Abstract

We demonstrate inverse design of plasmonic nanoantennas for directional light scattering. Our method is based on a combination of full-field electrodynamical simulations via the Green dyadic method and evolutionary optimization (EO). Without any initial bias, we find that the geometries reproducibly found by EO work on the same principles as radio-frequency antennas. We demonstrate the versatility of our approach by designing various directional optical antennas for different scattering problems. EO-based nanoantenna design has tremendous potential for a multitude of applications like nano-scale information routing and processing or single-molecule spectroscopy. Furthermore, EO can help to derive general design rules and to identify inherent physical limitations for photonic nanoparticles and metasurfaces.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]

2019 (1)

T. Zhang, J. Xu, Z.-L. Deng, D. Hu, F. Qin, and X. Li, “Unidirectional Enhanced Dipolar Emission with an Individual Dielectric Nanoantenna,” Nanomaterials 9(4), 629 (2019).
[Crossref]

2018 (5)

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

A. K. González-Alcalde, R. Salas-Montiel, H. Mohamad, A. Morand, S. Blaize, and D. Macías, “Optimization of all-dielectric structures for color generation,” Appl. Opt. 57(14), 3959–3967 (2018).
[Crossref]

C. Girard, P. R. Wiecha, A. Cuche, and E. Dujardin, “Designing thermoplasmonic properties of metallic metasurfaces,” J. Opt. 20(7), 075004 (2018).
[Crossref]

R. Kullock, P. Grimm, M. Ochs, and B. Hecht, “Directed emission by electrically driven optical antennas,” Proc. SPIE 10540, 1054012 (2018).
[Crossref]

P. R. Wiecha, “pyGDM—A python toolkit for full-field electro-dynamical simulations and evolutionary optimization of nanostructures,” Comput. Phys. Commun. 233, 167–192 (2018).
[Crossref]

2017 (6)

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref]

J. Hu, X. Ren, A. N. Reed, T. Reese, D. Rhee, B. Howe, L. J. Lauhon, A. M. Urbas, and T. W. Odom, “Evolutionary Design and Prototyping of Single Crystalline Titanium Nitride Lattice Optics,” ACS Photonics 4(3), 606–612 (2017).
[Crossref]

C. Yan, K.-Y. Yang, and O. J. F. Martin, “Fano-resonance-assisted metasurface for color routing,” Light: Sci. Appl. 6(7), e17017 (2017).
[Crossref]

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High–bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3(7), e1700007 (2017).
[Crossref]

S. P. Gurunarayanan, N. Verellen, V. S. Zharinov, F. James Shirley, V. V. Moshchalkov, M. Heyns, J. Van de Vondel, I. P. Radu, and P. Van Dorpe, “Electrically Driven Unidirectional Optical Nanoantennas,” Nano Lett. 17(12), 7433–7439 (2017).
[Crossref]

P. R. Wiecha, L.-J. Black, Y. Wang, V. Paillard, C. Girard, O. L. Muskens, and A. Arbouet, “Polarization conversion in plasmonic nanoantennas for metasurfaces using structural asymmetry and mode hybridization,” Sci. Rep. 7(1), 40906 (2017).
[Crossref]

2016 (8)

M. Mesch, B. Metzger, M. Hentschel, and H. Giessen, “Nonlinear Plasmonic Sensing,” Nano Lett. 16(5), 3155–3159 (2016).
[Crossref]

K. Yao and Y. Liu, “Controlling electric and magnetic resonances for ultracompact nanoantennas with tunable directionality,” ACS Photonics 3(6), 953–963 (2016).

