Plasmonic Nanoparticle Heating (2D): Coupled Heat-Diffusion Field

This is the 2D counterpart of the plasmonic-nanoparticle photothermal-heating simulator. It reuses the identical optical physics — a Drude dielectric function for gold combined with Gans theory for a prolate spheroid — to compute how much laser power each nanoparticle absorbs at its localized surface plasmon resonance. But instead of reading a temperature off the 3D scene's instantaneous single-particle steady-state formula, this page numerically integrates the real 2D transient heat-diffusion equation on a finite-difference grid, with each particle depositing its absorbed power as a volumetric heat source and a cold domain edge standing in for the surrounding fluid bath. Arrange the nanoparticles into a 1×1, 2×2 or 3×3 array and tighten the spacing to watch neighboring particles' thermal fields genuinely overlap — a real thermal-coupling effect the 3D model's per-particle formula explicitly ignores — and compare the simulated peak temperature rise against the isolated-particle analytic prediction in real time.