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Flatland Optics with Ultrathin Metasurfaces
J. Sebastian Gomez-Diaz
Department of Electrical and Computer EngineeringUniversity of California, Davis
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
2
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
3
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 4
Terahertz Science and Technology
DOTSEVEN, FP7 project
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 5
Terahertz Science and Technology
N. Llombart, et al, IEEE TAP, 2012
Security and screening
Imaging
C. Zhang, et al, IRMW THz
Biomedicine
K. Kawase, Rikken
Earth observation
P. Siegel, JPL, Caltech
Communications
Spectroscopy
Teraview
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 6
THz GAP
Sources Detectors
Wikipedia
Bolometers
Hamamatsu, Technical resport
HEB Antenna + Mixer
J. Bird, USAS meeting, 2011
Photomixer + Antennas
X. Yin, Springer, 2012
J. V. Moloney, et al, SPIE2011.
Manipulation of THz waves
Oxford, Johnston’s group
Quasi-optical components Lossy Bulky Heavy Expensive
TWT
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 7
Electromagnetic Metamaterials
Natural material
Güney, Opt. Express 18, 12348 Smith’s group Alu’s group
Metamaterials
Engineered “materials” with properties not found in natural materials
Cloaking
Pendry, Science
Negative refraction
Chen, Nature
Active devicesLenses
Pendry, PRL
Difficult fabrication High loss BW limitations 3D granularity
Veselago
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 8
Ultrathin Metasurfaces
Metasurface: 2D version of metamaterials
Nanostructured surfaces Simple fabrication Reduced losses
F. Capasso, V. Shalaev’s groups
Alu’s group
Gradient metasurfaces Meta-transmitarray
Grbic’s group
Huygens’ metasurfaces
Surface Plasmons
U. Levy’s group
Garcia Vidal’s group
d ≪ 𝜆
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Recent Advances on Material Science
Black PhosphorusGraphene
Ultrathin 2D materialsPlasmonic response at THz
Phase change materialsMulti quantum wells Varactors
Non-linear and active responses
Piezoelectric materials MEMs / NEMs
Micro/nanomechanical actuators
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 10
Motivation & Objectives
Towards a Flatland & Advanced Manipulation of EM waves
• Guided devices• Antennas• Sensors• On chip systems
• Reconfigurability• Non-linearity• Non-reciprocity• Hyperbolic
• Ultrathin artificial structures
• Strong light-matter interactions
• Suited at THz
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
11
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 12
Graphene Plasmonics
ധ𝜎(𝜔, 𝑇, 𝜏, 𝜇𝑐 𝐸𝑏𝑖𝑎𝑠, 𝐻𝑏𝑖𝑎𝑠 , 𝑘𝜌, )
𝐽𝑠 = ധ𝜎𝐸 d h
h d
Samsung
Vg
𝑬𝒃𝒊𝒂𝒔
Plasmons on noble metals @ optics
EM wave at the interface between a dielectric (Re[ɛm]> 0) and a metal (Re[ɛm]< 0)
Very confined waves Relatively large loss
Plasmons on graphene @ THz
Re[ɛm]< 0 Im[𝜎]< 0 (or Im[ZS]> 0)
Tunable Integration
Miniaturization Gyroscopy
Engheta’s group
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 13
Graphene Plasmonics
ധ𝜎(𝜔, 𝑇, 𝜏, 𝜇𝑐 𝐸𝑏𝑖𝑎𝑠, 𝐻𝑏𝑖𝑎𝑠 , 𝑘𝜌, )
𝐽𝑠 = ധ𝜎𝐸 d h
h d
Samsung
Vg
𝑬𝒃𝒊𝒂𝒔
Plasmons on noble metals @ optics
EM wave at the interface between a dielectric (Re[ɛm]> 0) and a metal (Re[ɛm]< 0)
Very confined waves Relatively large loss
Plasmons on graphene @ THz
Re[ɛm]< 0 Im[𝜎]< 0 (or Im[ZS]> 0)
Tunable Integration
Miniaturization Gyroscopy
Engheta’s group
X
Y
Z
Y
Graphene sheet
(Top view)
(Transversal view)
Example of plasmon propagation on a graphene sheet
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 14
Graphene-based THz Switches & Filters
Plasmonic switch
Switching: graphene field’s effect
TL model
Isolation > 40 dB
ON STATE
𝜇𝑐𝑜𝑢𝑡 = 0.5 𝑒𝑉𝜇𝑐𝑖𝑛 = 0.5 𝑒𝑉
OFF STATE𝜇𝑐𝑜𝑢𝑡 = 0.5 𝑒𝑉𝜇𝑐𝑖𝑛 = 0.1 𝑒𝑉
J.S. Gomez-Diaz and J. Perruisseau, “Graphene-based plasmonic switches at near infrared frequencies”, Optic Express, 2013.
