{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T18:46:20Z","timestamp":1760985980416,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T00:00:00Z","timestamp":1611705600000},"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 general model is developed to describe the polarization-resolved second harmonic scattering (SHS) response from a liquid solution of molecular aggregates. In particular, the molecular spatial order is introduced to consider the coherent contribution, also known as the retarded contribution, besides the incoherent contribution. The model is based on the description of a liquid suspension of molecular dyes represented by point-like nonlinear dipoles, locally excited by the fundamental field and radiating at the harmonic frequency. It is shown that for a non-centrosymmetrical spatial arrangement of the nonlinear dipoles, the SHS response is very similar to the purely incoherent response, and is of electric dipole origin. However, for centrosymmetrical or close to centrosymmetrical spatial arrangements of the nonlinear dipoles, the near cancellation of the incoherent contribution due to the inversion symmetry rule allows the observation of the coherent contribution of the SHS response, also known as the electric quadrupole contribution. This model is illustrated with experimental data obtained for aqueous solutions of the dye Crystal Violet (CV) in the presence of sodium dodecyl sulfate (SDS) and mixed water-methanol solutions of the dye 4-(4\u2013dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA), a cationic amphiphilic probe molecule with a strong first hyper-polarizability; both CV and DiA form molecular aggregates in these conditions. The quantitative determination of a retardation parameter opens a window into the spatial arrangements of the dyes in the aggregates, despite the small nanoscale dimensions of the latter.<\/jats:p>","DOI":"10.3390\/sym13020206","type":"journal-article","created":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T12:20:26Z","timestamp":1611750026000},"page":"206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Second Harmonic Scattering of Molecular Aggregates"],"prefix":"10.3390","volume":"13","author":[{"given":"Guillaume","family":"Revillod","sequence":"first","affiliation":[{"name":"Institut Lumi\u00e8re Mati\u00e8re, Universit\u00e9 de Lyon, UMR 5306 CNRS et Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Alfred Kastler, 10 Rue Ada Byron, CEDEX, 69622 Villeurbanne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julien","family":"Duboisset","sequence":"additional","affiliation":[{"name":"Institut Fresnel, Aix Marseille Universit\u00e9, UMR 6133 CNRS, Centrale Marseille et Aix Marseille Universit\u00e9, Avenue Escadrille Normandie-Ni\u00e9men, CEDEX, 13013 Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Isabelle","family":"Russier-Antoine","sequence":"additional","affiliation":[{"name":"Institut Lumi\u00e8re Mati\u00e8re, Universit\u00e9 de Lyon, UMR 5306 CNRS et Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Alfred Kastler, 10 Rue Ada Byron, CEDEX, 69622 Villeurbanne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0590-6998","authenticated-orcid":false,"given":"Emmanuel","family":"Benichou","sequence":"additional","affiliation":[{"name":"Institut Lumi\u00e8re Mati\u00e8re, Universit\u00e9 de Lyon, UMR 5306 CNRS et Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Alfred Kastler, 10 Rue Ada Byron, CEDEX, 69622 Villeurbanne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Jonin","sequence":"additional","affiliation":[{"name":"Institut Lumi\u00e8re Mati\u00e8re, Universit\u00e9 de Lyon, UMR 5306 CNRS et Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Alfred Kastler, 10 Rue Ada Byron, CEDEX, 69622 Villeurbanne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9097-0187","authenticated-orcid":false,"given":"Pierre-Fran\u00e7ois","family":"Brevet","sequence":"additional","affiliation":[{"name":"Institut Lumi\u00e8re Mati\u00e8re, Universit\u00e9 de Lyon, UMR 5306 CNRS et Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Alfred Kastler, 10 Rue Ada Byron, CEDEX, 69622 Villeurbanne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1166\/jnn.2014.8766","article-title":"Nanoarchitectonics of Molecular Aggregates: Science and Technology","volume":"14","author":"Ramanathan","year":"2014","journal-title":"J. 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