Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems

Area of Science:

• Photonics
• Optical Computing
• Integrated Optics

Background:

• Ordinary differential equations (ODEs) are fundamental in modeling linear time-invariant (LTI) systems.
• Traditional electronic solvers face limitations in speed and power consumption for complex computations.
• Photonic approaches offer potential for high-speed, low-power computation.

Purpose of the Study:

• To propose and demonstrate an all-optical temporal solver for ODEs.
• To design a compact photonic device for solving ODEs characterizing LTI systems.
• To enable tunable solutions for first-order ODEs with variable coefficients.

Main Methods:

• Implementation of an add-drop microring resonator (MRR) device.
• Integration of two tunable interferometric couplers on a silicon-on-insulator (SOI) wafer.
• Thermal tuning of phase shifts to control ODE solving capabilities.
• Theoretical analysis and experimental testing with 10-Gb/s optical pulses.

Main Results:

• Successful monolithic integration of the photonic ODE solver with a compact footprint (~60 μm × 120 μm).
• Demonstration of the device's capability to solve first-order ODEs with two variable coefficients via thermal tuning.
• Experimental verification of the device's effectiveness as a tunable photonic ODE solver using optical Gaussian-like pulses.

Conclusions:

• The fabricated microring resonator device functions as an effective all-optical temporal ODE solver.
• The proposed photonic approach offers a compact and tunable solution for LTI system analysis.
• This work paves the way for advanced optical computing architectures for differential equation solving.