Source mask optimization (SMO) is one of the required techniques for lithography below 32 nm. Source representation is one important factor that affects both the imaging simulation and optimization processes of SMO, especially the global SMOs such as the SMO using genetic algorithm (GA-SMO). We propose a source representation which accelerates the GA-SMO. The proposed representation uses a group of circular poles to describe the freeform illumination source whose pupil filling ratio (PFR) is small. Compared with conventional Cartesian-grid and polar-grid pixelated representations, the proposed multipole source representation can represent the low-PFR freeform illumination source with fewer variables, which speeds up both the GA convergence and lithography imaging simulation. Numerical experiments show that the GA-SMO using the proposed multipole source representation method is about seven times faster than that using polar-grid pixelated source representation on the premise that other simulation conditions are the same and optimization qualities are comparable.