Topological Dislocations for Plasmonic Mode Localization In

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Topological Dislocations for Plasmonic Mode Localization in Arrays of Nanoscale Rectangular Au Apertures: Implications for Optical Communications Eliav David Epstein, Leeju Singh, Maayan Fox, Shmuel Sternklar, and Yuri Gorodetski*

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ABSTRACT: We study the localization of plasmonic modes on topological dislocations obtained by an abrupt change in the geometry of unit cells in a plasmonic metasurface comprised of a nanoscale array of rectangular apertures. We experimentally demonstrate mode localization in line defects and point singularities in the topology. These results are conﬁrmed by numerical simulations of the near ﬁeld distributions along the topology boundaries. We present structures with line dislocations supporting dark and bright modes. Moreover, we show that in structures with point dislocations the localization strength can be further manipulated by modifying the topological order of the structure.

KEYWORDS: nanophotonics, surface plasmons, metasurfaces, topological photonics, photonic crystal, geometric phases

■ INTRODUCTION metamaterial comprising a periodic structure with effective − − 26 28 The field of topological photonics1 4 has gained much interest optical properties. Most commonly, such a system is lately in nanophotonics and optical communication commun- realized via nanometric apertures or particles periodically ities.5,6 Topology7,8 has, in fact, been recognized as a novel arranged on a metal surface. Similarly to the aforementioned degree of freedom in light−matter interactions, as it provides PhC, a specially designed doubly periodic metasurface can behave as a plasmonic crystal (PlC) with an accurately an almost lossless medium for optical signals. Efficient light fi designed band gap, where intentionally produced defects can con nement, guiding, and localization have been achieved by 29,30 Downloaded via ARIEL UNIV on January 23, 2021 at 17:18:11 (UTC). 9 localize and guide the SPs. Various configurations of PlC using photonic crystal (PhC) optical systems with topological 10,11 have been proposed for a variety of nanooptics applica- states. These optical modes have emerged within the 31,32 12 tions. It has been shown that such a mechanism provides a photonic band gap induced by the PhC periodicity at an promising platform for future nanophotonic circuitry as well as interface between two or more regions with different

See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. 1,13 variousactiveplasmonicdevicessuchaslasersand topological phases. The optical edge states were shown to − sensors.33 35 It has also been demonstrated that exciting SPs be topology protected and propagated with negligible by means of an anisotropic scatterer can lead to the geometric scattering losses, in analogy with currents in so-called 14,15 Berry phase that can further modify the propagation conditions topological insulators that have been recently discovered. − of the surface waves.36 38 The Berry phase has a topological Modern nanofabrication techniques facilitate the realization of origin, as it stems from the light’s polarization manipulation nanoscale periodic optical media with any desired geometry, deﬁned by a path on a conﬁgurational space represented by the which provides a practical advantage for the topology based Poincarésphere.39,40 In this context, one may inquire whether nanophotonics with respect to classical index-modulated the abrupt change of the Berry phase induced in the plasmonic systems.12,16 A special interest was focused on systems metasurface may lead to the topology induced edge states. In supporting surface plasmon (SP)17,18 modesexcitations of the bound electric charges in the vicinity of a metal−insulator interface.19,20 It has already been shown that these excitations Received: October 21, 2020 are intrinsically topological in nature and represent an edge Accepted: January 15, 2021 − state21 23 of two adjacent media with an abrupt sign change of the dielectric constant. Nevertheless, some further studies24,25 have discussed the possibility of further localizing the SP modes within a metasurfacethe 2D equivalent of a

