Photoexcited Graphene Metasurfaces: Significantly Enhanced and

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Photoexcited graphene metasurfaces: Significantly enhanced and tunable magnetic resonances Yuancheng Fan, Nian-Hai Shen, Fuli Zhang, Qian Zhao, Zeyong Wei, Peng Zhang, Jiajia Dong, Quanhong Fu, Hongqiang Li, and Costas M. Soukoulis ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00057 • Publication Date (Web): 27 Feb 2018 Downloaded from http://pubs.acs.org on February 27, 2018

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Photoexcited graphene metasurfaces: Significantly enhanced and tunable magnetic resonances Yuancheng Fan,∗,† Nian-Hai Shen,‡ Fuli Zhang,† Qian Zhao,¶ Zeyong Wei,§,k Peng Zhang,‡ Jiajia Dong,† Quanhong Fu,† Hongqiang Li,§,k and Costas M. Soukoulis‡,⊥ Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Department of Applied Physics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China, Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA, State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China, The Institute of Dongguan-Tongji University, Dongguan 523808, Guangdong, China, Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Science and Engineering, Tongji University, Shanghai 200092, China, and Institute of Electronic Structure and Laser, FORTH, 71110 Heraklion, Crete, Greece E-mail: [email protected]

Abstract ∗ To

whom correspondence should be addressed Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Department of Applied Physics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China ‡ Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA ¶ State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China § The Institute of Dongguan-Tongji University, Dongguan 523808, Guangdong, China k Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Science and Engineering, Tongji University, Shanghai 200092, China ⊥ Institute of Electronic Structure and Laser, FORTH, 71110 Heraklion, Crete, Greece † Key

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Artificially constructed metamaterials or metasurfaces with tailored resonant elements provide a revolutionary platform for controlling light at the subwavelength scale. Switchable or frequency-agile meta-devices are highly desirable in achieving more flexible functionalities and have been explored extensively by incorporating various materials, which respond to external stimuli. Graphene, a two-dimensional material showing extraordinary physical properties, has been found very promising for tunable meta-devices. However, the high intrinsic loss of graphene severely obstructs us from achieving high-quality resonance in various graphene metamaterials and metasurfaces, and the loss compensation can be considered as a straightforward strategy to take further advantages of enhanced light-graphene interactions. Here, we demonstrate that the photoexcited graphene, in which the quasi-Fermi energy of graphene changes corresponding to optical pumping, can boost the originally extremely weak magnetic resonance in graphene split ring metasurface, showing remarkable modulations in the transmission. Our work pioneers the possibilities of optically pumped graphene metasurfaces for significant enhancement of resonances and feasible modulations.

Keywords: graphene plasmonics, terahertz metamaterials, magnetic resonance, gain, loss compensation, surface conductivity

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Metamaterials, or its two-dimonsional counterpartałmetasurfaces, ˛ refer to a class of artificial microstructures that possesses unattainable properties in natural occurring medium. These microstructures usually consist of subwavelength metallic particles, so-called meta-atoms. 1–4 Since the first experimental demonstration of negative refraction with periodic metallic wire plasma and magnetic split ring resonators at microwave frequency, 5 many novel electromagnetic phenomena and extraordinary applications have been inspired ranging from microwave to visible frequencies, such as sub-diffraction lens, 6,7 optical cloak, 8 trapped rainbow, 9 polarizer, 10,11 perfect absorber 12 and wavefront engineering. 13–19 However, most of pre-designed metamaterials only work within fixed narrow frequency band, which limits many practical applications. 20,21 Therefore, in the past few years, there have reported various meta-devices with some materials responding to external stimuli (such as semiconductors 22 ) incorporated, to realize versatile switchable and frequency-agile functionalities. 23–30 Graphene 31 is attractive in nanoelectronics for myriad applications that profits from its high electronic mobility, 32 exceptional mechanical strength, 33 and thermal conductivity. 34 It is also promising for applications in photonics and optoelectronics. 35 Compared to the surface plasmons in bulk metals, the surface plasmons in two-dimensional (2D) graphene shows much stronger confinement of surface plasmons at the atomic scale, 36–40 implying that graphene is a novel platform for boosting light-matter interactions. 41,42 More importantly, the sensitivity of Fermi energy to the carrier density in the Dirac fermions results in ultra-wide tunable space in responding external light fields, 43 which makes it a feasible and outstanding platform for actively controllable plasmonics, 44 especially at terahertz and far-infrared frequencies. 43,45–49 Graphene metasurfaces were proposed to realize tailorable functionalities in transformation optics, 50 surface cloak, 51 plasmonic waveguides, 52,53 and absorbers. 54–59 However, the optical loss of graphene hinders many practical applications of the 2D plasmonic excitations. The large real-part of surface conductivity (i.e., the intrinsic loss) makes the propagating plasma decay fast, and the local resonant plasmonic modes weakly excited, especially the magnetic dipolar mode in graphene-based plasmonic metasurfaces. 60–62 Loss compensation with gain medium is a highly desirable and competitive strategy

