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European Quantum Electronics Conference (EQEC)

Giant nonlinearities via simultaneous electromagnetically- and self-induced transparencies in doped photonic crystals

Gershon Kurizki, David Petrosyan

Published Nov 15, 2004• 0 citations
Publisher

Abstract

This paper studies a strong modulation of the phase of a weak pulse subject to electromagnetically-induced transparency (EIT) by a control pulse in the form of an self-induced transparency (SIT) gap soliton (GS) moving at the same slow velocity. The aim of this work is to match the group velocities of the weak probe field subject to EIT and the free-propagating field having the form of a slow SIT GS.

DOI
10.1109/eqec.2003.1314061

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Modification of Self-Induced Transparency by a Coherent Control Field

Q‐Han Park, Robert W. Boyd

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.

Physical Review Letters•Mar 26, 2001•22 citations
This paper studies a strong modulation of the phase of a weak pulse subject to electromagnetically-induced transparency (EIT) by a control pulse in the form of an self-induced transparency (SIT) gap soliton (GS) moving at the same slow velocity. The aim of this work is to match the group velocities of the weak probe field subject to EIT and the free-propagating field having the form of a slow SIT GS.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
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.
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.
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.