Letter pubs.acs.org/NanoLett
Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface Ching-Fu Chen,† Chen-Ta Ku,† Yi-Hsin Tai,‡ Pei-Kuen Wei,‡ Heh-Nan Lin,§ and Chen-Bin Huang*,† †
Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan § Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan ‡
S Supporting Information *
ABSTRACT: Nanocavities inscribed in a gold thin film are optimized and designed to form a metasurface. We demonstrate both numerically and experimentally the creation of surface plasmon (SP) vortex carrying orbital angular momentum in the metasurface under linearly polarized optical excitation that carries no optical angular momentum. Moreover, depending on the orientation of the exciting linearly polarized light, we show that the metasurface is capable of providing dynamic switching between SP vortex formation or SP subwavelength focusing. The resulting SP intensities are experimentally measured using a near-field scanning optical microscope and are found in excellent quantitative agreements as compared to the numerical results. KEYWORDS: Orbital angular momentum, metasurface, optical vortex, plasmonics
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generated under circularly polarized excitations.12−20 This means that the functionality of the plasmonic devices were to convert the far-field SAM carried by the circularly polarized excitation beams into OAM in the SP near-field. We note here SP vortex can be generated by a radially polarized beam.21 However, the preparation of radially polarized beam typically requires a complicated setup. The aim of this Letter is to create optical near-field OAM at the metal−dielectric interface by using excitation wave carrying no angular momentum empowered by an optical metasurface. Metasurface is a new class of planar optical component comprised of designed subwavelength scatterers arranged with subwavelength separations. Recently, metasurfaces have demonstrated wide flexibilities in providing anomalous light bending,22−25 controllable propagation of surface plasmon polaritons,26 spin-controlled optical Rashba effect,27 the conversion from far-field SAM to far-field OAM,28−30 the conversion between far-field polarizations,31,32 as well as the generation of far-field optical vortex beam using linear polarization.32 The flexibility in designing a metasurface is exploited here and the functionality of a metasurface is extended to create near-field optical OAM. For the first time to our knowledge, we demonstrate both numerically and experimentally the creation of near-field vortex carrying OAM with uniform linear polarization. The metasurface is formed by
ptical waves carrying angular momenta have attracted immense research attentions in the past decades.1,2 Optical angular momenta are classified as either spin angular momentum (SAM) or orbital angular momentum (OAM). SAM is associated with circularly polarized light, where the spin of the photon leads to rotation of the instantaneous electric field vector as the wave propagates. In contrast, lightwave that carries OAM in free-space exhibits a helical phase front and is often referred to as an optical vortex. An optical vortex incorporates an azimuthal spatial phase in the mathematical form of ejqϕ, where ϕ is the azimuthal angle in the cylindrical coordinate, and q is the topological charge that determines the number of phase discontinuities (abrupt phase jumps from −π to π) within a 2π range.2 In free-space optics, optical vortex beams can be generated by converting fundamental Gaussian beams into Laguerre-Gaussian beams through diffractive optical elements,3 using Pancheratnam-Berry phase optical elements,4 combination of cylindrical lenses,5 or spatial light modulators.6,7 Free-space vortex beams have found applications in trapping8 and rotating microparticles9,10 and recently in high-capacity free-space data transmissions.11 On the other hand, the generation of vortices in the optical near-field has made much progress.12−20 These near-field vortices are typically generated through the excitation of surface plasmons (SPs) at the metal−dielectric interface as the result of collective free electron resonances induced by external electromagnetic waves. SP vortices have been generated in a wide variety of plasmonic geometries, such as in plasmonic Archimedes spiral,12−15 chiral plasmonic slits,16−19 and plasmonic rings.20,21 However, to date, SP vortices have been © XXXX American Chemical Society
Received: February 12, 2015 Revised: March 18, 2015
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DOI: 10.1021/acs.nanolett.5b00601 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Creating spinlike SP fields using optical linear polarizations. (a) A nanocavity formed by an asymmetric crossed air-slit is embedded in a gold thin film. The arm-lengths along x- and y-directions are denoted as L1 and L2, respectively. The slit width is defined as w. The optimized nanocavity is define by L1 = 500 nm, L2 =780 nm, and w = 200 nm. The green (blue) dot denotes the observation point at the gold−air interface for the air-slit along y (x)-direction. (b,c) The relative amplitude and phase relationships between the two observation points under −45 and 45° linearly polarized optical excitations, respectively. The time values are normalized to the carrier cycle. (d,e) Calculated instantaneous Ez field at 10 nm above the gold−air interface under −45 and 45° linearly polarized optical excitations, respectively. The orientation of the linearly polarized light is denoted by the arrow.
