Singular Nano-Photonics: hydrodynamics-inspired light trapping & routing Svetlana V. Boriskina Department of Mechanical Engineering Massachusetts Institute of Technology
2 Cat. F5 tornado (Manitoba, Canada, June 2007) Image credit: Juri Hahhal
Ray picture dominates conventional thinking about light propagation 3 A. Mavrokefalos et al, Nano Lett. 12, 2792-2796, 2012 Image credit: Teresa Matfield
Plasmonic design makes use of antenna theory Dipole antenna analog: Hertz dipole antenna analog: 50nm Dipole moment induced on nanoparticle generates secondary radiation field
Plasmonic design makes use of antenna theory Phased antenna array analogs: Dipole moments induced on each nanoparticle constructively interfere through far-field radiation
Light trapping schemes typically rely on constructive interference of light rays 6 scattering field enhancement waveguiding J. VanCleave, Colors & Thin-Film Interference, John Wiley & Sons, Inc. Atwater & Polman, Nature Mater. 2010
There is another way: making use of destructive interference 7 zero intensity = indefinite phase E ( r, t ) U ( r ) exp i ( ( r ) t ) phase vortex Black holes are where God divided by zero Steven Alexander Wright
There is another way: making use of destructive interference 8 zero intensity = indefinite phase E ( r, t ) U ( r ) exp i ( ( r ) t ) Credit: istockphoto.com/david Ciemny Black holes are where God divided by zero Steven Alexander Wright
There is another way: making use of destructive interference 9 Optical energy flows in the direction of the phase change phase vortex flow vortex Black holes are where God divided by zero Steven Alexander Wright
Hydrodynamic analogy of light trapping 10 Image credit: Teresa Matfield Image credit: http://www.forestwander.com S.V. Boriskina, Plasmonics with a twist, in Plasmonics: Theory & Applications (Shahbazyan & Stockman eds.) Springer, 2013
11 Hydrodynamic analogy of light flow Maxwell s equations: t t Ε J H H E H E 0 S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012 ) ( ) ( ) ( ) ( r r r v r ) ( ) ( ) ( r r v r v V mass conservation: momentum conservation: Navier-Stokes-like equations: (Madelung, 1926)
Hydrodynamic analogy of light flow (Madelung, 1926) Maxwell s equations: Navier-Stokes-like equations: material loss or gain 12 E H 0 E H t H J Ε t mass conservation: ( r ) v ( r ) ( r ) ( r ) momentum conservation: v ( r ) v ( r ) V ( r ) Photon fluid density: ( r ) I ( r ) U ( r ) 2 convective term potential created by the light trapping structure Photon fluid velocity: v (r ) S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
How can we generate optical tornadoes? 13
14 Back to basics: Surface Plasmon Polaritons on metal-dielectric interfaces k 0
Density of optical states is the number of states between iso-frequency surfaces separated by δω 15 Isotropic dielectric Momentum space @ fixed photon energy ε x =ε y =ε z >0 k z Dispersion k x k k y 2 c 2 k 2 x k 2 y k 2 z p k
Density of optical states is the number of states between iso-frequency surfaces separated by δω 16 M-D interface Momentum space @ fixed photon energy ε x =ε y =ε z >0 ε x =ε y =ε z <0 S.V. Boriskina et al, Plasmonic materials for energy: from physics to applications, Mater. Today, 2013
Electromagnetic energy density Photon energy U f ( ) D ( ) d E
Electromagnetic energy density Photon energy U f ( ) D ( ) d E Photon statistics f exp ( ) k T 1 1 ( ) B
Electromagnetic energy density U f ( ) D ( ) d Photon energy Density of states (DOS) E D ( k ) d k ( 2 ) 2 3 Photon statistics f exp ( ) k T 1 1 ( ) B
Electromagnetic energy density U f ( ) D ( ) d Density of states (DOS) D ( k ) d k ( 2 ) 2 3 Dispersion relation energy-to-momentum space: Photon energy: E Photon momentum: p k (k )
Transformation of the iso-frequency surface results in DOS sculpting
SPP waves generate highmomentum photons k 0 2 k k 2 0 E x
SPP waves generate highmomentum photons k 0 2 k k 2 0 k E x
Optical power flows in opposite directions along the M-D interface 1 S R e E H 2 * 2 S xˆ A e 2 0 2 2 k 2 z Z=0 E x S xˆ A e 2 2 0 1 2 k z 1
Optical power flows in opposite directions along the M-D interface 1 S R e E H 2 * Z=0 Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014
Instantaneous powerflow features vortices that recycle energy across the interface S 1 R e E H 1 R e E H e 2 2 * i t S in Z=0 Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014
Local k-vector is tangential to the powerflow streamlines S in Z=0 Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014
Vertical components cancel on average S in Z=0 Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014
29 Vortex powerflow is behind tight light localization and high photon momentum of SPP waves
From one interface to many: hyperbolic metamaterials ε x =ε y ε z ><0 Momentum space @ fixed photon energy k Dispersion 2 2 c c 2 2 2 2 2 k k k x y z 2 2 2 k k k x y z S.V. Boriskina et al, Plasmonic materials for energy: from physics to applications, Mater. Today, 2013
Dispersion characteristics & DOS of a multi-layer stack 31 S.V. Boriskina et al, Plasmonic materials for energy: from physics to applications, Mater. Today, 2013
