Letter pubs.acs.org/NanoLett
Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation Yuanmu Yang,† Wenyi Wang,‡ Parikshit Moitra,† Ivan I. Kravchenko,§ Dayrl P. Briggs,§ and Jason Valentine*,∥ †
Interdisciplinary Materials Science Program and ‡Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37212, United States § Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37212, United States S Supporting Information *
ABSTRACT: Plasmonic metasurfaces have recently attracted much attention due to their ability to abruptly change the phase of light, allowing subwavelength optical elements for polarization and wavefront control. However, most previously demonstrated metasurface designs suffer from low coupling efficiency and are based on metallic resonators, leading to ohmic loss. Here, we present an alternative approach to plasmonic metasurfaces by replacing the metallic resonators with high-refractive-index silicon cut-wires in combination with a silver ground plane. We experimentally demonstrate that this meta-reflectarray can be used to realize linear polarization conversion with more than 98% conversion efficiency over a 200 nm bandwidth in the shortwavelength infrared band. We also demonstrate optical vortex beam generation using a meta-reflectarray with an azimuthally varied phase profile. The vortex beam generation is shown to have high efficiency over a wavelength range from 1500 to 1600 nm. The use of dielectric resonators in place of their plasmonic counterparts could pave the way for ultraefficient metasurfacebased devices at high frequencies. KEYWORDS: Metamaterial, dielectric antenna, polarization conversion, vortex beam
A
One of the drawbacks of plasmonic metasurfaces is that they typically suffer from low efficiency due to weak coupling between the incident and cross-polarized fields. Methods to increase efficiency include the use of overlapped electric and magnetic resonances16 as well as the use of thicker metasurface sheets,17 though both of these proposals require materials with increased complexity. One can also employ antennae working away from their resonance positions to realize quarterwaveplates with polarization conversion efficiencies of close to 50% over large bandwidths.18 In another approach, it was shown that an array of metallic antennae in combination with a reflective ground plane can achieve efficiencies of up to 80% for anomalous reflection7,13,19 and linear polarization conversion10 by introducing multiple reflections within the film. While this design avoids complexity, the use of metallic antennae still limits metasurfaces from achieving unity efficiency at optical wavelengths due to the ohmic losses in metal.7 Resonant dielectric metamaterials offer one potential solution to the issue of loss. Formed from high refractive index resonators, dielectric metamaterial unit cells can support electric and magnetic dipole responses due to Mie
chieving full control over light propagation is an ever present issue in modern day optics. In order to realize such control it is necessary to create devices that allow 0 to 2π phase modulation and/or devices that allow control over the amplitude of light. In conventional optical elements such as birefringent waveplates and lenses, a significant propagation distance is needed to acquire disparate phase accumulation for different polarizations or spatial regions of the beam, thus requiring thick materials that are difficult to integrate into compact platforms.1 One solution to this issue is the use of reflect and transmit-arrays, originally developed at radio frequencies, that allow one to control the amplitude and phase of light using a single, or several, layers of ultrathin antennae.2,3 By changing the geometry of the antenna as a function of position, these arrays allow spatial control over the phase of light. Recently, similar materials, deemed metasurfaces, have been developed at optical frequencies.4 Metasurfaces typically utilize asymmetric electric dipole resonances to allow 0 to 2π phase control for the cross-polarized scattered light. As in transmitarrays, varying the geometry of the resonator as a function of position allows arbitrary control of the phase front of light using a subwavelength-thin film and has led to demonstrations including anomalous refraction,4−8 quarter and half waveplates,9,10 lensing,11−13 and manipulation of orbital angular momentum.14,15 © 2014 American Chemical Society
Received: December 1, 2013 Revised: February 14, 2014 Published: February 18, 2014 1394
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depositing a 380 nm thick amorphous Si (n = 3.7) thin film on quartz. The cut-wires were then created using electron beam lithography and reactive-ion etching. PMMA (n = 1.48) was then spin-coated onto the sample and planarized to serve as the low index dielectric spacer and a silver film was deposited on top, serving as the reflective mirror (see Supporting Information Section 1 and Figure S1 for details). The resulting PMMA thickness, measured with profilometry, was 200 nm. The scanning electron microscope (SEM) image of the fabricated sample is shown in Figure 1b. To experimentally characterize the performance of the polarization converter, we used a supercontinuum light source (Fianium SC400), incident normal to the sample surface with the polarization along the x-axis, which is tilted 45° with respect to the Si cut-wire axis. Two linear polarizers were employed in front and after the sample to measure the reflectance of the same polarization state as that of the incident wave, |rco|2, and that of the perpendicular polarization |rcross|2, as illustrated in Figure 2a. All reflectance measurements were normalized to the reflectance measured from a silver mirror. Figure 2b shows the measured reflectance for both polarizations and the corresponding polarization conversion rate (PCR), defined as |rcross|2/(|rcross|2 + |rco|2), is shown in Figure 2c. The experimental measurements demonstrate that the PCR remains above 98% from 1420 to 1620 nm, and