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to take further advantages of enhanced light-matter interactions in dynamically controllable 2D plasmonic excitations. Fortunately, the unique band structure of graphene offers the possibility of a new mechanism for loss compensation. The gapless and linear dispersion of the 2D Dirac Fermions could lead to negative dynamic conductivity in an ultra-wide frequency range under optical pumping, 63–66 which is significant for active photonics in 2D. The stimulated emission at terahertz and nearinfrared region has been experimentally demonstrated in graphene with inverted Dirac fermion population through time-resolved spectroscopy of fast nonequilibrium carrier relaxation dynamics. 64,65 These findings support the significance of graphene in active photonics applications. In this work, we theoretically study the loss compensation of resonant plasmonic excitations in photoexcited graphene metasurface. It is well known that the coupling of magnetic dipoles of natural atoms to external light-field are much weaker compared to electric dipoles especially at optical frequencies, which makes naturally occurring magnetic resonances are restricted to extremely low frequencies, the artificial optical magnetism is one main contribution of metamaterial. 67–71 We will focus our attention on the weakly excited magnetic resonance in a split ring resonator (SRR) array patterned graphene metasurface. It is shown in the scattering spectra and local-field distributions that photoexcitaion is a promising route to compensate the resonantly enhanced energy dissipation in graphene metasurfaces. It is found that the difficultly excited magnetic resonance in passive graphene can be boosted in photoexcited graphene metasurface with proper quasi-Fermi energy, and significant modulations in the transmission and absorption in the photoexcited graphene metasurfaces can be achieved. Our work pioneers the way toward various practical applications based on the active and dynamic plasmonic excitations in graphene metasurfaces due to strong lightgraphene interactions. The optical response of the pumped monolayer graphene under the local approximation can be

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60 Quasi-Fermi level (meV)

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60 77 K

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-6.000E-05

-5.400E-05

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Figure 1: Negative real-part of complex surface conductivity of the photoexcited graphene. Color plots of the surface conductivity as a function of frequency and quasi-Fermi level at the temperature of (a) 77 K and (b) 300 K. described with the complex surface conductivity [65] e2 σ (ω) = 4¯h

(

2 8kB T τ e ln 1 + exp π h¯ (1 − iωτ) 4¯h h¯ ω − εF + tanh 4kB T

4¯hω − iπ where G (ε, εF ) =

sinh(ε/kB T ) cosh(ε/kB T )+cosh(εF /kB T ) ,

Z ∞ G (ε, εF ) − G (¯hω/2, εF )

(¯hω)2 − ε 2

0

(1) ) dε ,

ω is the angular frequency of the incoming light wave,

e is the electron charge, h¯ is the reduced Planck constant, kB is the Boltzmann constant and T is the temperature. τ = 10−12 s is the phenomenological relaxation time representing the scatterings in graphene or the quality of the graphene, and εF is the quasi-Fermi energy representing the strength of photoexcitation. 65 Different from the Fermi energy of graphene that describes the tunable dynamic conductivity of graphene, the quasi-Fermi energy represents the intensity of pumping (photoexcitation) in graphene. The stimulated emission from graphene is corresponding to the transition of the real part of the optical conductivity from positive to negative. By taking Equation 1, we calculated the optical conductivities of photoexcited graphene at two featured temperatures in experiment: 77 K (liquid

