Research ArticleOPTICS

Metaform optics: Bridging nanophotonics and freeform optics

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Science Advances  30 Apr 2021:
Vol. 7, no. 18, eabe5112
DOI: 10.1126/sciadv.abe5112
  • Fig. 1 Conceptual diagram of the formation and function of a metaform.

    (A) The two metaform phase contributions are given by ϕfreeform (the phase imparted by the freeform substrate) and ϕmeta (the phase from the light interaction with the metasurface). (B) An example of a metaform where the metasurface is not properly rotated with respect to the freeform substrate, the tokens are not positioned properly along the freeform substrate, and some of the tokens are missing. These inconsistencies result in an additional undesired phase contribution ϕaberr and associated optical aberrations and blur artifacts in the final image. (C) Successful implementation of a metaform where the final phase ϕmetaform imparted to the incoming beam is given precisely by the sum of the as-designed phase contributions from the freeform substrate and the metasurface.

  • Fig. 2 Miniature imager design using a metaform mirror.

    (A) The object is positioned 85 mm away from the aperture stop. The image is relayed to a CMOS camera using a 51-mm working distance microscope objective (not shown). (B) The metasurface is conformed onto the freeform substrate. The metasurface has a predominantly linear phase and some coma contribution for aberration correction. The freeform substrate is an X-toroid as defined in CODE V software and given as Eq. 4.

  • Fig. 3 Design and experimental realization of the metaform mirror for the imager.

    (A) Technical drawing of the part. The dark rectangle in the center corresponds to the area where the metasurface grating is written. The scaled-up inset shows a set of tokens from the metasurface design. (B) Example drawing of a metaform with missing tokens and stitching/focusing errors between the different writing zones. An SEM image of a fabricated metaform with these issues is shown at the bottom inset. (C) Image of a successful metaform and a scaled-up view of an SEM image of a set of the fabricated nano-tokens. Photo credit: Daniel K. Nikolov, University of Rochester. The three nano-token insets are not necessarily from the same region on the sample, but they are good representatives given the predominantly linear phase nature of the metasurface. The scale on all three insets is 2 μm.

  • Fig. 4 Experimental imaging results from the metaform.

    The presented data are collected using the metaform from Fig. 3C. (A) Set of different regions of the resolution target imaged via the metaform. The object’s spatial frequencies range from 0.315 to >4.53 lp/mm, which corresponds to a range of 6.95 to >100 lp/mm in image space. The features decrease in size from left to right and from top to bottom. (B) Measured contrast as a function of spatial frequency (measured in image space). The length of the error bars corresponds to two SDs from the mean. The lines are smooth spline fits to the measured data for the horizontal (blue solid) and vertical (red dashed) frequencies, with fitting weights equal to one over the variance at each point.

  • Fig. 5 A top-down view sketch of an example AR eyeglasses architecture.

    A metaform imager similar to the one presented in this work can be used as an optical combiner.

  • Table 1 Optical system specifications for the miniature imager and the metaform.

    ParameterSpecification
    Object distance85 mm
    Object size8.5 mm by 5 mm
    Illumination wavelength632.8 nm
    Effective focal length4 mm
    F/#4.67
    Magnification0.0453
    Metasurface dimensions2 mm by 1.5 mm
    Freeform substrate shapeX-toroid
    Rx, Ry−8.24 mm, −7.78 mm
    α, β, γ0.2434, −0.0015 mm−2,
    −0.0017 mm−2

Supplementary Materials

  • Supplementary Materials

    Metaform optics: Bridging nanophotonics and freeform optics

    Daniel K. Nikolov, Aaron Bauer, Fei Cheng, Hitoshi Kato, A. Nick Vamivakas, Jannick P. Rolland

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