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Optics Express

Propagator operator for pulse propagation in resonant media

Felipe Morales, Maria Richter, Vlad Olvo, Anton Husakou

Published Aug 9, 2021• 1 citation
Publisher

Abstract

We show that, for the case of resonant media, the available models for unidirectional propagation of short pulses can face serious challenges with respect to numerical efficiency, accuracy, or numerical artifacts. We propose an alternative approach based on a propagator operator defined in the time domain. This approach enables precise simulations using short time windows even for resonant media and facilitates coupling of the propagation equation with first-principle methods such as the time-dependent Schödinger equation. Additionally, we develop a numerically efficient recipe to construct and apply such a propagator operator.

DOI
10.1364/oe.435012

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We show that, for the case of resonant media, the available models for unidirectional propagation of short pulses can face serious challenges with respect to numerical efficiency, accuracy, or numerical artifacts. We propose an alternative approach based on a propagator operator defined in the time domain. This approach enables precise simulations using short time windows even for resonant media and facilitates coupling of the propagation equation with first-principle methods such as the time-dependent Schödinger equation. Additionally, we develop a numerically efficient recipe to construct and apply such a propagator operator.
In this book, we focus on the stochastic nature of pulses to achieve a more realistic description of ultra-short optical pulses affected by noise. In order to simulate ultra-short pulses, various stochastic pulse models were applied. The effects of pulse amplitude and phase fluctuations on its propagation in various linear and non-linear media were studied based on optical coherence theory. The response of the medium atoms to the applied stochastic pulses was investigated for the particular resonant case in which the pulse frequency nearly coincides with the atom resonance frequency. Analytical and numerical propagation methods were applied to explore evolutions of ultra-short stochastic pulses in the vicinity of optical resonance.
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Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.