{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:13Z","timestamp":1760150893433,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym14020301","type":"journal-article","created":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T20:40:18Z","timestamp":1644180018000},"page":"301","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Propagation and Parametric Amplification in Four-Wave Mixing Processes: Intramolecular Coupling and High-Order Effects"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-7919","authenticated-orcid":false,"given":"Jos\u00e9 Luis","family":"Paz","sequence":"first","affiliation":[{"name":"Departamento Acad\u00e9mico de Qu\u00edmica Inorg\u00e1nica, Facultad de Qu\u00edmica e Ingenier\u00eda Qu\u00edmica, Universidad Nacional Mayor de San Marcos, Lima 15081, Peru"}]},{"given":"Patricio J.","family":"Espinoza-Montero","sequence":"additional","affiliation":[{"name":"Escuela de Ciencias Qu\u00edmicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Quito 170143, Ecuador"}]},{"given":"Marcos","family":"Loro\u00f1o","sequence":"additional","affiliation":[{"name":"Departamento Acad\u00e9mico de Qu\u00edmica Anal\u00edtica e Instrumental, Facultad de Qu\u00edmica e Ingenier\u00eda Qu\u00edmica, Universidad Nacional Mayor de San Marcos, Lima 15081, Peru"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7241-3582","authenticated-orcid":false,"given":"Fernando Javier","family":"Torres","sequence":"additional","affiliation":[{"name":"Grupo de Qu\u00edmica Computacional y Te\u00f3rica (QCT-UR), Facultad de Ciencias Naturales, Universidad del Rosario, Bogot\u00e1 111711, Colombia"},{"name":"Instituto de Simulaci\u00f3n Computacional (ISC-USFQ) and Grupo de Qu\u00edmica Computacional y Te\u00f3rica (QCT-USFQ), Departamento de Ingenier\u00eda Qu\u00edmica, Universidad San Francisco de Quito (USFQ), Quito 170143, Ecuador"}]},{"given":"Lenin","family":"Gonz\u00e1lez-Paz","sequence":"additional","affiliation":[{"name":"Laboratorio de Gen\u00e9tica y Biolog\u00eda Molecular (L.G.B.M), Departamento de Biolog\u00eda Facultad Experimental de Ciencias (F.E.C), Universidad del Zulia (LUZ), Maracaibo 4005, Venezuela"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7503-1528","authenticated-orcid":false,"given":"Edgar","family":"M\u00e1rquez","sequence":"additional","affiliation":[{"name":"Grupo de Investigaciones en Qu\u00edmica y Biolog\u00eda, Departamento de Qu\u00edmica y Biolog\u00eda, Facultad de Ciencias Exactas, Universidad del Norte, Carrera 51B, Km 5, V\u00eda Puerto Colombia, Barranquilla 081007, Colombia"}]},{"given":"Joan","family":"Vera-Villalobos","sequence":"additional","affiliation":[{"name":"Escuela Superior Polit\u00e9cnica del Litoral, Facultad de Ciencias Naturales y Matem\u00e1ticas, Guayaquil 999165, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6128-9504","authenticated-orcid":false,"given":"Jos\u00e9 R.","family":"Mora","sequence":"additional","affiliation":[{"name":"Instituto de Simulaci\u00f3n Computacional (ISC-USFQ) and Grupo de Qu\u00edmica Computacional y Te\u00f3rica (QCT-USFQ), Departamento de Ingenier\u00eda Qu\u00edmica, Universidad San Francisco de Quito (USFQ), Quito 170143, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6650-3549","authenticated-orcid":false,"given":"Fernando","family":"Moncada","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Circuito de la Investigaci\u00f3n Cient\u00edfica, Ciudad Universitaria, M\u00e9xico City 04510, Mexico"}]},{"given":"Ysaias J.","family":"Alvarado","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n y Tecnolog\u00eda de Materiales (CITeMA), Laboratorio de Caracterizaci\u00f3n Molecular y Biomolecular, Instituto Venezolano de Investigaciones Cient\u00edficas (IVIC), Maracaibo 4004, Venezuela"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1080\/09500340903230015","article-title":"Practical formula for the evaluation of high-order multiphoton absorption in thin nonlinear media","volume":"56","author":"Miret","year":"2009","journal-title":"J. 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