Modulated photonic-crystal surface-emitting lasers (M-PCSELs) are new semiconductor lasers that can emit a laser beam in arbitrary directions. Therefore, they can be regarded as a next-generation light source for light detection and ranging. In this manuscript, we numerically investigate the characteristics of M-PCSELs, including one- and two-dimensional optical coupling constants and radiation constants, by using three-dimensional coupled wave theory. We also carry out lattice point designs and show that the two-dimensional optical coupling can be enhanced by more than four times over our previous M-PCSEL devices by employing elliptical lattice points. Moreover, we find that two-dimensional optical coupling can be maintained even when large lattice point position modulations are introduced for large radiation constants. These results indicate that more stable two-dimensional oscillation and a higher slope efficiency are expected in M-PCSELs with elliptical lattice points. [ABSTRACT FROM AUTHOR]