Letter pubs.acs.org/NanoLett
Metafocusing by a Metaspiral Plasmonic Lens Grisha Spektor,* Asaf David, Bergin Gjonaj, Guy Bartal, and Meir Orenstein Department of Electrical Engineering, Technion, Israel Institute of Technology, 32000 Haifa, Israel S Supporting Information *
ABSTRACT: We designed and realized a metasurface (manipulating the local geometry) spiral (manipulating the global geometry) plasmonic lens, which fundamentally overcomes the multiple efficiency and functionality challenges of conventional in-plane plasmonic lenses. The combination of spirality and metasurface achieves much more efficient and uniform linear-polarization-independent plasmonic focusing. As for functionality, under matched circularly polarized illumination the lens directs all of the power coupled to surface plasmon polaritons (SPPs) into the focal spot, while the orthogonal polarization excites only diverging SPPs that do not penetrate the interior of the lens, achieving 2 orders of magnitude intensity contrast throughout the entire area of the lens. This optimal functional focusing is clearly demonstrated by near-field optical microscopy measurements that are in excellent agreement with simulations and are supported by a detailed theoretical interpretation of the underlying mechanisms. Our results advance the field of plasmonics toward functional detection and the employment of SPPs in smart pixels, near-field microscopy, lithography, and particle manipulation. KEYWORDS: Plasmonics, plasmonic focusing, plasmonic lens, metasurface, functional focusing
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optimized SPP focusing and high-contrast, large-collection-area circularly dichroic focusing. A plasmonic lens is formed by shaped boundaries engraved in a metal layer8 (e.g., Figure 1 a,e). Upon excitation by a vertically impinging light beam, the boundaries serve as secondary sources for SPPs propagating within the plane of the lens, and when the correct geometry is employed, they converge to a focal point (Figure 1d,f). The goal to focus the out-of-plane “transverse” field (Ez), which is by far the dominant SPP field component, carrying most of the electromagnetic energy.1,2,9 The electric field for an SPP propagating in the ±x̂ direction on a metal−dielectric interface defined in the x̂y ̂ plane is
urface plasmon polaritons (SPPs) are evanescent surface waves confined to metal−dielectric interfaces1,2 and hold promise3 in near-field imaging, sensing, lithography, and nanoparticle manipulations. Plasmonic lenses manifest a core significance of the field of plasmonics: confining SPPs to a surface in one dimension and focusing them to a tiny focal spot within the plane of the lens. Such lenses are a major avenue in substantiating those plasmonic promises and have already showed advances toward microscopy4,5 and maskless lithography.6 Moreover, using plasmonic lenses one can condition the generation of a focal spot on a parameter of the illumination, such as its wavelength or polarization state, resulting in functional focusing. By combining such structures with detectors, one can potentially obtain flat smart pixels. Of key importance to all of the aforementioned applications is the power directed toward the focal spot of a plasmonic lens, which ultimately determines the signal-to-noise ratio and the resolution. As will be shown, conventional plasmonic lenses, where the lensing is based on the global geometry of the boundaries, have deficiencies regarding the efficiency and signal-to-background ratio of the focusing. Here we present, both theoretically and experimentally, the deficiencies and functionality challenges of conventional plasmonic lenses. Subsequently we present the mitigation of these challenges by enhancement of the lens with the merit of metasurfaces7 to generate locally arbitrary polarization-dependent phases. We present the design and implementation of a metasurface-based spiral plasmonic lens that achieves both © XXXX American Chemical Society
± ⃗ Espp
⎛ ikz ⎞ ⎜ ⎟ ∝ ⎜ 0 ⎟ × exp( ∓iksppx) ⎜∓k ⎟ ⎝ spp ⎠
(1)
where k⃗ = (kspp, 0, kz) is the wave vector of the SPP. The out-ofplane components of counterpropagating SPPs generated at antipodal points of the lens boundary are in antiphase, and a necessary focusing condition is to compensate for this π phase shift before the focal point is reached. Therefore, using a lens having a mirror-symmetric geometry with respect to the desired Received: April 22, 2015 Revised: August 3, 2015
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DOI: 10.1021/acs.nanolett.5b01571 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Challenges posed by conventional plasmonic lenses. (a, e) Scanning electron microscopy (SEM) images of the (a) spiral and (e) halfcircles plasmonic lenses. The dotted arrows represent the inward−outward coupling symmetry of SPPs by a slit. (b, c) FDTD simulations demonstrating circular dichroism by the spiral lens,15 focusing the matched circular polarization state (c) and resulting in a dark focal spot for the orthogonal state (b). The insets demonstrate the difficulty of obtaining the very demanding spatial resolution required for high-contrast discrimination between the two states. (d) Experimental NSOM results for a spiral plasmonic lens illuminated with linear polarization (white arrow). (f, g) Experimental NSOM results demonstrating the linear dichroism of the half-circles lens between the (f) horizontal and (g) vertical linear polarization states.10 The dotted lines in (d), (f), and (g) emphasize the effective coupling of the angular slit sector to SPPs. (h) Schematic of the NSOM measurement. The plasmonic lenses (gold with engraved slits) are illuminated from the substrate side (red curly arrows). The SPPs generated at the top interface are scattered by the metal tip of the NSOM system. The scattered light is imaged by a self-homodyne detector.
