Harnessing Photons: an all-optical high-order ODE solver via cascaded microring resonators

This repository provides MATLAB scripts for simulating high-order ordinary differential equation (ODE) solvers implemented via cascaded microring resonators (MRRs) and performing Monte Carlo analysis to assess performance under parameter variations.

🗂️ Repository Structure

.
├── ODE_solver.m       % Main script: sets up parameters, computes ODE solutions, and plots results
├── MonteCarlo.m       % Function: runs Monte Carlo trials to analyze perturbations in coupling, loss, and detuning
└── README.md          % Project overview and usage instructions

📋 Prerequisites

• MATLAB R2018a or later
• Signal Processing Toolbox (for FFT and frequency-domain analysis)
• Statistics and Machine Learning Toolbox (for tinv in confidence intervals)

⚙️ Getting Started

1. Clone the repository

   git clone https://github.com/yourusername/photonic-ode-mrr.git
   cd photonic-ode-mrr

2. Open MATLAB and navigate to the project folder.

3. Configure user parameters in ODE_solver.m under the User parameters section:

   • order: system order (1, 2, or 3)
   • k: coupling rates per stage (ns⁻¹)
   • A: scaling factor (ns → s)
   • Tolerances for coupling (r_tolerances), intrinsic loss (loss_tolerance), and detuning (detuning_tolerance)
   • N_monte_carlo: number of Monte Carlo runs
   • Ring geometries (R) and effective index (neff)

4. Select input signal (step or sinusoid) by editing the Input signal block.

5. Run ODE_solver.m

   ODE_solver

   • Produces frequency-domain and time-domain plots comparing the ideal ODE solution against the cascaded MRR implementation
   • Executes Monte Carlo simulations and displays envelopes, density plots, and error statistics

🔧 Customization

• Order: Change order to simulate 1st, 2nd, or 3rd-order ODE behavior.
• Input Signal: Switch between unit-step (@(t) C*(t>0)) and sinusoid (@(t) C*sin(2*pi*f0*t)).
• Tolerances: Adjust r_tolerances, loss_tolerance, and detuning_tolerance to study robustness.
• Number of Trials: Increase N_monte_carlo for finer statistical accuracy (at the expense of runtime).

🖼️ Results and Visualization

• Frequency-Domain Plots: Compare ideal vs. MRR transfer functions; visualize input spectrum and -3 dB bandwidth.

• Time-Domain Plots: Show raw input, ODE45 solution, and MRR output, with power comparisons.

• Monte Carlo Figures:

  • Percentile envelopes (5–95%) and median of frequency/time responses
  • 2D density heatmap of time-domain outputs
  • RMSE error vs. coupling tolerance with confidence intervals

📜 License

This project is licensed under the MIT License. See LICENSE for details.

👷🏻‍♂️ Contributing

Feel free to open issues or submit pull requests for improvements, bug fixes, or new features.

📫 Contact

For questions or support, contact us at:

• [email protected]
• [email protected]