# Light propagation in systems involving two-dimensional atomic lattices

## TL;DR

This paper investigates how light interacts with two-dimensional atomic lattices, revealing collective effects, resonance shifts, and potential for emulating 1D waveguides, with implications for controlling light transmission in atomic systems.

## Contribution

It provides a detailed analysis of light propagation in 2D atomic lattices, including effects of dipole interactions and potential to mimic 1D waveguides, extending understanding of light-matter interactions in such structures.

## Key findings

- Lattice atoms exhibit multiple resonance frequencies due to dipole interactions.
- Stacks of 2D lattices can emulate 1D waveguides with lossless light propagation.
- Magnetic fields can induce transparency or opacity in the lattice at specific frequencies.

## Abstract

We study the optical response of a 2D square lattice of atoms using classical electrodynamics. Due to dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with cooperatively shifted resonances and altered transition linewidths. We show that when the distance between two 2D lattices is large enough and Bragg reflections are absent, the lattices interact among themselves as if they radiated a plane wave whose amplitude is in accordance with the radiation from a dipole moment continuously distributed in the lattice plane. We employ these results to study light propagation in stacks of 2D lattices, drawing on simple qualitative pictures of the response of a 2D lattice and light propagation in 1D waveguides. We show that a stack of 2D lattices may emulate regularly spaced atoms in a lossless 1D waveguide, and argue that in a suitable geometry the resonance shifts characteristic of 1D and 2D lattice structures may completely cancel to eliminate density dependent resonance shifts of atoms bound to a 3D lattice. A generalization to the case of anisotropic polarizability, such as in the presence of a magnetic field, reveals light frequencies induced by the magnetic field for which the lattice is either completely transparent, or completely opaque.