Terahertz Fingerprint: Phase Space & Cole-Cole View

This 2D counterpart runs the exact same driven damped-oscillator (Lorentz) model as the 3D terahertz fingerprinting simulator, but represents it with two dynamical-systems plots instead of a 3D dipole slab. The left disk integrates each vibrational mode's own equation of motion and plots its position against its velocity, so resonance shows up as a phase-space loop swelling in real time as you sweep the probe frequency across it. The right disk traces the mode's exact closed-form complex susceptibility χ(ω) = S/(ω0²−ω²+iγω) as a Cole-Cole arc — the same parametric plot real THz and dielectric spectrometers use to characterize a resonance — with a live marker showing exactly where the current probe frequency sits on that curve. Switch between lactose, aspirin, an RDX-like explosive analog and glucose, and raise the sample temperature to watch phonon damping shrink and blur both the phase-space loops and the Cole-Cole arcs.