An all-optical nonlinear joint-transform correlator that is based on a square-law receiver has been implemented for the first time to our knowledge without the use of a spatial light modulator and digital processing in the Fourier plane. The correlator uses energy transfer from two-beam coupling in the Fourier plane. We implement compressional nonlinearity in the hard-clipped regime by pumping a weak plane wave with the intense joint spectrum of the reference and the signal images. Operation of this device rivals or exceeds that of the phase-only filter for detecting objects in cluttered noise. Experimental results are compared with both plane-wave and beam-propagation simulations.