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Journal of Physics B Atomic and Molecular Physics

Propagation of a Gaussian pulse under two-photon near-resonant conditions

J.V. Moloney, Farhad H. M. Faisal

Published May 28, 1980• 1 citation
Publisher

Abstract

Evolution under two-photon near-resonance conditions of an adiabatic Gaussian pulse is considered in Rb vapour. Theoretical results show strong self-phase modulation and pulse deformation with increasing distance of propagation and intensity at a fixed detuning. At sufficiently large distances of propagation and/or input intensity pulse deformation is seen to develop into (two-photon) optical shocks. At a higher intensity double shock fronts are predicted to occur. The previously anticipated existence of an upper bound for the output maximum and of the vanishing of the self-phase modulation at the 'interaction time' between the output and the input profiles are shown explicitly to hold for the cases considered. A quasi free-wave like evolution occurs at asymptotically higher intensities.

DOI
10.1088/0022-3700/13/10/020

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 10, 1997•0 citations
Evolution under two-photon near-resonance conditions of an adiabatic Gaussian pulse is considered in Rb vapour. Theoretical results show strong self-phase modulation and pulse deformation with increasing distance of propagation and intensity at a fixed detuning. At sufficiently large distances of propagation and/or input intensity pulse deformation is seen to develop into (two-photon) optical shocks. At a higher intensity double shock fronts are predicted to occur. The previously anticipated existence of an upper bound for the output maximum and of the vanishing of the self-phase modulation at the 'interaction time' between the output and the input profiles are shown explicitly to hold for the cases considered. A quasi free-wave like evolution occurs at asymptotically higher intensities.
Coherent propagation of a circularly polarized pulse which is two-photon quasi-resonant with a medium of multi-level atoms is considered in the adiabatic following limit. The relevant pair of non-linear coupled partial differential equations are solved exactly for arbitrary pulse shapes. The development of the envelope and the phase of the pulse as it propagates through the medium is described analytically. Perturbation theoretical results are shown to apply only for small intensity or small distance of propagation or both. Qualitatively different results apply for higher intensities and longer distances of propagation. These include strong self-phase-modulation effects as well as reshaping of the pulse envelope.
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.
A numerical and analytic investigation is made of the self-interaction of Gaussian beams under two-photon resonance conditions when the pulse duration is shorter than the relaxation times and the frequency detuning from resonance exceeds appreciably the spectral width of the radiation (adiabatic model). An analysis is made of defocusing (up-detuning) and self-focusing processes (down-detuning) in two-photon resonance. Three characteristic adiabatic self-focusing regimes are identified: a steady-state waveguide and weak and strong quasiwaveguide propagation. Expressions are derived for the critical powers and minimal self-focusing length.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .