Anomalous Dispersion Modelling |
| The results of the empirical study prompted further investigation into the relationship between the absorbance and index of refraction. In almost every salt solution studied, the index of refraction and absorbance increased simultaneously. The association of the index of refraction and absorbance can be described by the Kramers-Kronig relationship, and both of these properties increase as the wavelength of incident light approaches an absorption peak. This phenomenon is known as normal dispersion and is evident in most of the salt solutions studied. However, at the edge of the absorption peak, while the absorbance is still low, the index increases almost to its maximum level. This phenomenon is called “anomalous dispersion.” If the position of the absorbance peak can be adjusted so that the high index/low absorbance state is at 193nm, any compound that would generate this peak would be an ideal immersion fluid candidate. |
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| Normal and Anomalous Disperison generated with a Lorentz Oscillator Model |
| This research involves exploiting the anomalous dispersion behavior surrounding an absorption peak and generating model absorption spectra. The Kramers-Kronig relationship is used to determine the dispersion curve (or index) from the absorption spectra. In this model the absorbance peaks are placed at wavelengths that will result in both a high index and low absorbance at 193nm. Working backwards in this way from the absorption spectrum and using quantum mechanical calculations allows identification of compounds that would have the ideal high index and low absorbance characteristics required of the next generation immersion fluid. |
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| Model index and absorbance spectra generated with three Gaussian absorption peaks and the solution to the Kramers-Kronig relation to find the index. |