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Physical Review Letters

Two-Photon Self-Induced Transparency of Different-Frequency Optical Short Pulses in Potassium

Naohiro Tanno, Kenichi Yokoto, Humio Inaba

Published Oct 30, 1972• 60 citations
Publisher

Abstract

Low-loss, coherent two-photon propagation and pulse breakup with peak amplification are observed resulting from two-photon resonant self-induced transparency of different-frequency optical pulses interacting with a three-level system in potassium vapor. Theoretical analysis yielding new area equations for two different-frequency pulses with computer solutions agrees well with the observed results.

DOI
10.1103/physrevlett.29.1211

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

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Physical Review A•Jul 1, 1984•9 citations
Low-loss, coherent two-photon propagation and pulse breakup with peak amplification are observed resulting from two-photon resonant self-induced transparency of different-frequency optical pulses interacting with a three-level system in potassium vapor. Theoretical analysis yielding new area equations for two different-frequency pulses with computer solutions agrees well with the observed results.
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.
We report on computer-generated solutions to the coupled matter-field equations which provide the first evidence for distortionless optical pulse propagation in an absorbing medium of three-level atoms. The associated phenomenon represents the three-level equivalent of self-induced transparency in two-level atoms. Results have application to the propagation of short, coherent optical pulses in a medium in which the atoms have two distinct transition frequencies in near resonance with the pulse carrier frequency. We relate in particular to the case of pulse propagation in a magnetically perturbed sodium vapor where the pulse carrier frequency is tuned near the frequencies of the well-known sodium DDD lines. Here we obtain particular solutions corresponding to three and five peak pulses with "areas" of approximately $6\ensuremath{\pi}$ and $10\ensuremath{\pi}$, respectively. The solutions are strongly supported by a number of analytical results. In particular, simple algebraic relations are found which give the populations of the levels in terms of the field variables.
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.