# Higher order multipoles in metamaterial homogenization

## TL;DR

This paper demonstrates that higher order multipoles beyond the electric quadrupole are significant in metamaterial homogenization, especially when considering second order spatial dispersion effects like magnetic response, and should not be overlooked.

## Contribution

It highlights the importance of including higher order multipoles in metamaterial homogenization, challenging the common practice of neglecting them.

## Key findings

- Higher order multipoles can significantly influence magnetic response.
- Neglecting these multipoles may lead to inaccurate homogenization models.
- They are as important as magnetization and quadrupole terms in certain conditions.

## Abstract

The higher order multipoles above the electric quadrupole are commonly neglected in metamaterial homogenization. We show that they nevertheless can be significant when second order spatial dispersive effects, such as the magnetic response, are considered. In this respect, they can be equally important as the magnetization and quadrupole terms, and should not automatically be neglected.