Large, high efficiency, volume Bragg gratings with dimensions of 5 mm× 5 mm and thickness between 1 and 7 mm with 20 μm pitch have been inscribed in poly (methyl) methacrylate (PMMA) with 180 fs, 387 nm parallel beams using both linear and circular polarizations. Linear polarization (perpendicular to the scan direction) produced the highest refractive index contrast, while circular polarization produced the lowest. The measured first-order diffraction efficiency with grating thickness L agrees well with theoretical expectations, and reached a maximum of 94% near L= 4 mm, the highest yet observed in pure PMMA. The source of the variation in refractive index contrast was investigated, and it was found to be due to the polarization-dependent nonlinear filamentation, the first such observation in a pure polymer.