These methods, while popular for other optical modeling applications, have not been used widely to model anti-reflective subwavelength structures, and will therefore not be discussed.Įxample images of moth-eye structures found in nature.
Some optical modeling methods are not covered here these methods include method of moments (MoM for background see Chapter 15 in reference ) and finite integral technique (FIT).
Although these methods are considered accurate and rigorous solutions to Maxwell’s equations, it is suggested that exploration of solutions through multiple modeling methods is most robust. The mathematical approach for each of these methods is different, resulting in different advantages and disadvantages in modeling capabilities, which are the topic of this review. Of those, all but TMM are capable of describing the geometry of subwavelength structures TMM relies on an effective media approximation for more complicated geometry. Currently, only four major modeling methods are commonly used in the field of ARSWS: finite-difference time-domain (FDTD), finite element method (FEM), transfer matrix method (TMM), and rigorous coupled-wave analysis or Fourier modal method (RCWA/FMM).
#Fem vs fdtd software#
Likewise, with the wide variety of optical modeling methods available, some methods have become more popular than others due to reasons other than their computational ability, such as availability of commercial software or abundant use in the literature. Optical modeling methods have developed over time and, with the introduction of advanced computing resources, have largely discarded methods that include non-rigorous assumptions. This paper is intended to be a review of the most commonly used methods for optical modeling of anti-reflective subwavelength structures. All rigorous numerical methods have accurately predicted the broadband reflection of ideal, graded-index anti-reflective subwavelength structures ideal structures are tapered nanostructures with periods smaller than the wavelengths of light of interest and lengths that are at least a large portion of the wavelengths considered. Initial disadvantages such as neglect of dispersion (FDTD), inaccuracy in TM polarization (RCWA), inability to model aperiodic gratings (RCWA), and inaccuracy with metallic materials (FDTD) have been overcome by most modern software. Analytical approaches such as TMM are appropriate for very simple thin films. Frequency-based solutions such as RCWA/FMM and FEM model one wavelength per simulation and are thus able to handle dispersion for regular geometries. Space-discretized methods such as FDTD and FEM output field strength results over the whole geometry and are capable of modeling arbitrary shapes. Time-based solutions to Maxwell’s equations, such as FDTD, have the benefits of calculating reflectance for multiple wavelengths of light per simulation, but are computationally intensive. Methods covered include effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), the Fourier modal method (FMM)/rigorous coupled-wave analysis (RCWA) and the finite element method (FEM). This paper reviews the current progress in mathematical modeling of anti-reflective subwavelength structures.