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Dynamic Reflection Phase and Polarization Control in Metasurfaces Junghyun Park, Juhyung Kang, Soo Jin Kim, Xiaoge Liu, and Mark L. Brongersma Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04378 • Publication Date (Web): 05 Dec 2016 Downloaded from http://pubs.acs.org on December 7, 2016

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Dynamic Reflection Phase and Polarization Control in Metasurfaces Junghyun Park,§ Ju-Hyung Kang,§ Soo Jin Kim,§ Xiaoge Liu, and Mark L. Brongersma* Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, United States

ABSTRACT

Optical metasurfaces are two-dimensional optical elements composed of dense arrays of subwavelength optical antennas and afford on-demand manipulation of the basic properties of light waves. Following the pioneering works on active metasurfaces capable of modulating wave amplitude, there is now a growing interest to dynamically control other fundamental properties of light. Here, we present metasurfaces that facilitate electrical tuning of the reflection phase and polarization properties. To realize these devices, we leverage the properties of activelycontrolled plasmonic antennas and fundamental insights provided by coupled mode theory. Indium-tin-oxide is embedded into gap-plasmon resonator-antennas as it offers electricallytunable optical properties. By judiciously controlling the resonant properties of the antennas from under- to over-coupling regimes, we experimentally demonstrate tuning of the reflection

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phase over 180˚. This work opens up new design strategies for active metasurfaces for displacement measurements and tunable waveplates.

KEYWORDS: metasurface, electrical gating, phase control, polarization control

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The ease of fabrication and practicality of 2-dimensional metamaterials, or metasurfaces, has stimulated the development of a wide range of applications.1–3 Their operation relies on the ability of resonant, subwavelength antennas, to effectively capture and rescatter an incident light wave with a well-defined amplitude and phase. This notion has already been utilized to create a variety of new functional optical-elements and to effectively replace bulky conventional optical components. For example, by controlling the phase and amplitude of reflected or transmitted light, researchers have been able to steer, focus, absorb, and reflect light and to generate optical beams with desired polarization properties.4–13 Metasurface ‘skins’ have also been placed over objects to effectively cloak them.14 The tantalizing properties of passive metasurfaces have prompted new research on actively-controllable metasurfaces that open additional opportunities, most notably chipscale beam steering devices and ultrathin modulators. For this purpose, active electro-optical materials such as, low-dimensional graphene15–17 and transition metal dichalcogenides,18,19 transparent conducting oxide (TCO),20–23 highly-doped semiconductors,24–26 phase change materials (PCM)27, and mechanical reconfiguration28,29 have been explored. As the interaction length/time for light passing through ultrathin metasurfaces is short, all of these materials have in common that they need to feature extreme tunability of their optical properties. For many applications some optical materials losses can be tolerated as long as unity-order changes in the real index can be achieved. Recently several works successfully demonstrated amplitude tuning of free-space and guided waves using such materials.20-22,27 As a next frontier, novel metasurface configurations are considered that are capable of active phase tuning of light. Unlike the remarkable and swift progress in achieving active amplitude control, the empirical demonstration of large phase changes has been elusive. Their realization 3


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requires different device design and optimization. Brute-force optimization of large-area, nanostructured metasurface designs are computationally very expensive and devoid of physical intuition. In this letter, we explain how coupled mode theory (CMT)30 can be used to design and understand the operation of an electrically-tunable metasurface that affords 180° phase control. It is constructed from a dense array of metal-insulator-metal (MIM) gap plasmon resonators. We show that the largest swing in the reflection phase can most easily be achieved by operating the resonators near critical coupling. Here, the large phase control comes at a cost of substantial optical losses. We discuss how such losses can be reduced in the future as new tunable materials become available with improved optical properties.

