Remarkable Predictive Power of the Modified Long Wavelength Approximation

The modified long-wavelength approximation (MLWA), a next order approximation beyond the Rayleigh limit, has been applied usually only to the dipole l = 1 contribution and for the range of size parameters x not exceeding x less than or similar to 1 to estimate far- and near-field electromagnetic properties of plasmonic nanoparticles. Provided that the MLWA functional form for the T-matrix in a given channel 1 is limited to the ratio T similar to iR/(F + D - iR), where F is the familiar size-independent Frohlich term and R similar to O(x(2l+1)) is a radiative reaction term, there is a one-parameter freedom in selecting the dynamic depolarization term D similar to O(x(2)) which preserves the fundamental feature of the MLWA that its predictions coincide with those of the Mie theory up to the order O(x(2)). By exploiting this untapped design freedom, we demonstrate on a number of different metals (Ag, Al, Au, Mg), and using real material data, that the MLWA may surprisingly yield very accurate results for plasmonic spheres both for (i) x = 1 and beyond, and (ii) higher order multipoles (l > 1), essentially doubling its expected range of validity. Because the MLWA obviates the need of using spherical Bessel and Hankel functions and allows for an intuitive description of (nano)particle properties in terms of a driven damped harmonic oscillator parameters, a significantly improved analysis and understanding of nanoparticle scattering and near-field properties can be achieved.

Automated summary

The modified long-wavelength approximation (MLWA) is an advanced method for estimating the electromagnetic properties of plasmonic nanoparticles, and by utilizing unexplored design flexibility, it can provide surprisingly accurate results within a certain range.