# Necessary conditions for out-of-plane lattice plasmons in nanoparticle arrays

## TL;DR

This paper identifies key design and environmental conditions necessary for supporting out-of-plane lattice plasmons in metallic nanoparticle arrays, enhancing their potential for advanced optical applications.

## Contribution

It systematically determines the combined effects of array period, dielectric environment, and incident angle on OLP excitation, providing practical guidelines for their engineering.

## Key findings

- Proper array period is crucial within a specific range.
- Homogeneous dielectric environment is necessary.
- Optimizing height and incident angle enhances OLPs.

## Abstract

Out-of-plane lattice plasmons (OLPs) supported by metallic nanoparticle arrays are promising for diverse applications due to their remarkably narrow linewidths and significant enhancement of local fields. Here we investigate the necessary conditions for metallic nanoparticle arrays to achieve OLPs. Our results show that, besides the prerequisites of large height, oblique incidence, and TM polarization, which have been pointed out by the literature; the array period should be properly designed within a limited range, the dielectric environment should be homogeneous, and the height and the angle of incidence need to be optimized. We expect this work will advance the understanding and engineering of OLPs in metallic nanoparticle arrays and promote their applications in nanolasers, ultrasensitive biochemical sensors, and nonlinear optics.