A new low-bandgap pi-conjugated D-A copolymer of squaraine and pyridopyrazine (P1) and a new small molecule squaraine-pyridopyrazine model compound (P2) were synthesized and compared. PI and P2 exhibit strong NIR absorption and low bandgap (1-1.3 eV). P2 in solution shows an intense and sharp absorption peak at 764 nm, while P1 in solution exhibits a red-shifted and broad absorption peak at 808 nm. The HOMO and LUMO levels of P1 were estimated to be -5.02 and -4.15 eV, while the HOMO and LUMO levels of P2 were estimated to be -5.27 and -3.22 eV, respectively. Polymer PI exhibits strong two-photon absorption (2PA) at telecommunication wavelengths with 2PA cross sections per repeat unit as high as 2300 GM, 3-5 times that for the small molecule P2. The higher HOMO, the lower LUMO levels, lower bandgap, red-shifted absorption, and stronger two-photon absorption of PI are attributed to higher degree of conjugation and delocalization of pi-electrons in the polymer.