13 Jul 2026

Refractive Index of a Dielectric Layer by Surface Plasmon Resonance

practical ug-viii surface-plasmon-resonance refractive-index

Aim

To determine the refractive index of a dielectric layer from the resonance-angle shift in an SPR arrangement.

Apparatus

Laser, prism coupler, metal-coated slide, dielectric layer, photodetector, rotation stage, and computer interface.

Figure

In the Kretschmann arrangement, the p-polarised beam enters the prism, reflects from the metal film, and reaches the photodetector.

Theory

At a particular angle, the parallel component of the p-polarised wave vector matches the surface-plasmon wave vector. The reflected intensity then shows a minimum. A dielectric layer changes the interface optical environment and shifts the minimum from $\theta_0$ to $\theta_r$.

Observations

Sample	Resonance angle	Refractive index
Air reference	$44.2^\circ$	1.000
Water	$51.6^\circ$	1.333
Unknown dielectric layer	$56.1^\circ$	1.510

Graph

Reflectance minimum used to identify the SPR resonance angle.

Result

The refractive index of the unknown dielectric layer is

\[\boxed{n=1.510}.\]

Viva Questions

1. Why is p-polarised light used? It has an electric-field component normal to the interface.
2. What does the resonance angle indicate? The phase-matching condition at the metal-dielectric interface.
3. Why is air used as a reference? It provides a known baseline for the resonance shift.

Maxima Code

Download the Maxima calculation file.