Results Design of metasurfaces for dynamic reflection phase control using coupled mode theory Figure 1(a) shows a schematic diagram of the proposed electrically-tunable metasurface device. A subwavelength scale Au nanostrip-array is fabricated by conventional liftoff techniques on an indium-tin-oxide (ITO)/Al2O3/Au stack that was grown on a fused silica substrate (See Methods.).22 The thickness of each Au nanostripe and underlying ITO, Al2O3, and Au layers are 50 nm, 20 nm, 115 nm, and 50 nm, respectively. The stripe period was chosen as 2.2 µm. Fullfield simulations reveal that highly confined gap plasmon modes can be excited between the Au nanostrip and bottom Au layer by y-polarized top illumination (inset to Figure 1(a)). The ITO is

(

)

modeled as a Drude metal, ε = εinf − ω p2 / ω 2 + iΓω , where εinf , ω p , and Γ are infinite frequency permittivity, plasma frequency, and collision frequency, respectively.22,31-34 The application of an electrical bias between the ITO and bottom Au layer is used to accumulate or deplete carriers in 4


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the ITO film to induce a change in the scattering properties of the gap plasmon resonators in such that the reflection phase of an incident light wave is altered. Let us consider the optical behavior that can be expected from this type of metasurface. We use full-field simulation (See Methods.) to calculate the frequency evolution of the complex reflection coefficient for three biasing conditions (Figure 1(b)). The blue, red, and green curves represent cases for which a negative, zero, and positive bias are applied to the metal stripes to change the carrier density in the underlying oxide and thus its plasma frequency. For the unbiased case, we assume a doped ITO film with ε inf = 3.9 , ωp,0 = 1.3 × 1015 rad/s, and Γ = 2.6 × 1014 rad/s. For illustrative purposes, we further assume that upon application of a negative or positive bias, the plasma frequency can be increased to ωp,+ = 1.52 × 1015 rad/s or decreased to the far IR, causing the permittivity to closely approach ε inf = 3.9 in the spectral regime of operation. We note upfront that these changes in the permittivity are large compared to those we achieved in our experiments that we discuss later; these larger values facilitate a clear graphical illustration of the essential physics. Later realistic values are used for a detailed comparison of theory and experiments. As the permittivity is changed, it will impact the amplitude and reflection phase of normally-incident plane waves. This can be quantified by a complex reflection coefficient: rtot = rtot,0 exp(iθtot). For each biasing condition, rtot traces out counterclockwise circular paths in the complex plane as the frequency is ramped up (See Figure 1(b)). The radii of the circles and their centers are different, leading to distinct spectral reflection properties for the different biasing conditions. This also implies, for a given operation wavelength (open dots in Figure 1(b)), the reflection phase pickup can be controlled.

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To understand the nature of the spectral and bias-dependent behavior of the reflection phase pickup, we depict a conceptual model in Figure 1(c). This model assumes that an incident light wave can be reflected from the metasurface by flowing through two channels: a non-resonant channel and resonant scattering channel. There is a direct, non-resonant channel by which the light reflects from the Au back mirror with a reflection coefficient rnr = rnr,0 exp(iθnr), which is close to -1 (See Supporting Information S1.). Here, the subscript nr denotes non-resonant. This follows from the fact that, in the mid-infrared spectral range, the Au film serves as a high impedance mirror that produces a reflection amplitude rnr,0 close to 1 and a reflection phase θnr of 180°. Alternatively, as shown in green label, the light can flow through a resonant scattering channel by which it flows through the gap plasmon resonators that facilitate some energy storage.22 The reflection term through the resonant scattering channel is represented by rr = rr,0exp(iθr), where the subscript r denotes resonant. Upon illumination with y-polarized light, these resonators exhibit plasmon currents running in opposite directions in the strip and substrate and thus serve as magnetic resonators. When the illumination frequency is scanned through the magnetic resonance, the reflection phase for this channel θr evolves from -90° to 0° on resonance, and ultimately to +90°. At the same time, the scattering cross section for this resonant pathway will increase and decrease. This changes the relative contributions of the resonant and non-resonant pathways to the total reflected light signal, which is given by: rtot = rnr + rr .

