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Dynamic Analysis and Reservoir Computing Application of a Nonlinear Microring Resonator.

Stefano Gretter1, Mattia Mancinelli1, Lorenzo Pavesi1

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This study simplifies analyzing nonlinear microring resonators for neuromorphic computing. A new linearization method efficiently predicts resonator performance, avoiding complex simulations for reservoir computing applications.

Keywords:
Jacobian eigenvaluesdynamical systemslocal stability analysisnonlinear microring resonatorreservoir computing

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Area of Science:

  • Photonics and Optical Engineering
  • Nonlinear Optics
  • Computational Neuroscience

Background:

  • Nonlinear microring resonators exhibit self-pulsing and memory effects crucial for neuromorphic computing.
  • These resonators are utilized as nonlinear nodes in reservoir computing (RC) architectures.
  • Previous methods for analyzing resonator dynamics and optimizing control parameters were computationally intensive.

Purpose of the Study:

  • To develop a computationally efficient method for analyzing the dynamical behavior of nonlinear microring resonators.
  • To identify optimal control parameters for efficient optical computation in RC systems.
  • To predict the performance of microring resonators in RC applications without extensive simulations.

Main Methods:

  • Governing differential equations for optical field, temperature, and free carrier concentration were analyzed.
  • A linearization and stability analysis of the system was performed.
  • An adiabatic approximation of the cavity field was used to calculate Jacobian eigenvalues.

Main Results:

  • The linearization and stability analysis successfully identified regions in the control parameter space corresponding to different dynamical behaviors.
  • Jacobian eigenvalues were calculated as reliable indicators of RC performance.
  • The proposed method offers a significant reduction in computational cost compared to traditional simulations.

Conclusions:

  • Linearization and stability analysis provide an efficient alternative to computationally intensive simulations for microring resonators.
  • This approach enables faster identification of optimal operating regimes for neuromorphic applications.
  • The findings facilitate the design and implementation of high-performance optical computing systems.