Plasmonic Nanoparticle Photothermal Heating

Illumination

Laser wavelength λ 532 nm

Irradiance I 5.0 mW/µm²

Nanoparticle

Equal-volume radius R 25 nm

Aspect ratio (sphere → rod) 1.0

Absorption Spectrum

Live Readouts

LSPR peak λ

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Q_abs (efficiency)

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Steady-state surface ΔT

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How it works

A metal nanoparticle much smaller than the light's wavelength responds to an oscillating field as a driven dipole. Its complex dielectric function is modeled with the Drude free-electron form:

ε(E) = ε∞ − Ep² / (E² + iγE)
E = 1239.84 / λ(nm)  [photon energy, eV]
Ep ≈ 9.0 eV (plasma energy), γ ≈ 0.07 eV (damping)

For a prolate spheroid (sphere → rod as aspect ratio AR increases, volume held fixed) the quasistatic depolarization factor along the long axis is

e² = 1 − AR⁻²
L = (1−e²)/e² · [ (1/2e)·ln((1+e)/(1−e)) − 1 ]   (L → 1/3 for a sphere)

The localized surface plasmon resonance (LSPR) occurs near ε(E) = −(1−L)/L · εm, and the absorption cross-section (Gans theory, reduces to Mie's dipole limit for L=1/3) is

σ_abs = 3kV · Im[ L(εp−εm) / (εm + L(εp−εm)) ],  k = 2πnm/λ
Q_abs = σ_abs / (πR²)

Absorbed light is converted to heat at the metal surface and conducted away through the surrounding medium. In steady state (Baffou & Quidant, 2013) the particle-surface temperature rise above ambient is

ΔT_surface = σ_abs · I / (4π·κm·R)

with κm the medium's thermal conductivity (water, 0.6 W/m/K, used here) and I the laser irradiance. The temperature then decays into the surrounding fluid as ΔT(r) = ΔT_surface · R/r — the glowing halo around each particle in the scene traces this 1/r conduction profile.

Wavelength — scans the driving photon energy across the LSPR; absorption (and heating) peaks when the resonance condition is met.
Radius — larger particles absorb more total power (σ_abs ∝ volume in this quasistatic limit) but the temperature rise scales only as R² since ΔT ∝ σ_abs/R.
Aspect ratio — elongating a sphere into a rod red-shifts the longitudinal LSPR peak, the mechanism used to tune gold nanorods into the near-infrared "tissue transparency window" for photothermal therapy.
Irradiance — scales ΔT linearly; this sim ignores particle-particle thermal coupling and interband transitions below ~500 nm, both real effects a full Mie/BEM calculation would add.

Nanoparticle (color = ΔT) Incident laser beam

Peak surface ΔT
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