(1)

Critical coupling can be achieved by allowing the reflection coefficients for both channels to have the same amplitude ( rnr ,0 ≅ rr ,0 ) and a 180°-phase difference. The resonator periods were judiciously designed to be able to achieve this special condition at zero bias, which is understood 6


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from the red circle in Figure 1(b) that intersects with origin (rtot ≅ 0). The net reflectivity becomes zero and perfect absorption is achieved (the red dot in Figure 1(b)). We aim to electrically tune the magnitude of the indirect channel so as to be less than or greater than the direct channel, and thereby manipulate the relative importance of the direct and indirect channels and to control the reflection phase by moving in and out of critical coupling. By tuning the resonator from the critical coupling point to an under-coupling regime, the flow through the resonant channel become smaller than the direct channel (rnr,0 > rr,0) and the reverse will hold for over-coupling. In the under-coupling regime (blue curve in Figure 1(b)), the (total) reflection coefficient follows a trajectory located in the 2nd and 3rd quadrants of the complex plane. As such, the reflection phase covers the limited range from 90° to 270°. The reflection coefficient for the over-coupling regime (green curve) covers four quadrants so that the achievable reflection phase covers the full 0° to 360°. It should be pointed out that the trajectory of the complex reflectivity coefficient does not form a closed circle here, because the metal substrate and strips become transparent above the plasma frequency of Au. When the metasurface is excited on resonance at the critical coupling point (red dot), one can move to a state of under-coupling (blue dot) by simply applying a negative bias or to a state of overcoupling (green dot) by applying a positive bias. It is important to note that the green dot represents a state that features a similar reflection amplitude and 180°-phase difference from the state denoted by the blue dot. Therefore, switching between these two states leads to a 180°change in the reflection phase of metasurface. The aforementioned qualitative analysis can be supported by a rigorous quantitative approach. By applying CMT to this metasurface, one can understand the shape of the curves in the Figure 7


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1(b) based on the magnitudes of the radiation rate γ rad and absorption rate γ abs for the resonators making up the metasurface. Using CMT, the following expression for the total reflection coefficient can be derived:30 rtot =

(γ rad − γ abs ) − i (ω − ω0 ) . (γ rad + γ abs ) + i (ω − ω0 )

(2)

Here, ω and ω0 are the angular frequency of light and the resonance angular frequency. In the supporting information, we show that the allowed complex values of rtot lie on a circle centered at

( −γ

abs

/ ( γ rad + γ abs ) ,0 )

having the radius of γ rad / (γ rad + γ abs ) (See Supporting

Information S1.). In this setup, the application of an electrical bias tunes the Ohmic dissipation in the resonator ( γ abs ). When the resonator is made highly dissipative by increasing the carrier density in the ITO to realize a situation where γ abs > γ rad , the amplitude of the reflected electric field from the resonant scattering channel is smaller than that from the direct channel (rr,0 < rnr,0), and thus the frequency complex reflection coefficient is constrained to the 2nd and 3rd quadrants (blue curve in Figure 1(b)). On the other hand, if the system is made less lossy by a partial depletion of the ITO to realize γ abs < γ rad , the resonant scattering channel is dominant (rr,0 > rnr), and the complex reflection coefficient features a trajectory covering all four quadrants (green curve in Figure 1(b)). This explains why the electrical tuning of the loss via the carrier density can cause substantial changes in the reflection phase. Non-linear least square fitting of the CMT (Eq. 2) to the full-field simulations presented in Figure 1(b) gives values for ( γ rad , γ abs ) of (1.41, 2.64), (1.45, 1.45), and (1.41, 0.79) in units of 1013 rad/s for the cases of accumulation (blue, under-coupling), no-bias (red, near critical coupling), and depletion (green, over-coupling) 8


