High precision, full-vector optical mode solving in waveguides via fourth-order derivative physics-informed neural...

Area of Science:

• Photonics and Computational Electromagnetics

Background:

• Conventional numerical methods for optical mode solving face challenges in geometric adaptability and computational efficiency.
• Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving forward and inverse problems in photonics.

Purpose of the Study:

• To introduce and validate fourth-order derivative PINNs (4DPINNs) for accurate full-vector waveguide eigenmode solutions.
• To demonstrate the capability of 4DPINNs in resolving tangential electric and magnetic field components for direct mode analysis and optical efficiency computations.

Main Methods:

• Developed 4DPINNs by integrating boundary conditions, initialization protocols, and a fourth-order derivative loss function derived from Maxwell's equations.
• Validated 4DPINNs by comparing electric field distributions and propagation constants against analytical benchmarks.
• Employed adaptive learning rate optimization for simultaneous prediction of propagation constants and field distributions.

Main Results:

• 4DPINNs achieved maximum absolute errors below -12 dB and minimum errors below -50 dB compared to analytical solutions for electric field distributions.
• Propagation constant errors were constrained to under 10^-4, with maximum field distribution errors below -12 dB.
• Demonstrated high accuracy and broad applicability for waveguide eigensolving.

Conclusions:

• 4DPINNs provide a highly accurate and computationally efficient method for full-vector waveguide eigenmode analysis.
• This approach offers significant advantages over conventional numerical methods for photonic device design.
• The developed 4DPINNs hold substantial value for applications in semiconductor devices and photonic integrated circuits.