Lei Zhou Physics Department, Fudan University, Shanghai , China

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1 Tunable Meta-surfaces for Active Manipulations of Electromagnetic Waves Lei Zhou Physics Department, Fudan University, Shanghai , China

2 Acknowledgements Key collaborators Yuanbo Zhang, Qiong Wu Key contributors Shaojie Ma, Ziqi Miao, Xin Li, Wujiong Sun, Weijie Luo, Jiaming Hao, Shulin Sun, Qiong He NSFC Shanghai Sci. Tech. Committee

3 Outline Backgrounds and recent works in my group Complete phase diagram for metal/insulator/metal meta-surfaces (PRL, 2015) Graphene meta-surfaces for full-range phase control (PRX, 2015) Conclusions

4 What is Metamaterial? Conventional material Metamaterial Structural unit: atom Structural unit: artificial microstructure In principle, there is no homogeneous medium except for vacuum. However, when >> unit, the medium can be viewed as a homogeneously effective medium, with definite and In principle, nothing is homogeneous except vacuum. However, as structural unit < < wavelength,a material is homogenized with effective, ; A natural material is homogeneous for visible light Change natural atom to subwavelength microstructure, a Metamaterial is formed

5 Metamaterials Metasurfaces Bulk MTM goes to single-layer metasurface Inhomogeonity provides more freedom to control EM waves

6 1) Gradient meta-surfaces to bridge PW and SW Generalized Snell s law k r sin k0 i PW SW conversion S. Sun et al., Nat. Mater. 11, 426 (2012) S. Sun et al., Nano Lett (2012)

7 Problems of the gradient coupler Driven SW flows on the inhomogeneous meta-surface Decouplings due to scatterings are inevitable Only works for small beam width Output Port SPP Metasurface Plasmonic Metal Q. Che et. al., EPL 101, (2013)

8 New concept: Meta-coupler for high-efficiency SPP conversion k r sin k0 i Transparent gradient meta-surface: No reflection No x -x symmetry, decoupling is forbidden More efficient to extract SPP

9 Realization in Microwaves NF characterizations Meta-coupler is the best, several times higher than others; Working bandwidth: GHz;

10 SPP excitation efficiency: Measured vs FDTD 73% efficiency (Expt.) Match well with FDTD (75%). W. Sun et al., Light: Science & Applications 5, (2016).

11 2) Spin-dependent meta-surfaces for 100%-efficiency PSHE Case 1: Symmetrical Case 2: Asymmetrical ruu rvv ruv rvu Half-wavelength plate 0 Luo et. al., Adv. Opt. Mater. 3, 1102, (2015) Establish a criterion to realize 100%-efficiency PSHE Experimentally demonstrated in microwaves

12 1) Tailor the functionalities of meta-surfaces based on a complete phase diagram 2) Toward full-range phase modulation with gatecontrolled graphene meta-surfaces

Reflectance modulation Change geometry/material Phase

13 What is Metal/Insulator/Metal Metasurface? Pattern Spacer Metal metal/insulator/metal Reflectance modulation Change geometry/material Phase modulation MIM Meta-surface can control reflectance and phase on resonance

14 Applications 1:Reflectance Modulation Perfect absorption N. I. Landy, et. al. PRB 78, (2008) Perfect absorption JM Hao et. al. APL (2010) Na Liu, et. al. NL 10, 2342(2010) Color Printing Alexander S. Roberts, et. al. Nano Lett. 14, 783 (2014) Active modulation Yu Yao, et. al. Nano Lett. 14, 6526 (2014) MIM metasurface triggers many applications through reflectance modulation

15 Application 2: Phase Modulation polarization control anomalous reflection J.M. Hao, et. al. PRL. 99, (2007) S.L. Sun, et. al. Nat Mater 11, (2012) holograms Wei Ting Chen, et. al. Nano Lett. 14, 225 (2014) flat-lens focusing Anders Pors, et. al. Nano Lett. 13, 829 (2013) MIM metasurface triggers many applications through phase control

al. Nat Mater 11, 426-431(2012) Why and when certain functionality?

16 Motivations Reflectance modulation Pattern Spacer Metal Phase modulation Na Liu, et. al. Nano Lett. 10, 2342(2010) Change geometry/material S.L. Sun, et. al. Nat Mater 11, (2012) Why and when certain functionality? Guidelines for designing MIM metasurfaces with desired functionalities

17 Coupled-mode theory for MIM metasurface Pattern Spacer Metal metal/insulator/metal Coupled mode theory: ( i0 ) 1 t a r e 2 r r0 1 e Response: r 1 1/ Qr i(1 ) 1 / 2Q 1 / 2Q S. Fan et. al., J. Opt. Soc. Am. A 20, 569(2003) 0 W. Suh et. al., IEEE J. Quantum Electron.,QE 40,1511(2004) a Qi r 0 i 2 CMT model describes response through lumped Q r and Q a

