Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions
Abstract
Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.
- Authors:
-
- Michigan State Univ., East Lansing, MI (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1252696
- Report Number(s):
- SAND-2016-1053J
Journal ID: ISSN 1084-7529; JOAOD6; 619145
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of the Optical Society of America. A, Optics, Image Science, and Vision
- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 4; Journal ID: ISSN 1084-7529
- Publisher:
- Optical Society of America (OSA)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Baczewski, Andrew David, Miller, Nicholas C., and Shanker, Balasubramaniam. Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions. United States: N. p., 2012.
Web. doi:10.1364/JOSAA.29.000531.
Baczewski, Andrew David, Miller, Nicholas C., & Shanker, Balasubramaniam. Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions. United States. https://doi.org/10.1364/JOSAA.29.000531
Baczewski, Andrew David, Miller, Nicholas C., and Shanker, Balasubramaniam. Thu .
"Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions". United States. https://doi.org/10.1364/JOSAA.29.000531. https://www.osti.gov/servlets/purl/1252696.
@article{osti_1252696,
title = {Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions},
author = {Baczewski, Andrew David and Miller, Nicholas C. and Shanker, Balasubramaniam},
abstractNote = {Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.},
doi = {10.1364/JOSAA.29.000531},
journal = {Journal of the Optical Society of America. A, Optics, Image Science, and Vision},
number = 4,
volume = 29,
place = {United States},
year = {Thu Mar 22 00:00:00 EDT 2012},
month = {Thu Mar 22 00:00:00 EDT 2012}
}
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