Polarization-Independent Silicon Metadevices for Efficient Optical

Page 1 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control Katie E. Chong,† Isabelle Staude,∗,† Anthony James,‡ Jason Dominguez,‡ Sheng Liu,‡ Salvatore Campione,‡ Ganapathi S. Subramania,‡,¶ Ting S. Luk,‡ Manuel Decker,† Dragomir N. Neshev,† Igal Brener,‡ and Yuri S. Kivshar† Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia, Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA, and Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA E-mail: [email protected]

Abstract We experimentally demonstrate a functional silicon metadevice at telecom wavelengths that can efficiently control the wavefront of optical beams by imprinting a spatially-varying transmittance phase independent of the polarization of the incident beam. Near-unity transmittance efficiency and full 0 − 2π phase coverage are enabled ∗

To whom correspondence should be addressed Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia ‡ Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA ¶ Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA †

1

ACS Paragon Plus Environment

Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

by utilizing the localized electric and magnetic Mie-type resonances of low-loss silicon nanoparticles tailored to behave as electromagnetically dual-symmetric scatterers. We apply this concept to realize a metadevice that converts a Gaussian beam into a vortex beam. The required spatial distribution of transmittance phases is achieved by a variation of the lattice spacing as a single geometric control parameter.

Keywords metasurface, metadevice, duality, Huygens’ surface, vortex beam, beamshaping

Silicon metasurfaces provide a CMOS compatible platform for the creation of arbitrary optical wavefronts with high transmission efficiencies, 1,2 opening new possibilities for e.g. beam steering and holographic encoding. Generally, such wavefront control applications usually ask for a spatially-varying transmittance phase to be imprinted on the incident beam with negligible amplitude modulation. Recently, a range of functional silicon metasurface devices, or metadevices, 3 have been demonstrated at near-infrared wavelengths, 1,2 including axicons, blazed gratings, and achromatic beam deflectors and lenses. However, the realized metadevices provide functionality for a defined circular 1 or linear 2 polarization of the incident light wave only. Furthermore, partial backreflection of the incident power due to impedance mismatch remains a challenge as it limits the device efficiencies. A route to overcome these limitations and to realize polarization independent silicon metasurfaces with near-unity transmission efficiency is provided by the strong localized electric and magnetic Mie-type resonances of silicon nanoparticles. 4–7 Metasurfaces composed of silicon nanoparticles are conceptually similar to designer metasurfaces harnessing localized surface plasmons. 8–14 As for plasmonic metasurfaces, the optical response of silicon metasurfaces can be tailored at will by the design and arrangement of its constituent building blocks. 6,15 However,

2


Page 2 of 19

Page 3 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

in contrast to plasmonic metasurfaces their high-index dielectric counterparts are not compromised by strong absorption losses. As such, for metasurfaces consisting of homogeneous two-dimensional arrangements of designed silicon nanoparticles a range of functionalities and effects have been demonstrated, including resonant forward scattering, 6 perfect 16 and broadband 17 reflectors, magnetic mirrors, 18 Fano resonances, 19,20 refractive-index sensing, 21 spontaneous emission control, 22 and polarization beam-splitting. 23 Nonetheless, since reflectance becomes very high at the resonance wavelength, graded metasurfaces based on individual localized modes of dielectric resonators have so far been mainly considered in reflection geometry, 24,25 with a few exceptions limited to theoretical proposals and implementations at mid-IR frequencies. 26,27 The concept of silicon Huygens’ metasurfaces, 7 solves this problem, enabling resonant silicon metasurfaces for operation in transmission. Ideal silicon Huygens metasurfaces are reflectionless due to matching of the electric and magnetic polarizabilities of their building blocks, 28 causing them to behave as electromagnetically dual-symmetric scatterers. 29,30 Electromagnetically dual-symmetric behaviour can be achieved in a resonant regime by simultaneous excitation of electric and magnetic dipole resonances in silicon nanoparticles. The two different resonances are tuned to occur at the same spectral position via the geometry of the nanoparticle for a given lattice constant 6 and adjusted in strength via the index contrast between the nanoparticle and the surrounding medium. 7 In addition to duality symmetry the zero back scattering condition has been shown to require a discrete rotational symmetry of degree higher than 2. 31 This second condition can be easily implemented by using disk-shaped nanoparticles arranged in two-dimensional square arrays. Silicon Huygens’ metasurfaces composed of such engineered magneto-electric nanoparticles are thus able to provide ideally unity transmission efficiency and full 2π phase coverage across the spectral bandwidth of the resonances. This complete phase coverage in homogeneous silicon Huygens’ metasurfaces was recently demonstrated experimentally for a metasurface composed of silicon nanodisks with an optimized geometry and index contrast. 7 In the same work, silicon

