Optical constants at complex energies: local deconvolution

Area of Science:

• Physics
• Materials Science
• Optics

Background:

• Causality dictates that optical constants are analytic functions in the complex photon energy plane.
• Kramers-Kronig relations utilize this analyticity to derive real from imaginary parts (e.g., n from k).
• Exploration of analytic continuation into the complex plane for optical constants has been limited.

Purpose of the Study:

• To investigate the analytic continuation of optical constants into the upper complex plane.
• To explore applications of this continuation, particularly for optical constant deconvolution.
• To develop a method for improving spectral resolution of optical measurements.

Main Methods:

• Analytic continuation of optical constants into the complex energy plane.
• Characterization of the smoothening effect using a Lorentzian weight function.
• Development of a local deconvolution procedure via Taylor expansion in complex energy.
• Proposal of an approach for Gaussian slit functions using Lorentz function powers.

Main Results:

• Optical constants exhibit progressive smoothening upon analytic continuation into the complex plane.
• This smoothening is analogous to convolution with a Lorentzian slit function.
• A local deconvolution method was developed, utilizing derivatives of optical constants.
• The method offers a way to enhance resolution of spectrophotometer and ellipsometer data.

Conclusions:

• Analytic continuation provides a powerful theoretical framework for understanding optical constants.
• The developed deconvolution technique can improve the resolution of measured optical constants.
• This approach offers a practical post-processing tool for optical spectroscopy and ellipsometry.