Remarkable Predictive Power of the Modified Long Wavelength Approximation

Abstract

The modified long-wavelength approximation (MLWA), a next order approximation\nbeyond the Rayleigh limit, has been applied usually only to the dipole $\\ell=1$\ncontribution and for the range of size parameters $x$ not exceeding $x\\lesssim\n1$ to estimate far- and near-field electromagnetic properties of plasmonic\nnanoparticles. Provided that the MLWA functional form for the $T$-matrix in a\ngiven channel $\\ell$ is limited to the ratio $T\\sim iR/(F+D-iR)$, where $F$ is\nthe familiar size-independent Fr\\"ohlich term and $R\\sim {\\cal O}(x^{2\\ell+1})$\nis a radiative reaction term, there is a one-parameter freedom in selecting the\ndynamic depolarization term $D\\sim {\\cal O}(x^2)$ which preserves the\nfundamental feature of the MLWA that its predictions coincide with those of the\nMie theory up to the order ${\\cal O}(x^2)$. By exploiting this untapped design\nfreedom, we demonstrate on a number of different metals (Ag, Al, Au, Mg), and\nusing real material data, that the MLWA may surprisingly yield very accurate\nresults for plasmonic spheres both for (i) $x$ up to $\\gtrsim 1$ and beyond,\nand (ii) higher order multipoles ($\\ell>1$), essentially doubling its expected\nrange of validity. Because the MLWA obviates the need of using spherical Bessel\nand Hankel functions and allows for an intuitive description of (nano)particle\nproperties in terms of a driven damped harmonic oscillator parameters, a\nsignificantly improved analysis and understanding of nanoparticle scattering\nand near-field properties can be achieved.\n