© XXXX American Chemical Society https://dx.doi.org/10.1021/acsanm.0c02815 A ACS Appl. Nano Mater. XXXX, XXX, XXX−XXX ACS Applied Nano Materials www.acsanm.org Article this paper, we demonstrate the appearance of such plasmonic The sample was illuminated by a laser whose beam edge states at the boundary between two zones of a PlC with polarization had been controlled using a set of polarizer (P) different topological phases. We design a Bragg type plasmonic and quarter-wave plate (QWP) and focused by an objective medium where no propagating SP modes are allowed. We use (O1) onto the structure (Figure 1b). The imaging objective anisotropic rectangular apertures as the metasurface unit cell (O2) that was brought into contact with the back side of the and excite it by circularly polarized light. This configuration sample by means of an index-matching oil produced leakage enables us to manipulate the topological phase of the excited radiation from the near-field plasmonic signal.41 This light then modes that can be simply controlled by the aperture angular passed through a series of imaging lenses L1−L3, and a final orientation. We experimentally investigate a number of image of the SP mode was captured by the camera. plasmonic metasurfaces comprised of two domains with an We started with a sample where the apertures had a constant abrupt change in topologya topological dislocation. Here we orientation of +45° in its upper half and −45° in the lower half. discuss line and point dislocations with trivial and nontrivial In Figure 2a,b, a scanning electron microscope (SEM) image topological phases. Our leakage radiation (LR) microscopy system allows us to track the excited SP modes directly. Our experimental results and numerical simulations indicate the appearance of plasmonic dark and bright modes at the domain boundaries, while their localization properties result solely from the topology. ■ RESULTS AND DISCUSSION Our proposed metasurface was a square array of rectangular apertures fabricated using a focused ion beam (FIB) in a 100 nm-thick gold film evaporated on a glass substrate. The structure was comprised of two domains with a relative aperture orientation difference of π/2, as shown in the conceptual scheme in Figure 1a. The grating period was

Figure 2. Experimental manifestation of the topological SP mode. (a, b) SEM images of the PlC lattice. The inset in part a shows the Figure 1. Schematic of optical interaction with the metasurface and boundary between +45 and −45° domains. (c, d) The transmitted the experimental setup. (a) Right and left polarized light incident on intensity distribution of the sample when illuminated with linear the plasmonic grating. (b) The 780 nm laser beam is polarized using a polarization at ±45°. (e, f) The measured distributions for the polarizer (P) and a quarter-wave plate (QW) and then focused by a incident right and left CP illumination. 20× objective (O1) with NA = 0.25. The leakage radiation is collected by the second objective (O2, NA = 1.25, 100×) and imaged through the lenses (L1−L3) at the camera (Cam). A spatial filter (SF) is used in the secondary Fourier plane to filter out the direct of the fabricated sample is presented. The boundary where the transmission. aperture orientation changes is marked by the dashed line in the inset. Parts c and d of Figure 2 show the transmission through the sample captured in our LR system when the illuminating beam was linearly polarized at ±45°, respectively. λ + ϵ designed according to the Bragg condition d = 0 1 m with By comparing the transmission intensity distribution, one can 2 ϵm conclude that, as expected, the aperture anisotropy leads to the λ ϵ respect to the incident wavelength 0 (here m is the dielectric strong polarization dependence. We then switched to the λ constant of gold). The incident wavelength was 0 = 780 nm, circularly polarized (CP) illumination. We used an additional and accordingly, the structure period was chosen to be d = 382 set of polarizing elements to filter out the desired polarization nm. state. Moreover, a spatial filter (SF) was placed in the