the cross-polarized reflection remains above 97% over this bandwidth, in good agreement with the simulations. Measurements beyond 1620 nm were not possible (shaded region in Figure 2b,c) due to the low quantum efficiency of the spectrometer’s indium gallium arsenide detector and reduced light source intensity at long wavelengths. However, the numerical simulation predicts that 90% PCR extends out to 1720 nm and given the good agreement with theory, we expect the experimentally achievable efficiency to also be preserved over this range. Numerical simulations also show that the waveplate is robust to variations of the dielectric spacer thickness, maintaining a conversion efficiency of >90% over a 300 nm bandwidth for a PMMA spacer layer thickness of 187 nm ±37 nm (Supporting Information Figure S2). The reflectarray also maintains near-unity polarization conversion efficiency for incident angles up to 10° for both s- and ppolarized light (Supporting Information Figure S3). However, the bandwidth of the response is reduced at off-normal incidence due to excitation of a photonic crystal mode in the short-wavelength region of the response. The sensitivity to the angle of incidence is one trade-off associated with using dielectric resonators possessing slightly larger unit cell size compared to their plasmonic counterparts. To better understand the response of the meta-reflectarray, the incident light, which is linearly polarized along the xdirection, can be decomposed into two perpendicular components, u and v, which correspond to the short and long axis of the resonator, respectively (Figure 2d). The numerically simulated reflection amplitude and phase for a resonator array illuminated with polarization along these axes are shown in Figure 2e,f. It can be observed that the reflection amplitudes in both polarizations are close to unity while the relative phase retardation is roughly π throughout the wavelength range where the linear polarization conversion occurs, leading to a 90° polarization rotation when light is incident with polarization along the x- or y-axis of the sample. The high conversion efficiency can also be understood by modeling the field evolution upon multiple reflections within the low-index spacer layer, resulting in constructive and
resonances.20−25 Dielectric metamaterials can be much less absorptive than their metallic counterparts and have been recently utilized to realize zero index metamaterials26 and directional light scatterers27 at optical frequencies. Closely related to this concept are high-contrast gratings (HCGs) and artificial dielectrics. In HCGs, Mie resonances are used to control the phase of transmitted or reflected light at a surface. HCGs have been used to achieve surfaces with near-unity reflection for applications such as mirrors in vertical-cavity surface-emitting lasers,28 quarter waveplates,29 and optical elements with spatial phase variation such as lenses30,31 and spiral phase plates.32 However, one of the drawbacks of this approach is that it is difficult to achieve full 2π phase control while preserving near-unity reflectance with a single layer grating, an issue that becomes more restrictive as the index of the resonator is reduced. In artificial dielectrics,33−35 high index materials are structured to achieve a gradient index along the surface of the film and have been demonstrated to have high diffraction efficiency, exceeding that of blazed gratings. However, strong resonances in the unit cells are not utilized which results in relatively low index contrast (compared to resonant structures) and the need to utilize structured films that have thicknesses that are greater than the free-space wavelength to acquire a 0 to 2π phase shift. This results in the structures with relatively high aspect ratios which can be challenging to fabricate. In this Letter, we demonstrate a broadband dielectric metareflectarray polarization convertor by utilizing structured silicon (Si) cut-wire resonators placed above a silver ground plane. The meta-reflectarray utilizes Mie resonances in the Si resonators, allowing the use of low aspect ratio structures with subwavelength thicknesses. Multiple reflections within the spacer layer also relaxes the required phase delay upon a single pass through the resonator layer, mitigating the trade-off between phase control and efficiency present in single layer HCGs. This allows the meta-reflectarray to serve as a halfwaveplate with near-unity reflectance and over 98% polarization conversion efficiency across a 200 nm bandwidth. Furthermore, by varying the resonator dimensions, broadband 0 to 2π phase control of the reflected cross-polarized light can be achieved while maintaining high conversion efficiency, opening the door to ultracompact reflective phase plates at optical wavelengths. A schematic of the polarization converter is illustrated in Figure 1a. It is composed of an array of Si cut-wires and a silver ground plane, with a low index poly(methyl methacrylate) (PMMA) spacer in between. Device fabrication began with
Figure 1. (a) Schematic of the meta-reflectarray with a unit cell period of p = 650 nm, a = 250 nm, b = 500 nm, t1 = 380 nm and t2 = 200 nm. In the fabricated sample, the resonators are embedded in PMMA and a quartz wafer caps the resonators. (b) SEM image of the sample before spin-coating PMMA and depositing the silver film. 1395
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Figure 2. (a) Schematic of the polarization conversion measurement setup. (b) Measured and simulated reflectance for co- and cross-polarized light. (c) Polarization conversion efficiency of the device. The shaded regions indicate the wavelength range where experimental measurements were not possible due to low detector quantum efficiency. (d) Schematic of the decomposition of linearly polarized incident and reflected light. (e,f) Reflectance and phase for light polarized along the v (purple curves) and u (red curves) axes demonstrating near-unity reflection and a broadband πphase shift.