D. Correas-Serrano, J. S. Gomez-Diaz, et al , ”Graphene based plasmonic tunable low pass filters in the THz band,” IEEE Trans. on Nanotechnology, 2014.
ℓ𝑜𝑢𝑡 = ℓ𝑖𝑛 = 1𝜇𝑚𝜏 = 0.15 𝑝𝑠𝑇 = 300° 𝐾
Plasmonic THz filters
Accurate & scalable model
Steepped impedance filter
Low-loss & tunable
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 15
Graphene-based THz Antennas
Planar configuration
0E
Vertical dipole
M. Tamagnone, J. S. Gomez-Diaz, et al, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” APL , 2012.
M. Tamagnone, J. S. Gomez-Diaz, et al, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” JAP , 2012.
D. Correas-Serrano, J. S. Gomez-Diaz, A. Alvarez-Melcon and A. Alù, “Electrically and Magnetically Biased Graphene-Based Cylindrical Waveguides:
Analysis and Applications as Reconfigurable Antennas”, IEEE Transactions on THz Science and Technology, 2015.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 16
Graphene-based THz Antennas
Planar configuration
0E
Vertical dipole
M. Tamagnone, J. S. Gomez-Diaz, et al, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” APL , 2012.
M. Tamagnone, J. S. Gomez-Diaz, et al, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” JAP , 2012.
D. Correas-Serrano, J. S. Gomez-Diaz, A. Alvarez-Melcon and A. Alù, “Electrically and Magnetically Biased Graphene-Based Cylindrical Waveguides:
Analysis and Applications as Reconfigurable Antennas”, IEEE Transactions on THz Science and Technology, 2015.
E-planeGain (no lens) = -4 dBiGain (lens) = 14 dBi
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 17
Graphene-based Leaky-wave Antennas
A. Oliner and A. Hessel, “Guided waves on sinusoidally-modulated reactance surfaces,” IRE Transactions on Antennas and Propagation , 1959
M. Esquius-Morote, J.S. Gomez-Diaz, and J. Perruisseau-Carrier, IEEE Trans. on Terahertz Science and Technology, vol. 4, pp. 116-122, 2014
J.S. Gomez-Diaz, M. Esquius-Morote and J. Perruisseau-Carrier, Optic Express, vol. 21, pp. 24856-24872, 2013
Sinusoidally modulated surfaces at THz
Several implementations based on graphene’s field effect
Beam scanning at fixed freq
V3 V4V5 V4 V3 V2 V1 V2 V3 V4 V5
TM Surface Wave
XSmin
Im{ZS}
XSmax
N = 8
y
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 18
Graphene-based Leaky-wave Antennas
A. Oliner and A. Hessel, “Guided waves on sinusoidally-modulated reactance surfaces,” IRE Transactions on Antennas and Propagation , 1959
M. Esquius-Morote, J.S. Gomez-Diaz, and J. Perruisseau-Carrier, IEEE Trans. on Terahertz Science and Technology, vol. 4, pp. 116-122, 2014
J.S. Gomez-Diaz, M. Esquius-Morote and J. Perruisseau-Carrier, Optic Express, vol. 21, pp. 24856-24872, 2013
Sinusoidally modulated surfaces at THz
Several implementations based on graphene’s field effect
Beam scanning at fixed freq
y
τ = 1 ps, T = 300°K, f0 = 2 THz, VDC = 6.5 − 45 V, εr = 3.8, s = 4.8μm and g = 0.2μm.
LWA theoryHFSS
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 19
Experimental Results (I)
Fabrication of graphene stacks
CVD of graphene
Metallic contacts DC biasing + dynamic reconfiguration
Single layer graphene
Graphene «quality»
Double-layer graphene stack
J. S. Gómez-Díaz, C. Moldovan, S. Capdevilla, L. S. Bernard, J. Romeu, A. M. Ionescu, A. Magrez, and J. Perruisseau-Carrier, “Self-biased reconfigurable
graphene stacks for terahertz plasmonics”, Nature Communications, 2015.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 20
Experimental Results (and II)
Graphene stacks
Enhanced reconfiguration capabilities + simple fabrication avoiding metals
Measured using THz time-domain spectroscopy Good agreement theory
Operation frequency: 1 THz
J. S. Gómez-Díaz, C. Moldovan, S. Capdevilla, L. S. Bernard, J. Romeu, A. M. Ionescu, A. Magrez, and J. Perruisseau-Carrier, “Self-biased reconfigurable
graphene stacks for terahertz plasmonics”, Nature Communications, 2015.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
21
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 22
Reciprocity and Why it Needs to be Broken
