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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Propagation of short pulses of polarized radiation in a resonant medium

Andrei I. Maimistov

Published Sep 26, 1997• 0 citations
Publisher

Abstract

The propagation of electromagnetic radiation pulses in a medium emulated by the two-level atoms is considered. Ground state is not degenerated, excited state is characterized by the angular moment j equals 1. The exact steady state solutions of the Maxwell - Bloch equations without slowly varying envelope and phases approximation were found, that are generalization of a known solutions by Bullough and Ahmad for the scalar case.

DOI
10.1117/12.287671

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 31, 2006•0 citations
The propagation of electromagnetic radiation pulses in a medium emulated by the two-level atoms is considered. Ground state is not degenerated, excited state is characterized by the angular moment j equals 1. The exact steady state solutions of the Maxwell - Bloch equations without slowly varying envelope and phases approximation were found, that are generalization of a known solutions by Bullough and Ahmad for the scalar case.
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 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.
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.