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Journal of the Optical Society of America B

Invariant pulse propagation and self-phase modulation in dense media

C. M. Bowden, R. Inguva, Aharon Postan

Published May 1, 1991• 46 citations
Publisher

Abstract

Analytical solutions for the slowly varying phase as well as the field amplitude are obtained for invariant pulse propagation in resonant absorbing media consisting of interacting two-level atoms. Such media, having many atoms within a cubic wavelength, have been shown to exhibit large frequency chirps in pulse propagation owing to near-dipole–dipole interactions. Departures from hyperbolic-secant pulse envelopes and pulse areas other than 2π have been shown to occur in invariant pulse propagation. We show that self-phase modulation results from the near-dipole–dipole interactions and can cause strong modification of pulse shapes, including temporal narrowing and multipulse behavior.

DOI
10.1364/josab.8.001081

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Analytical solutions for the slowly varying phase as well as the field amplitude are obtained for invariant pulse propagation in resonant absorbing media consisting of interacting two-level atoms. Such media, having many atoms within a cubic wavelength, have been shown to exhibit large frequency chirps in pulse propagation owing to near-dipole–dipole interactions. Departures from hyperbolic-secant pulse envelopes and pulse areas other than 2π have been shown to occur in invariant pulse propagation. We show that self-phase modulation results from the near-dipole–dipole interactions and can cause strong modification of pulse shapes, including temporal narrowing and multipulse behavior.
Resonant absorbing media having many atoms within a cubic resonance wavelength can exhibit large frequency chirps in pulse propagation due to dipole-dipole interactions among the atoms. Analytic solutions are obtained for invariant pulse propagation in such a medium consisting of interacting two-level atoms. Departures from the McCall-Hahn results include nonhyperbolic secant pulse shapes and different than 2π-area pulses. In addition, the excitation of the medium is comparatively suppressed for the same group velocity. The results are interpreted to suggest new experiments.
We analyze the phase modulation, or chirping, of coherent lossless light pulses propagating without distortion through resonant absorbers. In order to do this, we generalize the pioneering work of McCall and Hahn in two different directions. In the first place, of course, we abandon their assumption that the phase of the pulses has no temporal dependence. We prove that for slowly varying single pulses, chirping is not possible. However, we describe many multiple-pulse trains which are necessarily chirped, even under the slowly varying envelope restriction, and also describe the envelope modulations which produce large chirps. We show that certain zero-$\ensuremath{\pi}$ chirped pulse trains are contained as special cases of our general results. Our second generalization of the McCall-Hahn work concerns the background material in which the two-level resonant atoms are suspended. We allow the host medium to possess significant nonresonant nonlinearities. We find that undistorted lossless single pulses are possible in such a medium and that they are necessarily chirped.
In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.
We investigate ultrashort pulse propagation in a dense medium of two-level atoms. We numerically solve the coupled nonlinear Maxwell-Bloch equations by assuming that the fields are slowly varying in time only. We find that while intrinsic optical switching of the atomic inversion persists in extended media, self-phase-modulation effects, coherent energy transfer, and reflections can be large even for films that are only a small fraction of a wavelength thick. If the propagation distance is sufficiently large, a physical boundary that separates fully excited atoms from atoms in the ground state can be created within the medium. In turn, this leads to a rapid spatial modulation of the nonlinear polarization, and a deterioration of the intrinsic optical switching mechanism. We then show that, although the slowly varying envelope approximation in space may be preempted by the fast longitudinal variation of the field and atomic variables, the mean-field approximation remains valid in the regime of ultrafast optical switching, provided the film thickness is sufficiently small such that the medium is nearly uniformly excited. These results are generated by utilization of our calculational method that fully accounts for the longitudinal dynamics of the fields, including reflections.