destructive interference of the cross- and co-polarized light, respectively.10 The polarization conversion region is occurring primarily between long and short-axis resonances, similar to previously reported broadband plasmonic metasurface quarterwave plates.18 In our case, however, this is combined with smoothing of the phase variation across the resonance due to multiple reflections within the spacer layer, resulting in the 200 nm bandwidth over which the PCR remains above 98%. A more in-depth discussion of these phenomena can be found in the Supporting Information, Section 2d and Figures S4 and S5. More interestingly, by properly engineering the cut-wire geometry, a 0 to 2π phase shift can be achieved for the crosspolarized reflected light with near-unity efficiency. This is in contrast to plasmonic V-shaped antenna based metasurfaces, where the majority of scattered light remains in the ordinary component (copolarized), resulting in low signal-to-noise ratio (SNR).4 The two-dimensional colormap of the numerically simulated reflectance, |rcross|2, and phase, φcross, of the metareflectarray with varying Si cut-wire dimensions at a fixed wavelength of 1550 nm, are plotted in Figure 3a,b. In these simulations the PMMA spacer layer thickness is set to 150 nm to match the fabricated reflectarray discussed below. These simulations were performed using a finite-element frequencydomain solver (CST Microwave Studio) with periodic boundary conditions. It can be observed that there is a region of high reflectance in which four antenna dimensions were chosen (circles in Figure 3a,b) to provide an incremental phase shift of π/4 for cross-polarized reflected light. By simply rotating the structures by 90°, the additional π-phase shift can be attained for realizing full 2π coverage while maintaining near-unity efficiency. An additional feature of this reflectarray is that it can maintain high efficiency over a wavelength range of ∼100 nm within the telecommunications band as demonstrated by the
simulated reflection amplitude and phase for the eight resonators as a function of the incident wavelength between 1500 and 1600 nm (Figure 3d,e). Within this range, the crosspolarized reflectance remains above 75% with the greatest drop occurring for resonators 1 and 5 at long wavelengths. However, despite this drop, the average reflectance is 93.6% across this bandwidth. The phase gradient is calculated by taking resonator 1 as a reference at each wavelength and setting its phase advance to zero. Across the l00 nm bandwidth, it can be seen that the phase gradient across the resonators remains linear, ensuring the designed phase profile is maintained. It should also be noted that this meta-reflectarray can be designed using lower index resonator materials such as TiO2 (n = 2.27 at 632 nm) while maintaining high conversion efficiency (Supporting Information Figure S6). This is due to the fact that there are multiple reflections within the film, relaxing the need for achieving a full 2π phase shift from a single pass, which in turn allows one to use broader resonances. The use of lower index transparent dielectrics such as TiO2 permits the design to be potentially scalable to visible wavelengths though at higher frequencies conversion efficiency will be limited by loss in the silver mirror. In order to validate the performance of a variable phase metareflectarray, we fabricated a sample with a spiral phase profile ranging from 0 to 2π with a phase increment of π/4 along the azimuthal direction (shown in Figure 4a,b). The design is based on the eight Si cut-wire resonators modeled in Figure 3. The PMMA layer was measured to be 150 nm thick at the edge of the phase plate using profilometry, though some variation in PMMA thickness is expected due to the different resonator filling fractions across the sample. This particular phase profile leads to the generation of a Laguerre-Gaussian beam with a theoretical cross-polarized reflectance that is above 94.5% for each section of the reflectarray at the center wavelength of 1550 1396
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Figure 3. Simulated cross-polarized reflection (a) magnitude and (b) phase for resonators with varying geometry at a fixed wavelength of 1550 nm. The unit cell period is set as 650 nm and the PMMA spacer thickness is set to 150 nm. (c) Schematic of eight resonators that provide a phase shift from 0 to 2π. The dimension of resonators 1−4 are (1) a = 200 nm, b = 425 nm; (2) a = 225 nm, b = 435 nm; (3) a = 250 nm, b = 450 nm; (4) a = 275 nm, b = 475 nm. Resonators 5−8 are simply rotated by 90° with respect to resonators 1−4. Simulated cross-polarized reflection (d) amplitude and (e) phase for arrays of resonators 1−8 as a function of the incident wavelength. The phase delay of array 1 is set to 0 for each wavelength to serve as a reference.
two beams are tilted and collinear with respect to each other, respectively, as illustrated in Figure 4f−k. In the tilted interference measurement, we slightly rotated the beam in the reference arm such that the E-field of the Gaussian beam was along the transmission axis of the polarizer, preventing it from being filtered out. In order to qualitatively gauge the conversion efficiency of the meta-reflectarray, the linear polarizer placed before the camera was removed, resulting in the images shown in Figure 4l,m. It can be observed that the spiral patterns remain largely unaffected, though there is moderate noise in the center of the pattern that is most likely due to the imperfections in the cut-wire arrays and slight variations in the PMMA thickness across regions with different resonator filling fractions, leading to increased copolarized reflection. Finally, one important aspect that remains to be explored is the role of coupling between the resonators in the array. This has important ramifications for using this type of metareflectarray for realizing short focal length lenses, in which dissimilar resonators are placed adjacent to one another. To explore the role of coupling, we modeled a surface in which the eight resonators from Figure 3, each with a unit cell size of 650 nm × 650 nm, were placed adjacent to one another forming a linear phase gradient over a supercell with length S = 5.2 μm. On the basis of the generalized Snell’s law,4 the surface should
nm. The Laguerre-Gaussian beam has a helical wavefront with a phase singularity in the center characterized by an azimuthally dependent phase term, exp(ilϕ), where l represents the topological charge, which was chosen as l = 1, and ϕ is the azimuthal angle.36 This optical vortex beam carries an orbital angular momentum of ℏl, making it a platform for investigating fundamental physical phenomenon such as spin−orbit interaction in photonic systems,14,15 and such beams have various applications in optomechanics37 and information processing.38−41 The evolution of the vortex beam as a function of incident wavelength was measured by illuminating the sample with a linearly polarized and collimated tunable continuous wave diode laser. A linear polarizer oriented 90° with respect to the illumination polarization was placed in front of the camera to filter out any copolarized light. Images of the reflected crosspolarized beam are shown in Figure 4c−e and have the characteristic intensity minimum at the center that is a direct consequence of self-cancel-out associated with the corkscrew shaped beam. The reflected beam was also measured using a Michelson interferometer with the generated vortex beam and the copropagating Gaussian beam in the sample and reference arm, respectively (see Supporting Information Figure S7 for a schematic of the measurement setup). The dislocated fringe and spiral shape phase patterns are clearly observable when the 1397
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Figure 4. (a) Optical microscope image of the fabricated spiral phase plate composed of eight sections of Si cut-wires, providing an incremental phase shift of π/4. (b) SEM image showing the cut-wires at the center of the reflectarray. (c−e) Experimentally measured intensity profiles of the generated vortex beam with topological charge l = 1. The wavelengths of the incident light are (c) 1500, (d) 1550, and (e) 1570 nm. (f−h) Interference pattern of the vortex beam and the copropagating Gaussian beam when the beam axes are tilted with respect to one another. (i−k) Interference pattern of a vortex beam and a Gaussian beam which have collinear propagation. In (c−k), a linear polarizer is placed in front of the camera to filter out copolarized light. (l,m) Interference pattern of the vortex beam and the Gaussian beam in the absence of the linear polarizer.