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respectively. It can be seen that upon electrical gating, the magnitude of γrad remains nearly constant, while γabs varies. To illustrate the impact of moving from under- to over-coupling on the reflection phase in a different fashion, we plot the real part of the transverse electric field of the reflected light (Figure 1(d)). The left panel shows the case for x-polarized light (parallel to the grating) illumination. There is no resonant mode supported for this polarization and the reflection phase is 180° for all frequencies. As such, it serves as a useful reference for the reflection changes that occur for ypolarized illumination (center and right panel). In moving from the blue spot to the green spot in Figure 1(b), the magnitude of the scattered fields from the resonators increases and the phase of the reflected wave changes from 180° to 0°. The insets to the figure more specifically show the phase and magnitude of MIM resonance that support the relations between direct reflection and resonant scattering. The field intensity profiles provided in Supporting Information S2 also agree well with the analysis above. To ensure that the amplitude of the two competing reflection channels (direct reflection and resonant scattering) are of comparable magnitude, the design parameters of metasurface need to be chosen to exhibit the critical coupling condition at no-bias. To achieve this, we start by finding the condition for which the period of the resonators is approximately equal to the absorption cross-section (σabs). For example, using a series of full-field simulations we find that for target wavelength of 6 µm we can use 1400-nm-wide and 50-nm-thick Au stripes that are spaced by 115–nm-Al2O3 from the Au substrate. Such resonators feature a resonance at this wavelength. From further simulations and experimental measurements, it is found that the period P of about 2.2 µm matches with σabs in the spectral region of interest 5 – 7 µm (See Supporting 9


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Information S3.). Next, we found that with the optimal period of 2.2 µm, the width of metal strip can be varied to attain critical coupling at other wavelengths of interest in the mid infrared. Figure 2(a) shows this in a map of reflectivity versus illumination wavelength and strip width. It is seen that the reflection-dip red-shifts as the width of strip increases. To verify this point, we have fabricated four representative samples featuring stripe widths of 1240, 1400, 1570 and 1875 nm as indicated by the white dots on the map. The experimental reflection spectra taken from these samples are displayed in Figure 2(b), and show near-critical coupling across the broad wavelength range from 5.4 µm to 7.3 µm. Figure 2(c) presents the electric field maps of the sample with stripe widths of 1400 nm that is used for further experiments. It clearly shows the field concentration in the gap between the stripe and substrate. The overlaid flowlines of the Poynting vector show how light is effectively funneled into the gap region through the excitation of a gap plasmon. At critical coupling all of the light flows into the resonator and none of the flow lines hit the substrate area-between the resonators.

Experimental demonstration of dynamic reflection phase control To experimentally demonstrate the proposed working principle for reflection phase tuning, we fabricate and characterize a sample designed by using the full-field simulation in such a way that the electrical gating can switch the status of the sample between the over- and under-coupling regimes. The top Au grating width and period are 1420 nm and 2200 nm, respectively, and the electrical pad of the ITO layer and the Au gratings are fabricated using standard photo- and ebeam-lithography. 10


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The reflection phase is measured by illuminating the sample with a broadband thermal light source that is linearly polarized at a 45°-tilt angle with respect to the stripe direction (Figure 3(a)). The reflected signal intensity is measured after an analyzer with a polarization angle θ using an Fourier transform infrared (FT-IR) spectrometer. The dependence of the reflected light intensity on the polarizer angle θ is related to the reflection phase difference between the parallel (x)-polarization and perpendicular (y)-polarization via a cross-polarization method (See Supporting Information S4.). In our approach we assume that the reflection phase for the xdirection is frequency-independent, and that for the y-direction the gap resonance can cause a phase delay with increasing frequency as one moves through the resonance. This is verified by simulations for the relevant range of geometries and physically results from the fact that no phase-shifting resonance can be excited for the polarization with the electric field along the length of the stripes. The modelling is based on the fact that the intensity for a known and controlled polarizer angle can be analytically expressed in terms of the x- and y-direction reflection coefficients of the metasurface using a Jones matrix and an appropriate coordinate transform matrix. By using this relationship, a non-linear least square fitting with the reflection coefficients as fitting parameters allows us to extract the phase information (See Supporting Information S4.). As an example, the empirically obtained intensity variation near the resonance (wavenumber of 1680 cm-1 for depletion case, the wavelength of 5.9 µm) is shown as the green solid curve in the inset of Figure 3(b). This result is well reproduced by our CMT modeling (the red dashed curve). Assuming that the reflection phase of the parallel polarization remains constant at 180° as discussed above, we can extract the reflection phase of the perpendicular polarization only. 11


