# Quadrupolar susceptibility modeling of substrated metasurfaces with application to the generalized Brewster effect

## TL;DR

This paper develops a comprehensive modeling framework for substrate-based metasurfaces incorporating quadrupolar responses, enabling advanced control of wave reflection and transmission phenomena such as the generalized Brewster effect.

## Contribution

It introduces generalized sheet transition conditions including quadrupoles for metasurfaces on substrates, expanding the modeling capabilities for wave manipulation.

## Key findings

- Demonstrates multiple angles of suppressed reflection (generalized Brewster effect)
- Shows transmission suppression at specific angles (anti-Brewster effect)
- Validates the model for practical, non-homogeneous metasurfaces

## Abstract

We derive generalized sheet transition conditions (GSTCs) including dipoles and quadrupoles, using generalized functions (distributions). This derivation verifies that the GSTCs are valid for metasurfaces in non-homogeneous environments, such as for practical metasurfaces fabricated on a substrate. The inclusion of quadrupoles and modeling of spatial dispersion provides additional hyper-susceptibility components which serve as degrees of freedom for wave transformations. We leverage them to demonstrate a generalized Brewster effect with multiple angles of incidence at which reflection is suppressed, along with an ``anti-Brewster'' effect where transmission is suppressed.