A group led by Federico Capasso at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) has broadened the study of optical singularities to include to zero-dimensional (point) and 2D (sheet) optical singularities. The group developed a way to engineer 2D singularity sheets on demand. The advance could have practical value for numerous applications. To date, the study of optical singularities — regions of darkness surrounded by light — has centered on optical vortices. These beams have helical wavefronts and a 1D singularity along the optical axis. “Conventional holography techniques are good at shaping light, but struggle to shape the darkness,” Capasso said. “We have demonstrated on-demand singularity engineering, which opens up a vast set of possibilities in wide-ranging fields, from superresolution microscopy techniques to new atomic and particle traps.” The singularity engineering procedure was also applied to creating more exotic singularities, such as a polarization singularity sheet. Here, the polarization properties (e.g., polarization azimuth, ellipticity angle, and intensity) of the experimental structured light field are compared to the numerical predictions. Courtesy of Daniel Lim/Harvard SEAS. To produce dark sheets, the researchers directed large phase gradients to targeted singular locations. They performed phase gradient maximization in linearly polarized fields to produce phase singularities, and separately in paraxial vectorial electric fields to produce transverse polarization singularities. Because of their precise alignment requirements, these singularities otherwise could only be observed in rare scenarios with high symmetry, the researchers said. In experiments, team members used metasurfaces to create phase and polarization singularity sheets with heart-shaped cross-sections, and to implement the required wavefront profile. Titanium dioxide nanostructures embedded in the metasurfaces were used to precisely shape the wavefront. The researchers sculpted singularities based on the phase gradients at the position of the singularity itself. This enabled them to create dark regions with high contrast and fidelity. The technique enabled them to engineer singularities of many different shapes, beyond simple curved or straight lines, on demand. “The metasurface tilts the wavefront of light in a very precise manner over a surface so that the interference pattern of the transmitted light produces extended regions of darkness,” researcher Daniel Lim said. “This approach allows us to precisely engineer dark regions with remarkably high contrast.” Cross-section of the designed heart-shaped phase singularity sheet. The extended dark region in the center image is a cross-section of the singularity sheet. The phase is undefined on the singularity sheet. Courtesy of Daniel Lim/Harvard SEAS. On-demand singularity engineering could be used to trap atoms in dark regions. Also, it has the potential to improve superresolution imaging: Light can be focused only to the size of the diffraction limit (about half a wavelength), but darkness has no diffraction limit. Unlike light, darkness can be localized to any size. This would allow an optical singularity to interact with particles over length scales that are smaller than wavelengths to provide detailed information on the size, shape, and orientation of the particles. Singularity engineering could make it possible to design complex beams that combine structured light and structured dark, and could inspire exotic field topologies in wave physics. “You can also engineer dead zones in radio waves or silent zones in acoustic waves,” Lim said. “This research points to the possibility of designing complex topologies in wave physics beyond optics, from electron beams to acoustics.” The research was published in Nature Communications (www.doi.org/10.1038/s41467-021-24493-y).