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Quantum Electronics

Coherent propagation of a short polarised radiation pulse in a one-dimensional resonance Bragg grating

Andrei I. Maimistov, V V Polikarpov

Published Sep 30, 2006• 3 citations
Publisher

Abstract

The propagation of an optical ultrashort pulse in a resonance Bragg grating is considered taking into account the polarisation of electromagnetic radiation. It is assumed that the grating is formed by thin films containing two-level atoms with the triply degenerate upper energy level. The system of equations is derived for the envelopes of electromagnetic pulses counterpropagating in such a grating. In the long-wavelength (continual) approximation, the system of equations generalising the known system for scalar waves is obtained. The solutions corresponding to elliptically (in particular, linearly and circularly) polarised stationary pulses are found. An arbitrary degree of ellipticity is possible only in a medium with a preliminary prepared stage of resonance atoms.

DOI
10.1070/qe2006v036n09abeh013227

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The propagation of an optical ultrashort pulse in a resonance Bragg grating is considered taking into account the polarisation of electromagnetic radiation. It is assumed that the grating is formed by thin films containing two-level atoms with the triply degenerate upper energy level. The system of equations is derived for the envelopes of electromagnetic pulses counterpropagating in such a grating. In the long-wavelength (continual) approximation, the system of equations generalising the known system for scalar waves is obtained. The solutions corresponding to elliptically (in particular, linearly and circularly) polarised stationary pulses are found. An arbitrary degree of ellipticity is possible only in a medium with a preliminary prepared stage of resonance atoms.
An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j a = 1 → j b =0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell–Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.
A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.
The propagation of the solitary waves in the resonant birefringent amplifier with linear losses is considered. The birefringent optical linear medium contains two-level atoms with the upper state degenerated over projection of angular moment. It is assumed that population of resonance levels of atoms is inverted. The steady state pulse of polarized radiation that is vectonal generalization of the known π-pulse was analytically found. Numerical simulations demonstrate the formation dynamics solitary waves originated in birefringent amplifier.