Reciprocitysymmetry in transmission for opposite propagation directions
Duplexers
Rx
Tx
Isolators
IBM
A
B
A
B
𝑇BA = 𝑇AB
Slide courtesy of Dr. Dimitrious Sounas.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 23
General Conditions for Non-Reciprocity
Magnetic Field
Direct current
B 21 12T TLinear network
B Bt t
Onsager-Casimir Principle
Static Magnets Massive Devices
Tanaka, Proc. IEEE 53, 260 (1965) D. L. Sounas et al, IEEE TAP (2013)
Transistors
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 24
General Conditions for Non-Reciprocity
Magnetic Field
Direct current
B 21 12T TLinear network
B Bt t
Onsager-Casimir Principle
Static Magnets Massive Devices
Tanaka, Proc. IEEE 53, 260 (1965) D. L. Sounas et al, IEEE TAP (2013)
Transistors
Linear Momentum
p
Angular Momentum
L
Alternative approach? Momentum Bias
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 25
Non-Reciprocity with Momentum Bias
Linear Momentum
p
Angular Momentum
L
Lira et al, PRL 109, 033901 (2012)
Demonstrated @ microwaves and optics
R. Fleury et al, Science (2014)N. A. Estep et al,
Nature Phys. (2014)
Demonstrated @ acoustics, microwaves and optics
D. Sounas, et alACS Photonics (2014)
S. Qin et al, IEEE MTT (2014)
Isolators
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 26
Non-Reciprocity with Momentum Bias
Linear Momentum
p
Angular Momentum
L
Lira et al, PRL 109, 033901 (2012)
Demonstrated @ microwaves and optics
R. Fleury et al, Science (2014)N. A. Estep et al,
Nature Phys. (2014)
Demonstrated @ acoustics, microwaves and optics
D. Sounas, et alACS Photonics (2014)
S. Qin et al, IEEE MTT (2014)
Isolators
Potential application in growing areas?
• THz science and technology• Plasmonics
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 27
Non-Reciprocal Graphene Components
All non-reciprocal graphene THz devices rely on magnetic bias…
Bulky static magnets
D. L. Sounas et al, APL (2013)
Giant Faraday Rotation
2D material & highly-confined plasmons but massive devices
Non-reciprocal plasmonics
Sounas et al, APL (2011)
J.Yao Chin, et al. Nature Com. (2013) M. Tamagnone et al,Nature Phot. (2014)
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 28
Non-Reciprocal Graphene Components
All non-reciprocal graphene THz devices rely on magnetic bias…
Bulky static magnets
D. L. Sounas et al, APL (2013)
Giant Faraday Rotation
2D material & highly-confined plasmons but massive devices
Non-reciprocal plasmonics
Sounas et al, APL (2011)
J.Yao Chin, et al. Nature Com. (2013) M. Tamagnone et al,Nature Phot. (2014)
Motivation and objectives
Magnet-free non-reciprocal graphene plasmonics
Linear momentum through graphene’s field effect
Integrated, low-cost technology
Relatively easy fabrication
Potential applications
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 29
Graphene’s Field Effect
Reconfigurability through applied bias Implement static conductivity profiles
𝑛𝑠 = 𝐶𝑜𝑥(𝑉𝐷𝐶 − 𝑉𝐷𝑖𝑟𝑎𝑐)/𝑞𝑒
2 2 0(
2( ) )s d c d c
F
f dfnv
𝜇𝑐 ≈ ℏ𝑣𝐹𝜋𝐶𝑜𝑥𝑉𝐷𝐶
𝑞𝑒 Usual static operation
Moderately doped ( 𝜇𝑐 ≫ 𝑘𝐵𝑇)
Below interband threshold (2 𝜇𝑐 > ℏ𝜔) 𝜎 ∝ 𝑉𝐷𝐶
Up to ~100 GHz C. T. Phare et al, Nat. Phot. (2015)
V. Ginis et al, PRB Rapid Comm. (2015)
𝑬𝒃𝒊𝒂𝒔
𝜎 𝑡 ∝ 𝑉 𝑡
V 𝑡
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 30
Spatio-Temporal Modulation in Graphene
Linear Momentum
p
S. Qin et al, IEEE MTT (2014)
Isolators Implemented at microwaves
Time modulated varactors
Can we apply this at THz?
𝜎 𝑧, 𝑡 ≈ 𝜎0 1 + 𝑀 cos 𝜔𝑚𝑡 − 𝛽𝑚𝑧𝑉𝑛 𝑡 = 𝑉cos 𝜔𝑚𝑡 + 𝑛𝜙𝑚
Graphene: Ideal material to implement spatiotemporal modulation @ THz
D. Correas-Serrano, J. S. Gómez-Díaz, D. Sounas, A. Alvarez-Melcon and A. Alù, “Non-reciprocal graphene devices and antennas at THz based on spatio-
temporal modulation”, IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1529-1533, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Single layer implementation
Single Layer Graphene Isolator
𝑘𝑧
𝜔𝜎 𝑧 = 𝜎0[1 + 𝑀cos(𝛽𝑚𝑧)]𝜎 𝑧, 𝑡 = 𝜎0[1 + 𝑀cos(𝜔𝑚𝑡 − 𝛽𝑚𝑧)]
𝜔𝑚
𝑓0 𝑓0
𝑓0𝑓0 − 𝑓𝑚
𝑣 = 𝜔𝑚/𝛽𝑚
Forward propag.Backwards propag.