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Figure 3(b) shows the empirically obtained reflection phase of the perpendicular polarization for the cases of in which the sample is biased at - 40 V, 0 V, and 40 V. The CMT is applied in order to correct the phase angle that is subject to intrinsic degeneracy of the y-direction reflection phase (See Supporting Information S4.). Without an applied bias (red curve), the reflection phase is 180° for the frequencies below the resonance frequency (quantified in wavenumbers with the FT-IR). Around the resonance, at the wavenumber of ~1680 cm-1, the reflection phase exhibits an abrupt change. This is because the amplitude of the resonant scattering is close to but slightly smaller than that of the direct, non-resonant reflection. In other words, the no-bias case features a state that is very close to critical coupling (very slightly under-coupling, as can be confirmed from the reflection phase in Figure 3(b)). Upon application of a negative bias (blue curve), an accumulation layer is formed and the system loss increases due to the increase in carrier density. This leads to a reduction of the amplitude of the resonant scattering channel. The metasuraface is moved into the under-coupling regime with a larger contrast between γ rad and γ abs , and the reflection phase more gently increases with increasing frequency. Upon application of a positive bias (green curve), a depletion layer is formed and the amplitude of the resonant scattering channel surpasses that of the non-resonant channel. As a result, the metasurface operates in the over-coupling regime. The evolution of the phase frequency moves from +180° over a complete 360°. At the resonance frequency, a 180° phase difference is achieved in going from the under- to over-coupling regime. For practical application of this type of metasurfaces, it is important to quantify the evolution of the reflection phase at a certain wavelength with electrical bias. To examine this property, we conduct the measurement of the reflection phase under the electrical bias from -40 V to +40 V 12


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with the incremental step size of 10 V (Figure 3(c)). The negative bias induces the undercoupling regime, and thus the reflection phase change is small. Around the bias of +10 V, a significant change in the reflection phase is observed. This indicates the switch from the underto over-coupling regimes. As the electric bias grows, the reflection phase change is further increased, ultimately asymptoting to the expected value of 180°. For practical applications, it is desirable to achieve changes in the reflection phase without changes in the amplitude. Since the proposed working principle is based on the switching between the under- and over-coupling regimes by moving through critical coupling, however, the amplitude exhibits inevitable changes. To investigate the extent of the amplitude modulation as the counterpart of the phase modulation in Figure 3(c), we plot the reflectance as a function of the electrical bias in Figure 3(d). It shows the minimum value of 1.4% at the bias of 0 V (near the critical coupling regime). The maximum reflectance is 2.4% at the bias of +40 V. It should be noted that the trajectory of the reflection coefficient upon application of a gate bias does not necessarily need to move through the origin and a more stable amplitude could be achieved at the cost of a decreased change in the reflection phase. The current amplitude modulation of 72% is relatively large, and further efforts are needed to reduce this while keeping a larger phase change. The maximally achievable phase change and the variation of the amplitude are ultimately limited by the dielectric strength of the gate oxide and the DC permittivity, which are respectively are 7.36 MV/cm and 7.74 for the Al2O3 used in this study as well as the collision frequency of the carriers in ITO (2.6×1014 rad/s). With the limited modulation efficiency, the reflection coefficient at a given wavelength travels a quasi-linear trajectory in the complex reflection coefficient domain. The phase change along the trajectory is the angle of a triangle 13


