terahertz metamaterials: a bulk approach
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TERAHERTZ METAMATERIALS: A BULK APPROACH
Eric Lheurette 1, Frédéric Garet 2, Shenxiang Wang 1, Charles Croënne 1, Karine Blary 1,
Jean-Louis Coutaz 2 et Didier Lippens 1
1 IEMN - UMR CNRS 8520, Université de Lille 1, 59652 Vi lleneuve d'Ascq Cedex - France 2 IMEP LAHC - UMR CNRS 5130, Université de Savoie, 7337 6 Le Bourget du Lac Cedex - France
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Outline
• Negative Index Metamaterials (NIM)• Targeting the THz spectrum• Stacked subwavelength hole arrays
Design and fabrication
R & T measurements
Angular measurements
• ApplicationsEnvironment sensing
Polarization rotation
Focusing
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Negative Index Metamaterials (NIM)
• Negative permittivityDiluted metal in order to decrease the plasma frequency
• Negative permeabilityResonating current loops
J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely LowFrequency Plasmons in Metallic Mesostructures," Physical Review Letters, vol. 76, pp. 4773, 1996.
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," Microwave Theory andTechniques, IEEE Transactions on, vol. 47, pp. 2075-2084, 1999
H
Ek
D. R. Smith and S. Schultz, UCSD
The combination of wire and current loopsarrays permits one to synthesize a Negative Index Metamaterial
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Negative Index Metamaterials (NIM)
F. Zhang, D. P. Gaillot, C. Croenne, E. Lheurette, X. Melique, and D. Lippens, "Low-loss left-handed metamaterials at millimeter waves," Applied Physics Letters, vol. 93, pp. 083104, 2008.
Incident wave polarization requirement:
The substrates need to be stacked and illuminatedunder grazing incidence.
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Targeting the THz spectrum
• Stacked subwavelength arrays
M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express, vol. 16, pp. 560-566, 2008.
• « Fishnet » approach
S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express, vol. 13, pp. 4922-4930, 2005.
J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature, vol. 455, pp. 376-379, 2008
• « Nanorod » approach
V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett., vol. 30, pp. 3356-3358, 2005
B. Kante, S. N. Burokur, A. Sellier, A. d. Lustrac, and J. M. Lourtioz, "Controlling plasmonhybridization for negative refraction metamaterials," Physical Review B (Condensed Matterand Materials Physics), vol. 79, pp. 075121, 2009.
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
Fullwavesimulations
Eigenmode
Scatteringparameters
Typical size of the unit cell
Diameter of the aperture 125 µm
Elliptical Aspect Ratio (EAR) 1,8
Metal thickness 0,4 µm
Periodicity along k 26 µm
Periodicity along E : ay 340 µm
Periodicity along H : ax 340 µm
BenzoCycloButhene (BCB) / gold stackLimited thickness due to to the stress in BCB interlayers
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
C. Croënne, F. Garet, K. Blary, É. Lheurette, J.-L. Coutaz and D. Lippens, Bulk metamaterials at terahertz frequencies : thesubwavelength hole stacked arrays approach, EuMC 2009, Roma
Impedance matching for EAR > 1,6The dispersion diagrams do not fit.
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
2,121,12
2,222,111,221,121,222,122,221,112
2,122
1,1212 ))(cosh(2
SS
SSSSSSSSSSll
−−+++=−γ
1,ijS : structure of length l1
2,ijS : structure of length l2 B. Bianco and M. Parodi, "Determination of the propagation constant of uniformmicrostrip line," Alta Frequenza, vol. 2, pp. 107, 1976.
Description of the dispersion from a7-3 unit cell differential analysis
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
• BCB coating (13 µm)Dow-Cyclotene 3022-63
• BCB polymerisation
• Optical lithographyAznLOF 2070
• Metal evaporating, lift-offCr : 200 Å / Au : 4000 Å / Cr : 200 Å
C. Croënne, F. Garet, É. Lheurette, J-L. Coutaz, and D. Lippens, "Left handed dispersion of a stack of subwavelength hole metal arrays at terahertz frequencies," Applied Physics Letters, vol. 94, pp. 133112, 2009.