𝑆𝑓0−𝑓𝑚,𝑓0+𝑓𝑚 → 0
31
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 32
PPW Graphene-based Isolator
Isolator requirements
Modes are phase-matched @ one direction
Modulated length = Coherence length 𝐿𝑐
𝜎1 𝑧, 𝑡 = 𝜎0 1 + 𝑀 cos 𝜔𝑚𝑡 − 𝛽𝑚𝑧
𝑑𝑎1𝑑𝑧
= −𝑗𝑘𝑧1𝑎1 + 𝐶𝑎2e𝑗(𝑘𝑧1−𝑘𝑧2−𝛽𝑚)𝑧
𝑑𝑎2𝑑𝑧
= −𝑗𝑘𝑧2𝑎2 + 𝐶𝑎1e−𝑗(𝑘𝑧1−𝑘𝑧2−𝛽𝑚)𝑧
𝐿𝑐 = 𝜋/2|𝐶|
Coupled-mode analysis
where 𝐶 =M𝜎08
𝐸𝑧1 𝑥𝜎1 𝐸𝑧2∗ (𝑥𝜎1)
Graphene PPW: Two orthogonal modes Graphene PPW: Two orthogonal modes
PPW + ST modulation of one layer:
D. Correas-Serrano, J. S. Gómez-Díaz, D. Sounas, A. Alvarez-Melcon and A. Alù, “Non-reciprocal graphene devices and antennas at THz based on spatio-
temporal modulation”, IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1529-1533, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Numerical Simulations
PPW Graphene-based Isolator (and II)
𝒇𝟎
𝒇𝟎
𝒇𝟎
𝒇𝟎
𝒇𝟎
𝒇𝟎
𝒇𝟎 + 𝒇𝒎
𝒇𝟎 − 𝒇𝒎
𝒇𝟎
𝒇𝟎 + 𝒇𝒎
𝒇𝟎 − 𝒇𝒎
𝒇𝟎
𝐸𝑧 Transmission Isolation
33
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Sinusoidally modulated LWA
Spatiotemporally modulated LWA
34
Non-Reciprocal Graphene Leaky-wave Antenna
𝜎 𝑧 = 𝜎0[1 + 𝑀cos(𝛽𝑚𝑧)]
1 t 2 t 3 t
1DCV t
2DCV t 3DCV t
𝑓0
𝑓0 − 𝑓𝑚 𝑓0 − 𝑓𝑚
𝜃𝑇𝑋 ≠ 𝜃𝑅𝑋
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 35
Non-Reciprocal LWA Radiation/Reception
𝑬𝒛, 𝒇𝟎
𝑬𝒛, 𝒇𝟎 − 𝒇𝒎
Tx Rx
Rx Angle
𝜃(deg)
𝑬𝒛𝒊,𝟑𝟎∘ , 𝒇𝟎 − 𝒇𝒎
𝑬𝒛, 𝒇𝟎 − 𝟐𝒇𝒎∀𝑓
𝑬𝒛𝒊,𝟏𝟓∘ , 𝒇𝟎 − 𝒇𝒎
𝑬𝒛, 𝒇𝟎 − 𝟐𝒇𝒎
Non-reciprocity is two fold
Radiation diagram in Tx - Rx
Frequency conversion
D. Correas-Serrano, J. S. Gómez-Díaz, D. Sounas, A. Alvarez-Melcon and A. Alù,
“Non-reciprocal graphene devices and antennas at THz based on spatio-temporal
modulation”, IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1529-
1533, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
36
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 37
Hyperbolic and Isotropic Materials
Images from Lavrinenko’s group (DTU, Denmark). SPIE Newsroom. DOI: 10.1117/2.1201410.005626
, , 0x y z
Light line
, 0
0
x y
z
‘ zoo’ of propagating waves
Wav
evec
tor 𝑘W
avev
ecto
r 𝑘
2
k
are “bounded” !,k
0
k
0 0
0 0
0 0
x
y
z
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 38
Hyperbolic Wave Propagation & Applications
K. G. Balmain et al.IEEE TAP - AWPL
2003 – 2004
222 2
||
/kk
c
0 & 0 0 & 0
Natural and Artificial Hyperbolic media
A. Poddubny, I. Iorsh, P. Belov and Y. KivsharNature Photonics, 7,
113110 (2013)
E. E. Narimanov and A. V. Kildishev
Nature Photonics, 9, 214 (2015)
Negative refraction
A. Fang, T. Koschny, and C. M. Soukoulis,
Phys. Review B, 79,245127, (2009)
Canalization & thin structures
A. V. Kildishev, A. Boltasseva, V. M. Shalaev
Science 339, 1232009 (2013)
Topological transitions
H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V.
