Presets
Playback
Optics
Wavelength, gold thickness, buffer index and the beam angle.
Binding
Concentration and rate constants set the sensorgram shape.
Layers
Model checks
The science
Surface plasmons and the Kretschmann geometry
A p-polarised beam in a glass prism (index np) is totally internally reflected from a thin gold film. Its evanescent wave tunnels through the metal and can excite a surface plasmon polariton at the gold-liquid interface when the in-plane wave vector matches the plasmon dispersion:
np sinθ = Re √( εm ns2 / (εm + ns2) ), where εm is the permittivity of gold (negative real part) and ns the buffer index. At that angle energy goes into the plasmon and the reflectance R drops sharply.
Reflectance by transfer matrices
The page multiplies the 2x2 characteristic matrices of each layer (prism, gold of thickness d, adsorbed layer, buffer) with qj = kz,j/εj and kz,j = k0√(εj − np2 sin2θ), then R = |r|2. Gold permittivity is interpolated from Johnson and Christy (1972) data.
Binding kinetics
Langmuir 1:1 binding: dΓ/dt = ka C (1 − Γ) − kd Γ, with equilibrium Γeq = C/(C + KD) and KD = kd/ka. The adsorbed layer thickness is Γ times the full-coverage thickness (index 1.45), which shifts the resonance angle. That shift versus time is the sensorgram.
Honest simplifications: plane layers, no surface roughness or mass-transport limitation, a fixed layer index of 1.45, and gold optical data interpolated between six wavelengths. The layer thickness at full coverage is a free parameter, not derived from molecular mass. This is not a calibrated instrument model.
What to try
- Move the beam angle through the dip and watch R fall in the red reflected beam.
- Try 35, 50 and 70 nm gold: the dip is deepest near 50 nm (graph at lower left).
- Raise the analyte concentration: the plateau rises as C/(C+KD).
- Increase the buffer refractive index (like a sugar solution) and see the resonance angle rise.