## A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applicationsPublished in JOSA A, Vol. 30 Issue 11, pp.2175-2187 (2013) |

**Spotlight summary:**Suppose we want to predict the number of trees in a certain forest year after year. As a first approximation, we might assume that it’s a forest like any other forest, with no defining characteristics. But maybe this forest has a pond in it, which we expect to affect tree growth in its local environment. We could simply estimate how such a pond affects tree growth locally, and then add that to our estimate for the rest of the forest. The pond, in this case, causes a perturbation on our calculation. We could keep adding perturbations, like boulders, or a gorge, or a large field, until we had an answer that was as precise as we needed it to be. It would look like "total trees = trees for a typical forest + trees added by pond - trees subtracted by presence of field + …"

Sometimes, a change is too much for this so-called perturbation theory to handle. Instead of introducing a pond, suppose we introduce a huge lake. We expect such change to heavily affect tree growth on a forest-wide scale. To solve the problem now, we need to introduce new elements into the calculation, and our understanding of how a featureless forest works becomes less important.

In this paper, Reitich et al. attack a problem in the field of plasmonics, for which neither the standard "forest" model nor the standard perturbative model work. They look at metallic films covered in periodic ridges, called gratings. When such films are illuminated at certain angles and wavelengths of light, it is known that some of the light drives plasmons, or electronic waves, in the metal. It is important to know exactly which angles and wavelengths will couple to plasmonic modes, and how efficiently, so that devices can be constructed. But while it is known how to solve the problem for small perturbations on a smooth metal film, the problem becomes much harder if the ridges start to get deep, or have irregular shapes.

This paper solves the problem by using a subtle insight: If we make a tiny change to the metal film, it should cause a tiny change in the optical characteristics of the film. It turns out that this is equivalent to saying that if we graph the efficiency of light-plasmon coupling vs., say, the depth of the ridges, we will get a function that is smooth no matter how many derivatives we take of it. Such a function is called analytic, and it has a special property that if we know any piece of it, we know the whole function. Reitich et al. can then calculate the plasmonic characteristics of a film with small perturbations, and then use that knowledge to extend the answer out to what it would be for deep ridges, where perturbation theory doesn’t work.

They call the method "high order perturbation of surfaces" (HOPS), and show that it correctly predicts all of the standard optical properties of metallic gratings. They also claim that it’s much faster than using Maxwell’s equations to calculate an exact solution, which would be like cataloging every tree, stone, and drop of water in the forest to make predictions about tree growth. This work extends the domain of viable plasmonic devices a bit farther from flat surfaces, and lets us better tailor the device to the application.

--Brad Deutsch

**Technical Division:**Light–Matter Interactions

**ToC Category:**Optics at Surfaces

OCIS Codes:
| (240.6680) Optics at surfaces : Surface plasmons |

(050.1755) Diffraction and gratings : Computational electromagnetic methods |

Posted on October 29, 2013

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