Diffractive lens design for optimized focusing.

We utilized nonlinear optimization to design phase-only diffractive lenses that focus light to a spot, whose width is smaller than that dictated by the far-field diffraction limit. Although scalar-diffraction theory was utilized for the design, careful comparisons against rigorous finite-difference time-domain simulations confirm the superfocusing effect. We were able to design a lens with a focal spot size that is 25% smaller than that formed by a conventional lens of the same numerical aperture. An optimization strategy that allows one to design such lenses is clearly explained. Furthermore, we performed careful simulations to elucidate the effects of fabrication errors and defocus on the performance of such optimized lenses. Since these lenses are thin, binary, and planar, large uniform arrays could be readily fabricated enabling important applications in microscopy and lithography.