3


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

nanodisk metasurfaces were suggested for wavefront manipulation in transmittance based on direct scaling of the metasurface geometrical parameters as a function of position, in order to create a desired spatial distribution of transmittance phases as required for wavefront control. However, wavefront shaping based on this concept has not been demonstrated so far. This is mainly due to the fact that direct geometrical scaling is technologically challenging as it requires 2.5-dimensional structuring, i.e., control of the height of the nanoparticles depending on their position, instead of conventional planar fabrication where the resulting structures are fixed in height. Here, we present the first experimental realization of a functional, polarization-independent wavefront shaping metadevice, namely a Gaussian-to-vortex beam shaper, based on a graded silicon Huygens’ metasurface. We show that by varying the lattice periodicity a in the array we can control the coupling between the nanodisks and hence tune the spectral position of the two resonances. Therefore by using a as a single control parameter we can realize a Huygens’ metasurface with the desired spatial distribution of transmittance phases. Importantly, this allows us to avoid direct scaling of the metasurface geometrical parameters. To illustrate this powerful concept of wavefront engineering we demonstrate an important example of beam shaping, namely vortex-beam generation. This choice is motivated by the significance of beams carrying orbital angular momentum for a range of potential applications, especially in the field of both quantum and classical communication technology, where control of the topological charge of the beam offers exceptional possibilities for multi-space entanglement 32 and multi-mode spatial multiplexing, 33 respectively. In this context the use of metadevices is particularly attractive, as their small overall size and nanoscale thickness open new avenues for the integration of functional elements directly onto the facet of an optical fibre or a waveguide. Such metadevices will be able to generate and process orbital angular momentum beams with guided-wave optics. 34 Ideally, in order to generate a vortex beam from a Gaussian beam, a phase mask with spatially varying phase profile spanning the full 2π range in the azimuthal direction is required. With our metasurface design we thus

4


Page 4 of 19

Page 5 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

aim to provide a maximum coverage of transmittance phases at the operation wavelength, while preserving the dual-symmetric response characteristics of the Huygens’ metasurface at every realized phase value. To this end we performed comprehensive numerical simulations of the metasurface response using the commercial simulation software CST Microwave Studio, where we systematically varied the nanodisk diameter d and the lattice constant a. The nanodisk height h = 243 nm, defined by the thickness of the top silicon layer of the silicon-on-insulator (SOI) wafer used in the experiment, as well as the refractive index of the embedding medium n = 1.45 are kept constant according to experimental conditions. We identified a combination of nanodisk diameter d = 534 nm and operation wavelength λ = 1477 nm, which for a variation of the lattice periodicity a offers the maximum phase coverage while preserving near-unity transmittance efficiency as a result of a spectral overlap and matching polarizabilities of the electric and magnetic dipolar resonances of the silicon nanodisks. We note that our suggested design concept is not the only possible implementation that can meet the specified conditions, however, due to its inherent simplicity – all the constituent building blocks are identical in shape – our solution offers great ease for experimental realization. In order to identify the lattice periodicities required for the desired phase shifts we plot the transmittance intensity and phase of arrays of the silicon nanodisks metasurface for a systematic variation of the lattice periodicity. Figure 1a shows the calculated transmittance intensity of the nanodisk arrays in the infrared region, Figure 1b shows the corresponding data for the phase of the transmitted beam. For the silicon optical properties we have used dispersion data obtained experimentally by ellipsometry measurements. The operation wavelength is indicated by the white dashed lines. Figure 1 c and d show the transmittance intensity and phase at this wavelength for various lattice periodicities, confirming that a phase coverage of approximately 3π/2 is obtained in the plotted range of lattice periodicities, while the transmitted intensity is flat and close to unity. For vortex beam generation with any discretized spatial phase mask, a minimum of

