Surface Plasmon Resonance Angle Calculator

Kretschmann Surface Plasmon Resonance Stack

In the Kretschmann geometry a thin gold film is deposited on the base of a high-index prism, with the analyte (sample) medium on the far side. Sweeping the incidence angle, p-polarized light excites a surface plasmon at the metal/analyte boundary, producing a sharp reflectance dip whose angle reports the analyte refractive index.

Why This Design Works

Past the prism/analyte critical angle the light is evanescent in the analyte, but the prism lets the in-plane wavevector exceed what the analyte alone allows. When that wavevector matches the surface-plasmon wavevector at the metal/analyte interface, energy couples into the plasmon mode — a bound charge-density wave with a strongly enhanced evanescent field — and p-reflectance drops. Only p-polarization couples; s-polarization shows no plasmon dip and its reflectance stays near total, reduced only by weak absorption in the gold. Changing the analyte index shifts the matching angle, which is the sensing signal.

The prism-side in-plane wavevector \(n_p\sin\theta\) matches the surface-plasmon wavevector set by the metal (\(\varepsilon_m\)) and analyte (\(\varepsilon_d\)) permittivities. A thinner gold film deepens the dip toward zero (critical coupling); the dip angle tracks the analyte index.

Interactive design tool

This page includes a live transfer-matrix calculator for this design. Adjust the parameters to recompute spectra, layer stack, and performance figures in the browser, then open the design in the full calculator.