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Quantum Electronics and Laser Science Conference

Exact theory of energy exchange and conversion via four-wave mixing processes in a nondissipative media

B. Glushko, Boris Kryzhanovsky

Published May 10, 1992• 0 citations
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Without making the nondepleted pump approximation, we solve the problem of four-wave mixing (FWM) in a nondissipative ${\mathrm{\ensuremath{\chi}}}^{(3)}$ medium. Instead of describing the dynamics of FWM in terms of coupled wave amplitudes, we base our solution on canonical equations that describe the propagation of the field's intensities. This structure clearly identifies the conservative exchange of energy in the FWM process. Consequently, analysis of the FWM process is reduced to a single propagation equation that describes the energy exchange between the pump and amplified waves. This equation yields an elliptic integral solution. The conversion efficiency reduces to the simple analysis of a fourth-order polynomial, which we analyze to determine the conditions for optimization. The destructive influence of the optical Kerr effect on the phase-matching condition is shown to be eliminated by proper choice of nonzero initial wave-vector mismatch, dependent on the input intensity. Furthermore, we show that the conversion efficiency for pulses is limited by the splitting of the pulses into a set of subpulses.
Without making the nondepleted-pump approximation, we solve the problem of four-wave mixing (FWM) in a nondissipative ${\mathrm{\ensuremath{\chi}}}^{(3)}$ medium. Instead of describing the dynamics of FWM in terms of coupled wave amplitudes, we base our solution on canonical equations that describe the propagation of the field's intensities. This structure clearly identifies the conservative exchange of energy in the FWM process. Consequently, analysis of the FWM process is reduced to a single propagation equation that describes the energy exchange between the pump and amplified waves. This equation yields an elliptic-integral solution. The conversion efficiency reduces to the simple analysis of a fourth-order polynomial, which we analyze to determine the conditions for optimization. The destructive influence of the optical Kerr effect on the phase-matching condition is shown to be eliminated by proper choice of nonzero initial wave-vector mismatch, dependent on the input intensity. The effect of the nonuniform transverse pump-beam intensity profile on the process of conversion is considered. The direction of the energy exchange is shown to be a periodic function of the propagation distance. The transverse intensity distribution of the generating waves provides the characteristic spatial structure (the set of coaxial rings with or without the central spot; the number of rings is explicitly determined by the length of interaction). Several methods of process optimization are discussed, and nonuniformity in the pump-beam profile is shown to be the main reason that complete energy transfer is not achieved.