Phone: +33 1 69 15 32 75; Fax: +33 1 69 15 33 28 RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to) TITLE RUNNING HEAD Non uniqueness of parameters in NLO spectroscopiesAbstract Experimental data from second-order nonlinear optical spectroscopies (SFG, DFG, SHG) provide parameters relevant to the physical chemistry of interfaces and thin films. We show that there are in general 2 N or 2 N-1 equivalent sets of parameters to fit an experimental curve comprising N resonant features, of vibrational or electronic origin for example. We provide the algorithm to calculate these sets, among which the most appropriate has to be selected. The main consequences deal with the existence of "ghost resonances", the need of a critical analysis of fit results and the procedure to search for better sets of parameters coherent with applied constraints.

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