nanocavities embedded in a gold thin film. The design of the nanocavities is optimized to provide localized SP vortex source under linearly polarized excitation. The nanocavities are arranged in a chiral geometry to form a metasurface. Moreover, we show that depending on the orientation of the exciting linearly polarized light, the metasurface is capable of providing dynamic switching between SP vortex formation or SP subwavelength focusing. The resulting SP fields are experimentally measured using a near-field scanning optical microscope and are found in excellent agreement as compared to our numerical results both qualitatively and quantitatively. The ability to create and switch between SP OAM and focusing could find immediate interesting applications in plasmonicassisted optical trapping15,33−36 and particle rotation.15,37−40 Our metasurface is designed and optimized using the threedimensional finite-difference time-domain (FDTD) method simulations.41 Because our target is in creating SP vortex on a flat metal surface for future potential in selective particle trapping or rotation,15 our metasurface is therefore comprised of nanovoids embedded within a metallic thin film to preserve its flatness. This is in contrast to metasurfaces formed by metallic nanoscopic islands/antennas in prior demonstrations.22−32 We start explaining our design rule with the numerical optimization to the single element forming the metasurface. Figure 1a shows the schematics of such single nanocavity. The nanocavity is realized by embedding an asymmetric crossed air-slit onto a gold thin film of 200 nm thick over a silica substrate. Here L1 and L2 denote the arm lengths of the crossed air-slit in the x- and y-directions, respectively, and w is the width of the slits. The optical excitation source is a plane wave normally illuminating the nanocavity from the substrate side with a vacuum wavelength of 1545 nm. This results in surface plasmon polaritons (SPPs) propagating along the gold−air interface (x−y plane) that are mainly polarized in the z-direction (Ez field). In our simulations, the dielectric constant of gold is taken as −92.45-j11.02, giving a SPP wavelength of λspp = 1536 nm.
We note here our nanocavity can be viewed as the reciprocal structure of a crossed optical antenna that was used to create near-field SAM within the air gap,42 The optimization rule for our nanocavity follows closely to an optical antenna capable of generating far-field SAM under linearly polarized excitation.43 Because of the structural inversion, the design rule is related through the Babinet’s principle.44 We note here although the in-plane magnetic fields (Hx and Hy) dominate due to effective magnetic resonances, the electric field of the SPP is only polarized in the z-direction and its magnitude is a scaled version of the resonating magnetic field and is therefore used as the metric in the design optimization. Each slit can be viewed as a dipole oscillator giving rise to length-dependent SPP amplitude and phase responses. The lengths L1 and L2 are optimized by monitoring the SP fields at two observation points (blue and green dots at the gold−air interface) in Figure 1a for two attributes: (1) achieving a −π/2 (π/2) temporal phase delay in the y-slit (green dot) as compared to the x-slit (blue dot) when the optical source is 45° (−45°) linearly polarized, respectively; and (2) simultaneously approaching nearly equal SPP field amplitudes at the two observation points. The optimized nanocavity is defined by parameters L1 = 500 nm, L2 = 780 nm, and w = 200 nm. The recorded Ez fields as a function of time normalized to the carrier cycle at the two observation points are displayed in Figure 1b,c, confirming that the temporal phase delays are exactly π/2 or −π/2 when the optical excitation are linearly polarized in the −45 and 45°, respectively. The orientations of the linearly polarized optical excitations are labeled using the arrows. The colors of the traces correspond to that of the observation points. The unequal amplitude between the two observation points will be addressed later in the discussion of the metasurface. The resulting instantaneous Ez fields within the vicinity of the nanocavity are displayed in Figure 1d (−45° polarized) and Figure 1e (45° polarized). These figures illustrate distinct spatial and phase characteristics can be selectively excited depending on the source polarizations. Figure 1d shows that a B
DOI: 10.1021/acs.nanolett.5b00601 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 2. Design of the metasurface. (a) The optimized nanocavities are arranged as an Archimedes spiral defined by r0 = 3λspp and m = 1. (b,c) Resulting instantaneous Ez vortex field and spatial phase profile created in the metasurface under −45° linearly polarized excitation, respectively. (d,e) Resulting instantaneous Ez focusing field and spatial phase profile generated in the metasurface under 45° linearly polarized excitation, respectively. SP field profiles derived by analytical solutions are shown as insets in (b,d).
