SURFACE PLASMON RESONANCE AT A SILVER-AIR INTERFACE
HOME THEORY APPARATUS DATA ACQUISITION RESULTS AND CONCLUSIONS
Results and Conclusions
The value of Θint for which the intensity profiles were at a minimum was chosen as Θplasmon. These values are shown for all 21 wavelengths used in the figure below.
From these values of Θplasmon, the dispersion curve shown below was generated as a means of visualizing the experimentally determined resonance conditions. The kx values were found using
where Θplasmon = Θint as described in THEORY; together with the corresponding frequency of incident light, these kx values were compared to a dispersion curve generated using literature values [5].
All experimental values were within uncertainty of the literature predictions. However, the experimental kx values were all lower in magnitude than the literature. This hints at a systematic error obscuring the measured data as random error alone would deviate both positively and negatively from literature.
The dispersion curve alone was not sufficient to examine this error, though, as it is of a form not readily fit; the figure below, showing the dielectric function of silver calculated from experimental values of Θplasmon plotted against literature values [5], is linear and so does not have this same weakness. The black line shows a χ2 fit for the experimental data, which took the form y = (1.21 ± 0.02) x - (0.3 ± 0.1) with a reduced χ2 value of 0.781. The red line, however, shows the ideal fit of the two data sets; namely, if the experimental and literature values were in perfect agreement, points would fall on the line x=y. This is patently not the case, seen both visually in the separation of the red and black lines and through the slope of 1.21 in the fit.
The discrepancy between the experimental and literature values for the dielectric function of silver confirmed the suspicion of systematic errors suggested by the dispersion curve. One readily obvious potential source of such a systematic error lies in the assumptions about the geometry of the setup detailed when deriving Equation 11. As APPARATUS suggests, the setup was vertical. This introduced technical challenges in assuring the light beam and camera were directly perpendicular to the surface of the prism and that the prism was centered on them both; moreover, uncertainties associated with these issues were difficult to quantify. Rotating the setup to be horizontal could allow more efficient use of standard optics tools to ensure the geometry of the setup was as is claimed, or at the least, quantify any associated uncertainties.
In conclusion, the conditions on surface plasmon resonance at a silver-air interface were investigated with monochromatic light incident on the interface through a glass prism. The amount of light reflected off of the interface for the various incident angles of light was used to map the resonance conditions on the frequency and wavevector of the optical beam. These experimentally determined resonance conditions were within uncertainty of those predicted from literature. however, experimental results did not accurately reproduce the dielectric function of silver; they deviated systematically, not randomly, from literature values.
Molly Andersen & Jesse Grindstaff
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