M. Menon, Science , 336, (2012)
SER enhancement
J. Kim, V. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E.
Narimanov, and V. M. Shalaev, Optic Express, 20, 8100, (2012)
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 39
Hyperbolic Wave Propagation & Applications
K. G. Balmain et al.IEEE TAP - AWPL
2003 – 2004
222 2
||
/kk
c
0 & 0 0 & 0
Natural and Artificial Hyperbolic media
A. Poddubny, I. Iorsh, P. Belov and Y. KivsharNature Photonics, 7,
113110 (2013)
E. E. Narimanov and A. V. Kildishev
Nature Photonics, 9, 214 (2015)
Negative refraction
A. Fang, T. Koschny, and C. M. Soukoulis,
Phys. Review B, 79,245127, (2009)
Canalization & thin structures
A. V. Kildishev, A. Boltasseva, V. M. Shalaev
Science 339, 1232009 (2013)
Topological transitions
H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V.
M. Menon, Science , 336, (2012)
SER enhancement
J. Kim, V. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E.
Narimanov, and V. M. Shalaev, Optic Express, 20, 8100, (2012)
Hyperbolic Metamaterials Challenges:
Fabrication Access to the propagating waves Volumetric loss Integration with other components
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 40
Topologies of Uniaxial Metasurfaces
Im 0
Im 0
xx
yy
Elliptic topology
Hyperbolic topology Im 0
Im 0
xx
yy
Hyperbolic topology
Im 0
Im 0
xx
yy
𝜎-near zero topology Im 0
Im 0
xx
yy
Ƹ𝑒𝑧Ƹ𝑒𝑦Ƹ𝑒𝑥
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
തത𝜎 =𝜎𝑥𝑥 00 𝜎𝑦𝑦
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 41
Plasmon Propagation
0
2 22 2 2 2 2 2 2 2 20 04 0x xx y yy x y x yk k k k k k k k
0
0xx
yy
Ƹ𝑒𝑧𝜀0
𝜀0
Ƹ𝑒𝑥Ƹ𝑒𝑦
𝜑
TM mode:
TE mode:
0
2 22 2 2 2 2 2 2 2 20 04 0x y x y y xx x yyk k k k k k k k
TM mode - Example
y xk mk b xx
yy
m
2
00
21
yy
b k
Im 0.1
Im 5.0
xx
yy
i mS
i mS
Im 0.1
Im 5.0
xx
yy
i mS
i mS
Im 3.0
Im 3.0
xx
yy
i mS
i mS
H. J. Bilow, IEEE TAP 51, 2788, 2003. [2] A. M. Patel and A. Grbic, IEEE TAP. 61, 211, 2013
R. Quarfoth, and D. Sievenpiper, IEEE TAP, vol. 61, 3597, 2013
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 42
Practical Implementation of Hyperbolic MTSs
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
0
0
effxxeff
effyy
Ƹ𝑒𝑧Ƹ𝑒𝑦
Ƹ𝑒𝑥 𝑊 𝐿
A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, Nature, vol. 522, pp. 192-196, 2015
Experimental verification @ optics
𝜎𝐶 = −𝑖𝜔𝜀0𝐿
𝜋ln csc
𝜋𝐺
2𝐿
𝜎𝑥𝑥𝑒𝑓𝑓
=𝐿𝜎𝜎𝐶
𝑊𝜎𝐶 + 𝐺𝜎
𝜎𝑦𝑦𝑒𝑓𝑓
= 𝜎𝑊
𝐿
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 43
Practical Implementation of Hyperbolic MTSs
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
0
0
effxxeff
effyy
Ƹ𝑒𝑧Ƹ𝑒𝑦
Ƹ𝑒𝑥 𝑊 𝐿
A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, Nature, vol. 522, pp. 192-196, 2015
Experimental verification @ optics
𝜎𝐶 = −𝑖𝜔𝜀0𝐿
𝜋ln csc
𝜋𝐺
2𝐿
𝜎𝑥𝑥𝑒𝑓𝑓
=𝐿𝜎𝜎𝐶
𝑊𝜎𝐶 + 𝐺𝜎
𝜎𝑦𝑦𝑒𝑓𝑓
= 𝜎𝑊
𝐿
Graphene-based Hyperbolic Metasurfaces Benefits:
Easy fabrication (lithography) Easy access/extraction of energy Reduced loss Compatible with integrated circuits / optoelectronic components Tunable
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 44
SPPs & Electrical Reconfigurability
Surface Plasmons @ THz
2 μm2 μm0.5 μm
1
0
Ƹ𝑒𝑥
Ƹ𝑒𝑦
Ƹ𝑒𝑥
Ƹ𝑒𝑦
Ƹ𝑒𝑥
Ƹ𝑒𝑦
0.5
0
0.3
0
L
x
yz
W
L=50nm, W=10 nm, 𝜇𝑐 = 0.5𝑒𝑉
L=50nm, W=25 nm,𝜇𝑐 = 0.1𝑒𝑉
L=50nm, W=25 nm,𝜇𝑐 = 0.3𝑒𝑉
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
f= 5 THz
Electrical reconfigurabilityf=10 THzW=44 nm
Hyperbolic
𝜎-near zeroAnisotropic elliptic
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 45
Negative Refraction of SPPs
𝜃𝑜𝑢𝑡
Ƹ𝑒𝑧
Ƹ𝑒𝑦Ƹ𝑒𝑥
𝜃𝑖𝑛
𝜎𝑖𝑛𝜎𝑜𝑢𝑡
Transmission & reflection coefficient (approx.)
