Propagation and Parametric Amplification in Four-Wave Mixing Processes: Intramolecular Coupling and High-Order Effects

José Luis Paz, Patricio J. Espinoza-Montero, Marcos Loroño, Fernando Javier Torres, Lenin González-Paz, Edgar Márquez, Joan Vera-Villalobos, José R. Mora, Fernando Moncada, Ysaias J. Alvarado

Research output: Contribution to journalArticlepeer-review


A strong pump-power dependence of the four-wave mixing (FWM) signal for an aqueous solution of Malachite green is reported. The characteristics of the pump-power dependence of the nonlinear signal are reproduced by a theoretical model based on the coupling between pump-probe, considering signal fields and propagation effects. The effect of the intramolecular coupling on the nonlinear intensity of the FWM signal is studied using a model molecule consisting of two-coupled harmonic curves of electronic energies with minima displaced in energy and nuclear positions. Two-vibrational states are considered while including non-adiabatic effects for the two-state model. Moreover, the coupling among the field components, as well as the propagation effects, are studied by considering a constant pump-intensity. Our calculation scheme, considering both the intramolecular coupling effects in the description of the molecular structure and the effects produced by the propagation of the FWM signal along the optical length, allows the exponential dependence of the latter, as the intensity of the pumping beam increases. Our treatments do not require the inclusion of other non-resonant processes outside the RWA approximation, due to the consideration of an adiabatic basis.

Original languageEnglish
Article number301
Issue number2
StatePublished - Feb 2022

Bibliographical note

Funding Information:
The authors (JLP, ML) are grateful to the UNMSM collaboration, grants C21071281. For financial support of this research, F.J.T. thanks Alianza EFI-Colombia Científica grant, codes 60185 and FP44842-220-2018. The authors have used the high-performance computing system available in UNMSM and UNINORTE for the development of this project. The authors are grateful to the UNINORTE for collaboration in the HPC system and the invoice payment.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.


  • Intramolecular coupling
  • Parametric amplification
  • Propagation effects


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