Phase conjugate four-wave mixing in waveguide arrays

Abstract

An array of nonlinear, single-mode waveguides can produce a sampled, phase conjugate image signal through four-wave mixing. To produce a backpropagating phase conjugate, the pump beams must be counterpropagating and have uniform amplitude across the array. For a high fidelity conjugate image to be produced the waveguide spacing must be small relative to the spatial variations of the incoming beam. A novel feature of phase conjugation using an array occurs because pump beams will be confined to counterpropagate in each waveguide, even if they are not counterpropagating in free space, as long as they fall within the acceptance angle of the waveguide. Pump beam alignment is not critical for phase-matched four-wave mixing. However, the propagation direction of the phase conjugate beam generated by the array is controlled by pump beam alignment. Alternatively, if the pump beams are internally generated by, for example, a laser diode array, control of the phase between laser diodes produces the same ability to manipulate the propagation direction of the generated beam. Use of multimode waveguides in the array reduces image fidelity and limits the spatial and frequency bandwidth of the generated conjugate because of nonuniform coupling between modes.