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 46
Light-Matter Interactions
Spontaneous Emission Rate (SER) of emitters• Large enhancement expected from analogy with bulk HMTM
• Dedicated Green’s function approach
SER in graphene
0 00 0
61 Im , ,p S p
p
PSER G r r
P k
F. H. L. Koppens, D. E. Chang, and F. García de Abajo, Nanoletters, vol. 11, pp. 3370-3377, 2011
Ƹ𝑒𝑧
d
Ƹ𝑒𝑦Ƹ𝑒𝑥
eff
020 0 2, ,
8zi k z
S ss ss sp sp ps ps pp pp x y
iG r r M M M M e dk dk
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 47
Light-Matter Interactions in Metasurfaces
-0.2 0 0.2-0.2
0
0.2
Im[yy
] (mS)
Im[
xx]
(mS
)
2
4
6
Elliptic TopologyHyperbolic Topology
Hyperbolic TopologyElliptic TopologyTE - modes
Im yy
Im yy
SER of a z-oriented dipole over a uniaxial metasurface Topological transitions
Dramatic SER enhancement
Ƹ𝑒𝑧
d=10nm
Ƹ𝑒𝑦Ƹ𝑒𝑥
eff
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Physical Review Letters , vol. 114, pp. 233901, 2015
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 48
Canalization & Hyperlensing
Canalization over a surface
LDOS/SER enhancement
𝜎 near-zero topology
Application: Hyperlensing
Im 0
Im 0
xx
yy
-500 -250 0 250 5000
0.2
0.4
0.6
0.8
1
y axis (nm)
abs(
Ez/E
ma
x)
x=150 nmx=-150 nm
d ≈ 0.7𝜆1 ≈ 0.007𝜆0
-500 -250 0 250 5000
0.2
0.4
0.6
0.8
1
y axis (nm)
abs(
Ez/E
ma
x)
x=150 nmx=-150 nm
d ≈ 0.21𝜆1 ≈ 0.0021𝜆0
-500 -250 0 250 5000
0.2
0.4
0.6
0.8
1
y axis (nm)
abs(
Ez/E
ma
x)
x=150 nmx=-150 nm
d ≈ 0.1𝜆1 ≈ 0.001𝜆0
J. S. Gomez-Diaz and A. Alù, ACS Photonics, 2016
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 49
Practical Limitations
Losses
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Optic Express, vol. 5, 2313-2329, 2015
D. Correas-Serrano, J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Optic Material Express, vol. 23, 29434-29448, 2015
(2) (2)3 3xx yyi mS i mS (2)
(2)
0.055 3
0.055 3
xx
yy
i mS
i mS
(2)
(2)
0.3 3
0.3 3
xx
yy
i mS
i mS
(2)
(2)
3 3
3 3
xx
yy
i mS
i mS
Ƹ𝑒𝑧
d
Ƹ𝑒𝑦Ƹ𝑒𝑥
eff Nonlocality
W=0.5L Limited Fermi velocity
Wavenumber cutoff
Periodicity L=15 nm
L
x
yz
W
L
x
yz
W
L=50 nm
L
x
yz W
L=100 nm
Design of Practical Hyperbolic Metasurfaces
0f
Lc v k
0f
Lc v k
Nonlocality dominates and imposes a wavenumber cutoff.Periodicity can be increased Easier fabrication !
Periodicity dominates and imposes a wavenumber cutoff.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 50
Practical Limitations
Losses
J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Optic Express, vol. 5, 2313-2329, 2015
D. Correas-Serrano, J. S. Gomez-Diaz, M. Tymchenko and A. Alù, Optic Material Express, vol. 23, 29434-29448, 2015
(2) (2)3 3xx yyi mS i mS (2)
(2)
0.055 3
0.055 3
xx
yy
i mS
i mS
(2)
(2)
0.3 3
0.3 3
xx
yy
i mS
i mS
(2)
(2)
3 3
3 3
xx
yy
i mS
i mS
Ƹ𝑒𝑧
d
Ƹ𝑒𝑦Ƹ𝑒𝑥
eff Nonlocality
W=0.5L Limited Fermi velocity
Wavenumber cutoff
Periodicity L=15 nm
L
x
yz
W
L
x
yz
W
L=50 nm
L
x
yz W
L=100 nm
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Black Phosphorus
Thickness down to few nm
Variable bandgap
Anisotropic & plasmonic material
Hyperbolic response ?