numerical findings, the ± π/2 temporal phase difference created by the two arms is extremely critical. On the other hand, slightly unequal amplitudes as shown in Figure 1b,c play a less important role. To this end, the generation of SP vortex carrying OAM using linearly polarized excitation is successfully demonstrated via numerical analyses. We then examine the field and phase behaviors of our metasurface under 45° linearly polarized optical excitation. Figure 2d,e shows the resulting instantaneous SP field and the spatial phase patterns, respectively. The resulting Ez SP field forms a subwavelength focusing spot that carries neither phase singularity nor optical angular momentum. This can be understood as the left-hand localized SP vortex source SP field (spin σ = −1) is canceled by the geometrical charge of the Archimedes spiral, yielding a q = σ + m = 0 focusing spot. Spatial distributions of the vortex and focusing fields as derived through analytical solutions that conform to the Bessel functions of the first kind13,18 are provided as insets in Figure 2b,d. The propagation behaviors of SPP on the designed metasurface are experimentally measured using a near-field scanning optical microscope (NSOM). Our sample is prepared by thermally evaporating a gold film of 200 nm onto a glass substrate followed by focused ion beam milling (see Supporting Information for experimental setup and sample scanning electron microscope images). Such gold thickness helps to prevent saturating the photodetector when the NSOM probe approaches the nanocavities and enables later quantitative comparisons against our numerical results. We note here that the width of the slits in forming the nanocavity also affects the resulting vortex/focusing formation (see Supporting Information for details on the effect of w value). In our experiments, the metasurface is comprised of nanocavities arranged as a threeturn plasmonic Archimedes spiral (defined by ϕ ranging from 0 to 6π). The three-turn geometry is adopted to enhance the SPP field strength under the presence of optical damping to facilitate the near-field measurements as well as in creating SP vortex with better azimuthal uniformity. The resulting SP field intensities are experimentally measured using a commercial NSOM scanning head (NT-MDT NTEGRA Solaris) with homemade tapered fiber probes (see Supporting Information for NSOM probe preparation and concerns).45
counterclockwise localized SP vortex source (right-handed) is generated by −45° polarized excitation, while Figure 1e shows that SPPs with an opposite sense of rotation (left-handed) are excited by the 45° polarized source (see Supporting Information for movies for the sense of field rotations). These two examples already demonstrate that planar SP spin angular momenta can be generated using linearly polarized optical excitations. Our next step is to exploit the localized SP vortex source synthesized by a single nanocavity for the creation of SP vortex. As shown in Figure 2a, 20 length-optimized nanocavities are arranged geometrically as an Archimedes spiral12−15 to form a metasurface. A right-handed Archimedes spiral (with a geometrical charge of m = +1) is mathematically defined in the cylindrical coordinate as r(ϕ) = r0 + (ϕλspp)/2π, where r denotes the distance between the spiral and the origin O, r0 is the starting distance, ϕ is the azimuthal angle, and λspp is the SPP wavelength. We define here r0 = 3λspp to facilitate later near-field optical measurements. We first examine the field and phase behaviors of the designed metasurface under −45° linearly polarized optical excitation. In this case, SP vortex carrying OAM is successfully created. This can be understood as the right-handed (spin σ = +1) localized SP vortex source fields of the nanocavities add up with the geometrical charge of the Archimedes spiral, leading to the creation of SP vortex with a topological charge of q = σ + m = 2. This is indicated as four field petals within a 2π azimuthal range can be found in the instantaneous Ez SP field shown in Figure 2b. The four-petals revolve in a counterclockwise direction at the rate of the optical carrier cycle, in accordance with the chirality and the phase difference provided by a single nanocavity (see Supporting Information for movies). The fourpetal field distribution is associated with vortex with a topological charge of 2. This is corroborated in Figure 2c, where the instantaneous spatial phase profile reveals two evident abrupt phase jumps from −π to π within a 2π azimuthal range. We further confirmed that the spatial line-phase trace along the dotted circle in Figure 2c does exhibit a linear increment as a function of ϕ. This assures that the resulting SP vortex is having an integer topological charge of 2 (see Supporting Information for the line-phase plot). We note here the final fine-tuning to the nanocavity arm lengths is performed through monitoring the integer topological charge. In our C
DOI: 10.1021/acs.nanolett.5b00601 Nano Lett. XXXX, XXX, XXX−XXX
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revolves at the speed of optical carrier and thus cannot be measured. The ability to dynamically switch to subwavelength focusing is further investigated. The NSOM measurement and FDTD calculated time-averaged intensity for the metasurface under 45° linearly polarized excitation are shown as Figure 4a,b,
Figure 3a shows the experimentally measured NSOM result when the metasurface is illuminated with a −45° linearly
Figure 3. Creation of experimental SP OAM under −45° linearly polarized excitation. (a) NSOM measurement result. (b) Timeaveraged intensity calculated through FDTD method. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. (c) Comparison between NSOM measured and FDTD calculated intensities along the x-direction (green dashed lines in both (a) and (b)). (d) Comparison between NSOM measured and FDTD calculated intensities along the y-direction (blue dashed lines in both (a) and (b)). SP intensity profile derived by analytical solution is shown as inset in (b).
