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In this context, knowing the frequency-resolved first order molecular hyperpolarizability (\u03b2) is essential to identifying regions where this response is intense enough to allow for applications in commercial devices. Thus, herein, we have determined the \u03b2 spectral dependence of five new push\u2013pull cinnamylidene acetophenone derivatives using femtosecond laser-induced Hyper-Rayleigh Scattering (HRS). A considerable increase in \u03b2 values was observed in molecules. We found remarkable \u03b2 values in regions near the two-photon resonance, which are mediated by electron withdrawing and donating groups. This effect was mapped using wavelength-tunable femtosecond Z-scan technique. Furthermore, it was modeled in light of the sum-over-states approach for the second- and third-order nonlinearities. Finally, our outcomes suggest a strategy to obtain large \u03b2 values mediated by the 2PA transition.<\/jats:p>","DOI":"10.1063\/5.0151622","type":"journal-article","created":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T10:09:26Z","timestamp":1685614166000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Observation of the two-photon transition enhanced first hyperpolarizability spectra in cinnamaldehyde derivatives: A femtosecond regime study"],"prefix":"10.1063","volume":"158","author":[{"given":"Carlos H. 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