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Physical Review Letters

The Influence of Level Degeneracy on the Self-Induced Transparency Effect

C. K. Rhodes, A. Szöke, Ali Javan

Published Oct 14, 1968• 118 citations
Publisher

Abstract

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 $\ensuremath{\int}\mathcal{E}(z,t)dt=0$.

DOI
10.1103/physrevlett.21.1151

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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⇌jj\ensuremath{\rightleftharpoons}jj\ensuremath⇌j transitions (j>0j>0j>0) and for 0 \ensuremath{\rightleftharpoons} 1 and 12\ensuremath⇌32\frac{1}{2}\ensuremath{\rightleftharpoons}\frac{3}{2}21​\ensuremath⇌23​. Pulses which propagate without energy loss for any transition j\ensuremath⇌j\ensuremath′{j\ensuremath{\rightleftharpoons}j}^{\ensuremath{'}}j\ensuremath⇌j\ensuremath′ also include zero-degree pulses defined as \ensuremath∫E(z,t)dt=0\ensuremath{\int}\mathcal{E}(z,t)dt=0\ensuremath∫E(z,t)dt=0.
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.
The propagation of ultrashort coherent light pulses through a resonant atomic medium, modelled by a two-quantum level of absorbers, is studied including the effects of level degeneracy. The governing equations, a sequence of n-tuple sine-Gordon (SG) equations, are solved by quadrature for the Q-transition, with an approximate method indicated for the (mathematically) more difficult P- and R- transitions. It is shown, in particular, that there is a surprisingly close relation between the usual SG equation and the double SG equation. A simple theorem is proved which shows that each travelling wave solution of the former immediately leads to a solution of the latter, which thus admits a restricted Backlund transformation. This direct solution of nonlinear dispersive equations, which apparently cannot be solved by the inverse method, has an interesting by-product: an approximate method for finding travelling wave solutions of relatively arbitrary Klein-Gordon equations.
The influence of degeneracy on coherent pulse propagation in an inhomogeneously broadened attenuator is examined by computer calculations, and the connection with self-induced transparency in a nondegenerate system is described. Specific modifications that arise in a degenerate system are the development of pulse shapes characteristic of the degeneracy, the association of a finite loss with propagation, a reduction of pulse delay times, and the suppression of pulse separation of multi-$2\ensuremath{\pi}$ pulses. Additionally, results of calculations pertaining to experiments on pulse propagation in SF6{\mathrm{F}}_{6}F6​ are presented which indicate two basically different phenomena. One corresponds to delay phenomena qualitatively similar to nondegenerate self-induced transparency, while the other is a coherent saturation effect generally characteristic of degenerate media. The computed results fully substantiate our earlier experimental findings.