Photonics Beyond Diffraction Limit: Plasmon Cavity, Waveguide and Lasers Xiang Zhang University of California, Berkeley
Light-Matter Interaction: Electrons and Photons Photons Visible / IR ~ 1 m Electrons e ~ 1 nm Quantum dot Not efficient Interaction NV center 5 nm 0.36 nm
Challenges in Scaling Down of Photonics Intel The Photonic Chip M. Paniccia Intel Corp., Silicon Photonics (2005) Key Issues: Nanoscale Waveguides On Chip Light Source Ultrafast Modulation New approaes Hybrid Plasmon Waveguide Plasmon Nano Lasers Graphene, Plasmon Modulators
Outline Indefinite Nano Cavity Deep Sub Plasmon Waveguide and Lasers
Optical Fabry-Perot Cavity m=1 m=2 m=3 mirror mirror Resonance frequency m f m 2L c n c : speed of light in vacuum L : cavity size m: mode order (1, 2, 3, ) University of California, Berkeley 5
Quality factor Q and modal volume V Cavity mode mirror mirror Quality factor Q Q 2 Electromagnetic Energy Energy Dissipated per Stored cycle Modal Volume V Q/V Figure of Merit V Total Electromagnetic Energy max( Electromagnetic Energy Density) University of California, Berkeley 6
V [(λ) 3 ] 10 3 10 2 10 1 10-2 Subwavelength confinement Optical Micro- and Nano-cavities Plasmonic Fabry-Perot (V. Sorger et al) Plasmonic microdisk (B. Min et al) Q ~ 1,400 V ~ 6 () 3 Q/V~230 () -3 Microring resonator (M. Lipson et al) Q ~ 1.510 4 V ~ 10(/n) 3 Q/V~ 1,500(/n) -3 Photonic crystal (S. Noda et al) Q ~ 2.510 6 V ~ 1.4 (/n) 3 Q/V~1.8x10 6 (/n) -3 High Q 10-4 Q ~ 200 scale bar: 2 μm 100 nm Ref.: K. Vahala, Nature 424, 839 (2003); D. K. Armani et al., Nature 421, 925 (2003); 10-6 Enhancement of light-matter interactions: - Purcell factor for spontaneous emission: Q/V - Strong coupling for cavity QED: Q/V 1/2 - (3) optical nonlinearities: Q 2 /V - Optical forces and trapping: Q/V - Bio-sensing: Q/V Indefinite metamaterial nanocavity Q ~ 20 V ~ 0.0002 () 3 Q/V~100,000 () -3 V ~ 0.04 () 3 Q/V~5000 () -3 O. Painter et al., Opt. Exp. 13, 1515 (2005); M. Lipson et al., Nature 435, 325 (2005); S. Noda et al., Nature 425, 944 (2003); B. Min et al, Nature 457, 455 (2009); V. Sorger et al, Nano Lett., 9 3489 (2009). 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Microtoroid Microsphere 25 um 50 um (K. Vahala et al) Q ~ 10 8 10 10 V ~ 2000(/n) 3 Q/V ~ 5x10 6 (/n) -3 Q University of California, Berkeley 7
V [(λ) 3 ] 10 3 10 2 10 Q/V in Optical Cavities Enhancement of light-matter interactions: - Purcell factor for spontaneous emission: Q/V - Strong coupling for cavity QED: Q/V 1/2 - (3) optical nonlinearities: Q 2 /V - Optical forces and trapping: Q/V - Bio-sensing: Q/V Larger than wavelength scale Plasmonic microdisk Microring resonator (M. Lipson et al) Q ~ 1.510 4 V ~ 10(/n) 3 Q/V~ 1,500(/n) Photonic -3 crystal cavity: Air-hole tuning & mode gap Microtoroid Microsphere 25 um 50 um (K. Vahala et al) Q ~ 10 8 10 10 V ~ 2000(/n) 3 Q/V ~ 5x10 6 (/n) -3 1 Indefinite metamaterial nanocavity Plasmonic Fabry-Perot (S. Noda et al) Q ~ 2.510 6 V ~ 1.4 (/n) 3 Q/V~1.8x10 6 (/n) -3 scale bar: 2 μm (B. Min et al) (S. Noda et al) 10-2 Q ~ 1,400 Q ~ 10 5 ; V ~ (/n) 3 V ~ 6 () 3 Q/V ~ 100,000 (/n) -3 (V. Sorger et al) Q/V~230 () -3 10-4 Q ~ 200 100 nm V ~ 0.04 () 3 Ref.: K. Vahala, Nature 424, 839 (2003); D. K. Armani et al., Nature 421, 925 (2003); Q ~ 20 Q/V~5000 Deep subwavelength () -3 O. Painter et al., Opt. Exp. 13, 1515 (2005); M. Lipson et al., Nature 435, 325 (2005); V ~ 0.0002 () 3 S. Noda et al., Nature 425, 944 (2003); B. Min et al, Nature 457, 455 (2009); 10-6 confinement -3 V. Sorger et al, Nano Lett., 9 3489 (2009). 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Q rad University of California, Berkeley 8
