利用有限差分法研究栅格的光共振吸收

FDM INVESTGATION OF OPTICAL RESONANCED ABSORPTION ON CORRUGATED SURFACES

基于严格的电磁场理论应用有限差分法研究了栅格表面的光散射和吸收的理论，并计算了具有任意截面形状的一维栅格在平面散射及锥形散射情况下的光声角共振曲线．文中引入了依赖于两个形状参数的准正弦形模型来模拟实验条件下的栅格截面．针对实验条件用ｐ偏振或ｓ偏振的入射光，通过选择合适的形状参数，计算光声角谱曲线的结果和实验符合得非常满意．计算稳定可靠．因此，当栅格材料的物理参量（如介电常数等）已知的情况下，通过理论计算和实验曲线的拟合，可以估计栅状表面的几何参数（高度和周期）和表面形状．

In eighties, the photoacoustic (PA) angular spectroscopy has been used to study the optical resonance absorption in one or two dimensional metalcoated diffraction gratings, where the optical absorption spectra are measured by detecting the part of the absorbed energy dissipated as heat, while the incident angle is varied. The PA method can measure not only the resonance absorption of the planar diffraction of gratings, but also the conical diffraction with any azimuth angle, which is difficult to be measued by conventional optical methods.On the other hand, several theories have been presented for explaining the optical absorption phenomena on the corrugated surfaces. Generally, the gratings (grooves) were considered as regularly sinusoidal or rectangular. However, the shapes or profiles of gratings are always not regular in practical conditions. We find that the theoretical calculations based on these regular functions cannot be fitted satisfactorily to the experimental results. Therefore, simple regular functions are not suitable for describing the corrugation profiles. In this paper, an algorithm with the finite difference method (FDM) based on rigorous electromagnetic theory has been deduced to calculate the optical absorption and scattering on corrugated surfaces, in which a quasisinusoidal model with two shape factors has been introduced to describe the profile shape for fitting the experimental results. Then the photoacoustic angular resonance spectra of onedimensional gratings with arbitraryfunction profiles under the planar diffraction, as well as the conical diffraction, have been calculated. By adjusting the parameter factors, the PA angular spectra as functions of the incident angle for ppolarized and spolarized incident lights can be satisfactorily fitted to the experimental results. Moreover, all calculations show the algorithm is stable. Therefore, when the physical property (such as dielectric constant) is already known, the systematrical parameters (including the height and period of the grating) and the surface shape can be theoretically estimated by PA method.