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Figure 3. Plasmonic edge modes simulated by the Comsol Multiphysics software. The colormap represents the field amplitude in the 200 nm vicinity of the sample surface. (a) The sample is comprised of two ±45° domains with a simple boundary, and (b) the domains are separated by a zigzag boundary. intermediate Fourier plane of the system in order to block the emanating from each aperture is represented as a sum of the directly propagating light. original circular component and one with the opposite ϕ In Figure 2e,f, we show the SP distribution measured in our handedness with an additional geometric phase of g = LR system for incident right and left CP state, respectively. 2θ.47,48 As schematically shown in Figure 4,thelocal Here we notice some intensity localization along the boundary between the domains. We can also recognize fringes appearing parallel to the boundary (indicated on the figure by the arrow). We simulated the interaction of the optical field with the structure using Comsol Multiphysics software. In Figure 3a, the field amplitude in the vicinity of the metal surface is shown. First, it is clearly visible that each of the apertures indeed behaves as a localized SP source. Nevertheless, due to the Bragg periodicity,10,42 the field decays rapidly everywhere except at the domain boundary. The abrupt change in the aperture orientation behaves as a defect in the Bragg grating, inducing SP scattering similar to the one expected from a single groove. The fringes parallel to the boundary decay as they recede from it, indicating that the momentum of the plasmonic wave is preferably normal to the dislocation. From these results, one can deduce that the topological dislocation behaves as a defect in the Bragg grating, generating significant light scattering in the normal direction, with partial coupling to the SP waves that propagate away with a strong amplitude decay. This effect is achieved in our system thanks to the specific phase matching conditions arising along the boundary. We also note that there is a significant light concentration observed along the edges of the structure. We believe that this Figure 4. Artistic rendition of the topological Berry phase. The is resulting from the edge scattering which is obviously fi illumination of the Bragg lattice with an anisotropic aperture leads to enhanced through our dark- eld microscopy setup. the serial polarization state manipulation that is depicted as a path on To elucidate the physical mechanism of the system, we the surface of the Poincarésphere. The abrupt change in the aperture consider the geometric Berry phase.40 In general, the geometric orientation results in the topological (Berry) phase jump equal to the phase, also known as the Pancharatnam−Berry phase, arises as area enclosed by the two paths. a result of the polarization state manipulation leading to the closed path on the Poincarésphere.39,43,44 Numerous applications and physical systems based on this effect have polarization state manipulation in each domain is represented ff ́ been demonstrated in the last few decades in optics and by a di erent path on the Poincare sphere, resulting in the plasmonics.45,46 It has been shown that the geometric phase relative geometric phase equal to half the area enclosed by the emerges from the holonomy of the system’s configurational paths. The origin of this phase can be tracked back to the space; therefore, its origin is purely topological. Specifically, in Coriolis term in the Helmholz equation in a rotating reference our plasmonic system, we consider the rectangular apertures as frame which is analogous to the potential term in the Schrödinger equation.49 Accordingly, the Berry connection sources of the localized SPs excited by the incident light fi σΩ σ ± scattering. The incident CP light scattered at the rectangular can be de ned as A =2 , where = 1 is the spin number aperture is predominantly linearly polarized according to the representing the handedness of the circular polarization EiExy+ σ θ local orientation of the scatterer, θ. In the CP basis, the light eigenstates; E = and Ω = d is the aperture spatial ± 2 dχ

