Model & Assumptions Beta

Model: Exact Mie theory for absorption and scattering cross-sections, combined with the steady-state heat equation for a point source in a homogeneous medium: ΔT(R) = P_abs / (4πκR).
Assumptions: CW (continuous-wave) illumination, Gaussian beam profile (peak irradiance I = 2P/πw₀²), uniform and infinite host medium, temperature-independent thermal conductivity.
Validity: Accurate for single isolated nanoparticles in a uniform medium with moderate temperature rises (linear thermal regime).
Limitations: No collective heating, no substrate, no pulsed illumination, no temperature-dependent material properties. The point-source thermal model breaks down very close to the particle surface.
References: G. Baffou & R. Quidant, Laser Photonics Rev. 7, 171 (2013); Bohren & Huffman (1983).

Parameters

Material

Radius (nm)

n_host

λ (nm)

P_laser (mW)

1/e field waist w₀ (μm)

κ (W/m·K)

Cross-sections vs wavelength

σ_abs σ_sca laser λ

Apparent color

scattered

transmitted

σ_abs

— nm²

σ_sca

— nm²

σ_ext

— nm²

Albedo

—

Power at particle —

absorbed —

scattered —

T(r) − T_∞ vs. r / R · dots mark 1/e (r = e·R) and 1/e² (r = e²·R)

Notes

Model. I = 2P/(πw₀²) (Gaussian peak). P_abs = σ_abs·I. ΔT = P_abs/(4πκR) at the surface; T(r) − T_∞ = P_abs/(4πκr) for r ≥ R. σ_abs from exact Mie theory.

Examples

First column Columns 2 and 3

Column 1	Column 2	Column 3

References

[1]G. Baffou & R. Quidant, Thermo-plasmonics: using metallic nanostructures as nano-sources of heat, Laser & Photonics Reviews 7, 171 (2013).
[2]C. F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
[3]Optical constants: refractiveindex.info — Au/Ag: Johnson & Christy (1972); Al: Rakić (1995); Si: Aspnes & Studna (1983).

Photothermal Calculator

Parameters

Notes

Radial Temperature Profile

Confirm Material Import

References