5


Nano Letters

Transmittance (T)

Q1

Q4

Q2 Q3

Phase

b

d a

h

Wavelength ( m)

Wavelength ( m)

a

Q1

Q2 Q3

Q4

a

c

d Q2 Q3

Q4

Q1

Phase

Q1

T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 19

Q2 Q3 Q4

Lattice Periodicity a (nm)

Lattice Periodicity a (nm)

Figure 1: Numerical calculations of the transmittance intensity (a) and phase (b) of silicon nanodisk arrays with varying lattice periodicity embedded in a medium with refractive index of n = 1.45. The nanodisk diameter is d = 534 nm and their height is h = 243 nm. The inset in (a) shows a sketch of the silicon nanodisk arrays. The white line denotes the design operation wavelength of 1477 nm. (c) and (d) show the transmittance intensity and phase values at the operation wavelength. The white/red dots in (a,b)/(c,d), respectively, highlight the lattice periodicities chosen for experimental realization. three different sectors of constant phase 0, 2π/3, and 4π/3 are sufficient. Here, however, we exploit the capability of a Huygens’ metasurface to provide up to 2π phase coverage, 7 and we select four lattice periodicities providing a series of phase shifts spaced by π/2 radians. This allows for a simple metasurface layout organised in quadrants. The selected values for the lattice periodicity (aQ1 = 695 nm, aQ2 = 815 nm, aQ3 = 855 nm and aQ4 = 975 nm) are denoted by the white and red dots in Figure 1a,b and c,d, respectively. The circular symmetry of the nanodisks, the four-fold symmetry of the lattice, and the existence of a mirror symmetry containing the optical axis 31 are chosen to enable beam conversion for any polarization of the incident light field. We note, however, that, strictly speaking, rotational symmetry is not fulfilled any longer for the four quadrant metasurface as a whole. This is in contrast to the numerical calculations for each quadrant, where we assume an infinite array of silicon nanodisks. 6


Page 7 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 2: (a) Scanning-electron micrograph of a typical fabricated beam shaper before low-pressure chemical vapor deposition (LPCVD). The silicon nanodisks have diameters of 590 nm and are 243 nm high. The lattice periodicities for each quadrant are aQ1 = 695 nm, aQ2 = 815 nm, aQ3 = 855 nm and aQ4 = 975 nm. The insets show magnified and oblique views of a single nanodisk. (b) The transmittance of the 4 quadrants of the fabricated beam shaper after LPCVD (i) at 1490 nm and (ii) in the NIR range. The blue dashed line in (i) is the numerically calculated data (same result as Figure 1(a)) and the gray dashed line indicates the 70% transmittance level as a reference. The white dashed line in (ii) denotes the experimental operation wavelength of 1490 nm. For experimental realization of our silicon metasurface beamshaper we use electron beam lithography on back-side polished SOI wafers. After development, the samples undergo a reactive-ion etching process by using the obtained electron-beam resist pattern as an etch mask, followed by an oxygen plasma etch and an additional cleaning step using piranha solution for residual resist removal (see Supporting Information for details). Finally, lowpressure chemical vapor deposition (LPCVD) is applied to embed the sample into 580 nm of silica. Figure 2a shows scanning electron micrographs (SEMs) of a typical fabricated sample before LPCVD. 7