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Figure 5. Experimental and calculated SP edge state along the zigzag boundaries. (a, d) SEM images of the PlC lattice (the domain boundary is marked with the dashed frame). (b, e) The measured transmitted intensity distribution on the sample surface in comparison with (c, f) the distributions calculated using our Matlab solver. Yellow arrows indicate the guided plasmonic mode. rotation rate along the coordinate χ. The aforementioned We have tested a structure with two equal topological Berry phase can then be derived by integrating A along one domains occupying the upper and lower halves and also a rotation period. Here the aperture orientation change of π/2 structure in which one of the domains occupies just a quarter between the domains leads to an additional fractional Berry of the total grating (Figure 5). In both cases, the experimental phase of π at the boundary and 0 elsewhere. The fields pictures show a very pronounced mode localization along the scatterered from the apertures excite SP waves propagating on line dividing the domains, regardless of its geometry, as should the surface between the unit cells that serves as the coupling be expected from a topologically protected state. Unlike the channel. In our metasurface, the propagating SPs acquire a π previous case, the fringes appearing at the boundary indicate phase along one Bragg period which leads to the destructive that the momentum of the excited mode is now aligned with interference. However, the additional Berry phase then results the dislocation. We used a Matlab solver particularly designed fi 50 in the constructive interference along the domain boundary. to calculate the SP elds based upon the Huygens principle where each aperture was represented as a point source of SP This provides the condition for excitation of the SP mode that π can propagate along the boundary as long as the topology of waves. When we deliberately introduce a phase jump that is expected as a result of the topology dislocation, we obtain the domains is maintained. fi The light localization found in the first experiment is mostly distributions that are signi cantly similar to the experimental results (see Figure 5c,f). The edge plasmonic mode seems to contributed from the light scattered from the topological be strongly localized along the boundary in both simulated boundary. However, we note that the normally incident cases. planewave does not possess the necessary momentum to Next, we decided to extend our study to structures with launch the plasmonic waves along the boundary, and the edge radial geometry. First, we designed a metasurface where the state appears as a “dark” mode. This can also be deduced from ° fi +45 domain has a circular shape in the center of the structure the simulated eld distribution in Figure 3a having a minimum while outside of this area the aperture orientation was −45°. intensity at the boundary. The plasmonic waves scattered from Clearly, the distance between the unit cells along the boundary the line dislocation seem to propagate away toward the edges is no longer fixed at half the SP wavelength, which leads to of the sample. To obtain the conditions for exciting the SP weaker localization. Nevertheless, one can still recognize a bright mode, we designed another structure comprised of two rather pronounced edge mode appearing along the circle domains as before but having a zigzag type boundary (see circumference (Figure 6b). At the next stage, we introduced a Figure 3b and Figure 5a). In this fashion, every aperture along slow θ variation along the azimuthal angle, φ. In particular, we the boundary is rotated by π/2 radians with respect to the next let the aperture orientation change as θ(φ)=mφ/2, where m is one and the total phase between them is then matched. When the topological order keeping the same abrupt π/2 change we illuminate this structure by the incident CP light, the along the circular boundary (Figure 6d). Here we show the boundary itself leads to launching of the SP modes in both results of the structure with m = 2 which are expected to directions along the topological dislocation (see Figure 5b). induce the overall vortex-type geometric phase of ϕ = lφ, with l

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Figure 6. Study of plasmonic metasurfaces with nontrivial topology. The SEM images of the structures are given in parts a, d, and g, and the measured intensity distribution achieved in our LR system is presented in parts b, e, and h. The structure in part a is comprised of two trivial topological phases deﬁned by θ = ±45° separated by a circular boundary of the radius ρ =10μm. The structure in part d consists of apertures whose local orientation rotates with topological order m = 2 (see details in the text) but having a π/2 jump along the same circular boundary. The structure in part g is similar to the one in part e, but the topology change occurs at the lower right corner. (c, f, i) Field amplitude distributions simulated by the Matlab solver.

=2m being the total topological charge.51 Interestingly, in the the hypothesis that the presence of this point may act as a SP center of the structure, where the phase has a singularity, we launcher. Therefore, combining topological singularities of notice a very strong flower-like light localization (Figure 6e). different types might pave the way for more sophisticated  Similarly to the topological line dislocation the boundary nanophotonic circuitry and other practical devices for optical π  along which the rotation of the aperture occurs here we communication where the line dislocation may serve as a observe a point dislocation due to the phase structure. waveguide while a point dislocation could be used for optical However, as these singularities appear in the plasmonic data storage. The three latter cases were also simulated using Bragg grating, they appear as constructive interference and localize light. The difference between these two cases is that our Matlab solver and produced quite similar results (Figure the line dislocation suggests a local topological defect while the 6c,f,i). We note that the measured mode intensities in Figure appearance of the point dislocation is induced by a global 6b,e,h have some variations along the boundary which was azimuthal phase gradient. The appearance of these zero- found to be independent of the incident polarization and was dimension SP localizations at the point dislocation is not observed at all in the simulations. We attribute this effect reminiscent of the so-called higher-order topological corner to the measurement noise due to a possible tiny tilt of the modes found in systems with high-order multipole moments. structure plane with respect to the illumination. Such systems have been shown to host topological states of It should be noted that in the current configuration the 52,53 dimensions two or less than that of the bulk. system is degenerate with respect to the incident circular state. The last experiment was performed with a metasurface In other words, both circular polarizations lead to the same having the same azimuthal phase ramp as before, but this time mode excitation, propagating in both directions equally, as can the topology change occurred in a square domain at a corner of be seen in the first experiment. The reason for this is the trivial the sample (see Figure 6g). When this structure was (constant) topological phase induced in both domains by the illuminated by circularly polarized light, the line singularity Ω could be easily detected by the excited plasmonic state along zero aperture rotation rate, = 0. We believe that smart the domain edge (Figure 6h). In addition, we could also engineering of the domains can lift the spin degeneracy, for measure the point dislocation at the center of the structure instance, by designing a graphene-like metasurface with space- exactly at the Berry phase singular point. The excited mode in variant aperture orientation providing an overall spin-depend- this case seems to be much more pronounced, strengthening ent nontrivial Berry phase.