18 Coupled-mode analyses: Generic phase diagram Reflectance modulation Qr Qa Phase modulation Qr Qa r 1 1 / Qr ω=ω i (1 0 ) 1 / 2Qa 10 / 2Qr r0 1 Qr Qa 1 Qr Qa The competitions between two Q factors generate a variety of physical effects

19 Coupled-mode analysis on MIM metasurface r 1 1/ Qr i(1 ) 1 / 2Q 1 / 2Q 0 a r Question: what determines Q factors?

0 ] Y a a (3,2) cm cm Sm0 [ a0 a0 ] (2,3) III II S0m Ym [ cm cm ] Y0 [ a0 a0 ] m III III

20 Mode-expansion theory: Analytical results Ma et al, PRB (2016) to appear Conditions: Subwavelength: Thin-slit: d a d (1,2) 0 0,0 S00 [ a0 a0 ] (2,1) I II S00 Y 0 0 0,0 0 [ 0 0 ] Y a a (3,2) cm cm Sm0 [ a0 a0 ] (2,3) III II S0m Ym [ cm cm ] Y0 [ a0 a0 ] m III III cm exp( ikm, zh) cm exp( ikm, zh) 0 Resonance freq. & Q of MIM metasurfaces analytically obtained

Total Energy Im(ε) hd E 2 Loss in spacer 1 2 EH, ~ U, Q ~ E h h Ma et al, PRB (2016) to

21 Analytical expressions for Q factors Q r factor: Q a factor: (perturbation) Q Qr r 2 U P radiat cavity 1 F a, d kh 0 Q a Q a 2 U P absorb cavity Re hd hd d a Im 2 eff f Re(ε) hd E 2 Total Energy Im(ε) hd E 2 Loss in spacer 1 2 EH, ~ U, Q ~ E h h Ma et al, PRB (2016) to appear r, ~ UQ r 1 h d a δ E 2 d δ E 2 Concrete expressions of Q factors are obtained Loss in metal

22 Tailor MIM Metasurface Through Structural/Material Tuning Response: 1/ Qr r 1 i(1 ) 1 / 2Q 1 / 2Q Q r factor: Qr 1 F a, d kh 0 Q a factor: Re hd Qa Im hd 2d a 0 a eff r MIM properties Two Q factors Structure & Materials

23 Tailor MIM Metasurfaces via tuning h Q r factor: Q Q a factor: Q r a 1 F a, d kh 0 Re hd hd d a Im 2 eff Critical parameter Tuning h can dramatically change the property of a metasurface

24 Tailor MIM metasurfaces via tuning a Q r factor: Q a factor: 1 Q r F a, d kh Q a 0 Re hd hd d a Im 2 eff Critical parameter Tuning a can change the property of a metasurface

2 eff Gate-controlled graphene : Tune dielectric loss:

25 Tailor MIM Metasurfaces via tuning material loss Q r factor: Qr Q a factor: Q a 1 F a, d kh 0 Re hd hd 2 d a Im 2 eff Gate-controlled graphene : Tune dielectric loss: Tuning material can dramatically change the property of a metasurface

Q r, Q a THz experiments verification: l increase: Q r ~ C, Q a w

26 Extension to General Situations Q r factor: Q a factor: 1 Q r F ashape, d kh Q a 0 Re hd hd Sd a Im 2 metal eff eff l w h increase: Q r, Q a THz experiments verification: l increase: Q r ~ C, Q a w increase: Q r, Q a ~C Tuning can be extended to a general 2D metasurface

27 Re-interpreting previous works with our phase diagram Phase-modulation Polarization control Gradient MS Perfect absorbers

28 Conclusions Pattern Spacer Metal Response: 1/ Qr r 1 i(1 ) 1 / 2Q 1 / 2Q Q r factor: 0 a r Qr Q a factor: Q a 1 F a, d kh 0 Re hd hd d a Im 2 eff Guidelines for designing metasurfaces with desired functionalities: Perfect absorption, Phase modulation, Active control Qu et. al, Phys. Rev. Lett. 115, (2015)

29 1) Tailor the functionalities of metasurfaces based on a complete phase diagram 2) Toward full-range phase modulation with gatecontrolled graphene metasurfaces

$Refraction, polarization$ Background: Why need phase

30 Fermat-Huygens law: Phase distribution on a certain plane determines the far-field radiation Refraction, polarization control, hologram Background: Why need phase control? At the boundary of 2 homogeneous medium Phase control plays a central role in wave optics!

or MTMs: Bulk effect, difficult for photonics integration

31 How to realize phase control? Conventional techniques: Gradient-index natural materials or MTMs: Bulk effect, difficult for photonics integration Jin, Y. et al., J Appl. Polym. Sci. 103,1834 (2007) Larouche, S et al., Nat. Mater (2012).

