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Metasurface optics for on-demand polarization transformations along the optical path


Polarization plays a key role in science; hence its versatile manipulation is crucial. Existing polarization optics, however, can only manipulate polarization in a single transverse plane. Here we demonstrate a new class of polarizers and wave plates—based on metasurfaces—that can impart an arbitrarily chosen polarization response along the propagation direction, regardless of the incident polarization. The underlying mechanism relies on transforming an incident waveform into an ensemble of pencil-like beams with different polarization states that beat along the optical axis thereby changing the resulting polarization at will, locally, as light propagates. Remarkably, using form-birefringent metasurfaces in combination with matrix-based holography enables the desired propagation-dependent polarization response to be enacted without a priori knowledge of the incident polarization—a behaviour that would require three polarization-sensitive holograms if implemented otherwise. Our work expands the use of polarization in the design of multifunctional metasurfaces and may find application in tunable structured light, optically switchable devices and versatile light–matter interactions.

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Fig. 1: The concept of longitudinally variable polarization elements.
Fig. 2: Device implementation and characterization.
Fig. 3: Longitudinally variable analyser.
Fig. 4: z-Dependent HWP.
Fig. 5: z-dependent QWP.

Data availability

All key data generated and analysed are included in this paper and its Supplementary Information. Additional datasets that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The codes and simulation files that support the plots and data analysis within this paper are available from the corresponding author on reasonable request.


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We thank W.-T. Chen and X. Yin, both of Harvard University, for their helpful discussions. A.H.D. acknowledges the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant no. PDF-533013-2019. N.A.R. acknowledges support from the National Science Foundation Graduate Research Fellowship Program (GRFP) under grant no. DGE1144152. This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation under NSF award no. 1541959. CNS is part of Harvard University. Additionally, financial support from the Office of Naval Research (ONR) MURI program, under grant no. N00014-20-1-2450, and from the Air Force Office of Scientific Research (AFOSR), grant no. FA95550-19-1-0135, is acknowledged.

Author information




A.H.D. and N.A.R. developed the theoretical framework and fabricated the devices. A.Z. helped formulate the dual matrix holography theory. A.H.D. designed and measured the devices and analysed the data. M.T. contributed to the fabrication and characterization of the devices. A.H.D., N.A.R. and F.C. wrote the manuscript. F.C. supervised the project.

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Correspondence to Federico Capasso.

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The authors declare no competing interests.

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Nature Photonics thanks Philippe St-Jean and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–11 and Notes 1–9.

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Dorrah, A.H., Rubin, N.A., Zaidi, A. et al. Metasurface optics for on-demand polarization transformations along the optical path. Nat. Photonics 15, 287–296 (2021).

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