Abstract
For simulations of electromagnetic resonance spectra, where the locations of spectral features are unknown, and for wide-band simulations in general, a substantial number of wavelengths must be simulated for acceptable resolution, increasing computation time. This problem is exacerbated for spectra containing narrow-band features, as a high spectral resolution is required to even detect them. To address this challenge, a heuristic algorithm is presented for electromagnetic simulations, which adaptively refines the local resolution of spectral features during a simulation. The method supports parallel processing and plugs in with existing simulation systems, such as (RCWA). It can routinely reduce the computational load by two orders of magnitude. Program SummaryProgram Title:asasimProgram Files doi:http://dx.doi.org/10.17632/d6gty7kr2x.1Licensing provisions: CC By 4.0Programming language: MATLABNature of problem: Simulations are challenging when information is needed both on a long scale (broad interval) and on a short scale (high local resolution), such as wide-band electromagnetic spectra containing narrow-band features. When resolution is insufficient, narrow-band features may be downright absent from the spectrum, if neighboring points are simulated on either side of a narrow peak. When local resolution is sufficient, it will necessarily be excessive in flat regions, wastefully increasing computation time.Solution method: The presented method enables adaptive resolution, which ensures that all peaks of a given minimum width are always detected and maximally resolved, while feature-less regions remain minimally resolved. An optimum point spacing is derived for lorentzian peaks (descriptive of optical resonances) and is applied to optimize computation time.
Highlights
The ability to accurately simulate light-matter interactions in nanostructures has enabled breakthroughs in areas as diverse as optical biosensors [1], pigment-free coloration [2], and solar cells [3]
A heuristic algorithm is presented for electromagnetic simulations, which adaptively refines the local resolution of spectral features during a simulation
Rigorous coupled-wave analysis (RCWA) is a popular semi-analytical method for electromagnetic simulations originally described by Moharam and Gaylord in 1981 [4]
Summary
The ability to accurately simulate light-matter interactions in nanostructures has enabled breakthroughs in areas as diverse as optical biosensors [1], pigment-free coloration [2], and solar cells [3]. The method is computationally demanding, and this can be a limitation for high-resolution, wide-band simulations. This can be problematic for optimization methods, such as particle swarm optimization [5] or genetic algorithms [6], where an extensive number of simulations in a many-dimensional parameter space should be performed. A heuristic MATLAB-algorithm is demonstrated for achieving adaptive resolution in electromagnetic simulations. This effectively reverses the information emphasis to lay on the spectral features rather than the background, as illustrated in figure 2b. Optimal parameters are derived, and the speed of the method is evaluated
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