Analytical transfer function for the nonlinear response of a resonant medium in the spatiotemporal Fourier-transform domain

Mehjabin S. Monjur*, Mohamed F.F. Ouda, Selim M. Shahriar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The nonlinear response of a resonant medium has many applications. To model and find the response of such a medium requires solving the Schrödinger equation (SE), which is a computationally extensive task. In this paper, we develop an analytical model to find the response of a resonant medium due to an applied field by employing the spatio-temporal Fourier-transform (STFT)-domain-based transfer function. A key feature of this approach is the use of the resonant excitation approximation (REA), which amounts to assuming that a group of atoms (or other quantum systems) within a volume element in the STFT domain are excited by only the corresponding volume element in the STFT domain of the field. We first derive the one-dimensional transfer function using an inhomogeneously broadened atomic medium under the REA. Then, we develop the three-dimensional transfer function and show that the analytical model agrees closely with the results obtained via an explicit simulation of the atomic response. As a practical example of the analytical model, we show that it can be used to model a spatio-temporal-correlator-based automatic event recognition system at a speed that is many orders of magnitude faster than solving the SE.

Original languageEnglish (US)
Pages (from-to)397-403
Number of pages7
JournalJournal of the Optical Society of America B: Optical Physics
Volume34
Issue number2
DOIs
StatePublished - Feb 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics

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