exhibit an anomalous reflection peak at an angle of θr = sin−1[(λ0/nS) + sin(θi)], where n is the background index, equal to the index of quartz/PMMA (n = 1.5) in our case, and θi is the incident angle. Numerical simulations were performed to verify the meta-reflectarray performance by illuminating the array at normal incidence (θi = 0°) with a Gaussian beam with a waist size of 7 μm and wavelength of 1550 nm (device performance at 1500 and 1600 nm incident wavelength are also available in Supporting Information Figure S8). The crosspolarized reflected field is plotted in Figure 5a and demonstrates a well-defined phase front while the far-field scattered intensity was collected for both co- and crosspolarized reflection and is plotted as a function of scattered angle in Figure 5b. The peak cross-polarized scattering angle matches well with the theoretical angle of θr = 11.5° (dashed line) and the diffraction efficiency of the +1 order is 83% with the major source of inefficiency arising from light remaining in the zeroth order copolarized beam. The slight reduction in conversion efficiency, compared to the spatially homogeneous arrays, indicates that coupling between resonators plays a role in the response and must be taken into account when designing sharp phase gradients for applications such as lensing when dissimilar resonators are placed next to each another. In summary, we have experimentally demonstrated broadband linear polarization conversion and optical vortex beam generator by employing a meta-reflectarray based on dielectric antennae. Replacing plasmonic antennae with their dielectric counterparts allows loss to be reduced leading to increased efficiency. The trade-off is that dielectric based metasurfaces will invariably have a slightly larger unit cell size at optical frequencies and can be affected by resonator coupling, issues associated with the relatively modest refractive index of viable constituent materials. This may limit applications requiring off-
Figure 5. (a) Electric field plot of the meta-reflectarray illumined with a normally incident x-polarized Gaussian beam with a wavelength of 1550 nm and waist of 7 μm. The metasurface is composed of the eight Si cut-wire resonators from Figure 3 with a unit cell period of 650 nm. (b) Far-field scattered light as a function of angle for both co- and cross-polarizations. The dotted line corresponds to the solution of the generalized Snell’s law and matches well with the full-wave simulation.
normal incidence or sharp phase profiles. However, as shown here, this is not a significant limitation for polarization control 1398
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(21) Peng, L.; Ran, L.; Chen, H.; Zhang, H.; Kong, J.; Grzegorczyk, T. Phys. Rev. Lett. 2007, 98, 157403. (22) Popa, B.-I.; Cummer, S. Phys. Rev. Lett. 2008, 100, 207401. (23) Zhao, Q.; Zhou, J.; Zhang, F.; Lippens, D. Mater. Today 2009, 12, 60−69. (24) Ginn, J.; Brener, I.; Peters, D.; Wendt, J.; Stevens, J.; Hines, P.; Basilio, L.; Warne, L.; Ihlefeld, J.; Clem, P.; Sinclair, M. Phys. Rev. Lett. 2012, 108, 097402. (25) Shi, L.; Tuzer, T. U.; Fenollosa, R.; Meseguer, F. Adv. Mater. 2012, 24, 5934−5938. (26) Moitra, P.; Yang, Y.; Anderson, Z.; Kravchenko, I. I.; Briggs, D. P.; Valentine, J. Nat. Photonics 2013, 7, 791−795. (27) Staude, I.; Miroshnichenko, A. E.; Decker, M.; Fofang, N. T.; Liu, S.; Gonzales, E.; Dominguez, J.; Luk, T. S.; Neshev, D. N.; Brener, I.; Kivshar, Y. ACS Nano 2013, 7, 7824−7832. (28) Huang, M. C. Y.; Zhou, Y.; Chang-Hasnain, C. J. Nat. Photonics 2007, 1, 119−122. (29) Mutlu, M.; Akosman, A. E.; Kurt, G.; Gokkavas, M.; Ozbay, E. Opt. Express 2012, 20, 27966−27973. (30) Lu, F.; Sedgwick, F. G.; Karagodsky, V.; Chase, C.; ChangHasnain, C. J. Opt. Express 2010, 18, 12606−12614. (31) Fattal, D.; Li, J.; Peng, Z.; Fiorentino, M.; Beausoleil, R. G. Nat. Photonics 2010, 4, 466−470. (32) Biener, G.; Niv, A.; Kleiner, V.; Hasman, E. Opt. Lett. 2002, 27, 1875−1877. (33) Lalanne, P.; Astilean, S.; Chavel, P. Opt. Lett. 1998, 23, 1081− 1083. (34) Lalanne, P.; Astilean, S.; Chavel, P.; Cambril, E.; Launois, H. J. Opt. Soc. Am. A 1999, 16, 1143. (35) Sauvan, C.; Lalanne, P.; Lee, M.-S. L. Opt. Lett. 2004, 29, 1593. (36) Allen, L.; Beijersbergen, M.; Spreeuw, R.; Woerdman, J. Phys. Rev. A 1992, 45, 8185−8189. (37) Galajda, P.; Ormos, P. Appl. Phys. Lett. 2001, 78, 249−251. (38) Molina-Terriza, G.; Torres, J. P.; Torner, L. Nat. Phys. 2007, 3, 305−310. (39) Verbeeck, J.; Tian, H.; Schattschneider, P. Nature 2010, 467, 301−304. (40) Genevet, P.; Yu, N.; Aieta, F.; Lin, J.; Kats, M. A.; Blanchard, R.; Scully, M. O.; Gaburro, Z.; Capasso, F. Appl. Phys. Lett. 2012, 100, 013101. (41) Cai, X.; Wang, J.; Strain, M. J.; Johnson-Morris, B.; Zhu, J.; Sorel, M.; O’Brien, J. L.; Thompson, M. G.; Yu, S. Science 2012, 338, 363−366.
