A programmable Fresnel transform pulse shaper.

We demonstrate the first reprogrammable Fresnel transform pulse shaper based on a modified direct space-to-time pulse shaping apparatus. In our approach, the pulse shaping lens and mask are implemented by a dual-layer liquid crystal spatial light modulator. The input mask subsequently undergoes a free-space Fresnel transform which causes quadratic dispersion of the output temporal waveform. When used as a spectrometer, we demonstrate that the passband function of the apparatus (determined by the Fourier transform of the input spatial mask) may be chosen to exhibit a user-defined scale. Here we present the theory of operation, as well as experimental verification in both the time- and frequency-domains.