E https://dx.doi.org/10.1021/acsanm.0c02815 ACS Appl. Nano Mater. XXXX, XXX, XXX−XXX ACS Applied Nano Materials www.acsanm.org Article ■ CONCLUSIONS Author Contributions We have demonstrated the excitation of the edge plasmonic M.F. performed the simulations, M.F., E.D.E., and L.S. states along the domain boundary on a metasurface. The origin analyzed the data and performed the experiments, and all of of these states is purely topological, as it stems from the abrupt the authors have equally contributed to the paper writing. change of the unit cell geometry leading to the quantal Notes geometric Berry phase generation. We have shown that some The authors declare no competing financial interest. of our structures can support dark or bright SP edge modes fi con ned to the topological dislocation within the metasurface. ACKNOWLEDGMENTS By using a nontrivial (space-variant) topological phase, we ■ were able to generate a point dislocation which was then We acknowledge the Israeli Ministry of Science Technology shown to localize the SP waves. and Space for financial support.

■ METHODS ■ REFERENCES Element Fabrication. The basic plasmonic metasurfaces are (1) Lu, L.; Joannopoulos, J. D.; Soljacič,́ M. Topological photonics. designed according to the proposed geometry in Matlab and first are Nat. Photonics 2014, 8, 821−829. rigorously investigated by using numeric simulation software (2) Khanikaev, A. B.; Shvets, G. Two-dimensional topological Comsol and our simplified Matlab solver based on the Huygens photonics. Nat. Photonics 2017, 11, 763−773. principle. The structures of interest can then be fabricated as (3) Ozawa, T.; Price, H. M.; Amo, A.; Goldman, N.; Hafezi, M.; Lu, metasurfaces. As a substrate, we use a simple 160 μm-thick coverslip L.; Rechtsman, M. C.; Schuster, D.; Simon, J.; Zilberberg, O.; glass, cleaned in two-stage sonication followed by an ethanol Carusotto, I. Topological photonics. Rev. Mod. Phys. 2019, 91, overnight soaking. We evaporate a 100 nm-thick gold layer on the coverslip using a High Resolution Sputter Coater (Agar Scientific, 015006. AGB7234). The thickness of the gold is precisely controlled by the (4) Monticone, F.; Alu, A. Metamaterial, plasmonic and nano- built in QCM thickness meter. The nanofabrication process photonic devices. Rep. Prog. Phys. 2017, 80, 036401. incorporates focused ion milling of the patterns in the dual-beam (5) Kim, M.; Jacob, Z.; Rho, J. Recent advances in 2D, 3D and FEI system. The experiments are performed using the leakage higher-order topological photonics. Light: Sci. Appl. 2020, 9, 130. radiation microscopy system (see the details in the text). (6) Yang, Y.; Yamagami, Y.; Yu, X.; Pitchappa, P.; Webber, J.; Zhang, COMSOL Simulation. fi B.; Fujita, M.; Nagatsuma, T.; Singh, R. Terahertz topological The simulation is a full eld solution of the − time-invariant Maxwell’s equations over the volume of interest. The photonics for on-chip communication. Nat. Photonics 2020, 14, 446 metasurface geometry is assembled as a unit section of the periodic 451. structure; a floquet-periodic port excites the wave from above; (7) Rider, M. S.; Palmer, S. J.; Pocock, S. R.; Xiao, X.; Arroyo reflected waves are absorbed by this port, and transmitted waves are Huidobro, P.; Giannini, V. A perspective