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Neutral delay differential equation model of an optically injected Kerr cavity.

Andrei G Vladimirov1, Daria A Dolinina1

  • 1Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany.

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A new neutral delay differential equation model generalizes the Ikeda map, revealing dissipative soliton solutions in Kerr cavities. This model captures resonance overlaps missed by the Lugiato-Lefever equation.

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Area of Science:

  • Nonlinear optics
  • Theoretical physics
  • Cavity dynamics

Background:

  • The Ikeda map and Lugiato-Lefever equation are foundational for modeling nonlinear optical systems.
  • Understanding dissipative soliton formation and dynamics is crucial for optical technologies.
  • Standard models often struggle to capture complex resonance interactions in optical cavities.

Purpose of the Study:

  • To develop a generalized neutral delay differential equation (NDDE) model for a Kerr cavity with coherent injection.
  • To investigate the existence and properties of dissipative solitons within this extended framework.
  • To analyze the model's capability in describing resonance overlaps beyond the Lugiato-Lefever equation (LLE) limitations.

Main Methods:

  • Formulation of a neutral delay differential equation (NDDE) model.
  • Analysis of the model's solutions, including dissipative solitons.
  • Comparison with the Lugiato-Lefever equation (LLE) in low dissipation limits.
  • Investigation of phenomena like Cherenkov radiation and resonance overlap.

Main Results:

  • The NDDE model successfully predicts dissipative soliton solutions.
  • These solutions exist both in the low dissipation limit (reducible to LLE) and beyond.
  • The model accounts for second- and higher-order dispersion effects.
  • Unlike the LLE, the NDDE model describes the overlap of multiple cavity mode resonances.

Conclusions:

  • The developed NDDE model offers a more comprehensive description of nonlinear optical phenomena in Kerr cavities.
  • It provides a unified framework for studying dissipative solitons and complex resonance dynamics.
  • This generalization advances the theoretical understanding of optical cavity behavior and soliton formation.