Local response (q0)
51
2D Natural Hyperbolic Materials
D. Correas-Serrano, J. S. Gomez-Diaz, A. Alvarez Melcon, and A. Alù, “Black Phosphorus Plasmonics: From Anisotropic Elliptical Regimes to Nonlocality-
Induced Canalization”, Journal of Optics, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Black Phosphorus
Thickness down to few nm
Variable bandgap
Anisotropic & plasmonic material
Hyperbolic response ?
Local response (q0)
52
2D Natural Hyperbolic Materials
D. Correas-Serrano, J. S. Gomez-Diaz, A. Alvarez Melcon, and A. Alù, “Black Phosphorus Plasmonics: From Anisotropic Elliptical Regimes to Nonlocality-
Induced Canalization”, Journal of Optics, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Black Phosphorus
Thickness down to few nm
Variable bandgap
Anisotropic & plasmonic material
Hyperbolic response ?
Local response (q0)
Nonlocality induces a wideband canalization regime
53
2D Natural Hyperbolic Materials
D. Correas-Serrano, J. S. Gomez-Diaz, A. Alvarez Melcon, and A. Alù, “Black Phosphorus Plasmonics: From Anisotropic Elliptical Regimes to Nonlocality-
Induced Canalization”, Journal of Optics, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
54
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 55
Non-linear Responses
-+
+
E E
Dipole moment – Hooke’s law
𝑷
𝜖0= 𝜒 1 𝑬 + Ӗ𝜒 2 𝑬𝑬+ Ӗ𝜒 3 𝑬𝑬𝑬+⋯
Linear Nonlinear
Nonlinear material
Ӗ𝜒(1), Ӗ𝜒(2), Ӗ𝜒(3)
𝜔
Ӗ𝜒(2)𝜔
2𝜔
Second Harmonic Generation(SHG)
P. Franken, A. Hill, C. Peters, and G.Weinreich, Phys. Rev. Lett. 7, 118 (1961)
ħ(2ω)ħω
ħω
R. W. Boyd, ‘Nonlinear Optics’, Academic, 2008
Ӗ𝜒(2)
Differential Frequency Generation(DFG)
𝜔1
𝜔2
𝜔3 = 𝜔1-𝜔2
ħω1ħω2
ħ(ω1- ω2)
Pros:• Ultrafast response
• Coherent process
Challenges:• Relatively large
incident intensities
• Weak intrinsic response: Crystals, Metals, Diodes, Ferroelectrics, MQWs
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 56
Enhancing Non-linear Responses (I)
Phase matching: Bulk materials
𝐸 𝜔
𝐸(2𝜔)
𝜒(2)
n(2ω)>n(ω) !!𝑘𝑜𝑢𝑡
𝑘𝑖𝑛1 Δkkin2
1 2in in outk k k
𝑑
2222
2eff
I dE
I
𝜒𝑒𝑓𝑓(2)
≈ 1 − 100𝑝𝑚/𝑉
𝜂 ↑↑
𝐸𝜔 ↑↑
𝑑 ↑↑ Bulky/heavy structures
Material damage threshold
𝑛 𝜔 = −𝑛(2𝜔)
A. Rose, et al, PRL, 2011.
ENZ responseSuckowski et al,
Science, 2013
ENZ responseC. Argyropoulos,et al,
PRB, 2012
Periodically pooled material
Birefringence
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 57
Enhancing Non-linear Responses (and II)
Phase matching: Ultrathin Metasurfaces (SHG)
2
1 2in in outk k k
Relaxed conditions: in-plane
2222
2eff
I dE
I
Conversion efficiency Typical non-linear materials
2 1eff E 𝜒𝑒𝑓𝑓(2)
≈ 10 𝑝𝑚/𝑉 𝐼𝜔 ≈ 1 𝑃𝑊/𝑐𝑚2
@ 57 MW/cm2
Standard nonlinear metasurfaces: 2 1eff E
Linden et al, PRL, 2012
𝑑 ≪ 𝜆
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 58
Combining Two Worlds
Huge intrinsic NL response from MQWs
n-doped MQWs
Ӗ𝜒(2) = 𝜒𝑧𝑧𝑧(2)
Ƹ𝑒𝑧 Ƹ𝑒𝑧In0.53Ga0.47As/Al0.48In0.52As
Ultrathin plasmonic resonators
𝝎 𝟐𝝎
z pumpE E
3
1.5
0
-1.5
-3
𝟐𝝎
2
1
0
-1
-2
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 59
Nonlinear Plasmonic Metasurfaces
J. Lee, M. Tymchenko, C. Argyropoulos, et al, Nature , vol. 511, pp. 65-69, 2014
Nonlinear plasmonic metasurfaces
Vision: Flat nonlinear paradigm
Enhanced conversion efficiency
Manipulation of the generated beam
𝟐 ∙ 𝟏𝟎−𝟒% at 15 kW/cm2 !!