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse Design of Metal Nanoparticles’ Morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

X. Y. Z. Xiong, L. J. Jiang, W. E. I. Sha, Y. H. Lo, and W. C. Chew, “Compact Nonlinear Yagi-Uda Nanoantennas,” Sci. Rep. 6(1), 18872 (2016).
[Crossref]

K. Lindfors, D. Dregely, M. Lippitz, N. Engheta, M. Totzeck, and H. Giessen, “Imaging and Steering Unidirectional Emission from Nanoantenna Array Metasurfaces,” ACS Photonics 3(2), 286–292 (2016).
[Crossref]

G. C. des Francs, J. Barthes, A. Bouhelier, J. C. Weeber, A. Dereux, A. Cuche, and C. Girard, “Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources,” J. Opt. 18(9), 094005 (2016).
[Crossref]

B. L. Good, S. Simmons, and M. Mirotznik, “General optimization of tapered anti-reflective coatings,” Opt. Express 24(15), 16618 (2016).
[Crossref]

A. Abass, P. Gutsche, B. Maes, C. Rockstuhl, and E. R. Martins, “Insights into directional scattering: From coupled dipoles to asymmetric dimer nanoantennas,” Opt. Express 24(17), 19638 (2016).
[Crossref]

2015 (2)

A. Mirzaei, A. E. Miroshnichenko, I. V. Shadrivov, and Y. S. Kivshar, “All-Dielectric Multilayer Cylindrical Structures for Invisibility Cloaking,” Sci. Rep. 5(1), 9574 (2015).
[Crossref]

M. Ramezani, A. Casadei, G. Grzela, F. Matteini, G. Tütüncüoglu, D. Rüffer, A. Fontcuberta i Morral, and J. Gómez Rivas, “Hybrid Semiconductor Nanowire–Metallic Yagi-Uda Antennas,” Nano Lett. 15(8), 4889–4895 (2015).
[Crossref]

2014 (7)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar Interference for Directed Light Emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref]

D. Dregely, K. Lindfors, M. Lippitz, N. Engheta, M. Totzeck, and H. Giessen, “Imaging and steering an optical wireless nanoantenna link,” Nat. Commun. 5(1), 4354 (2014).
[Crossref]

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional Fluorescence Emission by Individual V-Antennas Explained by Mode Expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref]

M. Wersäll, R. Verre, M. Svedendahl, P. Johansson, M. Käll, and T. Shegai, “Directional Nanoplasmonic Antennas for Self-Referenced Refractometric Molecular Analysis,” J. Phys. Chem. C 118(36), 21075–21080 (2014).
[Crossref]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, , K. Kumar, C.-W. Qiu, and J. K. W. Yang, “Plasmonic Color Palettes for Photorealistic Printing with Aluminum Nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref]

A. Mirzaei, A. E. Miroshnichenko, I. V. Shadrivov, and Y. S. Kivshar, “Superscattering of light optimized by a genetic algorithm,” Appl. Phys. Lett. 105(1), 011109 (2014).
[Crossref]

F. Bigourdan, F. Marquier, J.-P. Hugonin, and J.-J. Greffet, “Design of highly efficient metallo-dielectric patch antennas for single-photon emission,” Opt. Express 22(3), 2337 (2014).
[Crossref]

2013 (2)

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and Chiroptical Effects in Plasmonic Nanostructures: Fundamentals, Recent Progress, and Outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref]

D. Vercruysse, Y. Sonnefraud, N. Verellen, F. B. Fuchs, G. Di Martino, L. Lagae, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Unidirectional Side Scattering of Light by a Single-Element Nanoantenna,” Nano Lett. 13(8), 3843–3849 (2013).
[Crossref]

2012 (3)

I. S. Maksymov, I. Staude, A. E. Miroshnichenko, and Y. S. Kivshar, “Optical Yagi-Uda nanoantennas,” Nanophotonics 1(1), 65–81 (2012).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary Optimization of Optical Antennas,” Phys. Rev. Lett. 109(12), 127701 (2012).
[Crossref]

2011 (2)

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances On-Demand for Plasmonic Nano-Particles,” Nano Lett. 11(6), 2329–2333 (2011).
[Crossref]

T. Shegai, S. Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun. 2(1), 481 (2011).
[Crossref]

2010 (2)

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref]

C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm optimization of broadband nanoplasmonic arrays,” Opt. Lett. 35(2), 133 (2010).
[Crossref]

2009 (1)

G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: Influence of morphology,” Appl. Phys. Lett. 94(15), 153109 (2009).
[Crossref]

2008 (1)

