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Physical Review A

Solitary wave solutions in coherent two-photon pulse propagation

Naohiro Tanno, Yoshihiro Higuchi

Published Nov 1, 1977• 8 citations
Publisher

Abstract

Solitary wave solutions of an electric power envelope for two-photon pulse propagation in a resonant medium are given under limited conditions. In addition, we show new types of periodic solutions without Jacobian elliptic functions and the well-known Lorentzian-shape solutions for a coherent two-photon amplifier.
DOI
10.1103/physreva.16.2181

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The propagation of an optical ultrashort pulse in a resonance Bragg grating is considered taking into account the polarisation of electromagnetic radiation. It is assumed that the grating is formed by thin films containing two-level atoms with the triply degenerate upper energy level. The system of equations is derived for the envelopes of electromagnetic pulses counterpropagating in such a grating. In the long-wavelength (continual) approximation, the system of equations generalising the known system for scalar waves is obtained. The solutions corresponding to elliptically (in particular, linearly and circularly) polarised stationary pulses are found. An arbitrary degree of ellipticity is possible only in a medium with a preliminary prepared stage of resonance atoms.
The resonant propagation of an optical pulse in a two-photon absorber with a coherent initial excitation of the medium may lead to a pulse steepening growing exponentially in space. In addition another example is given wherein the steepening is followed by flattening. These results are new although, principally, they could be obtained from the general solution of the respective Goursat problem of an amplitude-modulated initial wave (H Steudel and D J Kaup 1996 J. Mod. Opt. 43 1851). In addition, we also give a simple theorem whereby it is demonstrated that the spatial derivative of the phase of the electric field will always be bounded. Furthermore, it is also shown that there can be certain critical points at which the atomic state, as well as the electric field, can become stationary in time and the spatial direction. © 2012 IOP Publishing Ltd.