We propose an all-optical interconnection with cross-polarized double phase conjugate mirrors (CP-DPCMs). In the interconnection, spatially arrayed signal beams from an input port two-dimensionally intersect with control beams from an output port in the photorefractive crystal (PRC) where polarizations of these two beams are orthogonal each other. The CP-DPCM can function as the switching element by adjusting the intensity ratio of these two beams because it strongly depends on the intensity ratio of crossing two beams whether the CP-DPCM is built up in the PRC or not. Thus the signal beam is diffracted by the CP-DPCM and propagated to the output port, when the intensity ratio of signal beam and control beam is adjusted to proper value for buildup of the CP-DPCM. This technique offers the point-to-point interconnection in two-dimensional plane. It implies the possibility of miniaturization and the integration by stacking the planes with different wiring pattern in layers compared to the conventional interconnections with DPCMs. For configuring the arbitrary wiring pattern, it is important to determine the intensities of the signal beams and the control beams, so we investigate the optimum intensities of these beams for effective switching. We carry out basic experiment on 1x2 interconnection with BaTiO3 and Ar+ laser.