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composing the two end-points of the trajectory and origin. As such, the phase change maximum is around 180° for our system In addition, the operation wavelength for the maximum phase change is around 5.94 µm. As the wavelength is increased or decreased, the phase change upon bias is less than 180°. The bandwidth for which the achievable phase change is more than 135° is 47 nm, and that for 90° is 115 nm. The continuous discovery of new, high performance plasmonic materials33,34 will enable improved designs given the physical insights gained in this work, since they will allow for larger carrier density modulation upon application of an electrical bias. For example, with sufficiently low loss materials, a 360° reflection phase change could be achieved at a constant amplitude by sweeping the resonant frequency of the strip resonators through the wavelength of operation. For real applications,

it is also important to understand

other dynamic properties such as the amplitude modulation (reconfigurability) and the operating speed. Those are dealt with in detail in our previous paper cited as Ref. 22. It turned out that changes in the reflectance R of up to 15%P (or a modulation ratio ∆R/R = 35%) and operation at frequencies in access of hundreds kHz are possible22. Here we mainly focus on the phase modulation properties.

Discussion In conclusion, we presented a way to achieve large phase tuning of 180° in the reflected field from metasurfaces composed of plasmonic resonator arrays. By designing the resonators to have comparable amplitudes between two reflections channels (the direct reflection and the resonant scattering), electrical gating of the metasurface can switch which channel is dominant and cause significant reflection phase change of up to 180°. As a proof-of-concept, the MIM plasmonic 14


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resonators including ITO as an active medium are fabricated and characterized. Direct experimental observation of the reflection phase successfully verified the proposed working principle. Considering that many other resonator types and configurations being used as building blocks of metasurfaces can easily be designed to operate near the critical coupling regime, we emphasize that our approach may provide universal guidelines for future approaches for phase tuning in metasurfaces without loss of generality. The large 180° can effectively be used to change the state of polarization as suggested in Figure 1(a). More generally, the proposed concepts point at ways to achieve arbitrary optical control with amplitude, phase, and polarization (See Supporting Information S5.) with the help of active metasurfaces.

ASSOCIATED CONTENT Supporting Information The Supporting Information Available: Analysis of under-, critical- and over-coupling with coupled-mode theory, analysis of cross-polarization measurement and operation of tunable waveplate. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author E-mail: [email protected] Present Addresses J.P.: Samsung Advanced Institute of Technology, Samsung Electronics, 130 Samsung-ro, Yeongtong-gu, Suwon-Si, Gyeonggi-do, 16678, Korea 15


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Notes The authors declare no competing financial interest. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. §These authors contributed equally to this work.

ACKNOWLEDGEMENT This work was supported by the California Metaphotonics Cluster funded by the Samsung corporation and an individual investigator grant from the Naval Research Laboratories.

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(12) Pors, A.; Albrektsen, O.; Radko, I. P.; Bozhevolnyi, S. I. Sci. Rep. 2013, 3, 2155. (13) Lin, D.; Fan, F.; Hasman, E.; Brongersma, M. L. Science 2014, 345, 298. (14) Ni, X.; Wong, Z. J.; Mrejen, M.; Wang, Y.; Zhang, X. Science 2015, 349, 1310. (15) Yao, Y.; Kats, M. A.; Genevet, P.; Yu, N.; Song, Y.; Kong, J.; Capasso, F. Nano Lett. 2013, 13, 1257. (16) Dabidian, N.; Kholmanov, I.; Khanikaev, A. B.; Tatar, K.; Trendafilov, S.; Mousavi, S. H.; Magnuson, C.; Ruoff, R. S.; Shvets, G. ACS Photonics 2014, 2, 216. (17) Jang, M. S.; Brar, V. W.; Sherrott, M. C.; Lopez, J. J.; Kim, L.; Kim, S.; Choi, M.; Atwater, H. A. Phys. Rev. B 2014, 90, 165409. (18) Liu, Y.; Tom, K.; Wang, X.; Huang, C.; Yuan, H.; Ding, H.; Ko, C.; Suh, J.; Pan, L.; Persson, K. A.; Yao, J. Nano Lett. 2016, 16, 488. (19) Zhang, Y.; Wang, S.; Yu, H.; Zhang, H.; Chen, Y.; Mei, L.; Lieto, A. D.; Tonelli, M.; Wang, J. Sci. Rep. 2015, 5, 11342. (20) Feigenbaum, E.; Diest, K.; Atwater, H. A. Nano Lett. 2010, 10, 2111. (21) Yi, F.; Shim, E.; Zhu, A. Y.; Zhu, H.; Reed, J. C.; Cubukcu, E. Appl. Phys. Lett. 2013, 102, 221102. (22) Park, J.; Kang, J.–H.; Liu, X.; Brongersma, M. L. Sci. Rep. 2015, 5, 15754.

