Polarization-multiplexed isotropic and reconfigurable nonlinear differential imaging via dual-channel parametric upconversion

We investigate a polarization-multiplexed nonlinear differentiator that combines spatial-frequency processing with mid-infrared (MIR)-to-visible (VIS) parametric upconversion. Two orthogonally pumped quasi-phase-matching channels synthesize odd transfer functions proportional to the transverse wave-vector components qx and qy. Coherent control of their relative amplitudes and phase switches the effective operator among horizontal, vertical, diagonal, isotropic, and elliptically weighted first derivatives. For an input wavelength of 3.07 μm and a pump wavelength of 1.03 μm, the processed image is generated near 771 nm for detection with a VIS camera. Quadrature recombination yields a nearly rotationally invariant intensity response and recovers the principal contours of a two-dimensional test object. The optimized isotropy score exceeds 0.98 in the calculated design landscape. The orthogonally polarized outputs also encode the local gradient in spatial Stokes parameter and phase textures. Numerical perturbation tests give an edge-image correlation above 0.95 for detector signal-to-noise ratios of approximately 10 dB. The proposed architecture provides a reconfigurable route to nonlinear edge processing while translating MIR spatial information to the VIS band.