Rigorous coupled wave approximation

The optical behaviour of silver island films embedded in optical thin film materials has been studied by spectrophotometry. The silver cluster surface plasmon absorption line position and width strongly depend on deposition temperature and ambient material. Electron micrographs of the samples allow to establish the correlation between silver cluster geometry and optical behaviour. The first results of Rigorous Coupled Wave Approximation (RCWA) calculations reproduce the spectrophotometric experimental results. 

A rigorous method to calculate the optical loss of periodic planar cluster assemblies is offered by RCWA (Rigorous Coupled Wave Approximation) calculations commercially available in grating solver software [4]. In order to apply this method to the calculation of the optical response of planar silver cluster assemblies such as shown in Fig.l, one has to assume that the cluster arrangement is periodically continued in two dimensions. In practice, we assumed a 300 nm x 300 nm broad elementary cell which contains 55 silver islands of 7.8 nm height (Fig.2). 

Diffractive ARS are usually calculated either using the effective medium approximation, or the rigorous coupled-wave analysis [169]. Direct numerical solution of Maxwell equations and the approach using the plane wave theory were also used [174]. 

A comparison of the steady-state profiles predicted by the wave model and those predicted by a rigorous tray-by-tray column model is shown in Fig. 5.16 for a coupled column system which serves for the separation of a mixture of methanol, ethanol, and 1-propanol. The approximation by the wave model in Fig. 5.16 is fairly good, although the reduction of the system order is considerable. The state variables of the rigorous model are the concentration and temperatures on each column tray. In contrast to this the state variables of the wave model are only the front positions. 

---