Metamaterials: beyond natural materials atoms Natural materials Atomic lattice constant a ~ 5.65 Å Optical wavelength λ ~1μm Homogeneous medium Crystal structure of sodium chloride (NaCl) Metamaterials meta-atoms a a λ Artificially fabricated structures Unit cell a << wavelength λ a Effective-media theory is valid Material properties not existing in natural materials University of California, Berkeley 9
Indefinite Metamaterials Dispersion relation for uniaxial anisotropic media k z k 2 x z k 2 z x 2 2 c indefinite media Normal media 0 0 0 0 0 0 anisotropic air k 0 silicon 3.5*k 0 k x Indefinite media 0 0 0 0 0 0 Access high k deep sub-λ optical confinement Ref: I. V. Lindell et al, Micro. Opt. Tech. Lett. (2001); D. R. Smith and D. Schurig, PRL 90, 077405 (2003); Z. Jacob, et al., OE (2006); A. Salandrino, et. al., PRB (2006) University of California, Berkeley 10
Indefinite Metamaterial Examples Metal nanowires array Metal-dielectric multilayers z 0 0 0 0 0 0 z 0 0 0 0 0 0 x y z x y z top side Ag/Al 2 O 3 500 nm x y Ag/Ti 3 O 5 500 nm x y Negative refraction (J. Yao et al, Science, 2008) 3D IFC Hyperlens (Liu, et., al, Science 2007) 3D IFC J. Rho et al., Nature Comm. 1, 143, (2010). University of California, Berkeley 11
Ag-Ge multilayers as indefinite metamaterial Germanium Silver z y x Effective permittivity: ( ) p v x ( ) z y p where p is filling ratio of silver layer m (1 p) m m d (1 p) p d d Effective permittivity 50 0-50 -100 z x 0 0-150 p = 0.4-200 100 150 200 250 300 Frequency (THz) University of California, Berkeley 12
Indefinite Cavity and Resonances Nanocavity made of 20 nm Ag and 30 nm Ge multilayers z y x Same mode order (1, 1, 1); same resonance frequency f 1 = 150 THz (140, 100) nm (160, 150) nm (180, 200) nm (195, 250) nm (200, 300) nm z x k E Plane wave excitation University of California, Berkeley
Size-independent Resonances in Indefinite Cavities 20 15 150 THz (140, 100) nm 10 (160, 150) nm k z /k 0 5 0-5 m f m 2L (180, 200) nm (195, 250) nm c n -10 (200, 300) nm -15 FDTD Effective media -20-15 -10-5 0 5 10 15 k x /k 0 z x (1, 1, 1) mode University of California, Berkeley 15
Fabricated Ag-Ge multilayer indefinite cavities Cavity size: (L x, L z ) nm (135, 100) nm (170,150) nm (200, 200) nm University of California, Berkeley 18
1 Anomalous Scaling in Indefinite Cavities 191 THz 15 k k m 2L i 0 i 0 (170, 150) nm (1, 1, 2) i (1, 1, 1) Transmission 0.97 0.94 0.91 (135, 100) nm 140 THz (1, 1, 2) (170, 150) nm (1, 1, 1) (1, 1, 2) 145.5 THz (200, 200) nm (1, 1, 1) 0.88 100 150 200 250 k z /k 0 10 5 0 (200, 200) nm (1, 1, 2) (135, 100 nm) (1, 1, 1) (170, 150) nm (1, 1, 1) (200, 200) nm (1, 1, 1) k 2 x k 2 z 147 THz 191 THz 0 5 10 z x 2 2 c Frequency (THz) k x /k 0 University of California, Berkeley 20
4000 4000 Q rad, v ~ k 4 Measured Radiation Q (L z = 150 nm) (1, 1, 2) (L z = 200 nm) (1, 1, 2) (L z = 100 nm) (1, 1, 1) 5% Q rad T 1 Q T tot Q rad,v 400 400 (L z = 150 nm) (1, 1, 1) (L z = 200 nm) (1, 1, 1) T 2 T 1 40 Optical Index n = 17.4! T = T 2 /T 1 40 1000 10000 100000 10 3 10 4 10 5 (k/k 0 ) 4 The cavity sizes investigated include (110 185,100) nm, (140 215,150) nm and (185 255,200) nm for the (1,1,1) mode, and (140 170,150) nm and (185 210,200) nm for the (1,1,2) mode. 22
Q rad of Indefinite Optical Cavity Cavity radiation Q: Q rad ~ neff Radiation loss from total internal reflection: ~ e ikr e ik r 0 dv k 3 Effective index: n eff k / k 0 Radiation quality factor: Q rad ~ k neff 4 ~ 4 Ref: H.A. Wheeler, Proc IRE, p.1479 (1947); Englund D et al, Opt. Exp.13, 5961 (2005). University of California, Berkeley 24
