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Variational principle for scattering of light by dielectric particles

Yung, Yuk L. (1978) Variational principle for scattering of light by dielectric particles. Applied Optics, 17 (23). pp. 3707-3709. ISSN 0003-6935. https://resolver.caltech.edu/CaltechAUTHORS:YUNao78

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Abstract

We exploit two fundamental properties of the dipole interaction matrix A (symmetry with respect to reversal of incident beam direction and interchange of any pair of dipoles) to construct two functionals. The connection with the minimum energy theorem and cross section suggests that our numerical algorithm will search for a physical quantity, and hence it would be efficient and stable. In this Letter we have made the crudest use of the variational principle. The practical limit for the current version of our numerical scheme is a dipole array (with fourfold symmetry) of order N ~10,000 atoms. Since the phase difference between neighboring atoms should be ≤1/3 rad for reliable results, this limits the scattering parameter 2πa/λ to ≤10. The storage required is ~20N real numbers, and the time is ~1x10^-6 N^2 min on a CDC 7600. Note that the main advantage with the current method is that we do not need to store the A matrix with order N^2 elements.


Item Type:Article
Related URLs:
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http://www.opticsinfobase.org/abstract.cfm?URI=ao-17-23-3695OtherUNSPECIFIED
ORCID:
AuthorORCID
Yung, Yuk L.0000-0002-4263-2562
Additional Information:© Copyright 1978 Optical Society of America. Received 4 August 1978. The author thanks E.M. Purcell, and Tony Chan for valuable discussions, C.R. Pennypacker and P.R. Shapiro for giving him their computing codes, A.A. Lacis for a copy of Mie program, and Y.S. Yung, C.K. Shum, and H.K. Wong for programming assistance. The author also thanks the referee for a number of helpful suggestions. This research was supported by NASA NSG-7376. This Letter represents Contribution 3015 of the Division of Geological and Planetary Sciences, California Institute of Technology.
Issue or Number:23
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Deposited On:21 May 2008
Last Modified:09 Mar 2020 13:19

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