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E(x)

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P w

k(z)

H( y )

g d

Figure 2: Schematic of the studied magnetic metasurface: a periodic array of split ring resonators (SRRs) made of photoexcited monolayer graphene is located on the xy plane. In a unit, a square ring with outer dimensions d × d was split with a gap (g) in the middle of the right arm, the period of the structure and the line-width of SRR are P and w. nitrogen temperature) and 300 K (room temperature), as shown in Figure 1. It can be seen that with the increasing of quasi-Fermi energy, there are regions where the optical conductivities decreases to negative values for both temperatures, indicating that the dissipation in graphene can be compensated with optical pumping. Comparatively, the dissipation of graphene at 77 K can either be compensated at a relatively low qusai-Fermi energy, or yielding larger terahertz gain. The schematic of the studied magnetic metasurface is shown in Figure 2. The photoexcited monolayer graphene is patterned into a periodic array of split ring resonators (SRRs), a fundamental magnetic structure in the design of metamaterials/metasurfaces. The period of the square lattice is P = 0.36 µm, the SRR in each unit cell is a square ring with outer dimension d × d (d = 0.25 µm) split with a gap (g = 0.05 µm) in the middle of the right arm, and the line-width of the SRR is w = 0.05 µm. For simplicity, we present the results for graphene metasurfaces without substrate. In the view of experiments, graphene generally needs to be transferred onto some substrate for patterning. We found that the dielectric substrate will only shift the plasmonic resonance of graphene metasurface to lower frequency (results not shown here), and the substrate will not change the evolution trend of the plasmonic resonance when increasing the photoexcitation. We performed full-wave numerical simulations with a Finite-Element-Method (FEM) based electromagnetic package (COMSOL Multiphysics) to calculate the terahertz response of graphene

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no pump

80 99

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1.6

(b)

Frequency (THz)

0

-10 0.8

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1.2

1.4

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Figure 3: Magnetic resonances of photoexcited graphene metasurfaces with different quasi-Fermi level at 77K. The transmission and absorption spectra are plotted for unpumped graphene, pumped graphene with quasi-Fermi level of 5 meV, 8 meV, 10 meV, 10.3 meV and 15 meV.

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metasurfaces. In the simulations, the graphene layer is modeled as a conductive sheet with complex surface conductivity calculated from Equation 1. We first consider the resonant behavior of a photoexcited graphene metasurface at temperature of 77 K. The transmission (T ) and absorption (A = 1 − T − R, R is the reflection) spectra of an unpumped graphene metasurface are shown as black curves in Figure 3. A shallow resonance appears around 0.95 THz with transmission of 99% and absorption of 1%, and this resonance is confirmed to be a magnetic dipolar mode through the electromagnetic field and current distributions (results will be shown and discussed later). This weakly excited magnetic dipolar mode of unpumped graphene metasurface agrees well with previous studies by Papasimakis et al.,[59] Fan et al.,[60] and Shen et al.[61] As the pump beam is on, or the quasi-Fermi level increases from 0 meV to about 10 meV, the magnetic resonance of the photoexcited graphene metasurface is continuously strengthened. Especially when the quasiFermi is 10.3 meV, a pronounced dip is observed from the transmission spectrum at 1.5 THz. The corresponding absorption and transmission are 39% and 8% respectively, indicating that we can achieve a strong modulation in the transmission through the photoexcited magnetic metasurface. The modulation depth is over 90% (the transmission changes from 99% to 8%). We note that the absorption in the graphene metasurface is also boosted remarkably in synchrony with the enhancement of magnetic resonance of SRRs. When further increasing the photoexcitation, the strong magnetic resonance switches abruptly from the passive regime to the active one, as can be seen from the case of 15 meV in Figure 3. The transmitted signal even exceeds the incident beam, and the absorption at the resonant frequency 1.75 THz turns negative. The detailed evolution of the process is studied and illustrated in Figure 4. The evolution of the loss compensation in different photoexcited graphene metasurfaces at 77 K is investigated by studying the on-resonance transmission and absorption (transmission and absorption at resonant frequencies). The on-resonance transmission (red) and absorption (black) are plotted as a function of the quasi-Fermi levels in Figure 4. As the excitation power of the pump beam is increased with the quasi-Fermi level changing from 0 meV to 10.3 meV, the on resonance transmission undergoes a strong modulation from nearly unit to the minimum 8%, and

