Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: Finite-difference time-domain study

  • Slavcheva G
  • Arnold J
  • Wallace I
 et al. 
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We extend to more than one spatial dimension the semiclassical full-wave
vector Maxwell-Bloch equations for the purpose of achieving an adequate
and rigorous description of ultrashort, pulse propagation in optical
waveguides containing resonant nonlinearities. Our considerations
are based on the generalized pseudospin formalism introduced. by
Hioe and Eberly [Phys. Rev. Lett. 47, 83& (198 1)] for treatment
of the resonant coherent interactions of ultrashort light pulses
with discrete-multilevel systems. A self-consistent set of coupled
curl Maxwell-pseudospin equations in two spatial dimensions and time
for the special case of a degenerate three-level system of quantum
absorbers is originally derived. Maxwell's curl equations are considered
to be coupled via macroscopic medium polarization to the three-level
atom model for the resonant medium. Two distinct sets of pseudospin
equations are obtained corresponding to the TE- and TM-polarized
optical waves. For the case of TM polarization, the electromagnetic
wave is polarized in a general direction in the plane of incidence
inducing two dipole transitions in a degenerate three-level system
by each E-field component along the propagation axis and in transverse
direction. We introduce a dipole-coupling interaction Hamiltonian
allowing Rabi flopping of the population difference along and perpendicular
to the propagation axis with frequencies depending on the corresponding
field components. The relationship between the induced polarization
and the state vector components that describe the evolution of the
discrete-level system is derived in order to couple the quantum system
equations to the Maxwell's curl equations. The pseudospin equations
are phenomenologically extended to include relaxation effects by
introducing nonuniform decay times corresponding to the various dipole
transitions occurring in a three-level system. The system has been
discretized using finite differences on a Yee grid and solved numerically
by an iterative predictor-corrector finite-difference time-domain
method. Self-induced transparency soliton propagation through a degenerate
three-level quantum system of absorbers in two spatial dimensions
and time is demonstrated in planar parallel-mirror waveguide geometries.

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