Figure 4. Generation of experimental SP subwavelength focusing under 45° linearly polarized excitation. (a) NSOM measurement result. (b) Time-averaged intensity calculated through FDTD method. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. (c) Comparison between NSOM measured and FDTD calculated intensities along the x-direction (green dashed lines in both (a,b)). (d) Comparison between NSOM measured and FDTD calculated intensities along the y-direction (blue dashed lines in both (a,b)). SP intensity profile derived by analytical solution is shown as inset in (b).
polarized excitation. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. It is apparent that the origin is a dark intensity spot. Such singularity provides a direct evidence for the successful generation of SP vortex carrying OAM in our metasurface. The experimental NSOM scan result is further compared with the FDTD simulation result. Since what is measured through the NSOM is the time-averaged intensity, Figure 3b shows the FDTD timeaveraged intensity pattern obtained through integration over four optical carrier cycles. We note here the numerical result is obtained after performing numerical spatial convolution given a finite point spread function of the NSOM fiber probe (see Supporting Information for details on convolution mechanisms). Close examinations between the two figures reveal excellent qualitative agreements: they both show a dark origin being surrounded by annular bright and dark rings. The results are further compared quantitatively in the vicinity of the spiral origin: Figure 3c (d) depicts the measured NSOM (solid trace) and FDTD (dotted trace) intensity values along the green (blue) dashed lines in Figure 3a,b. Excellent quantitative agreements are observed both in terms of the positions of the intensity peaks and valleys, as well as the relative magnitudes. Furthermore, the NSOM measurement conforms to the second-order Bessel function, demonstrating an evident signature of near-field vortex with a topological charge of 2 as anticipated. We thus confirm that an OAM-carrying SP vortex with a topological charge of 2 is experimentally generated in our designed metasurface under linearly polarized optical excitation. We note here the spatial phase profile of SP vortex
respectively. A strong, bright intensity spot at the spiral origin can be clearly observed in both figures. The line intensity traces near the spiral origin shown in Figure 4c,d along the x- and ydirections again reveal excellent agreements between our NSOM scan and FDTD result. The resulting intensity distribution conforms to the expected zeroth-order Bessel function, demonstrating an evident a subwavelength focusing spot carrying no OAM. The deconvoluted full width halfmaximum spot diameter for the focused spot is 530 nm. We thus verify successful experimental demonstration on subwavelength focusing in our designed gold metasurface. In summary, unit nanocavity embedded in a gold thin film is optimized for the creation of localized SP vortex source fields under linearly polarized optical excitations. The nanocavities are then arranged as an Archimedes spiral to form a metasurface. We demonstrate both numerically and experimentally that SP vortex carrying optical orbital angular momentum in our designed metasurface can be created under linearly polarized optical excitation that carries no angular momentum. In our experiment, an SP vortex with an integer topological charge of two is created under a −45° linearly polarized optical excitation. A subwavelength focusing spot can be generated in the same metasurface when the orientation of the linearly polarization is changed to 45°. The resulting SP fields are experimentally measured using a nearD
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Nano Letters field scanning optical microscope and are found in excellent quantitative agreements as compared to the numerical results.
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AUTHOR INFORMATION
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S Supporting Information *
Additional information, figures, and movies. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. Author Contributions
C.-F.C. and C.-T.K. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the support from the Ministry of Science and Technology of Taiwan under Grant MOST 103-2112-M007-017-MY3, National Tsing Hua University under Grant 103N2081E, and the Ministry of Education, Taiwan (Aim for the Top University Program). Technical support on focusedion beam milling from NanoCore, the Core Facilities for Nanoscience and Nanotechnology at Academia Sinica in Taiwan, is acknowledged.
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REFERENCES
(1) Padgett, M.; Bowman, R. Nat. Photonics 2011, 5, 343−348. (2) Nye, J. F. Natural Focusing and Fine Structure of Light; IOP Press: Bristol, U.K., 1999. (3) Heckenberg, N. R.; McDuff, R.; Smith, C. P.; White, A. Opt. Lett. 1992, 17, 221−223. (4) Biener, G.; Niv, A.; Kleiner, V.; Hasman, E. Opt. Lett. 2002, 27, 1875−1877. (5) Beijersbergen, M. W.; Allen, L.; van der Veen, H.; Woerdman, J. P. Opt. Commun. 1993, 96, 123−132. (6) Wulff, K. D.; Cole, D. G.; Clark, R. L.; DiLeonardo, R.; Leach, J.; Cooper, J.; Gibson, G.; Padgett, M. J. Opt. Express 2006, 14, 4169− 4174. (7) Jesacher, A.; Schwaighofer, A.; Fürhapter, S.; Maurer, C.; Bernet, S.; Ritsch-Marte, M. Opt. Express 2007, 15, 5801−5808. (8) Friese, M. E. J.; Enger, J.; Rubinsztein-Dunlop, H.; Heckenberg, N. R. Phys. Rev. A 1996, 54, 1593−1596. (9) Simpson, N. B.; Dholakia, K.; Allen, L.; Padgett, M. J. Opt. Lett. 1997, 22, 52−54. (10) Friese, M.; Nieminen, T.; Heckenberg, N. R.; RubinszteinDunlop, H. Nature 1998, 394, 348−350. (11) Wang, J.; Yang, J.-Y.; Fazal, I. M.; Ahmed, N.; Yan, Y.; Huang, H.; Ren, Y.; Yue, Y.; Dolinar, S.; Tur, M.; Willner, A. E. Nat. Photonics 2012, 6, 488−496. (12) Gorodetski, Y.; Niv, A.; Kleiner, V.; Hasman, E. Phys. Rev. Lett. 2008, 101, 043903. (13) Yang, S.; Chen, W.; Nelson, R. L.; Zhan, Q. Opt. Lett. 2009, 34, 3047−3049. (14) Chen, W.; Abeysinghe, D. C.; Nelson, R. L.; Zhan, Q. Nano Lett. 2010, 10, 2075−2079. (15) Tsai, W.-Y.; Huang, J.-S; Huang, C.-B. Nano Lett. 2014, 14, 547−552. (16) Kim, H.; Park, J.; Cho, S.-W.; Lee, S.-Y.; Kang, M.; Lee, B. Nano Lett. 2010, 10, 529−536. (17) Cho, S.-W.; Park, J.; Lee, S.-Y.; Kim, H.; Lee, B. Opt. Express 2012, 20, 10083−10094. (18) Ku, C.-D.; Huang, W.-L.; Huang, J.-S.; Huang, C.-B. IEEE Photonics J. 2013, 5, 4800409. (19) Ku, C.-T.; Lin, H.-N.; Huang, C.-B. Appl. Phys. Lett. 2015, 106, 053112. E
