Sub-millisecond response time with a refresh rate higher than 2000 frames per second (fps) and no degradation of the contrast ratio or diffraction efficiency is demonstrated in working liquid crystal on silicon (LCOS) spatial light modulators (SLMs) with 8-bit grey levels of amplitude and phase modulations. This makes possible to achieve an information bandwidth of about 190 Gb s-1 with a 4k LCOS operating at 10-bit phase modulation levels. The normalised contrast stays at almost the unit level for a frame rate up to 1700 fps and at higher than 0.9 for 2500 fps. The diffraction efficiency stays above -1.0 dB for a frame rate up to 2400 fps. Such a fast response allows us to eliminate image blurring in replaying a fast movie.