Two-Photon Beer’s Law for Coherently Prepared Three-Level Media

  • A. Rahman
  • R. Grobe
  • J. H. Eberly


The propagation of pairs of laser pulses interacting with resonant media has been recently recognized1,2 to be of interest in connection with lasing without inversions3 and electromagnetically induced transparency4. Here we have studied two different-frequency weak laser pulses propagating in one- and two-photon resonance with a coherently prepared medium with damping. In contrast to a two level system where a single weak pulse decays after a characteristic distance, we have shown that a coherently prepared three level medium forces the two weak fields to cooperate and evolve into a coherent superposition that propagates without loss. This can be regarded as a direct generalization of Beer’s law to the situation of two coupled pulses when the medium is strongly damped. Our analytical theory is confirmed by comparison with computer simulations.


Laser Pulse Analytical Theory Pulse Shape Level Medium Weak Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J.H. Eberly, M.L. Pons, and H.R. Hag, Phys. Rev. Lett. 72, 56 (1994);Google Scholar
  2. R. Grobe, F.T. Hioe, and J.H. Eberly, ibid. 73, 3183 (1994);Google Scholar
  3. F.T. Hioe and R. Grobe, ibid. 73, 2559 (1994).Google Scholar
  4. 2.
    J.H. Eberly, Quant. and Semicl. Optics, (in press, 1995).Google Scholar
  5. 3.
    M.O. Scully, Quant. Opt. 6, 203 (1994).CrossRefGoogle Scholar
  6. 4.
    S.E. Harris, Phys. Rev. Lett. 72, 52 (1994).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • A. Rahman
    • 1
  • R. Grobe
    • 1
    • 2
  • J. H. Eberly
    • 1
  1. 1.Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  2. 2.Department of PhysicsIllinois State UniversityNormalUSA

Personalised recommendations