# Time response of a microring resonator to a rectangular pulse in different coupling regimes

## TL;DR

This paper analyzes the time response of a microring resonator to rectangular pulses across various coupling regimes, combining analytical solutions, simulations, and experiments to improve understanding and characterization methods.

## Contribution

It introduces an analytical approach to the temporal response of microring resonators and demonstrates how time dynamics can determine coupling regimes and Q-factors.

## Key findings

- Temporal response varies with coupling regime
- Time response can identify coupling regime
- Q-factor can be determined from time response

## Abstract

We discuss the analytical temporal response of a microring resonator excited through a bus waveguide by an optical rectangular pulse. Finite difference time domain (FDTD) simulations illustrate the analytical solution and help in understanding the meaning of the different coupling regimes. In addition, we show that the temporal dynamics allows determing the coupling regime while the commonly used spectral characterization in the stationary regime does not. We also take advantage of the simulation to highlight the phase shift between the input and the output signals in the different coupling regimes. Finally, measurements on a Si3N4 microring resonator are performed and analyzed in the case of under-coupling regime to illustrate how the time response study leads to the Q-factor determination.