focal spot (e.g., a circular lens) under conventionally polarized (linear, circular, elliptic) illumination would essentially result in destructive interference of the out-of-plane component.8,10,11 One can compensate for this phase shift by employing radially polarized vector beam illumination of the circular lens;9,12 however, it is of less practicality because natural light is not radially polarized, the center of the beam and the lens must coincide, and furthermore, multiple pixel applications are almost unattainable. Alternatively, one can introduce geometrical phase shifts by shaping the engraved boundaries of the lens, forcing SPPs originating at different loci on the boundaries to propagate different distances toward the desired focal spot and therefore to accumulate different phases.10,13,14 A possible mitigation is using an Archimedes spiral plasmonic lens (ASPL) with unity geometrical charge (Figure 1a), described mathematically by
r(θ ) = r0 ±
λspp 2π
·θ
However, the ASPL still poses several major challenges. First, although the spiral discriminates between left and right circular polarization, the actual realization of a circular polarization handedness detection instrument with a finite-size detector at the focal point area will have severe contrast limitations because of the spatial proximity of the lobes of the two focal patterns, as can be seen in Figure 1 b,c. Second, although all of the antipodal points have a path difference of λspp/2, fulfilling the necessary focusing condition, the radial distance toward the focal spot depends on the azimuthal position as defined by eq 2. This linear angular distance dependence perfectly compensates for the linear temporal angular phase delay of a matched circularly polarized illumination field, enabling simultaneous (same phase) arrival of all of the SPPs at the center. However, it is not perfect for linearly polarized illumination, which lacks a temporal phase, or for the instantaneous circular polarization field, where the geometrical spiral phase is dressed onto the SPPs excited at different locations along the arc, resulting in an asynchronous focal spot (see Movie S1). Complementarily this can be understood by the superposition principle. The focal field pattern resulting under illumination with the matched circularly polarized state can be mathematically described approximately by the Bessel function Ez ∝ J0(krr) (Figure 1b). Illumination with the orthogonal polarization state results in a dark focal spot (Figure 1c) and is approximated by Ez ∝ J2(krr). The focal field under linearly polarized illumination will be a linear superposition of the focal fields under the circularly polarized illuminations:
(2)
where r and θ are cylindrical coordinates, λspp is the SPP wavelength, and the sign determines the handedness of the spiral. To date this seems to be the favorable choice for such a lens since by definition the distances from opposite (or antipodal) points on the boundary to the center differ by half a wavelength, fulfilling the necessary focusing condition as described above. The ASPL thus focuses impinging light with arbitrary linear polarization14 and in addition serves as a selective lens for the proper handedness of circular polarization (circularly dichroic lens).15−17 B
DOI: 10.1021/acs.nanolett.5b01571 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 2. (a) SEM image of the MASPL and a structural schematic. (b) Linear phase dependence of the right-propagating (inward-propagating for the spiral) SPPs (blue) and left (outward)-propagating SPPs (black) as a function of the polarization orientation. (c, e) NSOM measurements of the MASPL under linearly polarized illumination (white arrows) and (d, f) FDTD simulations of the MASPL corresponding to the experimental conditions.