or in realizing reflective phase plates for complex beam formation.
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ASSOCIATED CONTENT
S Supporting Information *
Device fabrication, modeling, vortex beam characterization, and Figures S1−S8. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interests.
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ACKNOWLEDGMENTS This work was funded by the Office of Naval Research (ONR) under program N00014-12-1-0571. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.
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REFERENCES
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Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation Yuanmu Yang,† Wenyi Wang,‡ Parikshit Moitra,† Ivan I. Kravchenko,§ Dayrl P. Briggs,§ and Jason Valentine*,∥ †
Interdisciplinary Materials Science Program and ‡Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37212, United States § Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37212, United States S Supporting Information *
ABSTRACT: Plasmonic metasurfaces have recently attracted much attention due to their ability to abruptly change the phase of light, allowing subwavelength optical elements for polarization and wavefront control. However, most previously demonstrated metasurface designs suffer from low coupling efficiency and are based on metallic resonators, leading to ohmic loss. Here, we present an alternative approach to plasmonic metasurfaces by replacing the metallic resonators with high-refractive-index silicon cut-wires in combination with a silver ground plane. We experimentally demonstrate that this meta-reflectarray can be used to realize linear polarization conversion with more than 98% conversion efficiency over a 200 nm bandwidth in the shortwavelength infrared band. We also demonstrate optical vortex beam generation using a meta-reflectarray with an azimuthally varied phase profile. The vortex beam generation is shown to have high efficiency over a wavelength range from 1500 to 1600 nm. The use of dielectric resonators in place of their plasmonic counterparts could pave the way for ultraefficient metasurfacebased devices at high frequencies. KEYWORDS: Metamaterial, dielectric antenna, polarization conversion, vortex beam
A
One of the drawbacks of plasmonic metasurfaces is that they typically suffer from low efficiency due to weak coupling between the incident and cross-polarized fields. Methods to increase efficiency include the use of overlapped electric and magnetic resonances16 as well as the use of thicker metasurface sheets,17 though both of these proposals require materials with increased complexity. One can also employ antennae working away from their resonance positions to realize quarterwaveplates with polarization conversion efficiencies of close to 50% over large bandwidths.18 In another approach, it was shown that an array of metallic antennae in combination with a reflective ground plane can achieve efficiencies of up to 80% for anomalous reflection7,13,19 and linear polarization conversion10 by introducing multiple reflections within the film. While this design avoids complexity, the use of metallic antennae still limits metasurfaces from achieving unity efficiency at optical wavelengths due to the ohmic losses in metal.7 Resonant dielectric metamaterials offer one potential solution to the issue of loss. Formed from high refractive index resonators, dielectric metamaterial unit cells can support electric and magnetic dipole responses due to Mie
chieving full control over light propagation is an ever present issue in modern day optics. In order to realize such control it is necessary to create devices that allow 0 to 2π phase modulation and/or devices that allow control over the amplitude of light. In conventional optical elements such as birefringent waveplates and lenses, a significant propagation distance is needed to acquire disparate phase accumulation for different polarizations or spatial regions of the beam, thus requiring thick materials that are difficult to integrate into compact platforms.1 One solution to this issue is the use of reflect and transmit-arrays, originally developed at radio frequencies, that allow one to control the amplitude and phase of light using a single, or several, layers of ultrathin antennae.2,3 By changing the geometry of the antenna as a function of position, these arrays allow spatial control over the phase of light. Recently, similar materials, deemed metasurfaces, have been developed at optical frequencies.4 Metasurfaces typically utilize asymmetric electric dipole resonances to allow 0 to 2π phase control for the cross-polarized scattered light. As in transmitarrays, varying the geometry of the resonator as a function of position allows arbitrary control of the phase front of light using a subwavelength-thin film and has led to demonstrations including anomalous refraction,4−8 quarter and half waveplates,9,10 lensing,11−13 and manipulation of orbital angular momentum.14,15 © 2014 American Chemical Society
Received: December 1, 2013 Revised: February 14, 2014 Published: February 18, 2014 1394
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depositing a 380 nm thick amorphous Si (n = 3.7) thin film on quartz. The cut-wires were then created using electron beam lithography and reactive-ion etching. PMMA (n = 1.48) was then spin-coated onto the sample and planarized to serve as the low index dielectric spacer and a silver film was deposited on top, serving as the reflective mirror (see Supporting Information Section 1 and Figure S1 for details). The resulting PMMA thickness, measured with profilometry, was 200 nm. The scanning electron microscope (SEM) image of the fabricated sample is shown in Figure 1b. To experimentally characterize the performance of the polarization converter, we used a supercontinuum light source (Fianium SC400), incident normal to the sample surface with the polarization along the x-axis, which is tilted 45° with respect to the Si cut-wire axis. Two linear polarizers were employed in front and after the sample to measure the reflectance of the same polarization state as that of the incident wave, |rco|2, and that of the perpendicular polarization |rcross|2, as illustrated in Figure 2a. All reflectance measurements were normalized to the reflectance measured