Four new low-bandgap electron-accepting polymers-poly(4,10-bis (2-butyloctyl)-2-(2-(2-ethylhexyl)-1,1-dioxido-3-oxo-2,3-dihydrothieno [3,4-d] isothiazol-4-71)-thieno [2',3':5,6]pyrido[3,4-g]thieno[3,2-disoquinoline-5,11-(4H,10H-dione) (PNSW); poly(4,10-bis (2-butyloctyl) -2-(5-(2-ethylhexyl)-4,6-dioxo-5,6-dihydro-4H-thieno [3,4-c]pyrrol-1-yl)thieno [2',3':5,6'pyrido[3,4-g] thieno[3,2-c]isoquinoline-5,11 (4H,10H)-dione) (PNTPD); poly(5-(4,10-bis (2-butylo cty1)-5,11-dioxo -4,5,10,11-tetrahydrothieno [2',3':5,6]pyrido[3,4-g]thieno [3,2-c] isoquinolin-2-yl)-2,9-bis(2-decyldodecyl)anthra[2,1,9-def:6,5,10-d'e'f']- diisoquinoline-1,3,8,10(2H,9H)-tetraone) (PNPDI); and poly(9,9-bis (2-butyloctyl)9H-fluorene-bis ((1,10:5,6)2-(5,6-dihydro-4H-cydopenta[b]thiophene-4-ylidene)malonitrile) -2-(2,3-dihydrothieno[3,4-b] [1,4] dioxine)) (PECN)-containing thieno [2',3':5',6']pyrido [3,4-g] thieno [3,2-c] iso quinoline-5,11 (4H,10H)-dione and fluorenedicyclopentathiophene dimalononitrile, were investigated to probe their structure-function relationships for solar cell applications. PTB7 was also investigated for comparison with the new low-bandgap polymers. The steady-state, ultrafast dynamics and nonlinear optical properties of all the organic polymers were probed. All the polymers showed broad absorption in the visible region, with the absorption of PNPDI and PECN extending into the near-IR region. The polymers had HOMO levels ranging from -5.73 to -5.15 eV and low bandgaps of 1.47-2.45 eV. Fluorescence upconversion studies on the polymers showed long lifetimes of 1.6 and 2.4 ns for PNSW and PNTPD, respectively, while PNPDI and PECN showed very fast decays within 353 and 110 fs. PECN exhibited a very high two-photon absorption cross section. The electronic structure calculations of the repeating units of the polymers indicated the localization of the molecular orbitals in different co-monomers. As the difference between the electron affinities of the co-monomers in the repeating units decreases, the highest occupied and lowest unoccupied molecular orbitals become more distributed. All the measurements suggest that a large difference in the electron affinities of the co-monomers of the polymers,contributes to the improvement of the photophysical properties necessary for highly efficient solar cell performance. PECN exhibited excellent photophysical properties, which makes it to be a good candidate for solar cell device applications.