on topological nano- absorbed by a PML beneath the illuminated structure; the four sides photonics: current status and future challenges. J. Appl. Phys. 2019, of the model have floquet periodicity (y direction) and PML 125, 120901. absorbers (x direction). Once solved, an xy plane is sliced 200 nm (8) Proctor, M.; Huidobro, P. A.; Maier, S. A.; Craster, R. V.; above the gold surface (in the air side) and the phase and magnitude Makwana, M. P. Manipulating topological valley modes in plasmonic − of the Ez field are analyzed. metasurfaces. Nanophotonics 2020, 9, 657 665. (9) Yablonovitch, E. Photonic crystals. J. Mod. Opt. 1994, 41, 173− ■ ASSOCIATED CONTENT 194. (10) Li, C.-A.; Wu, S.-S. Topological states in generalized electric *ı s Supporting Information quadrupole insulators. Phys. Rev. B: Condens. Matter Mater. Phys. The Supporting Information is available free of charge at 2020, 101, 195309. https://pubs.acs.org/doi/10.1021/acsanm.0c02815. (11) Parappurath, N.; Alpeggiani, F.; Kuipers, L.; Verhagen, E. Matlab solver code and the simulated band gap structure Direct observation of topological edge states in silicon photonic of the metasurface (PDF) crystals: Spin, dispersion, and chiral routing. Science Advances 2020, 6, eaaw4137. (12) Yablonovitch, E. Photonic band-gap structures. J. Opt. Soc. Am. ■ AUTHOR INFORMATION B 1993, 10, 283−295. Corresponding Author (13) Haldane, F. D. M.; Raghu, S. Possible Realization of Directional Yuri Gorodetski − Department of Electrical and Electronic Optical Waveguides in Photonic Crystals with Broken Time-Reversal Engineering, Ariel University, Ariel 40700, Israel; Symmetry. Phys. Rev. Lett. 2008, 100, 013904. (14) Moore, J. E. The birth of topological insulators. Nature 2010, Department of Mechatronics and Mechanical Engineering, 464, 194−198. Ariel University, Ariel 40700, Israel; orcid.org/0000- (15) Yue, Z.; Wang, X.; Gu, M. Topological insulator materials for 0003-1245-4512; Email: [email protected] advanced optoelectronic devices. Advanced Topological Insulators 2019,45−70. Authors − (16) He, Q.; Zaquine, I.; Roosen, G.; Frey, R. Bragg diffraction in Eliav David Epstein Department of Electrical and Electronic thin 2D refractive index modulated semiconductor samples. J. Opt. Engineering, Ariel University, Ariel 40700, Israel Soc. Am. B 2009, 26, 390−396. Leeju Singh − Department of Electrical and Electronic (17) Ding, F.; Yang, Y.; Deshpande, R. A.; Bozhevolnyi, S. I. A Engineering, Ariel University, Ariel 40700, Israel review of gap-surface plasmon metasurfaces: fundamentals and Maayan Fox − Department of Electrical and Electronic applications. Nanophotonics 2018, 7, 1129−1156. Engineering, Ariel University, Ariel 40700, Israel (18) Proctor, M.; Craster, R. V.; Maier, S. A.; Giannini, V.; − Huidobro, P. A. Exciting Pseudospin-Dependent Edge States in Shmuel Sternklar Department of Electrical and Electronic − Engineering, Ariel University, Ariel 40700, Israel Plasmonic Metasurfaces. ACS Photonics 2019, 6, 2985 2995. (19) Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H.; Thio, T.; Wolff, P. A. Complete contact information is available at: Extraordinary optical transmission through sub-wavelength hole https://pubs.acs.org/10.1021/acsanm.0c02815 arrays. Nature 1998, 391, 667−669.

