  We demonstrate first- and second-order spatial differentiation of an optical
beam transverse profile using thin suspended subwavelength gratings. Highly
reflective one-dimensional gratings are patterned on suspended 200 nm-thick
silicon nitride membranes using Electron Beam Lithography and plasma etching.
The optical transmission of these gratings, designed for illumination with
either TM or TE polarized light, are experimentally measured under normal and
oblique incidence and found to be in excellent agreement with the predictions
of an analytical coupled-mode model as well as Rigorous Coupled Wave Analysis
numerical simulations. High quality first- and second-order spatial
differentiation of a Gaussian beam are observed in transmission at oblique and
normal incidence, respectively. Such easy-to-fabricate, ultrathin and loss-free
optical components may be attractive for beam shaping and optical information
processing and computing.