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Linear-optical transmittance spectra of each quadrant of our beam shaper are measured using a custom-built white-light spectroscopy setup connected to an optical spectrum analyzer. The incident light is linearly polarized. Furthermore, we measure the transmittance for an unstructured etched region on the wafer as a reference, allowing us to retrieve the transmitted power T through the combined system of the metasurface and the silica layer for each quadrant. We note that the effect of the silica layer cannot be fully eliminated by the referencing procedure, as the presence of the metasurface changes the transmittance properties of the silica layer itself (See Supporting Information for details). Figure 2b shows the retrieved transmittance T of the sample (i) at 1490 nm and (ii) in a spectrally resolved presentation in the near-infrared range. The experimental operation wavelength is slightly shifted with respect to the design wavelength due to fabrication inaccuracies. Importantly, the transmittance of our structure at 1490 nm exceeds 70% for all quadrants. Furthermore, Figure 2b(ii) confirms that the measured spectra show all the essential features expected from the numerical calculations for the ideal system shown in Figure 1a, in particular the broad wavelength region of high transmittance. The slightly lower transmittance values for the experimental data as compared to the numerical results are mainly due to the presence of the silica box layer in the fabricated structure, which is not accounted for in the simulations. In order to optically characterize the wavefront shaping capabilities of the fabricated silicon Huygens’ metadevice we use a home-built Mach-Zehnder interferometer setup (See Supporting Information for details). A tunable laser with its emission wavelength adjusted to the experimental operation wavelength of λ = 1490 nm is used as a light source. First, we block the reference beam of the interferometer and project the object beam onto the camera so that a microscope image of the sample is obtained (see Figure 3a). The outline of each quadrant is clearly visible. The fringes are caused by Febry-Perot oscillations between the upper and lower interfaces of the handle wafer, which are not perfectly parallel due to manual polishing. Remarkably, the sample area appears to have the same brightness as

8


Page 8 of 19

Page 9 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3: (a) Light-microscopy image of the Huygens’ metasurface beam shaper sample. (b) Interferogram at the sample plane. (c) Reconstructed phase of the beam at the sample surface at 1490 nm wavelength. (d) Average phase shift at each quadrant (red dots) in comparison to the numerical calculation for the ideal structure (blue dashed line, same result as in Figure 1(d)), and (e) the average phase shift at each quadrant as a function of polarization angle of the incident beam. the surrounding wafer, which directly demonstrates the high transmission efficiency of our Huygens’ metadevice. Next, we image the interference pattern obtained by superposition of the object beam with the co-propagating reference beam (Figure 3b). Phase discontinuities are immediately observed at the borders between quadrants and at the sample outlines as apparent in Figure 3b. To retrieve the phase of the transmitted light at each quadrant we use the four-frame interferometric measurement technique 35 where one of the arms of the interferometer is increased in length by a closed-loop piezo element. To this end a set of four interferograms Ij (x, y), (j = 1, 2, 3, 4) is recorded as the phase shifts between the object and reference beam 9


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 19

vary as (j − 1)π/2 (see Supporting Information for details). The phase is then reconstructed by using the following relation

φ(x, y) = tan

−1

!

" I4 − I2 . I1 − I3

(1)

After a baseline adjustment process, the phase of the beam propagating through the sample with respect to the incident light is obtained and imaged in Figure 3c. The four distinct colors visualize an increment in transmittance phase of approximately π/2 between subsequent quadrants (counterclockwise from the top left quadrant Q4, which shows a closeto-zero phase shift with respect to the reference beam). In Figure 3d the measured average phase shift values for the four quadrants (red dots) are directly compared to the theoretical expectations for our design (blue dashed line), showing very good agreement. The deviations from the exact equidistant spacing of the phase shift increments arise from fabrication inaccuracies, and in particular from imperfect compensation of the change of proximity effect for different lattice constants leading to slightly different nanodisk diameters. Furthermore, to demonstrate the polarization insensitivity of our design, we rotate the polarization direction of the incident beam from 0 degrees (corresponding to horizontal polarization) to 90 degrees (corresponding to vertical polarization) in 10 degree steps and repeat the phase retrieval procedure for each quadrant at each step. These results are shown in Figure 3e, confirming that our Huygens’ metadevice shows almost no sensitivity to the polarization angle of the incident light wave. This is of particular importance as most of the metasurfaces developed to date operate in cross-polarisation regime in order to take advantage of the geometric phase accumulation to achieve 2π phase coverage. 36 In order to verify that the generated beam is indeed a vortex beam we modify the setup such that the camera images the object beam at 4 cm beyond the sample. For a blocked reference beam the object beam intensity profile shows a pronounced minimum in the middle of a bright ring (see Figure 4a). While this intensity minimum is found at any

