Nonlocal Metasurfaces for Optical Signal Processing

Hoyeong Kwon, Dimitrios Sounas, Andrea Cordaro, Albert Polman, and Andrea Alù

Phys. Rev. Lett. 121, 173004 – Published 24 October 2018

Abstract

Optical analog signal processing has been gaining significant attention as a way to overcome the speed and energy limitations of digital techniques. Metasurfaces offer a promising avenue towards this goal due to their efficient manipulation of optical signals over deeply subwavelength volumes. To date, metasurfaces have been proposed to transform signals in the spatial domain, e.g., for beam steering, focusing, or holography, for which angular-dependent responses, or nonlocality, are unwanted features that must be avoided or mitigated. Here, we show that the metasurface nonlocality can be engineered to enable signal manipulation in the momentum domain over an ultrathin platform. We explore nonlocal metasurfaces performing basic mathematical operations, paving the way towards fast and power-efficient ultrathin devices for edge detection and optical image processing.

Received 5 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.173004

Physics Subject Headings (PhySH)

Geometrical & wave optics Imaging & optical processing Metamaterials Nanophotonics Photonics Transformation optics

Atomic, Molecular & Optical

Authors & Affiliations

Hoyeong Kwon^1,*, Dimitrios Sounas^1,*, Andrea Cordaro^2,3, Albert Polman³, and Andrea Alù^1,4,5,6,†

¹Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
²Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
³Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
⁴Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, USA
⁵Physics Program, Graduate Center, City University of New York, New York, New York 10016, USA
⁶Department of Electrical Engineering, City College of The City University of New York, New York, New York 10031, USA

^*These authors contributed equally to this Letter.
^†aalu@gc.cuny.edu

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Vol. 121, Iss. 17 — 26 October 2018

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Images

Figure 1
Nonlocal metasurface. (a) Schematic showing an array of split-ring resonators parallel to the $x - z$ plane. The metasurface is excited by TM-polarized waves propagating on the $x - z$ plane. (b) Transmission versus frequency and incident angle when all the SRRs in the metasurface are identical. (c) Transmission versus frequency for different incident angles when the SRRs are sinusoidally modulated in space parallel to the $x$ axis. The modulation is applied to the permittivity of the dielectric material in the SRR gaps. (d) Transmission versus frequency and incident angle for the same metasurface as in panel (c). The geometrical parameters are provided in Ref. [36].
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Figure 2
Second-derivative operation. (a) Transmission versus incident angle for the metasurface in Figs. 1 and 1 for $f = 0.92 f_{0}$ [red dashed line in Fig. 1]. We also present the response for an ideal second-derivative operation. The reference plane for the metasurface transmission is selected at a distance that leads to a 180° transmission phase at normal incidence. (b) Output of an ideal second-derivative operation and of the metasurface when the top panel signal is applied as input. For the ideal response, we consider a cutoff angle of 39° (angle of unitary transmission for the metasurface). Here, we have discretized the input signal with a pixel size of $0.79 λ$ assumed to be the distance over which the vertical jumps occur. (c) Same as in panel (b) but for a different input signal. The parameters used to obtain these results are provided in Ref. [36].
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Figure 3
First-derivative operation. (a) Limitations on the response of a metasurface with mirror symmetry with respect to the $x$ axis imposed by reciprocity. (b) Metasurface with broken $x$ and $z$ symmetry to obtain an asymmetric response with respect to positive and negative $k_{x}$ , as required in order to implement a first-derivative operation. (c) Transmission versus incidence angle for the metasurface in panel (b) and for an ideal first-derivative operation. The reference plane for transmission is selected at a distance that leads to a 0° transmission phase at normal incidence. (d) Output of an ideal first-derivative operation and of the metasurface when we apply the signal at the top panel as input. For the ideal response, we consider a cutoff angle equal to 56° (angle of unitary transmission for the metasurface). The input signal is discretized with a pixel size of $0.60 λ$ . (e) Same as in panel (d) but for a different input signal. The parameters used to obtain these results are provided in Ref. [36].
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Figure 4
Two-dimensional second-derivative operation. (a) Metasurface with a 90° rotational symmetry to implement the second derivative in 2D. (b) Transmission versus elevation and azimuthal angles $θ$ and $φ$ , respectively. (c) Image used to test the response of the metasurface at $f = 0.98 f_{0}$ , where $f_{0}$ is the resonance frequency of the unmodulated metasurface. For the calculation of these results, we have discretized the input signal with a pixel size of $0.86 λ$ in each direction. (d) Output from the metasurface for the input image in panel (c) and illumination with an $x$ -polarized wave from the normal direction. (e) Similar to panel (d) but for $y$ -polarized wave illumination. (f) Similar to panel (e) but for illumination with unpolarized light from the normal direction. The parameters used to obtain these results are provided in Ref. [36].
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