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

Abstract

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 (β-BaB2O4) endowed with second-order nonlinearity. If the corresponding wave fields are at the same frequency ω and the crystal is tuned for the phase-matched generation of 2ω, 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 2ω, a correspondingly high density of data is encodeable in the wave front at ω 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.