# Strong nonreciprocity in modulated resonator chains through synthetic electric and magnetic fields

## TL;DR

This paper demonstrates how spatiotemporal modulation in resonator chains creates synthetic electric and magnetic fields, enabling nonreciprocal transmission akin to the Hall effect, with experimental isolation exceeding 58 dB.

## Contribution

It introduces a novel approach to achieve nonreciprocity using synthetic fields in modulated resonator chains without extra components.

## Key findings

- Achieved over 58 dB of isolation contrast in experiments.
- Established the analogy between synthetic fields and Hall effect.
- Demonstrated nonreciprocity in chains of 2 and 3 resonators.

## Abstract

We study nonreciprocity in spatiotemporally modulated 1D resonator chains from the perspective of equivalent 2D resonator arrays with a synthetic dimension and transverse synthetic electric and magnetic fields. The synthetic fields are respectively related to temporal and spatial modulation of the resonator chain, and we show that their combination can break transmission reciprocity without additional elements. This nonreciprocal effect is analogous to the Hall effect for charged particles. We experimentally implement chains of 2 and 3 spatiotemporally modulated resonators and measure over 58 dB of isolation contrast.