We explored a series of squaraine homodimers with varying π-bridging centres to probe the relationship between the chemical structure and the two-photon absorption (2PA) characteristics. To this end, we designed and synthesised six linear homodimers based on two indolenine squaraine dyes with transoid configuration (SQA) which are connected by diverse bridges. In this regard, we investigated the effect of exciton coupling in these dimeric systems where the variation of the bridging units affects the magnitude of exciton coupling and leads to an alteration of their linear optical properties. Using two-photon absorption induced fluorescence measurements we determined the two-photon absorption cross section in this series of homodimers and found sizable values up to 5700 GM at ca. 11 000 cm-1 and 12 000 GM at 12 500 cm-1. The 2PA strength roughly follows the exciton coupling interaction between the squaraine chromophores which therefore may be used as design criteria to achieve high 2PA cross sections. The results were substantiated by polarization dependent linear and nonlinear optical measurements and by density functional theory calculations based on time dependent and quadratic response theory.