Abstract
We have developed iterative algorithms for the calculation of holograms for non-diffracting or self-imaging light beams. Our methods make use of the special Fourier-space properties of the target beams. We demonstrate experimentally the holographic generation of perhaps the most challenging type of beam: a self-imaging beam shaped in more than one plane. Potential applications include the generation of light "crystals" for optical trapping and atomic diffraction studies.
Highlights
Since their discovery [1], non-diffracting (ND) light beams have enjoyed great interest, for example in the areas of optical micro-manipulation [2, 3, 4] and medical imaging [5].It is easy to understand why ND beams do not change shape on propagation [1]
ND beams consist of plane-wave components that all have the same kz; on propagation, they change phase in exactly the same way, and retain their relative phase, which in turn means that their interference pattern – the beam – does not change
Equation (2) describes a circle in the kx-ky plane. This can be used to create ND light beams as follows (Fig. 1): illuminate a thin ring aperture in the front focal plane of a lens, and behind the lens the light will be approximately non-diffracting. (Note that experimentally created light beams are never perfectly non-diffracting; in the setup discussed here this is due to the fact that the intensity in the Fourier plane is a ring of finite width instead of a circle, and because the aperture of any real Fourier lens is of finite size [6])
Summary
Since their discovery [1], non-diffracting (ND) light beams have enjoyed great interest, for example in the areas of optical micro-manipulation [2, 3, 4] and medical imaging [5]. (Note that experimentally created light beams are never perfectly non-diffracting; in the setup discussed here this is due to the fact that the intensity in the Fourier plane is a ring of finite width instead of a circle, and because the aperture of any real Fourier lens is of finite size [6]) This method has been used in various experiments to create different ND beams [7, 8]. In two examples the algorithm modulated only the phase of source points, in one example it modulated only the intensity, and in another example both These examples demonstrate the creation of arbitrary non-diffracting point patterns, in our case in the shape of the stars in the constellation Orion, and “light crystals”: periodic light distributions in the shape of a series of simple crystallographic unit cells. The detailed intensity is not exactly the desired point pattern, but this can be improved with larger and/or more rings in Fourier space
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