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Bulletin of the Lebedev Physics Institute

Soliton Regime of Second Harmonic Generation in the Presence of Quasi-Resonant Impurities

Sazonov S.V.

Published Sep 1, 2025• 4 citations
Publisher

Abstract

Abstract We report a study of a soliton-like regime of second harmonic generation in a crystal containing impurity atoms with a quantum transition, which is quasi-resonant with respect to a laser pulse at the fundamental frequency. Mismatches of phase and group velocities are taken into account. It is shown that quasi-resonant impurities, on the one hand, lead to a decrease in the generation efficiency, and, on the other hand, they are capable of creating conditions for the implementation of a two-frequency soliton regime, which is impossible in their absence.

DOI
10.3103/s1068335625602985

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Abstract We report a study of a soliton-like regime of second harmonic generation in a crystal containing impurity atoms with a quantum transition, which is quasi-resonant with respect to a laser pulse at the fundamental frequency. Mismatches of phase and group velocities are taken into account. It is shown that quasi-resonant impurities, on the one hand, lead to a decrease in the generation efficiency, and, on the other hand, they are capable of creating conditions for the implementation of a two-frequency soliton regime, which is impossible in their absence.
The generation of zero and high-order harmonics in the spectrum of a laser pulse propagating through a medium containing quantum particles whose constant resonance transition dipole moment is nonzero is studied theoretically. The consideration is performed in the approximation of slowly varying envelopes modified for the case of the medium with the nonzero permanent dipole moment. It is shown that this modification requires consideration of antiresonance terms, in particular, the Bloch-Siegert shift in equations. The conditions are revealed for the efficient optical rectification and excitation of the second harmonic at a quasi-monochromatic signal applied to the medium.
An analysis is made of the propagation of ultrashort pulses in a fibre waveguide doped with resonant impurities. Equations describing the evolution of a pulse in the case of one-photon and two-photon resonances are derived on condition that the Rabi frequency is considerably less than the detuning from an exact resonance. The influence of impurity atoms on the parameters of a pulse and on the characteristics of its evolution (ultrashort pulse duration, 'soliton threshold', and ultrashort pulse collapse threshold) is determined. The corrections to these quantities have different signs for different types of resonance.
The propagation of extremely short (without high-frequency filling) pulses and nonresonant envelope solitons in a two-component medium comprising two-level atoms with substantially different quantum transition frequencies was studied. The dynamics of a pulse whose reciprocal time scale lay between these frequencies was shown to be described by the Kosevich-Kovalev equation, the one-way variant of which was the Konno-Kameyama-Sanuki equation. If the transition dipole moments of medium components were equal, the one-way equation became integrable. Soliton and soliton-like solutions to these equations were used to analyze pulse propagation regimes at various two-component medium initial states. The stability of these localized wave formations was analyzed. The possible existence of stable soliton-like pulses propagating in a nonequilibrium medium at group velocities exceeding the velocity of light in vacuum was discussed.