Asymmetric Free-Space Light Transport at Nonlinear Metasurfaces

Nir Shitrit, Jeongmin Kim, David S. Barth, Hamidreza Ramezani, Yuan Wang, and Xiang Zhang

Phys. Rev. Lett. 121, 046101 – Published 24 July 2018

Abstract

Asymmetric light transport has significantly contributed to fundamental science and revolutionized advanced technology in various aspects such as unidirectional photonic devices, optical diodes, and isolators. While metasurfaces mold wave fronts at will with an ultrathin flat optical element, asymmetric transport of light cannot be fundamentally achieved by any linear system including linear metasurfaces. We report asymmetric transport of free-space light at nonlinear metasurfaces upon transmission and reflection. Moreover, we theoretically derive the nonlinear generalized Snell’s laws that were experimentally confirmed by the anomalous nonlinear refraction and reflection. The asymmetric transport at optically thin nonlinear interfaces is revealed by the concept of a reversed propagation path. Such an asymmetric transport at metasurfaces opens a new paradigm for free-space ultrathin lightweight optical devices with one-way operation including unrivaled optical valves and diodes.

Received 12 March 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.046101

Physics Subject Headings (PhySH)

Metamaterials Photonics

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Nir Shitrit¹, Jeongmin Kim¹, David S. Barth¹, Hamidreza Ramezani^1,2, Yuan Wang¹, and Xiang Zhang^1,3,*

¹NSF Nanoscale Science and Engineering Center (NSEC), 3112 Etcheverry Hall, University of California, Berkeley, California 94720, USA
²Department of Physics and Astronomy, University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
³Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA

^*Corresponding author. xiang@berkeley.edu

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Vol. 121, Iss. 4 — 27 July 2018

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Figure 1
Generalized laws of refraction and reflection at nonlinear gradient metasurfaces. (a),(b) Schematics used to derive the generalized laws of refraction and reflection for NGMs, respectively, wherein the optical path differences and the rapid phase shift (grayscale pattern) introduced by the metasurface are depicted. Red and blue rays correspond to rays of light at the fundamental wavelength $λ_{1}$ and at the wavelength of the generated nonlinear harmonic $λ_{2}$ , respectively. $ϕ$ and $ϕ + d ϕ$ are the phase shifts at the two locations in which the rays cross the interface. The inset in (a) illustrates the temporal phase delay originating from the time difference $Δ t$ in the generation of the nonlinear harmonic between the two crossing locations. The three factors of optical path differences, spatial-temporal nonlinear phase delay, and metasurface-induced phase shift give rise to the nonlinear generalized Snell’s laws of refraction $n_{t} (λ_{2}) \sin θ_{t} - n_{i} (λ_{1}) \sin θ_{i} = (λ_{1} / 2 π n) (d ϕ / d x)$ and reflection $n_{i} (λ_{2}) \sin θ_{r} - n_{i} (λ_{1}) \sin θ_{i} = (λ_{1} / 2 π n) (d ϕ / d x)$ , where $n$ is the order of the generated nonlinear harmonic.
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Figure 2
Anomalous refraction and reflection from nonlinear gradient metasurfaces. (a) Scanning electron microscope image of the NGMs. The unit cell of the NGMs (yellow) comprises 12 gold nanorod antennas, where their orientation angles $θ (x, y)$ rotate linearly to generate a constant phase gradient. The width and length of each nanorod are 50 and 240 nm, respectively, and the thickness is 30 nm. The unit cell repeats with a periodicity $Γ$ of $4.8 μ m$ along the $x$ direction and 400 nm along the $y$ direction. The gold metasurface was coated with a 100-nm-thick PFO layer to form metal-organic hybrid nonlinear metasurfaces. (b) The same metasurface structure introduces different phase distributions for the FH and THG (resembling linear and NGMs, respectively). Colors filling the nanorods depict the local phase. The FH beam experiences a constant phase for the modes maintaining the polarizations ( $σ, σ$ modes), while the modes flipping the polarizations ( $σ, - σ$ modes) experience a linear phase profile from 0 to $2 π$ . The THG beam experiences linear phase profiles from 0 to $2 π$ and from 0 to $4 π$ for $σ, σ$ and $σ, - σ$ modes, respectively. The phase profiles portrayed by color correspond to right circular polarization (RCP) excitation ( $σ = + 1$ ); for left circular polarization (LCP) excitation ( $σ = - 1$ ), the trends of the phase profiles are similar but with the opposite slope. (c),(d) Angles of refraction ( $θ_{t}$ ) and reflection ( $θ_{r^{'}}$ ) versus the angle of incidence ( $θ_{i^{'}}$ ), respectively. Modes are labeled with the incident-analyzed polarization state. Lines correspond to theoretical calculations performed by the generalized laws of refraction and reflection for NGMs [Eqs. (2) and (3)], whereas dots refer to measured data. Error bars (not shown) are smaller than the size of the data points. All angles were measured in free space as shown in the insets.
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Figure 3
Asymmetric transport at nonlinear gradient metasurfaces. (a),(b) Schematics of the concept of AT at NGMs for refraction and reflection, respectively. We first consider the angle of refraction or reflection for a given angle of incidence $θ_{i_{1}}$ ; then, we excite the metasurface from the opposite side, where the angle of incidence is set to the obtained angle of refraction or reflection in the original excitation (i.e., RP path). Moreover, the handedness of the circular polarization of these two beams is identical owing to RP. The transport of light is asymmetric when the angle of refraction $θ_{t_{2}}$ or reflection $θ_{r_{2}}$ in the excitation from the opposite side is different from $θ_{i_{1}}$ . (c),(d) THG RP angles of refraction ( $θ_{t_{2}}$ ) and reflection ( $θ_{r_{2}}$ ) versus the angle of incidence in the original excitation ( $θ_{i_{1}}$ ), respectively. Lines correspond to calculations based on the generalized laws of refraction and reflection at NGMs, whereas dots refer to measured data. All angles were measured in free space. The polarization state of the modes refers to the original excitation. The insets in (c) and (d) are the corresponding results for the FH (linear metasurfaces).
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