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Figure 4: Magnetic resonances of photoexcited graphene metasurfaces with different quasi-Fermi levels at 77K. The on-resonance transmission (red) and absorption (black, with lossy and losscompensated regimes marked with green and blue shadows) values are plotted as a function of the quasi-Fermi level. the on-resonance absorption also undergoes a dramatically increment to the maximum 50% at the quasi-Fermi level of 10.2 meV. When the quasi-Fermi energy is further increased, the on-resonance transmission undergoes an increment reversely, and the photoexcited graphene metasurface becomes lasing with an amplified beam propagating through the SRRs. The on-resonance absorption becomes negative regarding the loss compensation in the magnetic resonant structure. We then distinct the evolution of the photoexcited process into two regimes: one with positive on-resonance absorption, marked as “lossy”, representing the regime where photoexcitation cannot completely compensate the loss of graphene metasurface, and the other with negative on-resonance absorption, marked as “loss-compensated”, representing the regime where losses are completely compensated.

To better understand the reinforcement of magnetic resonance assisted by loss compensation through photoexcitations, we straightforwardly studied the local-field distributions of magnetic modes for some representative photoexcitation levels. Figure 5 shows the on-resonance electric-

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 5: The on-resonance local field and surface current maps (under same display settings) of metasurfaces with (a) unpumped graphene, (b)-(f) pumped graphene with quasi-Fermi level of 10 meV, 10.3 meV, 10.7 meV, 11meV and 11.5 meV, respectively. field (amplitude) and surface current maps of metasurfaces with unpumped graphene (Figure 5a), pumped graphene with quasi-Fermi levels of 10 meV, 10.3 meV, 10.7 meV, 11meV, and11.5 meV (Figure 5b - 5f), respectively. We note that all the field maps are displayed under same setting. It is obvious that the magnetic resonance of the unpumped graphene is very weak, while the photoexcitation leads to arresting confinement on the graphene structure, especially at 10.3 meV and 10.7 meV consistent with that in Figure 3. The boosting of magnetic resonances in graphene SRRs is particularly clear from the surface current distribution on SRRs, where the strongest circular surface current can be induced with quasi-Fermi level around 10 meV, in comparison to the extremely weak response in the unpumped graphene. Besides the liquid nitrogen temperature 77 K, we also investigated the graphene metasurfaces with same geometry but with the photoexcited optical conductivity at room temperature 300 K. The calculated transmission and absorption spectra of unpumped graphene metasurface, and photoexcited graphene (with quasi-Fermi levels of 33 meV and 50 meV) metasurfaces are presented in Figure 6, the on-resonance electric-field (amplitude) and surface current maps are shown around corresponding resonances. It can be seen that the results at room temperature confirm the evolution process of the case at 77K by increasing the photoexcitation, the weak magnetic resonance without 10


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Figure 6: Magnetic resonances of photoexcited graphene metasurfaces with different quasi-Fermi levels at 300K. The transmission and absorption spectra are shown for unpumped graphene, pumped graphene with quasi-Fermi levels of 33 meV and 50 meV, respectively. The on-resonance local field and surface current maps (under same display settings) are plotted in the middle accordingly. photoexcitation becomes stronger with the photoexcitation, the strong magnetic response exhibits considerable modulated on transmission and enhanced terahertz absorption, the inset electric-field (magnitude) and surface current distributions around the magnetic resonances agree well with the scattering spectra regarding the excitation of magnetic mode of graphene SRRs. Thus we conclude that the photoexcited graphene provide us opportunity to take further advantages of tunability of graphene and strong confinement of plasmonic mode on the atomic scale, compared to the lossy plasmonic excitations in metasurfaces based on passive graphene. The magnetic resonance in graphene metasurfaces can benefit from photoexcitation-induced smaller positive or even negative real part on the resistivity. This fantastic behavior works at both liquid nitrogen boiling point and the room temperature. To quantitatively measure the resonant strength of the graphene metasurface with photoexcitations, we apply the sheet retrieval method 72 to extract the effective surface conductivity, the real (solid) and imaginary (dashed) parts of which are presented in Figure 7 under different quasi-Fermi levels at 300 K (corresponding to Figure 6). The surface conductivity for unpumped case indicates 11