10


Page 11 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

distance in the far-field behind the sample, the distance of 4 cm is chosen to optimize the size of the image at the camera, whose position is fixed by the arrangement on the optical table. Here, the previously measured deviations from an equidistant spacing of the phase shift increments lead to intensity variations in azimuthal direction of the beam profile and prevent the formation of a perfect doughnut shape. Next, we remove the beam blocker to interfere the far field transmitted through the metadevice with a plane wave. In the interferogram the characteristic fork feature of a vortex beam is formed, as shown in Figure 4b. The reconstructed phase in Figure 4c demonstrates the continuous vortex phase with the phase singularity in the middle of the beam. The horizontal fringes in the background next to the laser beam are caused by an artefact of the baseline adjustment process (see Supporting Information for details). Figure 4d shows the cross section of the reconstructed phase through the centre of the beam (white dashed line in the inset), where the vortex-beam specific π phase jump is seen. While these results were obtained for horizontal linear polarization of the laser beam, we repeated these measurements for a vertically polarized input beam. The corresponding results are included in the Supporting Information. Both measurements show identical features as presented in Fig. 4, providing direct evidence of the polarization insensitivity of our Huygens’ metadevice. Based on these observations we can conclude that the symmetry break induced by the four quadrant layout of the metasurface does not have a significant impact on the polarization insensitive performance of our metadevice. In conclusion, we have presented the first experimental realization of an optical metadevice based on a gradient silicon Huygens’ metasurface. We demonstrated efficient wavefront control, namely shaping a Gaussian beam into a vortex beam, with high transmission efficiency exceeding 70%. In contrast to conventional phase plates which employ the accumulation of phase delay through propagation in a medium, the functional layer of our device has only nanoscale thickness and fabrication is possible by a standard planar lithography process. Furthermore, the simplicity of our design concept makes our metadevice suitable for cost-effective large area lithography techniques, and, being composed of silicon and silica

11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Phase

Nano Letters

Figure 4: (a) Intensity profile (logarithmic scale) of the generated vortex beam showing a pronounced minimum at its center. (b) Interferogram showing the characteristic fork structure of a vortex beam. (c) Reconstructed phase of the object beam imaged at 4 cm beyond the sample, revealing the gradual phase change in the azimuthal direction of the beam with a phase singularity at the center. (d) The phase profile across the center of the beam denoted by the white dashed line in the inset. glass only, our metadevice is fully silicon photonics and CMOS compatible. Importantly, in contrast to the gradient silicon metasurfaces based on silicon nanobeams, 1,2 our silicon metadevice works for any input polarization of the incident light. As a consequence, it can be used with arbitrary light sources without the need for pre-conditioning of the polarization state of the input, which typically results in a loss of 50% of the light intensity for an unpolarized light input. Our approach can be generalized to address a range of other wavefront shaping problems including for example focusing, defocusing, beam deflection, and holography. Active control of the metadevice functionality may be achieved by using liquid crystals for tuning and switching of the metasurface optical response as recently demonstrated. 37 Such tunability would open the way for dynamically tunable phase modulators and holograms. Altogether our approach offers a viable route for implementing a range of

12


Page 12 of 19

Page 13 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

high-efficiency optical devices with nanoscale thickness.

Acknowledgement The authors thank Mr. Guangyao Li for useful discussions. K. E. C. thanks the Australian Nanotechnology Network and the Australian National University Vice Chancellor’s HDR Travel Grants for their funding support. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The authors also acknowledge a support from the Australian Research Council.

