Multiplexed computer-generated hologram with polygonal apertures.

Abstract

A novel type of multiplexed computer-generated hologram (CGH) is designed with more than one billion of pixels per period. It consists of elementary cells divided into arbitrary-shaped polygonal apertures, the division being identical in all cells. The cells are further digitized into pixel arrays to exploit the huge space-bandwidth product of electron-beam lithography. The polygonal apertures in the same location inside the cells constitute a subhologram. With the Abbe transform that has never, to our knowledge, been used in other CGH designs, the subhologram images (subimages) are obtained with fast Fourier transforms. It is therefore possible to design a multiplexed CGH that has a size thousands of times larger than the manageable size of a conventional CGH designed with the iterative Fourier transform algorithm (IFTA). A much larger object window than that of the conventional CGH can also be achieved with the multiplexed polygonal-aperture CGH, owing to its extremely large dimensions. The multiplexed polygonal-aperture CGH is designed with the novel iterative subhologram design algorithm, which considers the coherent summation of the subimages and applies constraints on the total image, subimages, and subholograms. As a result, the noise appearing in the preceding multiplexed-CGH designs is avoided. The multiplexed polygonal-aperture CGH has a much higher diffraction efficiency than that resulting from either the preceding multiplexed-CGH designs or the conventional CGH designed by the IFTA.