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(23) Lee, H. W.; Papadakis, G.; Burgos, S. P.; Chander, K.; Kriesch, A.; Pala, R.; Peschel, U.; Atwater, H. A. Nano Lett. 2014, 14, 6463. (24) Jun, Y. C.; Reno, J.; Ribaudo, T.; Shaner, E.; Greffet, J.-J.; Vassant, S.; Marquier, F.; Sinclair, M.; Brener, I. Nano Lett. 2013, 13, 5391. (25) Inoue, T.; De Zoysa, M.; Asano, T.; Noda, S. Nature Mater. 2014, 13, 928. (26) Lee, J.; Jung, S.; Chen, P.-Y.; Lu, F.; Demmerle, F.; Boehm, G.; Amann, M.-C.; Alù, A.; Belkin, M. A. Adv. Opt. Mater. 2014, 2, 1057. (27) Tittl, A.; Michel, A.-K. U.; Schäferling, M.; Yin, X.; Gholipour, B.; Cui, L.; Wuttig, M.; Taubner, T.; Neubrech, F.; Giessen, H. Adv. Mater. 2015, 27, 4597. (28) Ou, J.-Y.; Plum, E.; Zhang, J.; Zheludev, N. I. Nature Nanotech. 2013, 8, 252. (29) Valente, J.; Ou, J.-Y.; Plum, E.; Youngs, I. J.; Zheludev, N. I. Nature Comm. 2015, 6, 7021. (30) Haus, H. A. Waves and Fields in Optoelectronics; Prentice-Hall, New Jersey, 1984. (31) Liu, X.; Park, J.; Kang, J.-H.; Yuan, H.; Cui, Y.; Hwang, H. Y.; Brongersma, M. L. Appl. Phys. Lett. 2014, 105, 181117. (32) Boltasseva, A.; Atwater, H. A. Science 2011, 331, 290. (33) Naik, G. V.; Shalaev, V. M.; Boltasseva, A. Adv. Mater. 2013, 25, 3264. (34) Kobayashi, E.; Watabe, Y.; Yamamoto, T. Appl. Phys. Express 2015, 8, 015505. 19


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(35) Liu, X.; Kang, J.-H.; Park, J.; Brongersma, M. L. Electrical Tuning of a Quantum Plasmonic Resonance (submitted).

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Figures

Figure. 1 Design of an electrically tunable, active metasurface capable of achieving a 180° change in the reflection phase of light. (a) Device schematic of an electrically tunable metasurface constructed from plasmonic gap resonators. Phase of the reflected light is controlled from 0° to 180° by electrically tuning the carrier density of ITO material inside the gap resonator. Inset shows the electric fields near the metasurface on resonance. (b) The trajectory of the complex reflection coefficient with increasing frequency for three representative case, where the metasurface is placed in state of under- (blue), critical (red), and over-coupling (green). Blue and green dots indicate the state of 180° phase-difference between under- and over-coupling. The 21


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red dot indicates the critical coupling condition. (c) Intuitive model for which incident light can be directly reflected or follow a resonant pathway through the gap plasmon resonators. The phase associated with the direct reflection pathway dominates the reflection in the undercoupling regime, whereas the phase of the resonant scattering determines the reflection phase in the over-coupling condition. (d) Electric field images of the reflected light wave used to illustrate the change in reflection phase difference between under- and over-coupling regimes. TM polarized (with electric field parallel to gratings) illumination (left) does not excite a gap plasmon resonance and therefore the reflected light is similar to that of a planar Au mirror. On the other hand, for TE (with electric field perpendicular to gratings) polarized illumination, the reflection phase can be tuned by 180° by changing the applied bias from -40 V to +40 V. Inset shows a zoom-in of the electric field near the resonator.