F https://dx.doi.org/10.1021/acsanm.0c02815 ACS Appl. Nano Mater. XXXX, XXX, XXX−XXX ACS Applied Nano Materials www.acsanm.org Article

(20) Poddubny, A.; Miroshnichenko, A.; Slobozhanyuk, A.; Kivshar, (42) Liu, J.-Q.; Wang, L.-L.; He, M.-D.; Huang, W.-Q.; Wang, D.; Y. Topological Majorana States in Zigzag Chains of Plasmonic Zou, B.; Wen, S. A wide bandgap plasmonic Bragg reflector. Opt. Nanoparticles. ACS Photonics 2014, 1, 101−105. Express 2008, 16, 4888−4894. (21) Karch, A. Surface plasmons and topological insulators. Phys. (43) Cohen, E.; Larocque, H.; Bouchard, F.; Nejadsattari, F.; Gefen, Rev. B: Condens. Matter Mater. Phys. 2011, 83, 245432. Y.; Karimi, E. Geometric phase from Aharonov−Bohm to (22) Leykam, D.; Bliokh, K. Y.; Nori, F. Edge modes in two- Pancharatnam−Berry and beyond. Nature Reviews Physics 2019, 1, dimensional electromagnetic slab waveguides: Analogs of acoustic 437−449. plasmons. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 102, (44) Biener, G.; Niv, A.; Kleiner, V.; Hasman, E. Formation of 045129. helical beams by use of Pancharatnam−Berry phase optical elements. (23) Bliokh, K. Y.; Leykam, D.; Lein, M.; Nori, F. Topological non- Opt. Lett. 2002, 27, 1875−1877. Hermitian origin of surface Maxwell waves. Nat. Commun. 2019, 10, (45) Bliokh, K. Y.; Gorodetski, Y.; Kleiner, V.; Hasman, E. Coriolis 580. effect in optics: unified geometric phase and spin-Hall effect. Phys. (24) Downing, C. A.; Weick, G. Topological collective plasmons in Rev. Lett. 2008, 101, 030404. bipartite chains of metallic nanoparticles. Phys. Rev. B: Condens. Matter (46) Bliokh, K. Y. Geometrical optics of beams with vortices: Berry Mater. Phys. 2017, 95, 125426. phase and orbital angular momentum Hall effect. Phys. Rev. Lett. (25) Honari-Latifpour, M.; Yousefi, L. Topological plasmonic edge 2006, 97, 043901. states in a planar array of metallic nanoparticles. Nanophotonics 2019, (47) Bomzon, Z.; Biener, G.; Kleiner, V.; Hasman, E. Space-variant 8, 799−806. Pancharatnam−Berry phase optical elements with computer-gener- (26) Maguid, E.; Yulevich, I.; Veksler, D.; Kleiner, V.; Brongersma, ated subwavelength gratings. Opt. Lett. 2002, 27, 1141−1143. M. L.; Hasman, E. Photonic spin-controlled multifunctional shared- (48) Kang, M.; Feng, T.; Wang, H.-T.; Li, J. Wave front engineering aperture antenna array. Science 2016, 352, 1202−1206. from an array of thin aperture antennas. Opt. Express 2012, 20, (27) Tseng, M. L.; Jahani, Y.; Leitis, A.; Altug, H. Dielectric 15882−15890. Metasurfaces Enabling Advanced Optical Biosensors. ACS Photonics (49) Gorodetski, Y.; Nechayev, S.; Kleiner, V.; Hasman, E. 2021, 8, 47. Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux (28) Zhao, Y.; Alu,̀ A. Manipulating light polarization with ultrathin parameter. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, plasmonic metasurfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 125433. 