We have studied the interaction of a homologous series of symmetrical thiacyanine dyes (DTCI, DTDCI, DTTCI) with β-cyclodextrin. From absorption spectra we infer that all three dyes form β-CD complexes, either as dye cation monomer or dimer. Higher aggregates, e.g. H-aggregates, are observable in water alone for both DTDCI and DTTCI, as is well-known. The H-aggregate formed from DTTCI in water provides evidence of a unique pathway for thermalization of photoexcitation energy; excited aggregate ejects excited dye monomer. β-CD complexes of all three dyes exhibit technologically useful levels of second-order hyperpolarizability, measured by Hyper-Rayleigh scattering, and we assign the non-linear optical response to dimer complex. Second-order scattering is observed, however, only when the saturation concentration of dye monomer in water is exceeded; at lower concentrations we infer that complexes do not form. Computational modelling, carried out for DTCI, suggests that the dimer forms endergonically with a structure that both locks in a significant degree of bond alternation, as well as allowing considerable freedom for torsional relaxation.