# Diffractive Optical Elements A diffractive optical element is a flat and thin optical component that performs a complex operation on an optical input beam. The principle behind its operation is diffraction, as its name implies. This means that the wave nature of light is predominant , and by modifying the phase of the light wave, changes to intensity are achieved.

This modification is done by a diffractive optical element, which consists of an array of discrete features that impart a local phase change to the wavefront of an input beam. The phase change is induced by a change in optical path that in turn is created by a different height of the features in different areas . A pattern consisting of many such features with varying heights can be produced using conventional lithographic techniques.

The relation between a phase pattern like the one described above and its effect on the input beam can be accurately analysed by resorting to the well known mathematical formulae from wave optics and diffraction phenomena. In some instances which in fact are of ample relevance, the relation is reduced to a scaled Fourier Transform operation.

From the manufacturing point of view, there is constraint on the number of phase level changes that can be written onto the diffractive optical element. In fact, the phase values cannot be taken from a continuous range but from a discrete set of values. The most common approach is for the phase level changes to be binary, or in powers of two, as this approach is befitting the current lithographic techniques.

In order to overcome this manufacturing constraint related to phase levels, an optimisation algorithm needs to be implemented. The most common is the Iterative Fourier Transform Algorithm (IFTA).

Having surpassed the manufacturing and design constraints related to diffractive optical elements, there are myriad optical functions that can be encoded into a diffractive element. Among the most common we can cite the following:

• Beam shaping.

• Beam splitting.

• Foci shaping.

Beam shaping refers to an operation in which the irradiance of an input beam is altered in geometrical shape. It also refers to the operation in which a Gaussian input beam profile is turned into a Top Hat profile.

Beam splitting is an operation in which the input beam can be replicated into an array of beams with the same characteristics of the input beam. Such arrays can have any number of beams as well as different arrangements. The last example, foci shaping, is when the focal properties of a lens are modified in order to attain a longer depth of focus. One good example is a diffractive axicon.