[Paper Review] Electric quadrupole and magnetic dipole coupling in plasmonic nanoparticle arrays

Viktoriia E. Babicheva, Andrey B. Evlyukhin|arXiv (Cornell University)|Feb 22, 2018

Plasmonic and Surface Plasmon Research55 references47 citations

TL;DR

The paper analyzes how electric quadrupole and magnetic dipole moments in gold nanoparticles couple in periodic arrays to produce lattice resonances, leading to Kerker-like suppression of reflection. It combines semi-analytical multipole theory with full-wave simulations for spheres and disks in homogeneous and non-homogeneous environments.

ABSTRACT

Collective resonances in plasmonic nanoparticle arrays with electric dipole moment oriented along the lattice wave propagation are theoretically investigated. The role of electric quadrupole (EQ) and magnetic dipole (MD) moments of gold nanoparticles in the resonant features of the arrays is analyzed. We perform both semi-analytical calculations of coupled multipole equations and rigorous numerical simulations varying contributions of the electric and magnetic multipoles by changing particle size and shape (spheres and disks). The arrays in homogeneous and non-homogeneous environments are considered. We find that even very weak non-resonant EQ and MD moments of a single particle are significantly enhanced in the periodic lattice at the wavelength of collective (lattice) resonance excitation. Importantly, we show that in the infinite arrays, the EQ and MD moments of nanoparticles are coupled and affect each other resonant contributions. We also demonstrate that at the lattice-resonance wavelength, the enhanced EQ and MD moments have contributions to reflection comparable to the dipole one resulting in a significant decrease of reflection and providing the satisfaction of the generalized Kerker condition for reflection suppression.

Motivation & Objective

• Investigate collective lattice resonances in periodic plasmonic nanoparticle arrays with electric dipole moments aligned along the lattice wave propagation.
• Assess the role and enhancement of electric quadrupole (EQ) and magnetic dipole (MD) moments in resonant features.
• Explore how particle size/shape (spheres and disks) and environment (homogeneous vs non-homogeneous) influence EQ/MD contributions.
• Demonstrate conditions under which EQ/MD coupling yields reduced reflection (generalized Kerker condition).

Proposed method

• Develop semi-analytical coupled multipole equations including ED, MD, and EQ contributions.
• Use a dipole-quadrupole model with polarizabilities αp, αm, αq and corresponding Green’s tensors G, g, q to describe inter-particle coupling.
• Derive effective polarizabilities αp^eff, αm^eff, αq^eff under lattice coupling (S1–S5 terms).
• Compute reflection and transmission via far-field superposition of ED, MD, and EQ fields using analytical expressions (r, t).
• Validate analytical results with full-wave CST Microwave Studio simulations for spheres and disks in varying environments.
• research_questions

Experimental results

Research questions

• RQ1 How do EQ and MD moments of nanoparticles contribute to lattice resonances in periodic arrays under parallel polarization?
• RQ2 Can EQ/MD coupling produce strong, narrow lattice resonances and modify reflection via a generalized Kerker condition?
• RQ3 How do particle size/shape and environmental inhomogeneity affect the strength and position of EQ/MD lattice resonances?
• RQ4 Do EQ and MD lattice resonances interact with the ED response to yield directional scattering and reflection suppression?

Key findings

• EQ and MD lattice resonances can be excited in arrays even when single-particle EQ and MD moments are weak.
• Coupling between EQ and MD moments in infinite arrays leads to significant resonant contributions and affects linewidth and position.
• At lattice-resonance wavelengths, enhanced EQ and MD moments contribute to reflection suppression comparable to the dipole contribution, fulfilling a generalized Kerker condition.
• Analytical models including ED, EQ, and MD coupling agree well with numerical simulations, showing the necessity of EQ–MD coupling for accurate Kerker-type behavior.
• Disks and spheres both exhibit lattice resonances with strong absorption and reduced reflection, and non-homogeneous environments can split and shift these features.