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Soviet Journal of Quantum Electronics

Self-induced transparency in an anisotropic molecular gas

V. I. Rupasov

Published Feb 28, 1981• 0 citations
Publisher

Abstract

A theory is developed of the self-induced transparency (SIT) of an anisotropic molecular gas for which aspects of the orientation of the molecules are of decisive importance. It is found that in such a chaotic molecular gas, the SIT equations do not have self-similar solutions in the form of a solitary nonlinear wave (soliton). In a partially oriented gas, the solutions have a quasisoliton form. An estimate is made of the orienting electric field required to observe the predicted effect.

DOI
10.1070/qe1981v011n02abeh005894

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Physical Review A•Apr 1, 1993•9 citations
A theory is developed of the self-induced transparency (SIT) of an anisotropic molecular gas for which aspects of the orientation of the molecules are of decisive importance. It is found that in such a chaotic molecular gas, the SIT equations do not have self-similar solutions in the form of a solitary nonlinear wave (soliton). In a partially oriented gas, the solutions have a quasisoliton form. An estimate is made of the orienting electric field required to observe the predicted effect.
The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.
The optical solitons that play the role of information carriers, are moving, requiring careful experimental timing to achieve the desired logic operation. In contrast, self-induced transparency (SIT) is a strong resonant nonlinear effect, supporting the propagation of optical solitons and are usually associated with a two-level system. By the appropriate application of light fields, the optical soliton, resonant with the SIT transition, can generate an excited region with ground state coherence in the medium, allowing logic operations to be performed on this coherence.
We consider self-induced transparency (SIT) in a two-level atomic system in the presence of an additional control laser field. We find that the dynamics of the SIT process are profoundly modified by the control field, in a manner reminiscent of the modification of other nonlinear optical interactions through the process of electromagnetically induced transparency. The presence of the control field allows SIT to occur under a much broader range of conditions and leads to dramatically reduced values of the group velocity of the SIT soliton.
We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.
The self-induced transparency in the Kerr host medium has been studied beyond the slowly-varying-envelope approximation. An analytic solution is obtained. There exists a hyperbolic-secant soliton whose power, pulse width, group velocity, and propagation constant are uniquely determined for given parameters of the medium. The reductions of the group velocities of the solitons by the self-induced-transparency effect in the resonant medium with homogeneous and inhomogeneous broadening are also studied. It is found that there is negative dispersion induced by the self-induced transparency, which is not predicted by the theory with the slowly-varying-envelope approximation. The amount of the induced dispersion is determined by the total dispersion of the system required to be compensated by the Kerr effect. Numerical examples of the self-induced transparency in an erbium-doped fiber are shown. In a typical erbium-doped fiber, the soliton solution has not been found because the inhomogeneous-broadening linewidth of the medium is too large.