from a silver mirror. Figure 2b shows the measured reflectance for both polarizations and the corresponding polarization conversion rate (PCR), defined as |rcross|2/(|rcross|2 + |rco|2), is shown in Figure 2c. The experimental measurements demonstrate that the PCR remains above 98% from 1420 to 1620 nm, and the cross-polarized reflection remains above 97% over this bandwidth, in good agreement with the simulations. Measurements beyond 1620 nm were not possible (shaded region in Figure 2b,c) due to the low quantum efficiency of the spectrometer’s indium gallium arsenide detector and reduced light source intensity at long wavelengths. However, the numerical simulation predicts that 90% PCR extends out to 1720 nm and given the good agreement with theory, we expect the experimentally achievable efficiency to also be preserved over this range. Numerical simulations also show that the waveplate is robust to variations of the dielectric spacer thickness, maintaining a conversion efficiency of >90% over a 300 nm bandwidth for a PMMA spacer layer thickness of 187 nm ±37 nm (Supporting Information Figure S2). The reflectarray also maintains near-unity polarization conversion efficiency for incident angles up to 10° for both s- and ppolarized light (Supporting Information Figure S3). However, the bandwidth of the response is reduced at off-normal incidence due to excitation of a photonic crystal mode in the short-wavelength region of the response. The sensitivity to the angle of incidence is one trade-off associated with using dielectric resonators possessing slightly larger unit cell size compared to their plasmonic counterparts. To better understand the response of the meta-reflectarray, the incident light, which is linearly polarized along the xdirection, can be decomposed into two perpendicular components, u and v, which correspond to the short and long axis of the resonator, respectively (Figure 2d). The numerically simulated reflection amplitude and phase for a resonator array illuminated with polarization along these axes are shown in Figure 2e,f. It can be observed that the reflection amplitudes in both polarizations are close to unity while the relative phase retardation is roughly π throughout the wavelength range where the linear polarization conversion occurs, leading to a 90° polarization rotation when light is incident with polarization along the x- or y-axis of the sample. The high conversion efficiency can also be understood by modeling the field evolution upon multiple reflections within the low-index spacer layer, resulting in constructive and
resonances.20−25 Dielectric metamaterials can be much less absorptive than their metallic counterparts and have been recently utilized to realize zero index metamaterials26 and directional light scatterers27 at optical frequencies. Closely related to this concept are high-contrast gratings (HCGs) and artificial dielectrics. In HCGs, Mie resonances are used to control the phase of transmitted or reflected light at a surface. HCGs have been used to achieve surfaces with near-unity reflection for applications such as mirrors in vertical-cavity surface-emitting lasers,28 quarter waveplates,29 and optical elements with spatial phase variation such as lenses30,31 and spiral phase plates.32 However, one of the drawbacks of this approach is that it is difficult to achieve full 2π phase control while preserving near-unity reflectance with a single layer grating, an issue that becomes more restrictive as the index of the resonator is reduced. In artificial dielectrics,33−35 high index materials are structured to achieve a gradient index along the surface of the film and have been demonstrated to have high diffraction efficiency, exceeding that of blazed gratings. However, strong resonances in the unit cells are not utilized which results in relatively low index contrast (compared to resonant structures) and the need to utilize structured films that have thicknesses that are greater than the free-space wavelength to acquire a 0 to 2π phase shift. This results in the structures with relatively high aspect ratios which can be challenging to fabricate. In this Letter, we demonstrate a broadband dielectric metareflectarray polarization convertor by utilizing structured silicon (Si) cut-wire resonators placed above a silver ground plane. The meta-reflectarray utilizes Mie resonances in the Si resonators, allowing the use of low aspect ratio structures with subwavelength thicknesses. Multiple reflections within the spacer layer also relaxes the required phase delay upon a single pass through the resonator layer, mitigating the trade-off between phase control and efficiency present in single layer HCGs. This allows the meta-reflectarray to serve as a halfwaveplate with near-unity reflectance and over 98% polarization conversion efficiency across a 200 nm bandwidth. Furthermore, by varying the resonator dimensions, broadband 0 to 2π phase control of the reflected cross-polarized light can be achieved while maintaining high conversion efficiency, opening the door to ultracompact reflective phase plates at optical wavelengths. A schematic of the polarization converter is illustrated in Figure 1a. It is composed of an array of Si cut-wires and a silver ground plane, with a low index poly(methyl methacrylate) (PMMA) spacer in between. Device fabrication began with
Figure 1. (a) Schematic of the meta-reflectarray with a unit cell period of p = 650 nm, a = 250 nm, b = 500 nm, t1 = 380 nm and t2 = 200 nm. In the fabricated sample, the resonators are embedded in PMMA and a quartz wafer caps the resonators. (b) SEM image of the sample before spin-coating PMMA and depositing the silver film. 1395
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Figure 2. (a) Schematic of the polarization conversion measurement setup. (b) Measured and simulated reflectance for co- and cross-polarized light. (c) Polarization conversion efficiency of the device. The shaded regions indicate the wavelength range where experimental measurements were not possible due to low detector quantum efficiency. (d) Schematic of the decomposition of linearly polarized incident and reflected light. (e,f) Reflectance and phase for light polarized along the v (purple curves) and u (red curves) axes demonstrating near-unity reflection and a broadband πphase shift.
