Optics naturally provides us with some powerful mathematical operations. Here, we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorialfield computation and perform edge detection for ultrafast image processing.

Optical computing holds significant promise of information processing with ultrahigh speed and low power consumption. Recent developments in nanophotonic structures have generated renewed interests due to the prospects of performing analog optical computing with compact devices. As one prominent example, spatial differentiation has been demonstrated with nanophotonic structures and directly applied for edge detection in image processing. However, broadband isotropic two-dimensional differentiation, which is required in most imaging processing applications, has not been experimentally demonstrated yet. Here, we establish a connection between two-dimensional optical spatial differentiation and a nontrivial topological charge in the optical transfer function. Based on this connection, we experimentally demonstrate an isotropic two-dimensional differentiation with a broad spectral bandwidth, by using the simplest photonic device, i.e. a single unpatterned interface. Our work indicates that exploiting concepts from topological photonics can lead to new opportunities in optical computing.

As a new degree of freedom for optical manipulation, recently, spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentums have been experimentally demonstrated with pulse shapers. Here, a spatiotemporal differentiator is proposed to generate STOVs with transverse orbital angular momentum. In order to create phase singularity in the spatiotemporal domain, the spatiotemporal differentiator is designed by breaking spatial mirror symmetry. In contrast to pulse shapers, the device proposed here is a simple one-dimensional periodic nanostructure and thus it is much more compact. For a normal incident pulse, the differentiator generates a transmitted STOV pulse with transverse orbital angular momentum. Furthermore, the interference of the generated STOVs can be used to detect the sharp changes of pulse envelopes, in both spatial and temporal dimensions.

No abstract

Phase is a fundamental resource for optical imaging but cannot be directly observed with intensity measurements. The existing methods to quantify a phase distribution rely on complex devices and structures. Here we experimentally demonstrate a phase mining method based on so-called adjustable spatial differentiation, just generally by analyzing the polarization in light reflection on a single planar dielectric interface. With introducing an adjustable bias, we create a virtual light source to render the measured images with a shadow-cast effect. We further successfully recover the phase distribution of a transparent object from the virtual shadowed images. Without any dependence on resonance or material dispersion, this method directly stems from the intrinsic properties of light and can be generally extended to a board frequency range. arXiv:1911.00861v1 [physics.optics]