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arXiv:0712.0794 · Optics Express

A high-accuracy algorithm for designing arbitrary holographic atom traps

Matthew Pasienski, Brian DeMarco

Published Jan 1, 2008• 219 citations
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Abstract

We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with a fractional error from the target distribution at the percent level. We demonstrate that this new algorithm outperforms the most frequently used alternatives typically by one and two orders of magnitude in accuracy and roughness, respectively. The techniques described in this paper outline a path to creating arbitrary holographic atom traps in which the only remaining hurdle is physical implementation.

DOI
10.1364/oe.16.002176

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We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with a fractional error from the target distribution at the percent level. We demonstrate that this new algorithm outperforms the most frequently used alternatives typically by one and two orders of magnitude in accuracy and roughness, respectively. The techniques described in this paper outline a path to creating arbitrary holographic atom traps in which the only remaining hurdle is physical implementation.
We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with a fractional error from the target distribution at the percent level. We demonstrate that this new algorithm outperforms the most frequently used alternatives typically by one and two orders of magnitude in accuracy and roughness, respectively. The techniques described in this paper outline a path to creating arbitrary holographic atom traps in which the only remaining hurdle is physical implementation.
Abstract We show that a phase-only spatial light modulator can be used to generate non-trivial light distributions suitable for trapping ultracold atoms, when the hologram calculation is included within a simple and robust feedback loop that corrects for imperfect device response and optical aberrations. This correction reduces the discrepancy between target and experimental light distribution to the level of a few percent (root mean square error). We prove the generality of this algorithm by applying it to a variety of target light distributions of relevance for cold atomic physics.
We have formulated and experimentally demonstrated an improved algorithm for design of arbitrary two-dimensional holographic traps for ultracold atoms. Our method builds on the best previously available algorithm, MRAF, and improves on it in two ways. First, it allows for creation of holographic atom traps with a well defined background potential. Second, we experimentally show that for creating trapping potentials free of fringing artifacts it is important to go beyond the Fourier approximation in modelling light propagation. To this end, we incorporate full Helmholtz propagation into our calculations.
Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.
The development of new laser beam shaping methods is important in a variety of fields within optics, atomic physics and biophotonics. Spatial light modulators offer a highly versatile method of time-dependent beam shaping, based on imprinting a phase profile onto an incident laser beam that determines the intensity in the trapping plane laser field. The calculation of the required phase is a well-known inverse problem, which can be tackled with different approaches. Our method based on conjugate gradient minimisation [1] not only allows the calculation of smooth and accurate intensity profiles suitable for trapping cold atoms, but can also be used to generate multi-wavelength traps [2] and for simultaneous control over both the intensity and the phase of the light [3], with exceptionally high reconstruction fidelity. References: [1] T Harte, et al., "Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms" Opt. Express 22, 26548 (2014) [2] D Bowman, et al., "Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments" Opt. Express 23, 8365 (2015) [3] D Bowman, et al., "High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation" Opt. Express 25, 11692 (2017)
We are exploring the possibilities offered by Spatial Light Modulators to create dipole potentials with arbitrary shape in order to apply to cold atoms. As a first experiment we have realized a guide for atoms by shaping the laser beam into a Laguerre-Gaussian mode, creating a sort of tube, empty of light, where the atoms rest confined during their flight in the gravity field. We are, now, creating new potentials by modifying the Laguerre-Gaussian hologram in order to create new original traps for atoms.