Ezlinear ∝ J0 (krr ) + αJ2 (krr )
fields and unidirectional coupling of SPPs with the direction determined by the handedness of circularly polarized illumination. It was shown that by the addition of circular curvature to the structure, radially convergent and divergent SPP fields can be obtained. In order to employ these new coupling characteristics for SPP focusing, the phase of the SPP fields is of crucial importance. We conducted an analytical study of the basic slanted slit column supported by full finite-difference time domain (FDTD) simulations and obtained the polarizationdependent phase of the structure (see the Supporting Information). Plotting this phase as a function of the polarization orientation reveals a linear dependence (Figure 2b). This is equivalent to fixing the polarization orientation and adding curvature to the slanted slit structure, resulting in rotation of the elements with respect to the polarization direction. For a given linear polarization, such a structure would introduce a linear angular phase. The radial distance of the Archimedes spiral boundary from the focal spot, given by eq 2, is also a linear function of the angle. Thus, a correct combination of the metasurface and the spiral geometry annihilates the angular dependence, making all pairs of antipodal points on the boundary have the same effective optical distance and satisfy the basic π shift focusing prerequisite. This mitigates two of the aforementioned challenges posed for focusing of linearly polarized illumination. It should be noted that embedding the metasurface on a circular geometry does not result in focusing, as explained above, and shown both experimentally and theoretically in Chapter 7 in the Supporting Information. As a result, SPPs are generated uniformly by the entire perimeter of the lens and effectively travel the same distance toward the center, accumulate the same phase, and reach the focal spot at the same time, resulting in a synchronous focal spot (see Movie S2 and Movie S3). Figure 2c−f depicts the experimental results and the corresponding FDTD simulations for the metasurfacebased ASPL (MASPL) under linearly polarized illumination,
(3)
where α is a complex coefficient. While the presence of the first term guarantees a bright focal spot for each linearly polarized illumination (Figure 1d), the second term spoils the spatial definition of the focal spot, and even worse, it means that about half of the SPP energy goes into the J2(krr) mode with the dark focal spot instead of being focused. One way to mitigate this is to deform the spiral to get angularly independent radial propagation distances while maintaining the λspp/2 difference of antipodal pointsan approach implemented as a half-circles configuration4,10,13 (Figure 1e). For the half-circles structure, however, the circular dichroism property and the linear polarization orientation invariance are lost, and the resulting lens becomes linearly dichroic,10 focusing only a single linear polarization state (Figure 1f,g). Third, the local SPP generation efficiency at the lens boundary upon illumination by a field E⃗ is proportional to n̂· E⃗ , where n̂ is the normal to the engraved slit. Thus, even for closed lens structures covering the entire angular domain, effectively only ∼0.5 of the slit interacts with light to launch SPPs (intensity-wise), as is evident from the partially shaded plasmonic field patterns shown in Figure 1d,f,g. This is true for both linear polarization and the instantaneous circularly polarized field (which is “linear” for each given time). Finally, equal amounts of SPP power propagate inward and outward from the boundaries, reducing the efficiency by an additional factor of 2. We have found solutions to the above challenges by adding local manipulation of phases using chains of rotated nanoapertures engraved in metals, inspired by structures that have been employed to form metasurfaces with control over the wave fronts of SPP fields.18 The aspect ratio and orientation of the apertures as well as their relative positions allow the SPP wave front to be shaped by controlling the geometrical and temporal phases of the fields. The recently proposed metasurface composed of columns of slanted slits19 provides a uniform coupling efficiency for any orientation of linearly polarized C
DOI: 10.1021/acs.nanolett.5b01571 Nano Lett. XXXX, XXX, XXX−XXX
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tional SPP excitation. The other parameters can be optimized to obtain maximal energy in the focal spot while retaining the functionality of the metasurface. A simple optimization procedure was conducted to increase the density of the nanoapertures along the curve as described in the Supporting Information and can be further improved by including more structural parameters. A transmission-mode aperture-less near-field scanning optical microscope (NSOM) was used to directly map the amplitude of the near field on the gold−air interface side of the sample. The sample was positioned on a moving stage and illuminated from below with a linearly polarized beam at a wavelength λ0 = 671 nm. Because of the relatively large scanning area, the illumination beam was weakly focused to a 30 μm spot in order to maintain an approximately constant illumination phase and amplitude over the scanning area. A metallic (Pt/Ir) tip scattered predominantly the out-of-plane electric field component into a pseudoheterodyne detection unit, which was used to remove the background signals and to provide phase information on the measured field.21 The