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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 7, Pages 1277–1285 (Mi zvmmf12018)

Mathematical physics

Study of resonance properties of paired nanoparticles with mesoscopic boundary conditions by the discrete source method

Yu. A. Eremin, V. V. Lopushenko

Lomonosov Moscow State University

Abstract: The discrete source method was adapted to calculate the field intensity in a nanometer gap of a pair of plasmonic nanoparticles taking into account quantum effects described by mesoscopic boundary conditions with Feibelman parameters. Based on the computational experiment, it was found that for particles made of noble metals, taking into account the quantum effect leads to blue shift of the plasmon resonance and a damping its amplitude. In the case of an alkali metal, taking into account the quantum effect leads to red shift of the plasmon resonance, and when the gap is reduced to 1–2 nm, an enhancement of the intensity in the gap is observed. Analysis of the intensity distribution over the particle surface made it possible to determine that its highest values are achieved at the ends of the particles, with the absolute maximum observed at the ends facing inside the gap. In addition, it was found that the field intensity along the particle surface can vary by four orders of magnitude over a length of only 12 nm, which is only 1.5% of the wavelength of external excitation.

Key words: discrete source method, maxwell’s equations, mesoscopic boundary conditions, quantum nanoplasmonics, paired nanoparticles, alkali and noble metals.

DOI: 10.31857/S0044466925070155


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:7, 1709–1717

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© Steklov Math. Inst. of RAS, 2026