Hilbert transform: applications to atomic spectra

Whittaker, K.A.; Keveaney, J.; Hughes, I.G.; Adams, C.S.

doi:10.1103/physreva.91.032513

Hilbert transform: applications to atomic spectra

Whittaker, K.A.; Keveaney, J.; Hughes, I.G.; Adams, C.S.

Authors

K.A. Whittaker

J. Keveaney

Professor Ifan Hughes i.g.hughes@durham.ac.uk
Professor

C.S. Adams

Contributors

J Keaveney xbnv46@durham.ac.uk
Other

Abstract

In many areas of physics, the Kramers-Kronig relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index, and group delay while avoiding the use of complicated experimental setups.

Citation

Whittaker, K., Keveaney, J., Hughes, I., & Adams, C. (2015). Hilbert transform: applications to atomic spectra. Physical Review A, 91(3), Article 032513. https://doi.org/10.1103/physreva.91.032513

Journal Article Type	Article
Publication Date	Mar 25, 2015
Deposit Date	Nov 20, 2014
Publicly Available Date	Apr 8, 2015
Journal	Physical Review A
Print ISSN	1050-2947
Electronic ISSN	1094-1622
Publisher	American Physical Society
Peer Reviewed	Peer Reviewed
Volume	91
Issue	3
Article Number	032513
DOI	https://doi.org/10.1103/physreva.91.032513

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Copyright Statement
Reprinted with permission from the American Physical Society: Whittaker, K. A. and Keveaney, J. and Hughes, I. G. and Adams, C. S. (2015) 'Hilbert transform : applications to atomic spectra.', Physical review A., 91 (3). 032513 © 2015 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.