resolution of the NSOM is limited by the size of the tip apex and varies between 10 and 20 nm, a high resolution for our wavelength of interest. The results are presented in Figures 2 and 3 alongside the simulation results. Additional experimental results as well as quantitative and comparative analysis are provided in the Supporting Information. In order to study the relative efficiency, we compared the energies in the focal spots of the ASPL and the MASPL using FDTD simulations. To isolate the contribution of our designs, the radial parameter of the underlying Archimedes’ spiral structure, r0, was taken to be the same for the conventional and metasurface-based structures. The total slit area was swept by increasing the width of the slit of the ASPL and the density and width of the nanoapertures for the MASPL as described in the Supporting Information. Figure 4 shows the focal spot power in arbitrary units for both linearly and circularly polarized illumination. An improvement by a factor of ∼2 is achieved for both polarizations, which is sufficient as a proof of concept; however a more rigorous optimization procedure might produce slightly better results. The thickness of the gold layer was the same for the two lenses, and it can be further optimized
which clearly show the uniform generation of SPPs from the entire perimeter of the lens and the single focal spot. The circularly polarized illumination effectively experiences only the spiral linear angular phase, and thus, the MASPL retains its selective-handedness-focusing property. Moreover, the latter property is achieved here with enhanced efficiency and much higher spatial contrast. The MASPL directs all of the coupled power of the matched circular polarization inward, while the power of the opposite circular polarization is directed outward and does not penetrate the lens region (Figure 3). The
Figure 3. Experimental NSOM results (a,b) and corresponding FDTD simulations (c,d) of the MASPL under circularly polarized illumination (solid white arrows). The dotted arrows represent the SPP propagation direction inward only (c) and outward only (d).
MASPL solves all of the challenges related to SPP focusing of circularly polarized illumination, resulting in “perfect” focusing in the sense that all of the power coupled to SPPs reaches the focal spot. The experimental results demonstrate 2 orders of magnitude contrast in intensity between the focused and expelled fields’ situations. A minute residual field penetrates the interior of the lens (Figure 3b) as a result of scattering due to imperfect fabrication of the lens. The experimental results described above were measured on a lens fabricated by focused-ion-beam milling on a 175 nm thick gold layer sputtered on a glass substrate. The SPP wavelength at a gold−air interface at our operating wavelength of 671 nm was calculated using the optical constants of metals reported by Johnson and Christy20 and is λspp ≈ 650 nm. The parameters for the structure depicted in the inset of Figure 2b are S = λspp/4 = 162.5 nm, D = 325 nm, L = 250 nm, and W = 100 nm. The slits are slanted at θ1 = 135° and θ2 = 45° with respect to the horizontal axis, in accord with ref 19. The array of elements was placed on a curve defined by an Archimedes’ spiral (eq 2) with r0 = 5 μm. The basic requirement is that at least one arm of the spiral is constructed, i.e., that elements are placed on the curve for θ ∈ [0, 2π]. The critical parameter here is S, which determines the geometrical phase compensation of the temporal phase lag between the two slanted slit columns under circularly polarized illumination, leading to the unidirec-
Figure 4. Focal spot intensity in arbitrary units as a function of total slit area. The dotted lines represent the Archimedes spiral lens under linearly (blue) and circularly (red) polarized illumination, and the solid lines represent the correspondingly illuminated MASPL. D
DOI: 10.1021/acs.nanolett.5b01571 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters to improve the global efficiency of both structures.22 Finally, it was previously shown that the optimal SPP coupling efficiency is achieved for a slit width of 0.23λspp.23 This explains the saturation of the graphs of the ASPL in Figure 4. For the MASPL, however, we cannot increase the width of the apertures to reach this limit and obtain saturation because we are limited by geometrical constraints ensuring the proper functionality of the metasurface. It should be noted that this is fundamental for any invariant structure (i.e., operating indifferently for the two linear polarizations) to incur a 3 dB loss one way or another. To further enhance the power at the focal spot, several windings can be resonantly added to the lens by choosing θ ∈ [0, 2mπ] with m > 1 in eq 2, resulting in a Bragg-like enhancement. Experimental results for such a lens are presented in the Supporting Information. In summary, the proper combination of global and local geometries enables the MASPL to mitigate the efficiency and functionality challenges posed by conventional SPP lenses. It provides uniform, efficient, polarization-orientation-independent focusing for linear polarization. In addition, the lens distinguishes between right and left circularly polarized illumination, providing optimized focusing for the matched circular polarization. The high-contrast, large-area functional focusing allows seamless integration with actual detectors, encompassing a substantial portion of the lens interior, which is made possible with the incorporation of the metasurface.