C. Girard, E. Dujardin, G. Baffou, and R. Quidant, “Shaping and manipulation of light fields with bottom-up plasmonic structures,” New J. Phys. 10(10), 105016 (2008).
[Crossref]

2007 (3)

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, “Optimal design of integrally gated CNT field-emission devices using a genetic algorithm,” Nanotechnology 18(39), 395203 (2007).
[Crossref]

H. F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi–Uda antenna,” New J. Phys. 9(7), 217 (2007).
[Crossref]

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[Crossref]

2005 (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant Optical Antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref]

1995 (1)

C. Girard, A. Dereux, O. J. F. Martin, and M. Devel, “Generation of optical standing waves around mesoscopic surface structures: Scattering and light confinement,” Phys. Rev. B 52(4), 2889–2898 (1995).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1928 (1)

H. Yagi, “Beam Transmission of Ultra Short Waves,” Proc. IRE 16(6), 715–740 (1928).
[Crossref]

Abass, A.

Arbouet, A.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref]

P. R. Wiecha, L.-J. Black, Y. Wang, V. Paillard, C. Girard, O. L. Muskens, and A. Arbouet, “Polarization conversion in plasmonic nanoantennas for metasurfaces using structural asymmetry and mode hybridization,” Sci. Rep. 7(1), 40906 (2017).
[Crossref]

Baffou, G.

G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: Influence of morphology,” Appl. Phys. Lett. 94(15), 153109 (2009).
[Crossref]

C. Girard, E. Dujardin, G. Baffou, and R. Quidant, “Shaping and manipulation of light fields with bottom-up plasmonic structures,” New J. Phys. 10(10), 105016 (2008).
[Crossref]

Barthes, J.

G. C. des Francs, J. Barthes, A. Bouhelier, J. C. Weeber, A. Dereux, A. Cuche, and C. Girard, “Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources,” J. Opt. 18(9), 094005 (2016).
[Crossref]

Baumberg, J. J.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and Chiroptical Effects in Plasmonic Nanostructures: Fundamentals, Recent Progress, and Outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref]

Berkovitch, N.

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances On-Demand for Plasmonic Nano-Particles,” Nano Lett. 11(6), 2329–2333 (2011).
[Crossref]

Bigourdan, F.

Biscani, F.

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Supplementary Material (1)

NameDescription
» Visualization 1       Movie showing the convergence process of EO for an intensity-optimized plane wave illuminated directional optical antenna.

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Figures (9)

