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Dielectric RheoSANS — Simultaneous Interrogation of Impedance, Rheology and Small Angle Neutron Scattering of Complex Fluids
Published on: April 10, 2017
Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions
Andrew D Baczewski1, Nicholas C Miller, Balasubramaniam Shanker
1Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48825, USA. baczewsk@msu.edu
Summary
We present a new method for analyzing fields in periodic dielectric structures. This approach significantly reduces computational cost, enabling faster and more accurate simulations for photonic applications.
Area of Science:
- Electromagnetics and Optics
- Computational Physics
- Materials Science
Background:
- Periodic dielectric structures are crucial in advanced applications like photonic bandgaps, plasmonics, and metamaterials.
- Accurate field analysis in these structures necessitates dense spatial discretization, increasing computational expense for traditional methods.
- Integral-equation-based methods face high computational costs, often O(N^2), due to the number of spatial degrees of freedom (N).
Purpose of the Study:
- To introduce an efficient numerical method for solving volumetric electric field integral equations in doubly periodic dielectric structures.
- To accelerate the analysis of electromagnetic fields in complex periodic nanostructures.
- To provide a computationally feasible approach for photonic and plasmonic device design.
Main Methods:
- Development of a rapid solution method for volumetric electric field integral equations.
- Implementation of an accelerated Cartesian expansion algorithm to evaluate potentials.
- Achieving O(N) computational cost for the analysis, where N is the number of spatial degrees of freedom.
Main Results:
- Demonstrated significant acceleration in solving electric field integral equations for periodic dielectric structures.
- Validated the accuracy of the accelerated method, showing no compromise compared to traditional approaches.
- Successfully applied the method to analyze compelling applications in photonics.
Conclusions:
- The accelerated Cartesian expansion algorithm provides a computationally efficient solution for analyzing fields in periodic dielectric structures.
- This method offers a substantial reduction in computational cost from O(N^2) to O(N) without sacrificing accuracy.
- The technique is applicable to various advanced photonic and plasmonic applications, facilitating faster design and analysis.
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