DOI: 10.1021/acs.nanolett.5b00601 Nano Lett. XXXX, XXX, XXX−XXX
Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface Ching-Fu Chen,† Chen-Ta Ku,† Yi-Hsin Tai,‡ Pei-Kuen Wei,‡ Heh-Nan Lin,§ and Chen-Bin Huang*,† †
Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan § Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan ‡
S Supporting Information *
ABSTRACT: Nanocavities inscribed in a gold thin film are optimized and designed to form a metasurface. We demonstrate both numerically and experimentally the creation of surface plasmon (SP) vortex carrying orbital angular momentum in the metasurface under linearly polarized optical excitation that carries no optical angular momentum. Moreover, depending on the orientation of the exciting linearly polarized light, we show that the metasurface is capable of providing dynamic switching between SP vortex formation or SP subwavelength focusing. The resulting SP intensities are experimentally measured using a near-field scanning optical microscope and are found in excellent quantitative agreements as compared to the numerical results. KEYWORDS: Orbital angular momentum, metasurface, optical vortex, plasmonics
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generated under circularly polarized excitations.12−20 This means that the functionality of the plasmonic devices were to convert the far-field SAM carried by the circularly polarized excitation beams into OAM in the SP near-field. We note here SP vortex can be generated by a radially polarized beam.21 However, the preparation of radially polarized beam typically requires a complicated setup. The aim of this Letter is to create optical near-field OAM at the metal−dielectric interface by using excitation wave carrying no angular momentum empowered by an optical metasurface. Metasurface is a new class of planar optical component comprised of designed subwavelength scatterers arranged with subwavelength separations. Recently, metasurfaces have demonstrated wide flexibilities in providing anomalous light bending,22−25 controllable propagation of surface plasmon polaritons,26 spin-controlled optical Rashba effect,27 the conversion from far-field SAM to far-field OAM,28−30 the conversion between far-field polarizations,31,32 as well as the generation of far-field optical vortex beam using linear polarization.32 The flexibility in designing a metasurface is exploited here and the functionality of a metasurface is extended to create near-field optical OAM. For the first time to our knowledge, we demonstrate both numerically and experimentally the creation of near-field vortex carrying OAM with uniform linear polarization. The metasurface is formed by
ptical waves carrying angular momenta have attracted immense research attentions in the past decades.1,2 Optical angular momenta are classified as either spin angular momentum (SAM) or orbital angular momentum (OAM). SAM is associated with circularly polarized light, where the spin of the photon leads to rotation of the instantaneous electric field vector as the wave propagates. In contrast, lightwave that carries OAM in free-space exhibits a helical phase front and is often referred to as an optical vortex. An optical vortex incorporates an azimuthal spatial phase in the mathematical form of ejqϕ, where ϕ is the azimuthal angle in the cylindrical coordinate, and q is the topological charge that determines the number of phase discontinuities (abrupt phase jumps from −π to π) within a 2π range.2 In free-space optics, optical vortex beams can be generated by converting fundamental Gaussian beams into Laguerre-Gaussian beams through diffractive optical elements,3 using Pancheratnam-Berry phase optical elements,4 combination of cylindrical lenses,5 or spatial light modulators.6,7 Free-space vortex beams have found applications in trapping8 and rotating microparticles9,10 and recently in high-capacity free-space data transmissions.11 On the other hand, the generation of vortices in the optical near-field has made much progress.12−20 These near-field vortices are typically generated through the excitation of surface plasmons (SPs) at the metal−dielectric interface as the result of collective free electron resonances induced by external electromagnetic waves. SP vortices have been generated in a wide variety of plasmonic geometries, such as in plasmonic Archimedes spiral,12−15 chiral plasmonic slits,16−19 and plasmonic rings.20,21 However, to date, SP vortices have been © XXXX American Chemical Society
Received: February 12, 2015 Revised: March 18, 2015