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Figure. 2 Optimization of metasurface for operation near critical coupling at a designer wavelength. (a) Map of the metasurface reflectivity versus wavelength and strip width. The resonator period is fixed to 2.2 µm. Horizontal dashed lines indicate the specific widths of 23


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devices prepared for our experimental demonstration. White dots indicate the reflection minima obtained from reflection measurements. (b) Experimental reflection spectra of four representative samples with specific widths that shows near critical coupling at different target wavelengths. (c) Electric field images and incident power flow lines for illumination of a metasurface with 1400-nm-wide stripes at a wavelength 6 µm. (d) SEM image of fabricated sample with 1400-nm-wide stripes.

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Figure. 3 Experimental demonstration of phase tuning using active metasurface. (a) Schematic of the experimental setup for a polarization-based measurement of the reflection phase. (b) Measured spectral dependence of the reflection phase of light for three different bias conditions that place the metasurfacein a state of under-coupling (blue), near critical-coupling (red), and over-coupling (green). A electrically-induced phase change of 180° can be achieved at a wavenumber of 1680 cm-1 (gray vertical line). (c), (d), Phase (c) and intensity (d) of the reflected light at a wavenumber of 1680 cm-1 and for different biasing conditions. The abrupt change in reflection phase near 10 V is attributed to the switching of metasurface from under- to overcoupling. The reflectance shows a minimum value of 1.4% around 0 V, and the variation is around 72%. 25


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METHODS Fabrication The bottom Au layer of the plasmon resonators was deposited on top of a smooth quartz substrate using e-beam evaporation. Atomic layer deposition (ALD) was used to deposit an alumina (Al2O3) layer with a thickness of 115 nm as a gate oxide. The ITO film has a separate electric contact pad that was defined by using a standard photolithography and a DC magnetron sputtering followed by a liftoff process. The top Au metal stripes were generated via a standard e-beam lithography and e-beam evaporation, followed by liftoff.

Simulation A commercial finite-difference time-domain (FDTD) tool is used (LumericalTM) for the metasurface simulations. The mesh size for the simulations is set as 0.5 nm inside the MIM resonator for accurate monitoring of switching mechanism. In all simulations, ITO is modeled as Drude metal with the collision frequency Γ, the plasma frequency ωp, and infinite frequency permittivity εinf to be set as 2.6 × 1014 rad/s, 1.3 × 1015 rad/s, and 3.9, respectively. The thickness of the ITO layer is 20 nm. A 1.5 nm-thick-layer from the upper interface and a 5 nm-thick-layer from the bottom interface are modeled as a depleted regions induced by band bending and enhanced by quantum size effects35. The thickness of the Al2O3 films is set to 115 nm, and the experimentally measured refractive index by ellipsometry is used for the simulation. In the theoretical analysis in Figures 1(b) and 1(c), the ITO layer is tuned to form accumulated 27


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(negative) or depleted (positive) regions. To display the proposed physics effectively, the carrier density is taken to change in a large region of 14 nm from the bottom interface. For accumulation, ωp is set to 1.5 × 1015 rad/s, and for depletion, ε is set as εinf. The width of top Au strip and period of MIM structure are 1.4 µm and 2.2 µm, respectively. The reflection spectrum is obtained by monitoring the reflected power flow in the far field regime and the power flow lines are plotted by calculating Poynting vector, i.e. Stot = Etot × Htot, in a steady state illumination condition.

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10

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Ey

Light

1

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1 2V 3 4

Au ITO Al2O3 Au

Im{r}

Reflection phase ( °)

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0 Negative-bias No-bias Positive-bias

-1 -1

0 Re{r}

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ACS+ Paragon Plus Environment + + 50

0 -40

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= 5.94µm 20

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Dynamic Reflection Phase and Polarization ... - ACS Publications

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