An LLM-Orchestrated Agent for Directional-Coupler Design with Self-Consistent Eigenmode and FDTD Validation

2026-06-21

AI Summary

This study addresses the challenge of achieving consistency between simulation and physical models in silicon-based directional coupler design by proposing an automated framework coordinated by a large language model (LLM). In this approach, the LLM acts as an intelligent scheduler that generates geometric parameters and assesses convergence, while a frequency-domain eigenmode solver computes the coupling coefficient and a finite-difference time-domain (FDTD) method provides independent validation—both grounded in a unified two-dimensional effective index model. The key innovation lies in employing the LLM as a coordinator rather than an executor of the design process, coupled with a novel closed-loop length correction enabled by identifying a constant phase offset. The method successfully designs a 50/50 splitting-ratio coupler, with FDTD-validated cross-coupling of 0.498 (an error of only 0.0017), and demonstrates that the phase offset remains invariant across varying coupling strengths.

Abstract

We present a design agent which is a Large Language Model (LLM) that orchestrates, but does not perform, the numerical simulations to design a silicon-on-insulator (SOI) $2\times2$ directional coupler. We choose a symmetric phase-matched coupler where a lot of analytical results are available that help the design strategy. The LLM proposes candidate gap values (a geometrical dimension size) and judges convergence, while all physics is owned by deterministic solvers: a frequency-domain eigenmode solver estimates the coupling coefficient~$κ$ for the current design, and an independent Finite-Difference Time-Domain (FDTD) stage validates it. Both solvers operate on a common slab-projected two-dimensional (2D) effective-index reduction of the silicon film, so the design~$κ$ and the FDTD response are consistent by problem design; the residual between them is shown to be a single constant phase offset~$φ$, attributable to a fixed excess coupling length $L_{\mathrm{extra}}=\SI{2.837(11)}{\micro\meter}$ that we find invariant across a factor-of-two range in~$κ$. Folding this offset into a closed-loop length correction, the agent delivers a $50/50$ splitter whose FDTD-measured cross fraction is $0.498$ (target $0.500$), a residual of $0.0017$. Results are made self-consistent within the 2D effective-index model; and the LLM succeeds in delivering a suitable design over a number of attempts.

Problem

• directional coupler
• silicon-on-insulator
• eigenmode solver
• FDTD validation
• effective-index model

Innovation

• LLM-orchestrated design
• directional coupler
• self-consistent validation
• effective-index model
• FDTD-eigenmode co-simulation