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Optics Communications

Systems of non-linear, partial differential equations for coherent optical pulse propagation in an inhomogeneously broadened medium and associated conservation laws

Hanno Rund

Published Oct 1, 1974• 5 citations
Publisher
DOI
10.1016/0030-4018(74)90372-1

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The description of coherent optical pulse propagation in terms of coupled Maxwell and Schroedinger- Bloch equations in slowly varying envelope approximation possesses conservation laws in addition to those of field energy and field momentum. Comparison with preliminary numerical results has shown that these higher conservation laws can be used to predict the amplitude of each of the 2pi pulses into which an intense coherent pulse may decompose as it propagates through an attenuator. In the present paper a comparison with more extensive numerical results is carried out. It is shown that over a wide range of variation of the parameters involved the conservation laws yield results in agreement with those obtained through numerical computation.
Higher conservation laws associated with the phase-dependent Maxwell-Bloch equations are derived and employed to determine both amplitudes and frequency shifts of the final-state solitons produced in a resonant medium by an initially phase-modulated optical pulse of area $<5\ensuremath{\pi}$. The higher conservation laws are shown to provide a relatively efficient method of relating the parameters of the final pulses to those of the incident pulse. Connection is made to the computer work of Diels and Hahn.