destructive interference of the cross- and co-polarized light, respectively.10 The polarization conversion region is occurring primarily between long and short-axis resonances, similar to previously reported broadband plasmonic metasurface quarterwave plates.18 In our case, however, this is combined with smoothing of the phase variation across the resonance due to multiple reflections within the spacer layer, resulting in the 200 nm bandwidth over which the PCR remains above 98%. A more in-depth discussion of these phenomena can be found in the Supporting Information, Section 2d and Figures S4 and S5. More interestingly, by properly engineering the cut-wire geometry, a 0 to 2π phase shift can be achieved for the crosspolarized reflected light with near-unity efficiency. This is in contrast to plasmonic V-shaped antenna based metasurfaces, where the majority of scattered light remains in the ordinary component (copolarized), resulting in low signal-to-noise ratio (SNR).4 The two-dimensional colormap of the numerically simulated reflectance, |rcross|2, and phase, φcross, of the metareflectarray with varying Si cut-wire dimensions at a fixed wavelength of 1550 nm, are plotted in Figure 3a,b. In these simulations the PMMA spacer layer thickness is set to 150 nm to match the fabricated reflectarray discussed below. These simulations were performed using a finite-element frequencydomain solver (CST Microwave Studio) with periodic boundary conditions. It can be observed that there is a region of high reflectance in which four antenna dimensions were chosen (circles in Figure 3a,b) to provide an incremental phase shift of π/4 for cross-polarized reflected light. By simply rotating the structures by 90°, the additional π-phase shift can be attained for realizing full 2π coverage while maintaining near-unity efficiency. An additional feature of this reflectarray is that it can maintain high efficiency over a wavelength range of ∼100 nm within the telecommunications band as demonstrated by the
simulated reflection amplitude and phase for the eight resonators as a function of the incident wavelength between 1500 and 1600 nm (Figure 3d,e). Within this range, the crosspolarized reflectance remains above 75% with the greatest drop occurring for resonators 1 and 5 at long wavelengths. However, despite this drop, the average reflectance is 93.6% across this bandwidth. The phase gradient is calculated by taking resonator 1 as a reference at each wavelength and setting its phase advance to zero. Across the l00 nm bandwidth, it can be seen that the phase gradient across the resonators remains linear, ensuring the designed phase profile is maintained. It should also be noted that this meta-reflectarray can be designed using lower index resonator materials such as TiO2 (n = 2.27 at 632 nm) while maintaining high conversion efficiency (Supporting Information Figure S6). This is due to the fact that there are multiple reflections within the film, relaxing the need for achieving a full 2π phase shift from a single pass, which in turn allows one to use broader resonances. The use of lower index transparent dielectrics such as TiO2 permits the design to be potentially scalable to visible wavelengths though at higher frequencies conversion efficiency will be limited by loss in the silver mirror. In order to validate the performance of a variable phase metareflectarray, we fabricated a sample with a spiral phase profile ranging from 0 to 2π with a phase increment of π/4 along the azimuthal direction (shown in Figure 4a,b). The design is based on the eight Si cut-wire resonators modeled in Figure 3. The PMMA layer was measured to be 150 nm thick at the edge of the phase plate using profilometry, though some variation in PMMA thickness is expected due to the different resonator filling fractions across the sample. This particular phase profile leads to the generation of a Laguerre-Gaussian beam with a theoretical cross-polarized reflectance that is above 94.5% for each section of the reflectarray at the center wavelength of 1550 1396
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Figure 3. Simulated cross-polarized reflection (a) magnitude and (b) phase for resonators with varying geometry at a fixed wavelength of 1550 nm. The unit cell period is set as 650 nm and the PMMA spacer thickness is set to 150 nm. (c) Schematic of eight resonators that provide a phase shift from 0 to 2π. The dimension of resonators 1−4 are (1) a = 200 nm, b = 425 nm; (2) a = 225 nm, b = 435 nm; (3) a = 250 nm, b = 450 nm; (4) a = 275 nm, b = 475 nm. Resonators 5−8 are simply rotated by 90° with respect to resonators 1−4. Simulated cross-polarized reflection (d) amplitude and (e) phase for arrays of resonators 1−8 as a function of the incident wavelength. The phase delay of array 1 is set to 0 for each wavelength to serve as a reference.