$Anomalous refractions Vortex$ generations, Sun, Nat. Mater.

32 Meta-surfaces: full-range phase control in deep-subwavelength regime Yu, Science (2011). Anomalous refractions Vortex generations, Sun, Nat. Mater. (2012). PW-SW conversion, high-efficiency, single-mode All these are passive! Sun, Nano Lett. (2012). Wide-band, optical regime Chen, Nano. Lett., (2014) High-efficiency meta-holograms

33 Available active phase modulations Modulation depth 3% Kleine-Ostmann, T. et al., APL (2004). Chen et. al, Nat. Photonics (2008) Limited phase modulations far from full-range control, even enhanced by MTM

Using graphene an atomic-thin material with great tunability? Lee, S. et al., Nature Mater. 11, 936-941 (2012) Ju, L. et al., Nature Nano.

34 Using graphene an atomic-thin material with great tunability? Lee, S. et al., Nature Mater. 11, (2012) Ju, L. et al., Nature Nano. 6, (2011) Great tuning capability, loss --- low Q factor Combined with MTM: Tuning phase with 32.2 degrees Far away from full-wave control!

35 Our motivations Realize active and full-range phase control with gate-controlled graphene meta-surface Active?

meta-surface Working at THz domain The transmission

36 Our structure Graphene + Meta-surface d /10 Metallic sheet Combining Graphene with reflective meta-surface Working at THz domain The transmission port is blocked --- crucial! Top-gating graphene using Ion-Gel

37 Graphene identification and TDS-THz measurements

38 Amplitude/phase modulation (Expt.) e-doping Reference: Spectrum with highest n Essentially featureless As voltage increases, reflection amplitudes first decreases to 0, then increases to 1 Phase behaviors change from a magnetic (~360 variation) to electric (<180) resonance Phase modulation covering +/- 180 degrees

39 Amplitude/phase modulation (Expt.) -- hole doping Symmetrical behaviors compared to e-doping Slight asymmetry caused by band-structure deviations

40 Full-range active phase control (Expt.) A E B Two slightly different pixels lead to full-range phase modulation at a frequency interval Previous mechanism can never work, due to intrinsic limitations

41 Complete phase diagrams (Expt.) --- different spacers 85um 60um 40um Critical point determined by structure geometry Some system dose not support critical transition

42 Puzzles Why can we achieve full-range phase modulation? Why previous system can not? What s the role played by graphene?

43 Coupled-mode theory --- a clear & coherent picture The temporal coupled mode theory (Fan, 2003) da dt m ( if ) a k S 0 m mi ms m m, n m, n n S c S c a s a m, n m, n m, n m, n m Single resonance Single port r ( ) / ( ), f f r i r i 0 Different damping parameters yield different phase behaviors! Whether or not enclosing origin determines the phase variation range!

44 Generic phase diagram Typical behaviors in 3 regions (Reference: gold) Under-damped resonator: 360 variation Over-damped resonator: < 180 variation Critical coupling: Perfect absorber Qu, PRL (2015) Tuning the ratio S / i tune the system dramatically

45 Role of graphene upon gating (Fitting FDTD with CMT) Effects of gating graphene: 1) increasing 2) has little effect on 3) drives the system to transit from an under-damped to an over-damped resonator Gating graphene beaks the subtle balance between intrinsic and radiation losses!

46 Remaining puzzles: 1) Why some of our systems cannot? 2) Why previous systems fail? 40um Do we have a general design guideline?

47 1) Why small-spacer one does not work? Smaller d, stronger near-field coupling, higher Q, smaller Already in over-damped region even with graphene Graphene can only make it even more over-damped, no critical transition

48 2) Why previous one cannot cover full range? Lee, Nature Mater. 11, (2012) Double ports Two-ports system has no critical coupling Always E-resonance, can never be M-type!

49 An application: an active polarizer y x Only x polarized wave are modulated strongly

50 Tuning the polarization actively E 32 degrees Polarization state strongly tuned by gate voltage Miao et al., Phys. Rev. X 5, (2015).

51 Conclusions Based on a complete phase diagram, we can easily tailor the functionalities of MIM metasurfaces. Combining graphene with metasurface, we can realize active fullrange phase modulation in deepsubwavelength regime Qu et. al, Phys. Rev. Lett (2015) Miao et al., Phys. Rev. X 5, (2015) W. Sun et al., Light: Science & Applications 5, (2016) W. Luo, Adv. Opt. Mater., (2015)

52 Thanks & Questions?

Light Manipulation by Metamaterials

Light Manipulation by Metamaterials W. J. Sun, S. Y. Xiao, Q. He*, L. Zhou Physics Department, Fudan University, Shanghai 200433, China *Speaker: qionghe@fudan.edu.cn 2011/2/19 Outline Background of metamaterials