The authors declare no competing financial interest

Supporting Information Available: Details of the sample fabrication, description of the interferometry setup used for optical characterization of the fabricated metadevices, characterization of the generated vortex beam for two orthogonal input polarizations of the incident laser beam, details of the phase reconstruction, and details of the retrieval of the experimental transmittance values. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1) Lin, D.; Fan, P.; Hasman, E.; Brongersma, M. L. Science 2014, 345, 298–302. (2) Aieta, F.; Kats, M. A.; Genevet, P.; Capasso, F. Science 2015, 347, 1342–1345. (3) Zheludev, N. I.; Kivshar, Y. S. Nat. Mater. 2012, 11, 917–924. 13


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(4) Evlyukhin, A. B.; Novikov, S. M.; Zywietz, U.; Eriksen, R. L.; Reinhardt, C.; Bozhevolnyi, S. I.; Chichkov, B. N. Nano Lett. 2012, 12, 3749–3755. (5) Kuznetsov, A. I.; Miroshnichenko, A. E.; Fu, Y. H.; Zhang, J.; Luk’yanchuk, B. Sci. Rep. 2012, 2, 492. (6) Staude, I.; Miroshnichenko, A. E.; Decker, M.; Fofang, N. T.; Liu, S.; Gonzales, E.; Dominguez, J.; Luk, T. S.; Neshev, D. N.; Brener, I.; et al., ACS Nano 2013, 7, 7824–7832. (7) Decker, M.; Staude, I.; Falkner, M.; Dominguez, J.; Neshev, D. N.; Brener, I.; Pertsch, T.; Kivshar, Y. S. Adv. Opt. Mat. 2015, 3, 813–820. (8) Ni, X.; Emani, N. K.; Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Science 2012, 335, 427. (9) Larouche, S.; Tsai, Y. J.; Tyler, T.; Jokerst, N. M.; Smith, D. R. Nat. Mater. 2012, 11, 450–454. (10) Chen, X.; Huang, L.; M¨ uhlenbernd, H.; Li, G.; Bai, B.; Tan, Q.; Jin, G.; Qiu, C. W.; Zhang, S.; Zentgraf, . Nat. Commun. 2012, 3, 1198. (11) Huang, L.; Chen, X.; M¨ uhlenbernd, H.; Zhang, H.; Chen, S.; Bai, B.; Tan, Q.; Jin, G.; Cheah, K. W.; Qiu, C. W. Nat. Commun. 2013, 4, 2808. (12) Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Science 2013, 339, 1232009. (13) Yu, N.; Capasso, F. Nat. Mater. 2014, 13, 139–150. (14) Meinzer, N.; Barnes, W. L.; Hooper, I. R. Nature Photon. 2014, 8, 889–898. (15) Campione, S.; Basilio, L. I.; Warne, L. K.; Sinclair, M. B. Opt. Express 2015, 23, 2293–2307. (16) Slovick, B.; Yu, Z. G.; Berding, M.; Krishnamurthy, S. Phys. Rev. B 2013, 88, 165116. 14


