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Journal of the Optical Society of America B

Collisions of counterpropagating optical solitons

Michael J. Shaw, Bruce W. Shore

Published May 1, 1991• 23 citations
Publisher

Abstract

We present numerical simulations of colliding counterpropagating solitons traversing a relaxation-free atomic vapor. The collisions produce appreciable spatially localized inversion of the atomic population, even in the case of colliding solitary 2π hyperbolic-secant pulses. The energy deposited in the atoms and lost from the pulses determines the pulse widths, energies, and phase shifts of the postcollision pulses. This energy subsequently appears as fluorescence. We present results that illustrate the role of the residual atomic excitation energy on postcollisional solitary pulses. In addition, we show that for certain conditions a low-density medium is transparent to nonsolitary π pulses.

DOI
10.1364/josab.8.001127

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We present numerical simulations of colliding counterpropagating solitons traversing a relaxation-free atomic vapor. The collisions produce appreciable spatially localized inversion of the atomic population, even in the case of colliding solitary 2π hyperbolic-secant pulses. The energy deposited in the atoms and lost from the pulses determines the pulse widths, energies, and phase shifts of the postcollision pulses. This energy subsequently appears as fluorescence. We present results that illustrate the role of the residual atomic excitation energy on postcollisional solitary pulses. In addition, we show that for certain conditions a low-density medium is transparent to nonsolitary π pulses.
We examine the dynamics of counterpropagating self-induced transparency solitons in three-level media. In a multilevel system, self-induced transparency gives rise to soliton solutions if the propagation is unidirectional, but the collision of counterpropagating pulses destroys the integrability of the underlying equations. We consider the collision of a rightward and a leftward moving self-induced transparency solitary wave by solving the full Maxwell-Bloch equations numerically using a finite-difference time-domain approach. Depending on pulse duration, amplitude and relative polarizations of the initial solitary waves we observe different regimes of interaction. For high group velocities and orthogonal polarizations, secondary solitary waves are born during the interaction, whereas the collision of solitary waves with the same polarization never produces secondary solitary waves but leaves behind a population grating in the interaction region. Because the crucial parameters can be controlled, an experimental confirmation of the predicted interaction regimes should be feasible.
We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.
We study inelastic collisions of counterpropagating self-induced transparency solitons in a homogeneously broadened two-level medium. The energy of the pulse can be almost totally absorbed in the medium due to asymmetric collision with a properly chosen control pulse. The medium state thus prepared demonstrates the property of an all-optical diode which transmits pulses from one direction and blocks from another. The saturation process of a controlled absorption effect, local-field correction influence, and the parameter ranges for the diode action are studied as well.
We obtain an exact linearly polarized vector solitary solution for the amplification of an optical pulse with a time width short compared with both population and polarization decay time. This dissipative soliton results from the balance between the gain from inverted resonant two-level atoms and the linear loss of the host material. We suppose that the excited state of the active centers is degenerate on the projection of the angular momentum, with a symmetric state of inversion. Quite remarkably, we find that after the passing of the pulse, the atomic medium does not return to the ground state, and a finite Zeeman coherence is generated. Numerical simulations demonstrate the stability of vector π solitons with an arbitrary state of elliptical polarization in the presence of both linear birefringence and group-velocity dispersion of the host material.
Collision properties of optical solitons are studied experimentally using the technique of self-induced transparency. Numerical plane-wave simulations of collisions using parameters for the input pulses and the atomic system appropriate to the actual experimental situation are presented and compared to matching analytic solutions derived previously by other workers. Experimental studies of overtaking collisions in sodium vapor are presented for the first time and found to be in qualitative agreement with numerical results at intermediate optical absorption. At higher absorption, dynamic transverse effects cause a rapid attenuation of the pulses which prevents the observation of complete collisions. Attempts to compensate for losses by focusing the input beam are described.