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Physical Review A

Coupled-mode analysis of the self-induced-transparency soliton switch

Ángela M. Guzmán, F. S. Locati, M. Romagnoli, Stefan W. Wabnitz

Published Aug 1, 1992• 4 citations
Publisher

Abstract

The dynamics of a nonlinear resonant tapered coupler is analyzed by using coupled-mode equations. The constituent waveguides are made of a linear host material doped with resonant impurities. Such a system allows a mechanism for all-optical switching. It is shown that nonlinear exchange between coupled waveguides originates from the group-velocity dependence on the propagating pulse power and/or area. The transmitted signal is always a multiple of the self-induced-transparency fundamental soliton. The dynamics of the pulse tuned or detuned from the resonance and with the inclusion of the material relaxation terms is discussed. In the last section the problem of soliton collision in the coupling region is considered; in this case an initial interpulse phase difference may determine a power-dependent outport switching.

DOI
10.1103/physreva.46.1594

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arXiv:1009.2641•Sep 14, 2010•0 citations
The dynamics of a nonlinear resonant tapered coupler is analyzed by using coupled-mode equations. The constituent waveguides are made of a linear host material doped with resonant impurities. Such a system allows a mechanism for all-optical switching. It is shown that nonlinear exchange between coupled waveguides originates from the group-velocity dependence on the propagating pulse power and/or area. The transmitted signal is always a multiple of the self-induced-transparency fundamental soliton. The dynamics of the pulse tuned or detuned from the resonance and with the inclusion of the material relaxation terms is discussed. In the last section the problem of soliton collision in the coupling region is considered; in this case an initial interpulse phase difference may determine a power-dependent outport switching.
The possibility of observing a self-induced transparency (SIT) in an erbium-doped optical fiber is investigated. A general equation that includes the SIT, the group-velocity dispersion (GVD) of the fiber, and the nonlinear refractive index is discussed. It is shown that for one particular value of waveguide parameters the nonlinear index can balance the GVD, that is, the nonlinear Schr\"odinger equation (NLS), while maintaining a SIT soliton. This is called a SIT-NLS soliton. The phase change of the SIT-NLS soliton is governed solely by the NLS component, and the pulse delay due to resonance is determined solely by the SIT component when the detuning is zero. Practical parameters for silica-based fibers do not allow the coexistence of a mixed soliton state. A simple derivation of a condition for a SIT-NLS soliton is also presented. The SIT-NLS soliton is computer-run, and it is shown that a stable 2\ensuremath{\pi}/N=1 SIT-NLS soliton exists. However, high-order SIT-NLS solitons always split into multiple 2\ensuremath{\pi}/N=1 solitons. The NLS property can be preserved when Zsp{\mathit{Z}}_{\mathrm{sp}}Zsp​\ensuremath{\ll}Labs.{\mathit{L}}_{\mathrm{abs}.}Labs.​ Finally, the NLS soliton that interacts coherently with erbium ions is studied, and the coherent pulsation that produces multiple narrow pulses is described.
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.
We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.
Fiber guided optical signal propagating in a Erbium doped nonlinear resonant medium is known to produce cleaner solitonic pulse, described by the self induced transparency (SIT) coupled to nonlinear Schroedinger equation. We discover two new possibilities hidden in its integrable structure, for amplification and control of the optical pulse. Using the variable soliton width permitted by the integrability of this model, the broadening pulse can be regulated by adjusting the initial population inversion of the opant atoms. The effect can be enhanced by another innovative application of its constrained integrable hierarchy, proposing a system of multiple SIT media. These theoretical predictions are workable analytically in details, correcting the limitation of a well known result.