## A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications |

JOSA A, Vol. 30, Issue 11, pp. 2175-2187 (2013)

http://dx.doi.org/10.1364/JOSAA.30.002175

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### Abstract

In this paper we demonstrate that rigorous high-order perturbation of surfaces (HOPS) methods coupled with analytic continuation mechanisms are particularly well-suited for the assessment and design of nanoscale devices (e.g., biosensors) that operate based on surface plasmon resonances generated through the interaction of light with a periodic (metallic) grating. In this connection we explain that the characteristics of the latter are perfectly aligned with the optimal domain of applicability of HOPS schemes, as these procedures can be shown to be the methods of choice for low to moderate wavelengths of radiation and grating roughness that is representable by a few (e.g., tens of) Fourier coefficients. We argue that, in this context, the method can, for instance, produce full and precise reflectivity maps in computational times that are orders of magnitude faster than those of alternative numerical schemes (e.g., the popular “C-method,” finite differences, integral equations or finite elements). In this initial study we concentrate on the description of the basic principles that underlie the solution scheme, including those that relate to analytic continuation procedures. Within this framework, we explain how, in spite of conventional wisdom to the contrary, the resulting perturbative techniques can provide a most valuable tool for practical investigations in plasmonics. We demonstrate this with some examples that have been previously discussed in the literature (including treatments of the reflectivity and band gap structure of some simple geometries) and extend this to demonstrate the wider applicability of the proposed approach.

© 2013 Optical Society of America

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: June 17, 2013

Manuscript Accepted: August 22, 2013

Published: October 3, 2013

**Virtual Issues**

Vol. 9, Iss. 1 *Virtual Journal for Biomedical Optics*

October 29, 2013 *Spotlight on Optics*

**Citation**

Fernando Reitich, Timothy W. Johnson, Sang-Hyun Oh, and Gary Meyer, "A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications," J. Opt. Soc. Am. A **30**, 2175-2187 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-11-2175

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