Abstract
The calculation of the electromagnetic field in nanostructured materials and nano-optoelectronic devices, when the wavelength of the incident radiation is comparable with the size of the structural elements, requires the exact solution of Maxwell's equations. In this case, a very promising numerical approach is the spectral element method, which combines the geometric flexibility of finite elements with high precision of spectral methods. In this paper the implementation of the spectral element method based on the Dirichlet-to-Neumann map for solving Maxwell’s equations is discussed. The application of the method for two-dimensional periodic structures, such as diffraction gratings and a metal nanowire array in a dielectric matrix, is demonstrated.
Highlights
IntroductionThe calculation of the electromagnetic field in nanostructured materials and nanooptoelectronic devices including image sensors, nanostructured solar cells, photonic crystals and diffraction gratings, when the wavelength of the incident radiation is comparable with the size of the structural elements, requires an exact numerical solution of Maxwell's equations
A very promising numerical approach is the spectral element method, which combines the geometric flexibility of finite elements with high precision of spectral methods
The calculation of the electromagnetic field in nanostructured materials and nanooptoelectronic devices including image sensors, nanostructured solar cells, photonic crystals and diffraction gratings, when the wavelength of the incident radiation is comparable with the size of the structural elements, requires an exact numerical solution of Maxwell's equations
Summary
The calculation of the electromagnetic field in nanostructured materials and nanooptoelectronic devices including image sensors, nanostructured solar cells, photonic crystals and diffraction gratings, when the wavelength of the incident radiation is comparable with the size of the structural elements, requires an exact numerical solution of Maxwell's equations. If the structure includes various materials the permittivity and permeability are not continuous functions and the convergence is only algebraic, in other words the absolute values of the coefficients decrease only as a certain power of the coefficient number In this case, the spectral domain decomposition methods have the advantage, when the domain of interest is divided into smaller subdomains in each of which ε and μ are uniform and the decomposition of solution by local basis functions occurs separately in each of the subdomains. Due to apt turn of phrase another authors [3] use the term “spectral element methods” in wider sense for all methods that implement spectral approach inside the elements by analogy with finite element method. In the part of the paper we shall demonstrate the application of the method to the two-dimensional periodic structures such as diffraction grating and metal nanowire array in a dielectric matrix; this approach can be extended to arbitrary three-dimensional calculations
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