2011, 84, 205428. (50) Katardjiev, I.; Carter, G.; Nobes, M. The application of the (29) Kim, D. S.; Hohng, S. C.; Malyarchuk, V.; Yoon, Y. C.; Ahn, Y. Huygens principle to surface evolution in inhomogeneous, anisotropic H.; Yee, K. J.; Park, J. W.; Kim, J.; Park, Q. H.; Lienau, C. Microscopic and time-dependent systems. J. Phys. D: Appl. Phys. 1989, 22, 1813. OriginofSurface-PlasmonRadiationinPlasmonicBand-Gap (51) Niv, A.; Biener, G.; Kleiner, V.; Hasman, E. Manipulation of the Nanostructures. Phys. Rev. Lett. 2003, 91, 143901. Pancharatnam phase in vectorial vortices. Opt. Express 2006, 14, − (30) Kelf, T. A.; Sugawara, Y.; Baumberg, J. J.; Abdelsalam, M.; 4208 4220. Bartlett, P. N. Plasmonic Band Gaps and Trapped Plasmons on (52) Mittal, S.; Orre, V. V.; Zhu, G.; Gorlach, M. A.; Poddubny, A.; Nanostructured Metal Surfaces. Phys. Rev. Lett. 2005, 95, 116802. Hafezi, M. Photonic quadrupole topological phases. Nat. Photonics − (31) Kocabas, A.; Ertas, G.; Senlik, S. S.; Aydinli, A. Plasmonic band 2019, 13, 692 696. gap structures for surface-enhanced Raman scattering. Opt. Express (53) Kim, M.; Jacob, Z.; Rho, J. Recent advances in 2D, 3D and 2008, 16, 12469−12477. higher-order topological photonics. Light: Sci. Appl. 2020, 9, 130. (32) Biener, G.; Dahan, N.; Niv, A.; Kleiner, V.; Hasman, E. Highly coherent thermal emission obtained by plasmonic bandgap structures. Appl. Phys. Lett. 2008, 92, 081913. (33) Bozhevolnyi, S. I.; Erland, J.; Leosson, K.; Skovgaard, P. M. W.; Hvam, J. M. Waveguiding in Surface Plasmon Polariton Band Gap Structures. Phys. Rev. Lett. 2001, 86, 3008−3011. (34) Okamoto, T.; H’Dhili, F.; Kawata, S. Towards plasmonic band gap laser. Appl. Phys. Lett. 2004, 85, 3968−3970. (35) Grande, M.; Vincenti, M. A.; Stomeo, T.; Morea, G.; Marani, R.; Marrocco, V.; Petruzzelli, V.; D’Orazio, A.; Cingolani, R.; Vittorio, M. D.; de Ceglia, D.; Scalora, M. Experimental demonstration of a novel biosensing platform via plasmonic band gap formation in gold nanopatch arrays. Opt. Express 2011, 19, 21385−21395. (36) Shitrit, N.; Bretner, I.; Gorodetski, Y.; Kleiner, V.; Hasman, E. Optical spin Hall effects in plasmonic chains. Nano Lett. 2011, 11, 2038−2042. (37) Shitrit, N.; Yulevich, I.; Maguid, E.; Ozeri, D.; Veksler, D.; Kleiner, V.; Hasman, E. Spin-Optical Metamaterial Route to Spin- Controlled Photonics. Science 2013, 340, 724−726. (38) Chervy, T.; Azzini, S.; Lorchat, E.; Wang, S.; Gorodetski, Y.; Hutchison, J. A.; Berciaud, S.; Ebbesen, T. W.; Genet, C. Room temperature chiral coupling of valley excitons with spin-momentum locked surface plasmons. ACS Photonics 2018, 5, 1281−1287. (39) Pancharatnam, S. Generalized theory of interference and its applications. Proc. - Indian Acad. Sci., Sect. A 1956, 44, 398−417. (40) Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 1984, 392,45−57. (41) Drezet, A.; Hohenau, A.; Koller, D.; Stepanov, A.; Ditlbacher, H.; Steinberger, B.; Aussenegg, F. R.; Leitner, A.; Krenn, J. R. Leakage radiation microscopy of surface plasmon polaritons. Mater. Sci. Eng., B 2008, 149, 220−229.

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