by fitting the dip wavelengths in the reflectance spectra. In addition, a laser scatterometer was employed to measure the angle-resolved reflectance at the wavelength of 891 nm. The emissivity calculated from the measured reflectance exhibits temporal and spatial coherence; see Fig. 2(b). Since the laser beam is highly collimated, the measured reflectance exhibits a very sharp dip with a minimum at θ = 54º less than 0.05, which is even lower than that predicted, although the calculated width of the valley is somewhat narrower. The key to enabling coherent emission is by exciting a surface wave at the PC-Ag interface in the stop band of the PC. When surface waves are excited, the electromagnetic field is highly localized near the PC-Ag interface. Coherent emission sources based on truncated 1D PC may be used to improve the design of wavelength-selective coatings for energy harvesting and thermal control applications.


References

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

[2] Lee, B. J., Fu, C. J., and Zhang, Z. M., 2005, “Coherent Thermal Emission from One-Dimensional Photonic Crystals,” Applied Physics Letters, 87, p. 071904.

[3] Lee, B. J., and Zhang, Z. M., 2009, “Indirect Measurements of Coherent Thermal Emission from a Truncated Photonic Crystal Structure,” Journal of Thermophysics and Heat Transfer, 23, pp. 9-17.

[4] Lee, B. J., Chen, Y.-B., and Zhang, Z. M., 2008, “Surface Waves Between Metallic Films and Truncated Photonic Crystals Observed with Reflectance Spectroscopy,” Optics Letters, 33, pp. 204-206.