two beams are tilted and collinear with respect to each other, respectively, as illustrated in Figure 4f−k. In the tilted interference measurement, we slightly rotated the beam in the reference arm such that the E-field of the Gaussian beam was along the transmission axis of the polarizer, preventing it from being filtered out. In order to qualitatively gauge the conversion efficiency of the meta-reflectarray, the linear polarizer placed before the camera was removed, resulting in the images shown in Figure 4l,m. It can be observed that the spiral patterns remain largely unaffected, though there is moderate noise in the center of the pattern that is most likely due to the imperfections in the cut-wire arrays and slight variations in the PMMA thickness across regions with different resonator filling fractions, leading to increased copolarized reflection. Finally, one important aspect that remains to be explored is the role of coupling between the resonators in the array. This has important ramifications for using this type of metareflectarray for realizing short focal length lenses, in which dissimilar resonators are placed adjacent to one another. To explore the role of coupling, we modeled a surface in which the eight resonators from Figure 3, each with a unit cell size of 650 nm × 650 nm, were placed adjacent to one another forming a linear phase gradient over a supercell with length S = 5.2 μm. On the basis of the generalized Snell’s law,4 the surface should
nm. The Laguerre-Gaussian beam has a helical wavefront with a phase singularity in the center characterized by an azimuthally dependent phase term, exp(ilϕ), where l represents the topological charge, which was chosen as l = 1, and ϕ is the azimuthal angle.36 This optical vortex beam carries an orbital angular momentum of ℏl, making it a platform for investigating fundamental physical phenomenon such as spin−orbit interaction in photonic systems,14,15 and such beams have various applications in optomechanics37 and information processing.38−41 The evolution of the vortex beam as a function of incident wavelength was measured by illuminating the sample with a linearly polarized and collimated tunable continuous wave diode laser. A linear polarizer oriented 90° with respect to the illumination polarization was placed in front of the camera to filter out any copolarized light. Images of the reflected crosspolarized beam are shown in Figure 4c−e and have the characteristic intensity minimum at the center that is a direct consequence of self-cancel-out associated with the corkscrew shaped beam. The reflected beam was also measured using a Michelson interferometer with the generated vortex beam and the copropagating Gaussian beam in the sample and reference arm, respectively (see Supporting Information Figure S7 for a schematic of the measurement setup). The dislocated fringe and spiral shape phase patterns are clearly observable when the 1397
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Figure 4. (a) Optical microscope image of the fabricated spiral phase plate composed of eight sections of Si cut-wires, providing an incremental phase shift of π/4. (b) SEM image showing the cut-wires at the center of the reflectarray. (c−e) Experimentally measured intensity profiles of the generated vortex beam with topological charge l = 1. The wavelengths of the incident light are (c) 1500, (d) 1550, and (e) 1570 nm. (f−h) Interference pattern of the vortex beam and the copropagating Gaussian beam when the beam axes are tilted with respect to one another. (i−k) Interference pattern of a vortex beam and a Gaussian beam which have collinear propagation. In (c−k), a linear polarizer is placed in front of the camera to filter out copolarized light. (l,m) Interference pattern of the vortex beam and the Gaussian beam in the absence of the linear polarizer.
exhibit an anomalous reflection peak at an angle of θr = sin−1[(λ0/nS) + sin(θi)], where n is the background index, equal to the index of quartz/PMMA (n = 1.5) in our case, and θi is the incident angle. Numerical simulations were performed to verify the meta-reflectarray performance by illuminating the array at normal incidence (θi = 0°) with a Gaussian beam with a waist size of 7 μm and wavelength of 1550 nm (device performance at 1500 and 1600 nm incident wavelength are also available in Supporting Information Figure S8). The crosspolarized reflected field is plotted in Figure 5a and demonstrates a well-defined phase front while the far-field scattered intensity was collected for both co- and crosspolarized reflection and is plotted as a function of scattered angle in Figure 5b. The peak cross-polarized scattering angle matches well with the theoretical angle of θr = 11.5° (dashed line) and the diffraction efficiency of the +1 order is 83% with the major source of inefficiency arising from light remaining in the zeroth order copolarized beam. The slight reduction in conversion efficiency, compared to the spatially homogeneous arrays, indicates that coupling between resonators plays a role in the response and must be taken into account when designing sharp phase gradients for applications such as lensing when dissimilar resonators are placed next to each another. In summary, we have experimentally demonstrated broadband linear polarization conversion and optical vortex beam generator by employing a meta-reflectarray based on dielectric antennae. Replacing plasmonic antennae with their dielectric counterparts allows loss to be reduced leading to increased efficiency. The trade-off is that dielectric based metasurfaces will invariably have a slightly larger unit cell size at optical frequencies and can be affected by resonator coupling, issues associated with the relatively modest refractive index of viable constituent materials. This may limit applications requiring off-
Figure 5. (a) Electric field plot of the meta-reflectarray illumined with a normally incident x-polarized Gaussian beam with a wavelength of 1550 nm and waist of 7 μm. The metasurface is composed of the eight Si cut-wire resonators from Figure 3 with a unit cell period of 650 nm. (b) Far-field scattered light as a function of angle for both co- and cross-polarizations. The dotted line corresponds to the solution of the generalized Snell’s law and matches well with the full-wave simulation.
normal incidence or sharp phase profiles. However, as shown here, this is not a significant limitation for polarization control 1398
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or in realizing reflective phase plates for complex beam formation.
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ASSOCIATED CONTENT
S Supporting Information *
Device fabrication, modeling, vortex beam characterization, and Figures S1−S8. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interests.
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ACKNOWLEDGMENTS This work was funded by the Office of Naval Research (ONR) under program N00014-12-1-0571. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.
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REFERENCES
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