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Quantum Electronics

Propagation of ultrashort pulses of polarised radiation in a resonant medium

Andrei I. Maimistov

Published Nov 30, 1997• 7 citations

Abstract

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.

DOI: 10.1070/qe1997v027n11abeh001092

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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.

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.

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.

Nonstationary polarisation effects in a medium with the Λ-scheme of energy levels with the quantum numbers of the total angular momentum equal to 0, 2, and 1 are numerically simulated. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. It is assumed that the lower-frequency (signal) radiation at the input to a resonance medium is considerably weaker than the higher-frequency (pump) radiation. It is shown that the polarisation of the signal pulse inside the medium is quasi-elliptic in the general case and is independent of the input-pulse polarisation. If the 'area' of the input pump pulse in the absence of signal radiation admits the formation of only one 2π-pulse, then the major axes of polarisation ellipses for the signal inside the medium and input pump radiation are collinear, however, the directions of rotation of the electric field strengths of these radiations are mutually opposite. For higher-power pump pulses, the polarisation structure of the signal pulse in the medium becomes considerably more complicated.

The effects are observed of propagation of an ultimately short (in one or several oscillation) electromagnetic pulse in a medium whose resonance transition characterized both by diagonal and non-diagonal matrix elements of dipole operator. The Maxwell-Bloch set of equation is employed without the approximation of slowly varying amplitudes. The analog of MacCall and Hahn area theorem is discussed corresponding to the process of the initial ultimately short pulse break up into subpulses. A novel solution is found in the form of a stable solitary bipolar signal, whose pulse area is not zero- non-zero breather.