Superdirectivity-based superoscillatory waveform design: A practical path to far-field sub-diffraction imaging

Recent interest in superoscillations has led to theoretical investigations as well as proposed applications in imaging and signal processing. In this paper, we elucidate the relationship between superoscillation and the closely related concept of superdirectivity. Key similarities and differences are highlighted, which showcase windows of possibility for practical superoscil-latory waveform design. Thereafter, through the example of the Optical Super-Microscope - a far-field super-resolution microscope, we demonstrate how established antenna array theory can be leveraged to design a practical superoscillatory filter, which enables far-field sub-diffraction optical imaging. We end by reporting our current progress with the Optical Super-Microscope and suggest future directions to improve its imaging capability.