Surface Plasmon Resonance Based Measurement of the Dielectric Function of a Thin Metal Film

Abstract

A spectral method based on surface plasmon resonance (SPR) in air is used to measure the dielectric function of a thin metal film. The method utilizes the spectral dependence of the ratio of the reflectances of p- and s-polarized waves measured in the Kretschmann configuration at different angles of incidence. By processing these dependences in the vicinity of a dip, or equivalently near the resonance wavelength, and using the dispersion characteristics of a metal film according to a proposed physical model, the real and imaginary parts of the dielectric function of the metal can be determined. The corresponding dielectric function of the metal is obtained by a least squares method for such a thickness minimizing the difference between the measured and theoretical dependence of the resonance wavelength on the the angle of incidence. The feasibility of the method is demonstrated in measuring the dielectric function of a gold film of an SPR structure comprising an SF10 glass prism and a gold coated SF10 slide with an adhesion film of chromium. The dielectric function according to the Drude⁻Lorentz model with two additional Lorentzian terms was determined in a wavelength range from 534 to 908 nm, and the results show that the gold film is composed of homogenous and rough layers with thicknesses 42.8 nm and 2.0 nm, respectively. This method is particularly useful in measuring the thickness and dielectric function of a thin metal film of SPR structures, directly in the Kretschmann configuration.

Keywords: Drude–Lorentz model; Kretschmann configuration; dielectric function; gold; reflectance ratio; resonance wavelength; surface plasmon resonance.

Figure 1

Experimental set-up: an SPR structure in the Kretschmann configuration; collimating lens (CL), polarizer (P), analyser (A).

Figure 2

AFM image of a thin gold film on an SF10 glass substrate.

Figure 3

An SPR structure under study.

Figure 4

Measured reflectance ratio $R_p\left(\lambda \right)/R_s\left(\lambda \right)$ as a function of the wavelength for different angles of incidence $\alpha$: ${33}^{\circ }$ to ${41}^{\circ }$ (a), ${41.1}^{\circ }$ to ${42.6}^{\circ }$ (b).

Figure 5

Measured (solid curves) reflectance ratio $R_p\left(\lambda \right)/R_s\left(\lambda \right)$ as a function of the wavelength for angle of incidence $\alpha ={40.6}^{\circ }$ together with the fitted one (a), and with the modelled one (b). Lower solid curve corresponds to a different loop diameter of a read optical fibre.

Figure 6

Dielectric function of the gold film (crosses) with a fit according to a modified Drude–Lorentz model: a real part (a), an imaginary part (b).

Figure 7

Measured (crosses) and modelled resonance wavelength as a function of the angle of incidence.