plasmonic cubes

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Maxim Yurkin

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Jun 2, 2026, 12:26:16 PM (2 days ago) Jun 2

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Dear colleagues,

Let me bring your attention to the recent paper:
Makarenko A.O., Yurkin M.A., Shcherbakov A.A., and Lapine M. Electromagnetics of deeply subwavelength metamaterial particles, Phys. Rev. B 113, 195153 (2026). (PDF)

This paper looks at a question that sounds simple but turns out to be surprisingly tricky: What happens when you build an object out of tiny resonant elements? In metamaterials, the usual answer is: “We homogenize it,” i.e. we pretend the object is just a smooth material with some effective parameters. Our original goal was merely to study how fast this homogenization limit is reached as the sample size increases. While this worked as expected for a sphere, the situation was drastically different for a cube much smaller than the wavelength. The attached figure shows DDA simulations compared with a semi-analytical reference method (which, fortunately, exists for this geometry). We do see some convergence in an integral sense, but it looks nothing like the standard DDA behavior one would anticipate. Simulations that resolved the detailed metamaterial structure (each unit cell consisting of three ring resonators) further demonstrated that the result depends strongly on the boundary structure of the sample (which rings are retained).

We could trace this behavior to the combination of sharp edges and the effective material properties typical of low-loss metals in the optical range (such as silver), guided by a detailed analysis of the integral-operator spectrum. But the overall conclusion is that great care must be exercised both when designing such volumetric metamaterials and when attempting to simulate metallic nanoparticles with sharp edges. Note, however, that low losses is an important condition, since DDA simulations for gold cubes are completely fine, as was shown long ago in https://doi.org/10.1117/1.3335329 .

If you're interested in detailed distribution of currents inside such magnetic metamaterials with varying frequency, take a look at supplementary videos (they are also freely available at https://www.researchgate.net/publication/405410973_Electromagnetics_of_deeply_subwavelength_metamaterial_particles - see Linked Data there).

And if you are interested in an almost analytical reference for polarizability of a cube in quasi-static limit (robust for any permittivity), take a look at https://doi.org/10.5281/zenodo.18721913 .