DelineTu/Lumerical-FDTD-EME-edge-couplers-for-TFLN-waveguides — reverse-engineered prompt

Build me a clean simulation project for designing inverse tapers and edge lens couplers for thin film lithium niobate and silicon nitride waveguides. I want it to help optimize fiber to chip coupling for balanced homodyne detection, using Lumerical FDTD and EME simulations plus FreeCAD style parametric 3D modeling.

The project should let me scan taper and lens parameters, compare TFLN and SiN cases, and calculate transmission times mode overlap against Gaussian targets. Include cases for a 2.5 μm lensed fiber mode and a 1.0 μm free space waist. I also want scripts for aligning the beam center, doing 2D mode overlap scans, and running 3D parameter scans for aspheric or elliptical edge lenses.

Please organize it so someone can open the scripts, change the main dimensions, rerun the simulations, and save plots or results showing the best coupling designs. Add a simple README explaining the workflow and what each script is for.