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Phase-space measurement and coherence synthesis of optical beams

Abstract

Phase-space optics allows the simultaneous visualization of both space (x) and spatial frequency (k) information. Previous experiments have focused mainly on coherent beams, which are fully described by a two-dimensional complex field (amplitude and phase). In contrast, partially coherent beams inherently have more degrees of freedom and require a four-dimensional description. This description is particularly important for propagation, in which coherence properties determine the intensity evolution. Despite this, most measurements in linear optics, and all those in nonlinear optics, have recorded only the intensity and power spectrum projections (x-space or k-space only). Measuring local coherence remains a challenging problem, especially in the full four-dimensional phase space. In turn, the recording difficulty has limited efforts to generate arbitrary, spatially varying patterns of coherence, despite their usefulness for imaging, illumination and display. We remedy both problems here, using spatial light modulators to create beams with locally varying spatial coherence and to measure their phase-space properties.

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Figure 1: Set-up for phase-space synthesis and measurement of nonlinear propagation.
Figure 2: Linear propagation results in a shear of phase space for both coherent and partially coherent light.
Figure 3: Nonlinear propagation depends on the entire phase space.
Figure 4: Experimental phase-space measurement of modulation instability.
Figure 5: Experimental measurement of a coherence wave localized in phase space.
Figure 6: Experimental measurements of four-dimensional coherence synthesis.

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Acknowledgements

The authors thank L. Tian and S. Muenzel for valuable discussions. This work was supported by the Department of Energy and the Air Force Office of Scientific Research.

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L.W. and J.W.F. conceived and designed the experiments. L.W. performed the experiments and simulations. G.S. helped with the set-up of the experiments. All authors analysed the data and contributed to the preparation of the manuscript.

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Correspondence to Jason W. Fleischer.

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The authors declare no competing financial interests.

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Waller, L., Situ, G. & Fleischer, J. Phase-space measurement and coherence synthesis of optical beams. Nature Photon 6, 474–479 (2012). https://doi.org/10.1038/nphoton.2012.144

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