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DOI: 10.1021/acs.nanolett.5b00601 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Creating spinlike SP fields using optical linear polarizations. (a) A nanocavity formed by an asymmetric crossed air-slit is embedded in a gold thin film. The arm-lengths along x- and y-directions are denoted as L1 and L2, respectively. The slit width is defined as w. The optimized nanocavity is define by L1 = 500 nm, L2 =780 nm, and w = 200 nm. The green (blue) dot denotes the observation point at the gold−air interface for the air-slit along y (x)-direction. (b,c) The relative amplitude and phase relationships between the two observation points under −45 and 45° linearly polarized optical excitations, respectively. The time values are normalized to the carrier cycle. (d,e) Calculated instantaneous Ez field at 10 nm above the gold−air interface under −45 and 45° linearly polarized optical excitations, respectively. The orientation of the linearly polarized light is denoted by the arrow.
nanocavities embedded in a gold thin film. The design of the nanocavities is optimized to provide localized SP vortex source under linearly polarized excitation. The nanocavities are arranged in a chiral geometry to form a metasurface. Moreover, we show that depending on the orientation of the exciting linearly polarized light, the metasurface is capable of providing dynamic switching between SP vortex formation or SP subwavelength focusing. The resulting SP fields are experimentally measured using a near-field scanning optical microscope and are found in excellent agreement as compared to our numerical results both qualitatively and quantitatively. The ability to create and switch between SP OAM and focusing could find immediate interesting applications in plasmonicassisted optical trapping15,33−36 and particle rotation.15,37−40 Our metasurface is designed and optimized using the threedimensional finite-difference time-domain (FDTD) method simulations.41 Because our target is in creating SP vortex on a flat metal surface for future potential in selective particle trapping or rotation,15 our metasurface is therefore comprised of nanovoids embedded within a metallic thin film to preserve its flatness. This is in contrast to metasurfaces formed by metallic nanoscopic islands/antennas in prior demonstrations.22−32 We start explaining our design rule with the numerical optimization to the single element forming the metasurface. Figure 1a shows the schematics of such single nanocavity. The nanocavity is realized by embedding an asymmetric crossed air-slit onto a gold thin film of 200 nm thick over a silica substrate. Here L1 and L2 denote the arm lengths of the crossed air-slit in the x- and y-directions, respectively, and w is the width of the slits. The optical excitation source is a plane wave normally illuminating the nanocavity from the substrate side with a vacuum wavelength of 1545 nm. This results in surface plasmon polaritons (SPPs) propagating along the gold−air interface (x−y plane) that are mainly polarized in the z-direction (Ez field). In our simulations, the dielectric constant of gold is taken as −92.45-j11.02, giving a SPP wavelength of λspp = 1536 nm.
We note here our nanocavity can be viewed as the reciprocal structure of a crossed optical antenna that was used to create near-field SAM within the air gap,42 The optimization rule for our nanocavity follows closely to an optical antenna capable of generating far-field SAM under linearly polarized excitation.43 Because of the structural inversion, the design rule is related through the Babinet’s principle.44 We note here although the in-plane magnetic fields (Hx and Hy) dominate due to effective magnetic resonances, the electric field of the SPP is only polarized in the z-direction and its magnitude is a scaled version of the resonating magnetic field and is therefore used as the metric in the design optimization. Each slit can be viewed as a dipole oscillator giving rise to length-dependent SPP amplitude and phase responses. The lengths L1 and L2 are optimized by monitoring the SP fields at two observation points (blue and green dots at the gold−air interface) in Figure 1a for two attributes: (1) achieving a −π/2 (π/2) temporal phase delay in the y-slit (green dot) as compared to the x-slit (blue dot) when the optical source is 45° (−45°) linearly polarized, respectively; and (2) simultaneously approaching nearly equal SPP field amplitudes at the two observation points. The optimized nanocavity is defined by parameters L1 = 500 nm, L2 = 780 nm, and w = 200 nm. The recorded Ez fields as a function of time normalized to the carrier cycle at the two observation points are displayed in Figure 1b,c, confirming that the temporal phase delays are exactly π/2 or −π/2 when the optical excitation are linearly polarized in the −45 and 45°, respectively. The orientations of the linearly polarized optical excitations are labeled using the arrows. The colors of the traces correspond to that of the observation points. The unequal amplitude between the two observation points will be addressed later in the discussion of the metasurface. The resulting instantaneous Ez fields within the vicinity of the nanocavity are displayed in Figure 1d (−45° polarized) and Figure 1e (45° polarized). These figures illustrate distinct spatial and phase characteristics can be selectively excited depending on the source polarizations. Figure 1d shows that a B
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Figure 2. Design of the metasurface. (a) The optimized nanocavities are arranged as an Archimedes spiral defined by r0 = 3λspp and m = 1. (b,c) Resulting instantaneous Ez vortex field and spatial phase profile created in the metasurface under −45° linearly polarized excitation, respectively. (d,e) Resulting instantaneous Ez focusing field and spatial phase profile generated in the metasurface under 45° linearly polarized excitation, respectively. SP field profiles derived by analytical solutions are shown as insets in (b,d).
