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# Diffractive Optical Elements

Diffractive Optical Elements (DOE) , also known as computer generated holograms (CGH), are optical components that exploit the wave nature of light to shape it. In geometrical optics, light beams are represented by rays that travel along a defined direction and only bend (refract) when going through a media change, like air-glass for example.  In contrast, in the wave description of light a beam is described by a propagating electromagnetic wave with a phase profile and intensity that can be distorted by obstacles in its path. That distortion leads to modifications of the phase profile of this wave, also referred to as wavefront, that then gives rise to physical optics phenomena like interference and diffraction.

The most basic optical element in which this behaviour can be seen is a diffraction grating. In fact, this element can be regarded as the simplest of DOEs. A grating is a microstructure composed of obstacles or apertures that are equally spaced. According to ray optics, when a beam of light traverses such a structure it should simply cast a periodic shadow arising from each obstacle. This is not what really happens since what comes into play is the wave nature of light. The beam’s wavefront is modulated by this periodic structure and at some distance away from the element some beam replicas, which are clearly discerned from each other, are formed. These beam replicas are referred to as diffraction orders. The mathematical relation between the light intensity in the far field and the DOE plane is given by the solution of the diffraction integral. For many cases of interest this relation can be reduced to a scaled Fourier Transform in spatial coordinates. Thus, in the case of a diffraction grating the angular direction of the orders (beam replicas) is directly proportional to the periodicityof the grating.

## Applications of DOEs

The fact that the relation between the far field intensity and the pattern on the DOE is well known, when coupled with modern lithographic techniques, leads to a myriad of applications for DOEs. They can be designed and manufactured to perform almost any desired transformation on coherent beams.

One application of DOE is beam shaping in which the intensity distribution of a light field can be  modifiedto become some optimised target profile, for example a flat-top profile. Another application is a multispotbeam splitting DOE, also referred to as a fan-out DOE or CGH, in which the beam can be replicated into a 1 dimensional or 2 dimensional array of beams that in turn can be arranged in any desired geometrical configuration. These types of DOEs are used inparallel material processing applications, fractional aesthetic treatments, metrology and free space optical interconnects, for example. DOEs can also be designed to create some less conventional light fields like vortex beams or Bessel beams.  These types of beams are finding new niche applications at the forefront of modern optical technologies such as focal beam shaping used to stretch the beam waist to create a longer focus area, useful for laser glass cutting.

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