32 What is the local field topology behind a global topological phase transition in metamaterials?
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 33
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 34
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 35
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 36
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 37
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 38
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 39
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 40
Singular & Chiral Nano-Plasmonics (Boriskina & Zheludev Eds.) Pan Stanford, 2014 Optical tornadoes change energy density in hyperbolic metamaterials 41
42 Local optical tornadoes are behind plasmonic field localization and topological transitions in metamaterials
43 Can we design custom-tailored vortex-trapping nanostructures with low losses?
Yes we can - by strategically positioning obstacles in the light flow path 44 Zero intensity S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
Example of a vortex-pinning nanostructure 45 50-nm radius Au nanoparticles S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90 (2012) W. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)
Example of a vortex-pinning nanostructure 46 50-nm radius Au nanoparticles S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90 (2012) W. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)
Optical energy is circulating outside the metal volume! 47 S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90 (2012) W. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)
What is the origin of the strong field enhancement? 48
Optical vortices generate local velocity fields 49 compressible fluid potential steadystate flow local convective acceleration possible v ( r ) v ( r ) V ( r ) r Tangential velocity ~1/r
Photon fluid is convectively accelerated in the vortex velocity field 50 compressible fluid potential steadystate flow local convective acceleration possible v ( r ) v ( r ) V ( r )
and when threaded through nanoscale gaps, generates hydraulic jumps - areas of high field intensity 51
and when threaded through nanoscale gaps, generates hydraulic jumps - areas of high field intensity 52
Vortex-pinning nanostructures are photonic analogs of turbopumps 53
Optical vortices can be moved and stretched by repositioning the obstacles 54
Tunable or broadband light trapping possible 55
E-beam SERS platforms fabricated with vortex-trapping VNTs surfaces Nano Lett. 12, 219-227 (2012) Adv. Mat., 25(1), 115 119, 2013
Reconfigurable vortex transmissions S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
58 Nanoscale light switching S.V. Boriskina & B.M. Reinhard, Opt. Express, vol. 19, no. 22, pp. 22305, 2011
59 Nanoscale light switching S.V. Boriskina & B.M. Reinhard, Opt. Express, vol. 19, no. 22, pp. 22305, 2011
60 Nanoscale light switching S.V. Boriskina & B.M. Reinhard, Opt. Express, vol. 19, no. 22, pp. 22305, 2011
61 Nanoscale light switching S.V. Boriskina & B.M. Reinhard, Opt. Express, vol. 19, no. 22, pp. 22305, 2011
62 Nanoscale light switching S.V. Boriskina & B.M. Reinhard, Opt. Express, vol. 19, no. 22, pp. 22305, 2011
Advantages of the hydrodynamicsinspired design approach Optical chip High-Q (narrow linewidth) modes with high field intensity in sub-wavelength device footprints
Advantages of the hydrodynamicsinspired design approach Hydrodynamic picture of conventionally-designed optical chip High-Q (narrow linewidth) modes with high field intensity in sub-wavelength device footprints
Advantages of the hydrodynamicsinspired design approach Hydrodynamic picture of vortex-pinning optical chip High-Q (narrow linewidth) modes with high field intensity in sub-wavelength device footprints
Conclusions and outlook New way of designing light absorbers & routers via the hydrodynamic analogy Higher field concentration than traditional schemes based on constructive interference Strong energy flow outside of the metal volume of nanoparticles possible PV applications
Acknowledgements Prof. Gang Chen & MIT NanoEngineering group 67 Funding: Students & Colleagues: Collaborations & Discussions: Prof. Bjoern Reinhard, Boston University Dr. Anton Desyatnikov, Australian National University
Nanoscale, 4, 76-90, 2012 Nano Lett. 12, 219-227, 2012 Adv. Mat., 25(1), 115 119, 2013 Opt. Express 19(22), 22305-22315, 2011 Read more: www.bio-page.org/boriskina Plasmonics with a twist: taming optical tornadoes on the nanoscale, to appear in Plasmonics: Theory & Applications, T.V. Shahbazyan & M.I. Stockman Eds., Springer 2012