numerical findings, the ± π/2 temporal phase difference created by the two arms is extremely critical. On the other hand, slightly unequal amplitudes as shown in Figure 1b,c play a less important role. To this end, the generation of SP vortex carrying OAM using linearly polarized excitation is successfully demonstrated via numerical analyses. We then examine the field and phase behaviors of our metasurface under 45° linearly polarized optical excitation. Figure 2d,e shows the resulting instantaneous SP field and the spatial phase patterns, respectively. The resulting Ez SP field forms a subwavelength focusing spot that carries neither phase singularity nor optical angular momentum. This can be understood as the left-hand localized SP vortex source SP field (spin σ = −1) is canceled by the geometrical charge of the Archimedes spiral, yielding a q = σ + m = 0 focusing spot. Spatial distributions of the vortex and focusing fields as derived through analytical solutions that conform to the Bessel functions of the first kind13,18 are provided as insets in Figure 2b,d. The propagation behaviors of SPP on the designed metasurface are experimentally measured using a near-field scanning optical microscope (NSOM). Our sample is prepared by thermally evaporating a gold film of 200 nm onto a glass substrate followed by focused ion beam milling (see Supporting Information for experimental setup and sample scanning electron microscope images). Such gold thickness helps to prevent saturating the photodetector when the NSOM probe approaches the nanocavities and enables later quantitative comparisons against our numerical results. We note here that the width of the slits in forming the nanocavity also affects the resulting vortex/focusing formation (see Supporting Information for details on the effect of w value). In our experiments, the metasurface is comprised of nanocavities arranged as a threeturn plasmonic Archimedes spiral (defined by ϕ ranging from 0 to 6π). The three-turn geometry is adopted to enhance the SPP field strength under the presence of optical damping to facilitate the near-field measurements as well as in creating SP vortex with better azimuthal uniformity. The resulting SP field intensities are experimentally measured using a commercial NSOM scanning head (NT-MDT NTEGRA Solaris) with homemade tapered fiber probes (see Supporting Information for NSOM probe preparation and concerns).45
counterclockwise localized SP vortex source (right-handed) is generated by −45° polarized excitation, while Figure 1e shows that SPPs with an opposite sense of rotation (left-handed) are excited by the 45° polarized source (see Supporting Information for movies for the sense of field rotations). These two examples already demonstrate that planar SP spin angular momenta can be generated using linearly polarized optical excitations. Our next step is to exploit the localized SP vortex source synthesized by a single nanocavity for the creation of SP vortex. As shown in Figure 2a, 20 length-optimized nanocavities are arranged geometrically as an Archimedes spiral12−15 to form a metasurface. A right-handed Archimedes spiral (with a geometrical charge of m = +1) is mathematically defined in the cylindrical coordinate as r(ϕ) = r0 + (ϕλspp)/2π, where r denotes the distance between the spiral and the origin O, r0 is the starting distance, ϕ is the azimuthal angle, and λspp is the SPP wavelength. We define here r0 = 3λspp to facilitate later near-field optical measurements. We first examine the field and phase behaviors of the designed metasurface under −45° linearly polarized optical excitation. In this case, SP vortex carrying OAM is successfully created. This can be understood as the right-handed (spin σ = +1) localized SP vortex source fields of the nanocavities add up with the geometrical charge of the Archimedes spiral, leading to the creation of SP vortex with a topological charge of q = σ + m = 2. This is indicated as four field petals within a 2π azimuthal range can be found in the instantaneous Ez SP field shown in Figure 2b. The four-petals revolve in a counterclockwise direction at the rate of the optical carrier cycle, in accordance with the chirality and the phase difference provided by a single nanocavity (see Supporting Information for movies). The fourpetal field distribution is associated with vortex with a topological charge of 2. This is corroborated in Figure 2c, where the instantaneous spatial phase profile reveals two evident abrupt phase jumps from −π to π within a 2π azimuthal range. We further confirmed that the spatial line-phase trace along the dotted circle in Figure 2c does exhibit a linear increment as a function of ϕ. This assures that the resulting SP vortex is having an integer topological charge of 2 (see Supporting Information for the line-phase plot). We note here the final fine-tuning to the nanocavity arm lengths is performed through monitoring the integer topological charge. In our C
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revolves at the speed of optical carrier and thus cannot be measured. The ability to dynamically switch to subwavelength focusing is further investigated. The NSOM measurement and FDTD calculated time-averaged intensity for the metasurface under 45° linearly polarized excitation are shown as Figure 4a,b,
Figure 3a shows the experimentally measured NSOM result when the metasurface is illuminated with a −45° linearly
Figure 3. Creation of experimental SP OAM under −45° linearly polarized excitation. (a) NSOM measurement result. (b) Timeaveraged intensity calculated through FDTD method. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. (c) Comparison between NSOM measured and FDTD calculated intensities along the x-direction (green dashed lines in both (a) and (b)). (d) Comparison between NSOM measured and FDTD calculated intensities along the y-direction (blue dashed lines in both (a) and (b)). SP intensity profile derived by analytical solution is shown as inset in (b).
