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Optics and Spectroscopy

The effect of initial inversion of resonant atoms on the propagation dynamics of laser pulses in a continuous resonant photonic crystal

Фролова Лидия Владимировна, Boris I. Mantsyzov

Published Sep 1, 2013• 0 citations
Publisher

Abstract

The nonlinear interaction of high-intensity coherent optical radiation and a continuous resonant photonic crystal is analytically and numerically studied in the framework of the semiclassical approximation using the two-wave Maxwell-Bloch equations at various initial excitations of resonant atoms. It is demonstrated that the initially unexcited resonant photonic crystal with an arbitrary concentration function of resonant atoms allows the propagation of the Bragg soliton of the self-induced transparency. The Bragg reflection is suppressed at zero initial inversion when the number of atoms in the excited state is equal to the number of atoms in the stationary state.

DOI
10.1134/s0030400x13090075

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B. Kalithasan, Kuppusamy Porsezian, Krishnamoorthy Senthilnathan +1 more

We consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.

Physical Review A•May 3, 2010•7 citations
The nonlinear interaction of high-intensity coherent optical radiation and a continuous resonant photonic crystal is analytically and numerically studied in the framework of the semiclassical approximation using the two-wave Maxwell-Bloch equations at various initial excitations of resonant atoms. It is demonstrated that the initially unexcited resonant photonic crystal with an arbitrary concentration function of resonant atoms allows the propagation of the Bragg soliton of the self-induced transparency. The Bragg reflection is suppressed at zero initial inversion when the number of atoms in the excited state is equal to the number of atoms in the stationary state.
Nonlinear interaction of coherent intensive optical radiation with continuous resonant photonic crystal (RPC) is analytically and numerically studied in the framework of semiclassical approach using the two-wave Maxwell–Bloch equations. The analytical solution being the gap soliton of self-induced transparency is obtained in the case of an initially unexcited continuous RPC. This solution is confirmed numerically. Influence of both initial inversion and resonant atom concentration function profile on the pulse dynamics in continuous RPC is analyzed. Suppression of the Bragg reflection and a “quasi-linear” 2π pulse propagation in the case of zero initial inversion in continuous RPC is shown. The possibility of laser pulse compression using slow spatial changing of resonant atom concentration is demonstrated.
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.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.
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 consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.