This is the 2D counterpart of the plasmonic-heating simulator. Both pages compute absorbed power from the identical optical physics — a Drude model of gold's dielectric function combined with Gans theory for a prolate spheroid — but where the 3D scene reads off an instantaneous analytic steady-state formula per isolated particle, this page actually integrates the 2D transient heat-diffusion equation on a finite-difference grid, so neighboring particles' temperature fields add up exactly as real heat conduction would:
∂T/∂t = α∇²T + q(x,y)/(ρc) (explicit FTCS, Dirichlet ΔT=0 at the domain edge = ambient fluid bath)
α = κ_water/(ρc) = 0.6 / (1000·4186) ≈ 1.43×10⁻⁷ m²/s
q = Q / (πR²·2R) inside each particle's footprint, Q = σ_abs·I (same σ_abs as the 3D Gans/Drude model)
Each particle deposits its absorbed power Q as a volumetric heat source over a disk of its own equal-volume radius R (footprint depth taken as one particle diameter); the grid then carries that heat away purely through diffusion into the surrounding fluid, exactly like a real photothermal experiment. The cold domain edge stands in for the bulk fluid reservoir far from the array, so the field genuinely relaxes to a steady profile rather than heating forever.
- Array / spacing — this is the physics the 3D page explicitly can't show: bringing particles closer than a few thermal diffusion lengths lets their fields overlap, so each particle's local ΔT ends up higher than an isolated particle at the same power would reach. Compare "Simulated peak ΔT" against "Isolated-particle ΔT (analytic)" — the ratio is the coupling enhancement, and it should sit near 1.0 for a lone particle (1×1) and climb as you tighten the spacing on a 2×2 or 3×3 array.
- Wavelength / aspect ratio — shift the LSPR exactly as in the 3D model (same σ_abs formula), which rescales Q and hence the whole diffusion field's source strength.
- Simulated time — the solver runs the real stability-limited time step (CFL-bound on the diffusion term) at an accelerated number of steps per rendered frame, so you watch the field build from a cold start toward equilibrium over a few seconds instead of the microseconds it actually takes.
- Limitations carried over from the reduced 2D model: the particle footprint is a disk of the equal-volume radius (rod elongation isn't reproduced spatially, only through σ_abs), and the "slab thickness" used to convert absorbed power to a volumetric source is an assumed one-diameter depth.