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(3) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Nature 2003, 424, 824−830. (4) Gjonaj, B.; David, A.; Blau, Y.; Spektor, G.; Orenstein, M.; Dolev, S.; Bartal, G. Nano Lett. 2014, 14, 5598−5602. (5) Frank, B.; Weiss, T.; Kahl, P.; Horn-von Hogen, M.; Meyer zu Heringdorf, F. J.; Fu, L.; Sigle, W.; Giessen, H. Presented at NanoMeta 2015: 5th International Topical Meeting on Nanophotonics and Metamaterials, Seefeld, Tirol, Austria, January 2015; paper TUE2s-O04. (6) Pan, L.; Park, Y.; Xiong, Y.; Ulin-Avila, E.; Wang, Y.; Zeng, L.; Xiong, S.; Rho, J.; Sun, C.; Bogy, D. B.; Zhang, X. Sci. Rep. 2011, 1, 175. (7) Genevet, P.; Capasso, F. Rep. Prog. Phys. 2015, 78, 024401. (8) Liu, Z.; Steele, J. M.; Srituravanich, W.; Pikus, Y.; Sun, C.; Zhang, X. Nano Lett. 2005, 5, 1726−1729. (9) Lerman, G. M.; Yanai, A.; Levy, U. Nano Lett. 2009, 9, 2139− 2143. (10) Spektor, G.; David, A.; Gjonaj, B.; Gal, L.; Orenstein, M. 2014, arXiv:1406.0115. arXiv.org e-Print archive. http://arxiv.org/abs/1406. 0115. (11) Steele, J. M.; Liu, Z.; Wang, Y.; Zhang, X. Opt. Express 2006, 14, 5664−5670. (12) Chen, W.; Abeysinghe, D. C.; Nelson, R. L.; Zhan, Q. Nano Lett. 2009, 9, 4320−4325. (13) Fang, Z.; Peng, Q.; Song, W.; Hao, F.; Wang, J.; Nordlander, P.; Zhu, X. Nano Lett. 2011, 11, 893−897. (14) Li, J.; Yang, C.; Zhao, H.; Lin, F.; Zhu, X. Opt. Express 2014, 22, 16686−16693. (15) Gorodetski, Y.; Niv, A.; Kleiner, V.; Hasman, E. Phys. Rev. Lett. 2008, 101, 043903. (16) Bachman, K.; Peltzer, J.; Flammer, P.; Furtak, T.; Collins, R.; Hollingsworth, R. Opt. Express 2012, 20, 1308−1319. (17) Yang, S.; Chen, W.; Nelson, R. L.; Zhan, Q. Opt. Lett. 2009, 34, 3047−3049. (18) Shitrit, N.; Bretner, I.; Gorodetski, Y.; Kleiner, V.; Hasman, E. Nano Lett. 2011, 11, 2038−2042. (19) Lin, J.; Mueller, J. B.; Wang, Q.; Yuan, G.; Antoniou, N.; Yuan, X.-C.; Capasso, F. Science 2013, 340, 331−334. (20) Johnson, P. B.; Christy, R.-W. Phys. Rev. B 1972, 6, 4370−4379. (21) Ocelic, N.; Huber, A.; Hillenbrand, R. Appl. Phys. Lett. 2006, 89, 101124. (22) Takakura, Y. Phys. Rev. Lett. 2001, 86, 5601−5603. (23) Lalanne, P.; Hugonin, J.; Rodier, J. J. J. Opt. Soc. Am. A 2006, 23, 1608−1615.
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b01571. Theoretical calculations of the polarization-dependent phase of the slit column, intermediate FDTD simulation results, Bragg-enhanced MASPL experimental results, description of the optimization procedure, and a detailed quantitative and comparative analysis of the experimental results (PDF) Movie S1 showing the asynchronous focal spot obtained upon illumination of the ASPL with linearly polarized light (MPG) Movie S2 showing the synchronous focal spot obtained upon illumination of the MASPL with vertically polarized light (MPG) Movie S3 showing the synchronous focal spot obtained upon illumination of the MASPL with horizontally polarized light (MPG) Movie S4 showing the MASPL under illumination with linearly polarized light in various orientations (MPG)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Maier, S. A. Plasmonics: Fundamentals and Applications; Springer: New York, 2007. (2) Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings; Springer: Berlin, 1988. E
DOI: 10.1021/acs.nanolett.5b01571 Nano Lett. XXXX, XXX, XXX−XXX
