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Physical Review Letters

Propagation of Ultrashort Optical Pulses in Degenerate Laser Amplifiers

Ildar R. Gabitov, S. V. Manakov

Published Feb 14, 1983• 26 citations
Publisher

Abstract

The shape and area of the output from physically realizable amplifiers of inverted $Q(2)$-degenerate two-level atoms are calculated analytically. The ($4\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}$)- or $\ensuremath{\delta}$-pulse output is made up from a sequence of $\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}$ double-humped pulses followed by $\ifmmode\pm\else\textpm\fi{}(4\ensuremath{\pi}\ensuremath{-}2\ensuremath{\delta})$ pulses, where $\ensuremath{\delta}=2invcos(\ensuremath{-}\frac{1}{4})$.

DOI
10.1103/physrevlett.50.495

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The shape and area of the output from physically realizable amplifiers of inverted Q(2)Q(2)Q(2)-degenerate two-level atoms are calculated analytically. The (4\ensuremathπ\ensuremath−\ensuremathδ4\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}4\ensuremathπ\ensuremath−\ensuremathδ)- or \ensuremathδ\ensuremath{\delta}\ensuremathδ-pulse output is made up from a sequence of \ifmmode±\else\textpm\fi4\ensuremathπ\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}\ifmmode±\else\textpm\fi4\ensuremathπ double-humped pulses followed by \ifmmode±\else\textpm\fi(4\ensuremathπ\ensuremath−2\ensuremathδ)\ifmmode\pm\else\textpm\fi{}(4\ensuremath{\pi}\ensuremath{-}2\ensuremath{\delta})\ifmmode±\else\textpm\fi(4\ensuremathπ\ensuremath−2\ensuremathδ) pulses, where \ensuremathδ=2invcos(\ensuremath−14)\ensuremath{\delta}=2invcos(\ensuremath{-}\frac{1}{4})\ensuremathδ=2invcos(\ensuremath−41​).
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.