Applied Digital Optics: From Micro-optics to Nanophotonics

6

Digital Diffractive Optics: Numeric Type

Designing, calculating and optimizing numeric-type diffractive lenses essentially boils down to finding the best phase surface-relief profile (a black box) that will perform a specific wavefront transformation task [1–3], without having too many amplitude variations, as depicted in Figure 6.1.

6.1 Computer-generated Holograms

A Computer-Generated Hologram (CGH) is the typical numeric-type digital element. It is designed with a numeric optimization procedure and fabricated by digital microlithographic fabrication tools.

6.1.1 What is a CGH?

A CGH is basically a complex wavefront processor. In the CGH design task, typically, an incoming wavefront description as well as the desired diffracted wavefront, or part of it, in the near or far field, are specified. The task in hand is then to find, by any means available, the best phase (or amplitude or even complex) mapping that will perform the diffraction job in an acceptable way considering the requirements of the final application.

Therefore, numeric-type elements can implement much more complicated optical functionalities than analytic-type elements are able to perform. Figure 6.2 shows some of the elements comprising the realm of numeric-type diffractives.

However, the fact that numeric-type elements can implement more complex optical functions than analytic types has to be weighed against the fact that analytic-type elements are designed in an absolute way (an analytic description of the ...