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Physical Review A

Propagation of phase-controlled lasers in a two-level medium

Takashi Nakajima

Published Sep 13, 2001• 7 citations
Publisher

Abstract

We study the propagation effects of phase-controlled two-color lasers in a two-level medium under a weak pumping condition. By solving the coupled equations for atoms and fields simultaneously, it is found that the propagation effects significantly modify the atom-field interactions. A time-dependent analysis is also undertaken to explain the numerical results.

DOI
10.1103/physreva.64.043406

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Physical Review A•Dec 1, 1999•158 citations
We study the propagation effects of phase-controlled two-color lasers in a two-level medium under a weak pumping condition. By solving the coupled equations for atoms and fields simultaneously, it is found that the propagation effects significantly modify the atom-field interactions. A time-dependent analysis is also undertaken to explain the numerical results.
We study the role of atomic coherence in the propagation dynamics of two-color lasers in an autoionizing medium. By solving the coupled equations for atoms and fields simultaneously, it is found that the asymptotic value of the phase difference after a long propagation distance critically depends on the detuning from an autoionizing resonance and the asymmetry parameter, suggesting that inherent atomic coherence of an autoionizing system, which is absent in a bound state system, plays an important role during the propagation processes. Our numerical findings are consistent with our theoretical analysis using a series expansion method of the coupled equations.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
The phase-dependent feature of few-cycle pulsed laser propagation in a resonant two-level atom medium is demonstrated by solving the full Maxwell-Bloch equations. Even in the perturbative region, the propagating carrier field and the corresponding spectra of the few-cycle pulsed laser are sensitive to the initial phase due to self-phase modulation. For the larger pulse area, the fact that the carrier-wave reshaping comes from the carrier-wave Rabi flopping is also responsible for this sensitivity, and the phase-dependent feature is more evident.
We present a theory of a continuous-wave light propagation in a medium of atoms with a double-$\ensuremath{\Lambda}$ configuration of levels. This is a configuration with a closed cycle of radiation-induced transitions. An interference of excitation channels in such closed-loop systems leads to a strong dependence of the atomic state on the relative phase and the relative amplitudes of applied electromagnetic waves. Therefore, the medium response may be controlled by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the propagation of four-frequency laser radiation through the double-$\ensuremath{\Lambda}$ medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the field evolve into a nonabsorbing state. This state implies specific coherent superposition for atoms (``dark state''), and particular relations for the field phases, amplitudes, and frequencies. In this way, the propagation results in the phase, amplitude, and frequency matching of the laser waves. In the second case, one $\ensuremath{\Lambda}$ system in double-$\ensuremath{\Lambda}$ atoms is excited resonantly, while the second $\ensuremath{\Lambda}$ system is far off resonance. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dissipated very weakly, whereas each individual laser wave can vary considerably along the propagation path. We have found that the resonant fields change as much as the far-detuned ones. The intensities oscillate sinusoidally with the optical length, with the energy being transferred back and forth between two waves in each frequency pair, resonant and far detuned. This gives the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them.