Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order nonlinear interactions

Boolean algebra operations such as AND or XOR are performed on optical bits encoded as amplitude modulations in two wave fronts that are made interact in a crystal (beta -BaB2O4) endowed with second-order nonlinearity. If the corresponding wave fields are at the same frequency omega and the crystal is tuned for the phase-matched generation of 2 omega, we show that the generated wave front reconstructs a holographic image containing the outputs of the desired operations. Since a nearly diffraction-limited optical resolution can be easily achieved in the holographic image at 2 omega, a correspondingly high density of data is encodeable in the wave front at omega playing the role of object wave front. The experiments demonstrate the feasibility of the operation of a parallel half-adder performing the sum of multiple data with a one-digit binary number, which is encoded in the reference wave front. (C) 2001 American Institute of Physics.