Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Instantaneous modes in dispersive laser cavities

Kristian Seegert, Yi Yu, Mikkel Heuck, Jesper Mørk

TL;DR

The paper addresses complex dynamics in lasers with dispersive mirrors by introducing an instantaneous-mode expansion, where the field is projected onto a small set of instantaneous modes defined by a local eigenproblem. This leads to a reduced, transparent description in terms of a dominant mode with a dynamically evolving confinement factor determined by the effective reflectivity, and extends from an ODE formulation to traveling-wave equations while preserving the core 2D reduction. The approach clarifies the conditions for dispersive instabilities and self-pulsing, provides a unified framework for reduced modeling and stability analysis, and offers practical tools for dispersion engineering and bifurcation analysis in laser cavities. Together, these results enable efficient, physically intuitive analysis of dispersive laser dynamics across both discrete and distributed representations, with direct relevance to Fano lasers and similar dispersion-engineered devices.

Abstract

We develop a unified instantaneous-mode description for lasers with dispersive cavities, exploiting the separation of timescales between fast cavity fields and slow carrier dynamics. The resulting reduced rate equations retain the essential effects of frequency-dependent mirrors through a dynamic modal gain and an effective confinement factor determined directly by the mirror reflectivity. Applied to a Fano laser, the reduced description accurately reproduces the full dynamics and clarifies the physical origin of dispersive instabilities. More generally, the approach provides a transparent framework for reduced modeling and stability analysis of dispersive laser cavities.

Instantaneous modes in dispersive laser cavities

TL;DR

The paper addresses complex dynamics in lasers with dispersive mirrors by introducing an instantaneous-mode expansion, where the field is projected onto a small set of instantaneous modes defined by a local eigenproblem. This leads to a reduced, transparent description in terms of a dominant mode with a dynamically evolving confinement factor determined by the effective reflectivity, and extends from an ODE formulation to traveling-wave equations while preserving the core 2D reduction. The approach clarifies the conditions for dispersive instabilities and self-pulsing, provides a unified framework for reduced modeling and stability analysis, and offers practical tools for dispersion engineering and bifurcation analysis in laser cavities. Together, these results enable efficient, physically intuitive analysis of dispersive laser dynamics across both discrete and distributed representations, with direct relevance to Fano lasers and similar dispersion-engineered devices.

Abstract

We develop a unified instantaneous-mode description for lasers with dispersive cavities, exploiting the separation of timescales between fast cavity fields and slow carrier dynamics. The resulting reduced rate equations retain the essential effects of frequency-dependent mirrors through a dynamic modal gain and an effective confinement factor determined directly by the mirror reflectivity. Applied to a Fano laser, the reduced description accurately reproduces the full dynamics and clarifies the physical origin of dispersive instabilities. More generally, the approach provides a transparent framework for reduced modeling and stability analysis of dispersive laser cavities.
Paper Structure (9 sections, 53 equations, 3 figures)

This paper contains 9 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Instantaneous modes in the ODE model
  3. Stability analysis
  4. Instantaneous modes in the TWE model
  5. Conclusion
  6. Acknowledgements
  7. Instantaneous modes in the ODE model
  8. Instantaneous modes in the TWE model
  9. Noise

Figures (3)

  • Figure 1: (a) Sketch of a Fano laser with $M$ side-coupled cavities. (b) Sketch of a dispersive cavity with one broadband mirror and one dispersive mirror.
  • Figure 2: A trajectory in phase-space $(N,|A^+|^2,|a_1|^2)$ for the Fano laser. The slow manifold is marked in grey, the orange dot shows the steady-state point, the arrows indicate the flow on the slow manifold, and the black lines indicate the nullclines.
  • Figure 3: Comparisons of the full ODE model (continuous blue line) with the single-mode approximation (dashed orange line). (a) Parameters leading to stable relaxation oscillations. (b) Parameters leading to a self-pulsing regime.