Fig. 1.
Fig. 1. (a) Scheme illustrating evolutionary optimization. (b) Plasmonic antenna structure model for EO of directional scattering. $40$ gold-blocks (B$_i$), each $40\times 40\times 40\,$nm$^{3}$ large are placed on a $n_{\textrm {s}}=1.5$ substrate (in the $XY$ plane) within an area of $1 \times 1\,$µm$^{2}$. Plane wave illumination at normal incidence ($\mathbf {k}$ along $-z$), with $\lambda _0=800\,$nm, linearly polarized along $OX$. (c) Sketch of the directionality problem: Maximize the ratio of scattered intensity through a narrow window (green) and scattering to the remaining solid angle (red).
Fig. 2.
Fig. 2. (a) Fitness vs. EO iteration with a population of $N_{\textrm {pop}}=500$ individuals. Best and average fitness are indicated by a green, respectively red line. (b-h) Best solutions at selected iterations between random initialization (b) and final solution (h). Iteration numbers are indicated at the upper right. Scattering patterns in $XZ$-plane are shown in the top panels by blue lines, a green segment indicates the optimization target. The corresponding gold cube arrangements are shown in the panels below. (i) Phase of the electric field $X$ component relative to the driving element’s center. (j) Functional components: feed (blue), reflector (green) and director (red). The distances between the centers of gravity (dashed lines) are indicated at the top. (k) Impact on the directionality ratio in decibel ($10 \log _{10} (R_{\textrm {direct}}$)) when each block is toggled (gold block $\leftrightarrow$ no gold block). Scale bars are $200\,$nm.
Fig. 3.
Fig. 3. Examples of directional EO (maximize $R_{\textrm {direct}}$) for various target solid angles (green areas in top plots). Bottom plots show top views of the optimized geometries, where scale bars are $200\,$nm. Center plots show scattering patterns for the full hemisphere of a normally incident plane wave at $\lambda _0 = 800\,$nm, linearly $X$-polarized. (a) towards a loose focal area, (b) towards $90^{\circ }$, (c) bidirectionally and (d) towards a “donut” target area. (a-d) are set in a vacuum environment and show backscattering. (e-f) are set on an $n_{\textrm {s}}=1.5\,$ dielectric, hemispherical substrate in order to reflect the conditions in oil immersion microscopy. In these two cases, forward scattering into the glass substrate is maximized for areas at the critical angle.
Fig. 4.
Fig. 4. EO for maximization of the absolute backscattered intensity $I_{\textrm {direct}}$ to the target solid angle centered at a polar angle of (a) $45^{\circ }$ and (b) $90^{\circ }$. Target solid angles, backscattering radiation patterns and top views of the optimized geometries are shown respectively from top to bottom. Scale bars are $200\,$nm. Normally incident plane wave, linearly $X$-polarized with $\lambda _0 = 800\,$nm, the structures lie in vacuum on an $n=1.5$ substrate. A visualization of the optimization convergence for case (a) can be found online (Visualization 1).
Fig. 5.
Fig. 5. Optimized antennas for dipole emitter directional emission. The quantum emitter is oriented along $OY$, radiates at $\lambda _0 = 800\,$nm and has a minimum distance to the gold structure of $20\,$nm. Emission is maximized at the critical angle of scattering inside the $n_{\textrm {s}}=1.5$ substrate. (a) maximize directionality ratio $R_{\textrm {direct}}$. (b) maximize absolute intensity $I_{\textrm {direct}}$ at target solid angle. (c) simulation of reference antenna from Ref. [15]. (d) spectrum of total dipole emission intensity, normalized to the intensity $I_{\textrm {dp}}$ of an isolated dipole emitter (no antenna). The inset shows directionality spectra for the three antennas. Radiation patterns are evaluated on a hemispherical screen inside the substrate. Scale bars are $200\,$nm.
Fig. 6.
Fig. 6. Symmetry analysis, showing optimization results of directional quantum emitter gold antennas in vacuum environment ($n_{\textrm{env}}=1$) for different orientations of the dipole transition. (a) and (d): dipole emitter along $OX$, (b) and (e): dipole emitter along $OY$, (c) and (f): dipole emitter along $OZ$. In (a-c), the geometry is unconstrained, in (d-f), the same optimizations were repeated, imposing an axial mirror symmetry at the $x$-axis for the geometry of the antenna. Emitter placed at $(x=0\,\textrm {nm}, y=0\,\textrm {nm}, z=20\,\textrm {nm})$, indicated by a red arrow. Scale bars are $200\,$nm.
Fig. 7.
Fig. 7. Demonstration of reproducibility and convergence: Top row shows antenna geometries and their directivity ratios for $5$ independent runs of the same optimization, with random initial EO populations. Bottom row shows the relative phase of the $E_x$ field component.
Fig. 8.
Fig. 8. Analysis of functional elements for the antenna in Fig. 2. Top row: Top view of the considered sub-part of the full antenna geometry. Bottom row: backscattering pattern. Scale bars are $100\,$nm, the colorscale represents the scattering intensity in arbitrary units (normalized to the peak intensity of the full structure).
Fig. 9.
Fig. 9. Backscattering patterns of an identical gold nanostructure but using different discretization steps (geometry shown on the right, same as in Fig. 2). $\lambda =800\,$nm plane wave illumination from the top, linear polarized along $X$. Each elementary block in the structure was discretized from left to right by $2\times 2\times 2$ dipoles with $20\,$nm step, $4\times 4\times 4$ dipoles with $10\,$nm step and $6\times 6\times 6$ dipoles with $6.67\,$nm step. The results are very similar, hence we can conclude that a step of $20\,$nm is a good approximation.

Equations (1)

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R direct = ( Ω direct I ( Ω ) d Ω ) / Ω direct ( Ω rest I ( Ω ) d Ω ) / Ω rest = I direct I rest .

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