Topology-Optimized Multilayered Metaoptics

Zin Lin, Benedikt Groever, Federico Capasso, Alejandro W. Rodriguez, and Marko Lončar

Phys. Rev. Applied 9, 044030 – Published 20 April 2018

Abstract

We propose a general topology-optimization framework for metasurface inverse design that can automatically discover highly complex multilayered metastructures with increased functionalities. In particular, we present topology-optimized multilayered geometries exhibiting angular phase control, including a single-piece nanophotonic metalens with angular aberration correction, as well as an angle-convergent metalens that focuses light onto the same focal spot regardless of the angle of incidence.

Received 17 June 2017
Revised 23 February 2018

DOI:https://doi.org/10.1103/PhysRevApplied.9.044030

Physics Subject Headings (PhySH)

Geometrical & wave optics Metamaterials Nanophotonics Optical materials & elements

Devices Multilayer thin films Nanostructures

Electromagnetic field calculations

Condensed Matter, Materials & Applied PhysicsGeneral PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Zin Lin^1,*, Benedikt Groever¹, Federico Capasso¹, Alejandro W. Rodriguez², and Marko Lončar¹

¹John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
²Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA

^*zinlin@g.harvard.edu

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Vol. 9, Iss. 4 — April 2018

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Images

Figure 1
Schematics (not to scale) of (a) a single-piece nanophotonic aberration-corrected metalens and (b) an angle-convergent metalens. The metalens ensures diffraction-limited focusing under general oblique incidence $θ_{inc}$ either (a) onto a laterally shifted focal spot or (b) onto the same on-axis focal spot.
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Figure 2
(a) Multilayered miniature 2D lens ( $NA = 0.35$ , $f = 30 λ$ ) which is aberration corrected for four incident angles ${0 °, 7.5 °, 15 °, 20 °}$ . Note that, by virtue of symmetry, the lens is automatically corrected for the negative angles as well ${- 7.5 °, - 15 °, - 20 °}$ . The lens materials consist of five layers of silicon (black) in alumina matrix (gray). (Inset) A portion of the lens is magnified for easy visualization; the smallest features (such as those encircled within the blue dotted oval lines) measure $0.02 λ$ , while the thickness of each layer is $0.2 λ$ . (b) FDTD analysis of the far-field profiles (density plots) reveal focusing action for the four incident angles. Note that the location of the focal plane is denoted by a white dashed line. (c) The field intensities (the circle points) at the focal plane follow the ideal diffraction limit (the solid lines). Note that the intensities are normalized to unity for an easy comparison of the spot sizes. (d) The corresponding phase profile (the red circle data points) for each angle is measured at a distance of $1.5 λ$ from the device, showing good agreement with the ideal profile (the black solid line). (e) Near-field profiles with almost perfect outgoing spherical wave fronts.
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Figure 3
(a) Multilayered miniature 2D lens ( $NA = 0.35$ , $f = 30 λ$ ) that exhibits on-axis focusing for the incident angles ${0 °, \pm 3 °, \pm 6 °, \pm 9 °}$ . The lens materials consist of ten layers of silicon (black) in silica matrix (gray). (Inset) A portion of the lens is magnified for easy visualization; the smallest features (such as those encircled within blue dotted oval lines) measure $0.02 λ$ , while the thickness of each layer is $0.05 λ$ . (b) FDTD analysis of the far-field profiles (density plots) reveal the same focal spot for the different incident angles. Note that the location of the focal plane is denoted by a white dashed line. (c) The intensities (symbolic data points) at the focal plane follow the on-axis ideal diffraction limit for all of the incident angles (the solid line). (d) The corresponding phase profile (the red circle data points) for each angle is measured at a distance of $1.5 λ$ from the device, showing good agreement with the ideal profile (the black solid line). (e) Near-field profiles with almost perfect outgoing spherical wave fronts.
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