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Physical Review A

Coherent pulse propagation and self-induced transparency on degenerate transitions in atomic iodine

Gan Xu, Terence A. King

Published Jul 1, 1984• 9 citations
Publisher

Abstract

Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.

DOI
10.1103/physreva.30.354

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Self-induced transparency effects are examined in an absorbing medium having degenerate optical transitions. Undistorted propagating light pulses exist under restrictive conditions for $j\ensuremath{\rightleftharpoons}j$ transitions ($j>0$) and for 0 \ensuremath{\rightleftharpoons} 1 and $\frac{1}{2}\ensuremath{\rightleftharpoons}\frac{3}{2}$. Pulses which propagate without energy loss for any transition ${j\ensuremath{\rightleftharpoons}j}^{\ensuremath{'}}$ also include zero-degree pulses defined as $\ensuremath{\int}\mathcal{E}(z,t)dt=0$.

Physical Review Letters•Oct 14, 1968•118 citations
Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the 2P12\ensuremath−2P32^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}2P21​​\ensuremath−2P23​​, F=3\ensuremath↔F\ensuremath′=4F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4F=3\ensuremath↔F\ensuremath′=4, \ensuremathΔMF=0,\ifmmode±\else\textpm\fi1\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\ensuremathΔMF​=0,\ifmmode±\else\textpm\fi1 and F=2\ensuremath↔F\ensuremath′=2F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2F=2\ensuremath↔F\ensuremath′=2, \ensuremathΔMF=0,\ifmmode±\else\textpm\fi1\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\ensuremathΔMF​=0,\ifmmode±\else\textpm\fi1 transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.
Self-induced transparency has been observed on a Q(2)Q(2)Q(2)-degenerate transition for the first time. Coherent interaction occurs as a short pulse from the $^{2}P_{\frac{1}{2}}F=2\ensuremath{\rightarrow}^{2}P_{\frac{3}{2}}{F}^{\ensuremath{'}}=2$, magnetic dipole transition of the atomic-iodine laser passes through a self-resonant iodine vapor. High transparency and considerable pulse delay at input pulse areas $\ensuremath{\theta}>\ensuremath{\pi}$, and small-pulse splitting at $\ensuremath{\theta}\ensuremath{\simeq}\ensuremath{\pi}$ characterized the phenomena.
Self-induced transparency (SIT) has been observed on a Q(J)-branch transition (J=2) for the first time. Coherent field-matter interaction was studied using a photodissociation atomic iodine laser system operating on the 2P1/2 F=2 →2P3/2 F′=2 magnetic dipole hyperfine transition and a self-resonant iodine vapour. With linearly polarized radiation the propagation phenomena are characterized by high transparency and large time delay at pulse areas θ > π and small-pulse splitting at θ ≃ π. With circularly polarized radiation, non-degenerate SIT is observed. The results can be explained by the dynamic effects of the different dipole moments involved in the process.
The observation of self-induced transparency on the magnetic dipole 2P1/2 F = 3 5 2P3/2 F′ = 4, j MF = 0 transition of atomic iodine has been extended to cover pulse areas up to 4 ~. Laser pulses of various areas have been shown to be reshaped considerably by the coherent field-matter interaction. Pulses have been found to narrow by two-thirds for a 3 ~ -pulse. The lower limit of the homogeneous relaxation time T′2 of atomic iodine vapour is determined from pulse broadening and transmission measurements.
Self-induced transparency has been observed for the degenerate, $F=3\ensuremath{\rightarrow}4$, hyperfine component of the 1.315-\ensuremath{\mu}m magnetic dipole transition of atomic iodine, at high optical power levels, up to 50 MW ${\mathrm{cm}}^{\ensuremath{-}2}$. For pulse areas approaching $2\ensuremath{\pi}$, the dynamics of the strong coherent resonant self-focusing which accompanies self-induced transparency have been studied with a streak camera to provide time-dependent analysis of the spatial beam profile.
Above a critical power threshold for a given pulse width, a short pulse of coherent traveling-wave optical radiation is observed to propagate with anomalously low energy loss while at resonance with a two-quantum-level system of absorbers. The line shape of the resonant system is determined by inhomogeneous broadening, and the pulse width is short compared to dissipative relaxation times. A new mechanism of self-induced transparency, which accounts for the low energy loss, is analyzed in the ideal limit of a plane wave which excites a resonant medium with no damping present. The stable condition of transparency results after the traversal of the pulse through a few classical absorption lengths into the medium. This condition exists when the initial pulse has evolved into a symmetric hyperbolic-secant pulse function of time and distance, and has the area characteristic of a "$2\ensuremath{\pi}$ pulse." Ideal transparency then persists when coherent induced absorption of pulse energy during the first half of the pulse is followed by coherent induced emission of the same amount of energy back into the beam direction during the second half of the pulse. The effects of dissipative relaxation times upon pulse energy, pulse area, and pulse delay time are analyzed to first order in the ratio of short pulse width to long damping time. The analysis shows that the $2\ensuremath{\pi}$ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "$\ensuremath{\pi}$ pulse area" solution is presented in the limit of a sharp leading edge of the pulse. The dynamics of self-induced transparency are studied for the particular effects of Doppler velocities upon a resonant gas. The analysis of transparency for random orientations of dipole moments associated with degenerate rotational states yields modified forms of self-induced transparency behavior, which indicates a finite pulse energy loss as a function of distance in some cases. The effect of self-induced transparency on the photon echo is considered. Experimental observations of self-induced transparency have been made in a ruby sample at resonance with a pulsed ruby-laser beam. Single and multiple $2\ensuremath{\pi}$ pulse outputs have been observed, and pulse areas measured in the range of $2\ensuremath{\pi}$. The experimental results are compared with the predictions of the ideal-plane-wave theory. Deviations from the ideal-plane-wave theory are discussed. An analysis is made of the effect of a transverse mode of the propagating beam upon the transparency properties of the pulse.
Self-induced transparency effects are examined in an absorbing medium having degenerate optical transitions. Undistorted propagating light pulses exist under restrictive conditions for $j\ensuremath{\rightleftharpoons}j$ transitions (j>0j>0j>0) and for 0 \ensuremath{\rightleftharpoons} 1 and $\frac{1}{2}\ensuremath{\rightleftharpoons}\frac{3}{2}$. Pulses which propagate without energy loss for any transition ${j\ensuremath{\rightleftharpoons}j}^{\ensuremath{'}}$ also include zero-degree pulses defined as $\ensuremath{\int}\mathcal{E}(z,t)dt=0$.