Page 14 of 19

Page 15 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(17) Moitra, P.; Slovick, B. A.; Yu, Z. G.; Krishnamurthy, S.; Valentine, J. Appl. Phys. Lett. 2014, 104, 171102. (18) Liu, S.; Sinclair, M. B.; Mahony, T. S.; Jun, Y. C.; Campione, S.; Ginn, J.; Bender, D. A.; Wendt, J. R.; Ihlefeld, J. F.; Clem, P. G.; et al., Optica 2014, 1, 250–256. (19) Wu, C.; Arju, N.; Kelpp, G.; Fan, J.; Dominguez, J.; Gonzales, E.; Tutuc, E.; Brener, I.; Shvets, G. Nat. Comm. 2014, 5, 3892. (20) Chong, K. E.; Hopkins, B.; Staude, I.; Miroshnichenko, A. E.; Dominguez, J.; Decker, M.; Neshev, D. N.; Brener, I.; Kivshar, Y. S. Small 2014, 10, 1985–1990. (21) Yang, Y.; Kravchenko, I. I.; Briggs, D. P.; Valentine, J. Nat. Commun. 2014, 5, 5753. (22) Staude, I.; Khardikov, V. V.; Fofang, N. T.; Liu, S.; Decker, M.; Neshev, D. N.; Luk, T. S.; Brener, I.; Kivshar, Y. S. ACS Photonics 2015, 2, 172–177. (23) Khorasaninejad, M.; Zhu, W.; Crozier, K. B. Optica. 2015, 2, 376–382. (24) Zou, L.; Withayachumnankul, W.; Shah, C. M.; Mitchell, A.; Bhaskaran, M.; Sriram, S.; Fumeaux, C. Opt. Express. 2013, 21, 1344–1352. (25) Yang, Y.; Wang, W.; Moitra, P.; Kravchenko, I. I.; Briggs, D. P.; Valentine, J. Nano Lett. 2014, 14, 1394–1399. (26) West, P. R.; Stewart, J. L.; Kildishev, A. V.; Shalaev, V. M.; Shkunov, V. V.; Strohkendl, F.; Zakharenkov, Y. A.; Dodds, R. K.; Byren, R. Opt. Express 2014, 22, 26212– 26221. (27) Cheng, J.; Ansari-Oghol-Beig, D.; Mosallaei, H. Opt. Lett 2014, 39, 6285–6288. (28) Person, S.; Jain, M.; Lapin, Z.; Sanz, J. J.; Wicks, G.; Novotny, L. Nano Lett. 2013, 13, 1806–1809. (29) Fernandez-Corbaton, I.; Molina-Terriza, G. Phys. Rev. B 2013, 88, 085111. 15


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(30) Fernandez-Corbaton, I.; Fruhnert, M.; Rockstuhl, C. ACS Photonics 2015, 2, 376–384. (31) Fernandez-Corbaton, I. Opt. Express 2013, 21, 29885–29893. (32) Bozinovic, N.; Yue, Y.; Ren, Y.; Tur, M.; Kristensen, P.; Huang, H.; Willner, A. E.; Ramachandran, S. Science 2013, 340, 1545–1548. (33) Willner, A. E.; Huang, H.; Yan, Y.; Ren, Y.; Ahmed, N.; Xie, G.; Bao, C.; Li, L.; Cao, Y.; Zhao, Z.; et al., Adv. Opt. Photonics 2015, 7, 66–106. (34) Cai, X.; Wang, J.; Strain, M. J.; Johnson-Morris, B.; Zhu, J.; Sorel, M.; OBrien, J. L.; Thompson, M. G.; Yu, S. Science 2012, 338, 363–366. (35) Creath, K. Progress in Optics, E. Wolf ed.; Elsevier Science Publishers: Amsterdam, 1988; Vol. XXVI. (36) Minovich, A. E.; Miroshnichenko, A. E.; Bykov, A.; Murzina, T.; Neshev, D. N.; Kivshar, Y. S. Laser & Photonics Rev. 2015, 9, 195–213. (37) Sautter, J.; Staude, I.; Decker, M.; Rusak, E.; Neshev, D. N.; Brener, I.; Kivshar, Y. S. ACS Nano 2015, 9, 4308–4315.

16


Page 16 of 19

Page 17 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

For Table of Contents Use Only

Manuscript title: Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control Names of authors: Katie E. Chong, Isabelle Staude, Anthony James, Jason Dominguez, Sheng Liu, Salvatore Campione, Ganapathi S. Subramania, Ting S. Luk, Manuel Decker, Dragomir N. Neshev, Igal Brener, and Yuri S. Kivshar

Figure 5: ToC-image

17


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry We experimentally demonstrate a functional silicon metadevice at telecom wavelengths that converts a Gaussian beam into a vortex beam independent of the polarization of the incident beam. Near-unity transmittance efficiency is enabled by utilizing the localized resonances of low-loss silicon nanoparticles tailored to behave as electromagnetically dual-symmetric scatterers, thereby eliminating all major loss channels of metasurfaces such as polarization-conversion, diffraction, reflection, and absorption losses. The required spatial distribution of transmittance phases is achieved by a variation of a single geometrical parameter only, namely the spacing between the silicon nanoparticles.

18


Page 18 of 19

Page 19 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

85x34mm (300 x 300 DPI)


Polarization-Independent Silicon Metadevices for Efficient Optical

Recommend Documents