A large language model orchestrates the design of a silicon-on-insulator 2x2 directional coupler by proposing gap values and assessing convergence. The design is validated through eigenmode and FDTD simulations on a common 2D effective-index model, showing a consistent phase offset of 2.837(11) micrometers that is corrected in a closed-loop process. The final device achieves a 50/50 split with a cross fraction of 0.498, within 0.0017 of the target.