Anomalous Scaling Physics in Indefinite Cavity Cavity size can be scaled well below diffraction limit (/20) Anomalous Scaling: smaller size, higher Q rad ~ k 4 ~ (L) -4 Size-independent resonant frequency High order mode has lower resonance frequency Effective Optical Refractive Index: n =17.4 The total Q, however, is unchanged (metal loss dominated), but Q/V still increases. (Yang et al., Nature Photon. 6, 450, 2012) University of California, Berkeley 25
Outline Indefinite Nano Cavity Deep Sub Plasmon Waveguide and Lasers
Plasmonics and Its Critical Challenge Surface plasmons dilemma ω Photon ω=ck Surface Plasmon Dispersion Small Mode Size, Short Range ω sp Large Mode Size, Long Range kx Can we have the best of two worlds?
Our Approach: Hybride Plasmons Lifting the field out of metal and confined it!
Small Mode Size and Relative Long Propagation! Si / SiO 2 / Ag @ = 1550 nm Mode area ~ 2 /400 L sp ~ 50 microns Oulton, et. al., Nature Photonics (2008) Alam, et., al., CLEO (2007)
Measurement of Deep Sub Mode profile Apertureless NSOM Measured Mode Size (53x65nm) = 633 nm 125nm = 600 1450 nm (Sorger et al. Nature Comm. 2012 ) Mode Area = 1/50 th of Diffraction Limit Comparable to Transistor or Virus
Plasmon Laser Realization d = 90 nm h = 5 nm Oulton, et. al, Nature, (2009)
Spontaneous Emission to Laser oscillation 0.8 nm i ii iii i ii iii
Single mode plasmon laser @ Room Temperature 36
Multiplexed and Electrically Modulated Plasmon Laser Circuit o Directional emission o Multi colored laser array o Wavelengths multiplexing o Direct electrical modulation Ma, et. al., Nano Lett (2012)
Coherent Light Source at Single Molecule Size Single Molecular Bio Sensors Optical Modulators (Sorger, et al., Nanophotonics, 2012) 5 nm Quantum Photonics Signal Control Beam (Gate) Emitter (Chang, et al., PRB, 2010)
Possibility of Ultrafast Plasmonic Devices from Broadband Percell Effect Spontaneous emission enhancement (Purcell effect) F 3 4 2 n Q V Plasmonics offers: d = 100 nm h = Ultra-small 5 nm modal volume and low Q Broadband Purcell Factor Conventionally, dielectrical cavities (PBG, etc.) pursue High Q due to the diffraction limit High Q > low bandwidth! Ultra Fast Plasmon LED and lasers with Ideally, modulation speed up to 10 THz!
Graphene Optical Modulator Graphene contains monolayer of carbon atoms, and absorbs the incident light over a broadband (UV to mid-ir). By modulating the Fermi Level of graphene, optical absorption can be turned. Advantages of graphene modulator: Fast (1-100GHz) Broadband (1350-1600 nm) Compact (25 um 2 ) Athermal (Liu, et. al, Nature, 2011)
Photonic Spin Hall Effect in Metamaterials Strong spin orbital interaction ( kˆ kˆ or Ψ) separates light with different helicity Helicity of light: S z I( ) I( ) I( ) I( ) Yin, et., al, Science, (2013)
Valley Optoelectronics of 2D WS2 (Spin Valley LED)
Acknowledgement Former and Current Members of group: Jun Rho, Renmin Ma, Ong Pholchai, Tongcang Li, Peng Zhang Jie Yao (UC Berkeley) Maiken Mikkelsen (Duke Univ.) Volker Sorger,(George Washington Univ) Rupert Oulton (Imperial College, UK) Xiaobo Yin (Univ. Colorado) Xiaodong Yang (University of Missouri), Yongmin Liu (Northeastern) Peter Park (Samsung), Pavel Kochin (KLA) Collaborators: Prof. Lun Dai of Peking University (CdS nanowire for plasmon laser) Support from: NSF Center for Scalable and Integrated Nao Manufacturing (SINAM) DoD MURIs, DOE