Alternative discretization in the aperiodic Fourier modal method leading to reduction in computational costs

Abstract

The Fourier modal method (FMM), also referred to as Rigorous Coupled-Wave Analysis (RCWA), is based on Fourier-mode expansions and is inherently built for periodic structures such as diffraction gratings. When the infinite periodicity assumption is not realistic, the finiteness of the structure has to be incorporated into the model. In this paper we discuss the recent extensions of the FMM for finite structures. First, we explain how an efficient FMM-based method for finite structures is obtained by a reformulation of the governing equations and incorporation of perfectly matched layers (PMLs). Then we show that the computational cost of the method can be further reduced by employing an alternative discretization instead of the classical one. Numerical results demonstrate the characteristics of the discussed FMM-based methods and include a discussion of computational complexities.

Through-focus scanning optical microscopy with the Fourier modal method

“…However, the influence of the degree of coherence has not been well studied and remains an unexplored research topic. From the results of [5], the OIR of the TSOM, as well as the DTIs, increase with decreasing INA, showing that TSOM sensitivity increases with decreasing INA.…”

“…It is known that the sensitivity of TSOM can be enhanced by optimizing the INA and CNA [3]. A decrease in INA leads to an interference or diffraction optical signal in TSOM images [5,[11][12][13][14] due to increased optical coherence of the illuminating field. However, the influence of the degree of coherence has not been well studied and remains an unexplored research topic.…”

“…FMM is a well-known frequency domain method for Maxwell equations. The efficiency of TSOM image reference buildup can be improved by representing the Maxwell equations in the frequency domain using Fourier transform and calculating the scattering matrix of the target sample structure [5][6][7][8][9][10]. Using the FMM requires that the frequency domain is discretized, but a range of spatial domain parameters can be dealt with in a continuous support accurately and efficiently.…”

Multiple parametric nanoscale measurements with high sensitivity based on through‐focus scanning optical microscopy

“…According to the previous analysis, under the condition of ideal Kohler illumination, each point of the field of view receives consistent converging light, and each converging light can be decomposed into a series of plane waves with different incident angles. If the lengths of the rectangular calculation region are and respectively, the decomposition principle is (Pisarenco et al ., ; Golani et al ., ; Park et al ., ) where and are the wave vector components along x and y directions of the m th and n th plane waves, respectively, both and are integers, and is the INA.…”