Fabry-Perot optical cavities

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An asymmetric Fabry-Perot resonance cavity can enhance absorption as well as thermal emission at particular wavelength and can be used to build a coherent emission source [1,2]. The structure involves a thin metallic layer over a dielectric film (which functions as an optical cavity) on a thick metal film (which functions as a mirror). As shown in Fig. 1, the top metal layer has to be ultrathin (on the order of the radiation penetration depth) to let infrared radiation to penetrate through into the cavity and thus enable resonance. High reflection from the boundaries of the resonance cavity is also essential for the sharp spectral peak at the resonance condition. SiO2 is employed to form the optical cavity and Au as the reflective coating on both sides of the dielectric cavity.

Figure 1. Schematic of the asymmetric Fabry-Perot structure for coherent thermal emission and the reflection and transmission coefficients.

To experimentally investigate the coherent emission from proposed Fabry-Perot optical cavities, several samples were fabricated on a 500-μm thick Si wafer. After proper surface cleaning, a thin Ti adhesive layer and a 200-nm Au film were deposited subsequently using an e-beam evaporator under high vacuum environment. Afterwards, a SiO2 film was deposited at 250ºC in a plasma-enhanced chemical vapor deposition chamber. The thickness of SiO2 film was monitored by measuring the oxide film deposited on a bare Si piece at the same time. Finally, a thin Au film (less than 30 nm) was coated on the sample surface using the e-beam evaporator. The thickness of top Au film and SiO2 layer were determined from fitting the optical properties.

Figure 2. (a) Normal reflectance of a fabricated specimen; (b) TE-wave reflectance at incidence angles of 30° and 45°; from [2].

The spectral directional reflectance of the fabricated sample was measured by an FTIR spectrometer at 10º, 30º and 45º angles of incidence, similar to the experiments described in the previous section. Figure 2(a) shows the measured reflectance spectrum at 10º incidence from 3 000 to 13 000 cm–1 with 4 cm–1 resolution. There are two reflectance dips due to the cavity resonance since the SiO2 layer thickness is dc = 622 nm. Note that the top Au layer thickness is df = 21 nm. According to Kirchhoff’s law, two emission peaks were suggested by the reflectance spectrum, indicating the Fabry-Perot resonator can be used as a coherent emission source. The quality factor, a measure of sharpness of the emissivity peak or reflectance dip, is defined as Q = Δω / δω, where the free spectral range Δω is the frequency interval between two consecutive reflectance dips. The Q factor at 10º incidence angle is 49.5 and 21.7 for the lower and higher frequency resonances, respectively. The reflectance dips (or emissivity peaks) were also observed at oblique angles, shown in Fig. 2(b) for TE waves only. The resonance frequencies shift to higher frequency and the free spectral range becomes larger with larger incidence angles. Similar to the spectra for truncated PCs, the predicted reflectance minima with fitted parameters are lower than the measurement, which may be caused by the beam divergence. The reflectance at oblique angles for TM waves exhibits similar behavior as TE waves.

Two different approaches, i.e., the “indirect” and “direct” methods, are commonly used for computing the emissivity of an object. For an opaque surface at a uniform temperature, the indirect method involves calculating the spectral directional-hemispherical reflectance to deduce the spectral directional emissivity based on Kirchhoff’s law. Wang et al. [3] utilized a combination of Maxwell’s equations with the fluctuation-dissipation theorem to directly calculate the emissivity. The equivalence between the spectral directional emissivity and absorptivity of each layer can be viewed as the generalized Kirchhoff’s law. This allows the thermal emission from and brightness temperature of a multilayered structure with a nonuniform temperature distribution to be evaluated using the indirect method.


[1] Lee, B. J., and Zhang, Z. M., 2006, “Design and Fabrication of Planar Multilayer Structures with Coherent Thermal Emission Characteristics,” Journal of Applied Physics, 100, 063529.

[2] Wang, L. P., Lee, B. J., Wang, X. J., and Zhang, Z. M., 2009, “Spatial and Temporal Coherence of Thermal Radiation in Asymmetric Fabry-Perot Resonance Cavities,” International Journal of Heat and Mass Transfer, 52, pp. 3024-3031.

[3] Wang, L. P., Basu, S., and Zhang, Z. M., 2011, “Direct and Indirect Methods for Calculating Thermal Emission from Layered Structures with Nonuniform Temperatures,” Journal of Heat Transfer, 133, p. 072701.