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 60
Analysis of Nonlinear MTSs
Rigorous analysis of nonlinear Metasurfaces
J. S. Gomez-Diaz, M Tymchenko, J Lee, M. A. Belkin, A Alù, Physical Review B, vol. 92, pp. 125429, 2015
2
[ ] [ ] [ ](2) (2) (2)[ ] 2
[ ] [ ] [ ]
1
UC
z a z b z meff mab zzz zzz overlap
inc a inc b inc mV
E E EI d MI I
V E E E
r r
(2)effective It
ab
t
ab
Effective non-linear susceptibility
MQWs saturation
d ≪ 𝜆
𝜔
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 61
Enhancing Efficiency: Approaches
(2)effective I
Plasmonic resonator design overlapMI
MQWs design (2) ,zzz SATI
2eff
J. S. Gomez-Diaz, M Tymchenko, J Lee, M. A. Belkin, A Alù, Physical Review B, vol. 92, pp. 125429, 2015.
2222
2eff
I dE
I
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 62
Highly-Efficient Non-Linear Metasurfaces
(2) 55 /zzz nm V
1 2 20.5 /SatI MW cm
0.55overlapMI
(2) 275 /zzz nm V
1 2 22 /SatI MW cm
4.25overlapMI
(2) 137 /zzz nm V
1 2 21.25 /SatI MW cm
2.1overlapMI
J. Lee, N. Nookola, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, M. Belkin, Advanced Optical Materials,
doi: 10.1002/adom.201500723, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 63
Manipulating the Generated NL Beams
M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, Physical Review Letters, vol. 115, pp. 207403, 2015
ω
2ω
2ω
y
xz
E
2LE
2RE
Pancharatnam-Berry approach
o Local control of the phase by rotation subwavelength resolution!
o High conversion efficiency
o Enhanced functionalities for the SH beam Beam steering
Focusing
Generation of vortex beam
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 64
Advanced Functionalities (I)
Steering the generated SH beam
ω
2ω
2ωy
xz
RCP pumpω
2ω
2ωy
xz
LCP pump
Focusing the generated SH beam
Rω
RCP pump
Lω
LCP pump
M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, Physical Review Letters, vol. 115, pp. 207403, 2015
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 65
Advanced Functionalities (and II)
M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù , “Advanced Control of Nonlinear Beams with Pancharatnam-Berry
Metasurfaces”, Physical Review B, 2016.
Nonlinear generation of Vortex beams
Polarization-dependent angular momentum Wikipedia
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 66
Experimental Results
J. Lee, N. Nookola, M. Tymchenko, J. S. Gomez-Diaz, F. Demmerle, G. Boehm, M. Amann, A. Alu, M. Belkin, Optica, Vol. 3, Issue 3, pp. 283-288, 2016.
L2ωR2ω
0.01%
RωRCP pump
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
67
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 68
Nems Metasurfaces
Y. Hui, J. S. Gomez-Diaz, A. Alù, and M. Rinaldi, Nature Communications, 2016.
Infrared detector Ultrathin metasurface Body of a nanomechanical resonator
Combination of mechanical and electromagnetic resonances
Room temperature
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 69
Nems Metasurfaces: Features
Infrared detector Low noise, fast response
High electromechanical coupling coefficient
Y. Hui, J. S. Gomez-Diaz, A. Alù, and M. Rinaldi, Nature Communications, 2016.
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces
Introduction
Graphene plasmonics: THz devices & antennas
Non-reciprocal metasurfaces
Hyperbolic metasurfaces
Non-linear metasurfaces
Multidisciplinary
Conclusions
70
Outline
J. S. Gomez-Diaz - Flatland Optics with Ultrathin Metasurfaces 71
Conclusions
Hyperbolic metasurfaces
NEMS
Reconfigurable THz graphene devices
Flat nonlinear paradigm
Towards a Flatland & Advanced Manipulation of EM waves
Non-reciprocal plasmonics
Thank you!J. Sebastian Gomez-Diaz
Department of Electrical and Computer EngineeringUniversity of California, Davis
Collaborators:
• Mr. Diego Correas-Serrano – University of Califonia, Davis, USA
• Prof. Andrea Alù – The University of Texas at Austin, USA
• Prof. Mikhail Belkin – The University of Texas at Austin, USA
• Dr. Dimitrious Sounas – The University of Texas at Austin, USA
• Prof. Mateo Rinaldi – Northeastern University, USA
• Prof. Juan Mosig – École Polytechnique Fédérale de Lausanne, Switzerland
• Dr. Michele Tamagnone – École Polytechnique Fédérale de Lausanne, Switzerland
• Prof. A. Alvarez-Melcon – Technical University of Cartagena, Spain.