Abstract

Synthesis of arbitrarily shaped femtosecond optical waveforms has recently been achieved by masking the optical frequency components that are spatially dispersed within a simple grating and lens apparatus.¹ The spatial mask acts as a linear filter that manipulates the phases and amplitudes of the spatially dispersed spectral components; the shaped pulse corresponds to the Fourier transform of the pattern transferred by the mask onto the spectrum. In this paper we demonstrate additional signal processing operations, such as time-reversal, correlation, and convolution, which cannot be achieved using simple linear filtering. Our demonstration relies on spectral holography within a femtosecond pulse shaping apparatus. Two input beams are incident on the holographic pulse shaper—a shaped signal beam, generated using a CPM dye laser and a second, programmable pulse shaper,² and an unshaped 100-fsec reference beam. The interference pattern between these two beams, which are spectrally dispersed within the pulse shaping apparatus, is recorded on a thermoplastic plate. The resulting spectral hologram can be read out using an unshaped reference pulse to yield both real and time-reversed (virtual) replicas of the original signal pulse. Convolution and correlation operations are performed by using shaped pulses for readout.

© 1991 Optical Society of America