Optical Computation of a Second-Order Mixed Derivative Using a Layered Structure

It is theoretically shown that a layered structure possessing a reflection zero allows the optical computation of the second-order mixed derivative of the profile of a linearly polarized incident beam with respect to spatial coordinates. The derivative is computed at normal incidence in the cross-polarized component of the reflected beam. The presented design and numerical simulations results of a layered structure demonstrate that high-quality computation of the second-order mixed derivative is possible, and such a structure can be used for optical detection of corners and edges in an image.