Figure 4. Generation of experimental SP subwavelength focusing under 45° linearly polarized excitation. (a) NSOM measurement result. (b) Time-averaged intensity calculated through FDTD method. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. (c) Comparison between NSOM measured and FDTD calculated intensities along the x-direction (green dashed lines in both (a,b)). (d) Comparison between NSOM measured and FDTD calculated intensities along the y-direction (blue dashed lines in both (a,b)). SP intensity profile derived by analytical solution is shown as inset in (b).
polarized excitation. The origin of the Archimedes spiral is labeled by the intersection of the two dashed lines. It is apparent that the origin is a dark intensity spot. Such singularity provides a direct evidence for the successful generation of SP vortex carrying OAM in our metasurface. The experimental NSOM scan result is further compared with the FDTD simulation result. Since what is measured through the NSOM is the time-averaged intensity, Figure 3b shows the FDTD timeaveraged intensity pattern obtained through integration over four optical carrier cycles. We note here the numerical result is obtained after performing numerical spatial convolution given a finite point spread function of the NSOM fiber probe (see Supporting Information for details on convolution mechanisms). Close examinations between the two figures reveal excellent qualitative agreements: they both show a dark origin being surrounded by annular bright and dark rings. The results are further compared quantitatively in the vicinity of the spiral origin: Figure 3c (d) depicts the measured NSOM (solid trace) and FDTD (dotted trace) intensity values along the green (blue) dashed lines in Figure 3a,b. Excellent quantitative agreements are observed both in terms of the positions of the intensity peaks and valleys, as well as the relative magnitudes. Furthermore, the NSOM measurement conforms to the second-order Bessel function, demonstrating an evident signature of near-field vortex with a topological charge of 2 as anticipated. We thus confirm that an OAM-carrying SP vortex with a topological charge of 2 is experimentally generated in our designed metasurface under linearly polarized optical excitation. We note here the spatial phase profile of SP vortex
respectively. A strong, bright intensity spot at the spiral origin can be clearly observed in both figures. The line intensity traces near the spiral origin shown in Figure 4c,d along the x- and ydirections again reveal excellent agreements between our NSOM scan and FDTD result. The resulting intensity distribution conforms to the expected zeroth-order Bessel function, demonstrating an evident a subwavelength focusing spot carrying no OAM. The deconvoluted full width halfmaximum spot diameter for the focused spot is 530 nm. We thus verify successful experimental demonstration on subwavelength focusing in our designed gold metasurface. In summary, unit nanocavity embedded in a gold thin film is optimized for the creation of localized SP vortex source fields under linearly polarized optical excitations. The nanocavities are then arranged as an Archimedes spiral to form a metasurface. We demonstrate both numerically and experimentally that SP vortex carrying optical orbital angular momentum in our designed metasurface can be created under linearly polarized optical excitation that carries no angular momentum. In our experiment, an SP vortex with an integer topological charge of two is created under a −45° linearly polarized optical excitation. A subwavelength focusing spot can be generated in the same metasurface when the orientation of the linearly polarization is changed to 45°. The resulting SP fields are experimentally measured using a nearD
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AUTHOR INFORMATION
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S Supporting Information *
Additional information, figures, and movies. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. Author Contributions
C.-F.C. and C.-T.K. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the support from the Ministry of Science and Technology of Taiwan under Grant MOST 103-2112-M007-017-MY3, National Tsing Hua University under Grant 103N2081E, and the Ministry of Education, Taiwan (Aim for the Top University Program). Technical support on focusedion beam milling from NanoCore, the Core Facilities for Nanoscience and Nanotechnology at Academia Sinica in Taiwan, is acknowledged.
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