Surface Plasmon Wave In this experiment you will learn about a surface plasmon wave. Certain metals (Au, Ag, Co, etc) exhibit a negative dielectric constant at certain regions of the electromagnetic spectrum. Maxwell s equations predict that an interface of two materials: one with a positive dielectric constant and another with a negative dielectric constant can support a p-polarized surface electronic wave, known in the literature as surface plasmon wave. In this experiment we use a gold film as it shows a negative dielectric for long wavelengths (red) in the visible spectral region. For a positive dielectric constant we will simply use air. This experiment will show how you can use light to excite such surface wave. Instead of being reflected (usually metals are good reflectors), light will be almost completely transferred toward the excitation of the plasmon wave. You will learn that to excite such unique wave there are requirements about the polarization, the angle of incidence, and even from which side light must be incident on the structure. From applications of Maxwell s equation, the dispersion relation, k SPR (ω) and ω, for the surface plasmon wave is shown to be given by: k SPR (ω) = 2 π ε air(ω) ε metal (ω) ε air (ω) + ε metal (ω) Experiment: Using a rotation stage, a laser beam (He-Ne laser, 632.8 nm), a plastic sheet polarizer, and a power meter, in this experiment you
will perform reflectance measurements of a thin film of gold (about 40-50 nm) on a glass substrate. In Part 1, light will be incident from the air side. In Part 2, light will be incident from the glass side. You should observe important differences. Do the following measurements: 1. Reflectance R pol (θ a ) versus angle of incidence θ a for light polarized perpendicular and parallel to the plane of incidence for an air/metal/glass as shown in Figure below. With a plastic polarizer, select a particular polarization. Measure the incident light power I o after the polarizer. Align the rotation stage to get back-reflected light. Write down the offset angle you read in the rotation stage; all angles of incidence will be measured with respect to this reference angle. Vary the angle of incidence from the smallest (as close to 0 as possible) to the highest (as close to 90 as possible) you can get under the mechanical constraints of the setup. Measure the reflected light intensity I pol (θ a ). Perform power intensity measurements at steps of 5 or smaller.
2. Reflectance R pol (θ a ) versus angle of incidence θ a for light polarized perpendicular and parallel to the plane of incidence for a glass/metal/air as shown in Figure below, which is known as the Kretschmann s configuration. With a plastic polarizer, select a particular polarization (first s-polarized, then p-polarized). Measure the incident light power I o after the polarizer. As before, align the rotation stage to get backreflected light. Write down the offset angle on the rotation stage. Vary the angle of incidence from the smallest (as close to 0 as possible) to the highest (as close to 90 as possible) you can get under the mechanical constraints of the setup. Have steps of 5 or smaller. Measure the reflected light intensity I pol (θ a ) so later you can determine the reflectance R pol (θ a ) = I pol (θ a ). Do a quickly analysis of your data. For the p-polarized light you should notice a deep in the reflectance at a particular angle of incidence. Zoom to this angle of incidence and perform additional measurements around the angle of minimum reflectance at a much smaller step (e.g. 1 ). I o
Analysis: For data in Part 1, tabulate your data: θ a, I pol (θ a ), R pol (θ a ). Create a plot of Reflectance, R pol (θ a ), versus Angle of Incidence, θ a, for each polarization. Discuss your experimental results. For data in Part 2, derive the relation between θ a and θ p. θ p = α + sin 1 [ n asin(θ a ) n p ] For the right-angle prism made of BK-7 glass, you have: α = 45 and n p 1.51 at = 632.8 nm. Tabulate your data: θ a, θ p, I pol (θ p ), R pol (θ p ). Create a plot of Reflectance, R pol (θ p ), versus Angle of Incidence, θ p, for each polarization. Discuss your experimental results. Determine the
polarization and the angle of resonance to excite the surface plasmon mode. Consider that the tangential component of the k-vector for the incident light is described by: k x = 2 π n g sin(θ g ) = 2 π n p sin(θ p ) As for the resonant condition, k SPR (ω) = k x, calculate the dielectric constant of the gold metal at 632.8 nm. Questions to consider: 1. What would happen if instead of air we had water? 2. Why cannot we excite the surface plasmon wave with light coming from the air side? 3. Explain why the surface plasmon resonance is highly sensitive and useful to detect surface binding of molecules.