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Figure 7: Extracted surface conductivities for photoexcited graphene metasurfaces with different quasi-Fermi levels at 300 K. The real (solid) and imaginary (dashed) parts of the surface conductivity (in unit of η0 , the characteristic impedance of vacuum) are shown for unpumped graphene, pumped graphene with quasi-Fermi levels of 33 meV and 50 meV (corresponding to the cases in Fig. 6). a Lorentz resonant response around 1.85 THz, with the damping frequency of the Lorentz resonance about 0.18 THz. When the quasi-Fermi level is 33 meV, the surface conductivity increases 60 times compared to the unpumped case. The Lorentz resonance becomes much sharper with damping frequency being 0.01 THz. Similar to metamaterials with gain-medium layer, 27 the resonant strength of the graphene metasurface is significantly enhanced. When the quasi-Fermi level increases to 50 meV, the real part of the effective surface conductivity, the quantity representing the loss, becomes negative, suggesting that the graphene metsurface to be active under photoexcitation. The analysis on the effective sheet agrees well with the distributions of magnetic field, an intuitive indication that the resonance of graphene metasurface can be remarkably boosted with photoexcitation in graphene. We have devoted our attention to the boosted and tunable magnetic resonance of photoexcited graphene metasurface. There may exist many other novel mechanisms contributing to the photoexcited responses of graphene plasmonic structures particularly when the scales are down to nanometer regime. For example, the plasmon resonance in doped graphene patterns with different graphene edges, 73 and nonlocal response arised from spatial inhomogeneity 74 will affect magnetic resonances in graphene nanostructures; the time-dependent photoexcitation processing could 12


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also affect the plasmonic response in graphene. 66 It is also worth noting that the photoexcited graphene-based metasurface has several distinctive advantages in comparison to recent studies on loss compensation with quantum dots, quantum wells, and dyes. 75–80 i) Atomically thin graphene is more compatible with planar nanostructured metasurfaces and is helpful in miniaturizing optical devices; ii) Photoexcited graphene provides optical gain in wide frequency ranges and the gain is relatively large compare to its low carrier concentration. In summary, we propose a strategy of boosting the originally weak plasmonic resonances in graphene metasurfaces via photoexcitation induced inverted Dirac Fermion population for intrinsic loss compensation. Taking the well-known split ring pattern as an example for graphene metasurface, we demonstrate a significantly enhanced magnetic resonance under optical pumping, and remarkable modulations in transmission and absorption. The proposed mechanism may also apply to all other 2D conductive materials in format of various micro- and nano-structures. Our work therefore paves the way toward more efficient control of terahertz waves with many potential applications.

Acknowledgement The authors would like to acknowledge financial support from the National Science Foundation of China (NSFC) (Grants No. 11674266, 61771402, 61505164, 51575297, 11674248, and 11404213) and the Fundamental Research Funds for the Central Universities (Grant No. 3102017zy033). Work at Ames Laboratory was partially supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering (Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under contract No. DE-AC0207CH11358), by the U.S. Office of Naval Research, award No. N00014-14-1-0474 (simulations). The European Research Council under the ERC Advanced Grant No. 320081 (PHOTOMETA) supported work (theory) at FORTH.

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Graphical TOC Entry

Magnetic resonance in graphene metasurface is commonly rather weak due to the intrinsic dissipation in graphene, this study exploits the inverted Dirac fermion population in photoexcited graphene to compensate the loss in graphene metasurface. It is shown that the magnetic resonance of a split ring resonator patterned graphene layer can be boosted to be even active. The transmission through and absorption in the photoexcited graphene merasurface can be significantly modulated.

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Photoexcited Graphene Metasurfaces: Significantly Enhanced and

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