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
• BCB coating (26 µm)
• BCB polymerisation
• Optical lithography
• Metal evaporating, lift-off
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
• BCB coating (13 µm)
• BCB polymerisation
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysdesign and fabrication
GaAs substrate wet etchingH2SO4 : 1 / H2O : 1 / H2O2 : 8
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysR & T measurements
transmission reflexion
• Pump-probe methodPhase information
• Transmission and reflection measurementsDefinition of the generalized Sij matrix
L. Duvillaret, F. Garet and J.L. Coutaz., « A reliable method for extraction of material parameters in THz Time-Domain Spectroscopy»IEEE Journal of Selected Topics in Quantum Electronics, 1996, Vol. 2, pp. 739 – 746.
-20
-10
0
10
20
30
40
50
0 12 24 36 48 60
sign
al (
a.u.
)
time (ps)
0.001
0.01
0.1
1
10
0 1 2 3 4 5 6
THz
field
(u.a
.)
frequency (THz)
IMEP-LAHC, Chambéry, University of Savoie
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysR & T measurements
Transmission properties of a 3-cell structure
Bandgap between the left- and right-handed bands
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysR & T measurements
Transmission properties of a 5-cell structure
Continuous evolution from the left- to the right-handed ba nds
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysR & T measurements
S. Wang, F. Garet, K. Blary, C. Croënne, E. Lheurette, J.-L. Coutaz, and D. Lippens, "Composite left/right-handed stacked hole arrays at sub-millimeter wavelengths," Journal of Applied Physics 107, 074510 (2010)
Refractive index dispersion
3-cell structure 5-cell structure
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
Radiation boundary
Wave port
Perfect electric boundary
5 step-prism
10 step-prism
Electric field mapping
Output plane refracted angle
FEM simulations conditions
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
FEM simulations: 5-step prism
f = 0.456 THz
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
f = 0.492 THz
FEM simulations: 5-step prism
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
f = 0.490 THz
FEM simulations: 10-step prism
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
f = 0.630 THz
FEM simulations: 10-step prism
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
THz – Time Domain Spectroscopy
Ti:Sa laser excitation (50 fs pulse duration for a repetition rate of 100 MHz )
Low temperature-grown GaAs substrates integratingdipole antennas
High resistivity silicon hyper hemispherical lenses
Characterization of 5 and10-step prisms
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
Experimental results: 5-step prism
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Stacked subwavelength hole arraysAngular measurements
Experimental results: 10-step prism
S. Wang, F. Garet, K. Blary, E. Lheurette, J.-L. Coutaz, and D. Lippens, "Experimental verification of negative refraction for a wedge-type negative index metamaterial operating at terahertz," Applied Physics Letters, vol. 97, pp. 181902, 2010
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
ApplicationsEnvironment sensing
ay 29 µm
ax ax = 2*ay
Metal thickness 0,4 µm
BCB thickness : az 13 µm
dy 170 µm
dx 170 µm
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
ApplicationsPolarization rotation
E-vector orientation for mode 1
E-vector orientation for mode 2
Cylindrical coefficients
)(
)(
TyxTxyiTyyTxxT
TyxTxyiTyyTxxT
−−+=−−++=+
T
T
−
+ Right-Handed CircularPolarization (RCP)
Left-Handed CircularPolarization (LCP)
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
ApplicationsPolarization rotation
[ ])arg()arg(2
1−+ −= TTθ
Rotary power ~ 1035 /λ
100 degrees rotation for a 3-layer structure
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
ApplicationsFocusing
1 THz focusing with gradient refractive index lens
Structure:Number of layes: 5ax=ay=170 µmaz=13 µmThickness of gold: 400 nmElliptical ratio: 2Diameter of short axis: ~59 µm 8.00x1011 9.00x1011 1.00x1012 1.10x1012 1.20x1012
-5
-4
-3
-2
-1
0
1
2
Rea
l (n)
Frequency (Hz)
n_53um n_54um n_55um n_56um n_57um n_58um n_59um n_60um n_61um n_62um n_63um
A. O. Pinchuk and G. C. Schatz, "Metamaterials with gradient negative index of refraction," J. Opt. Soc. Am. A, vol. 24, pp. A39-A44, 2007.
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
ApplicationsFocusing
1 THz focusing with gradient refractive index lens
Simulation of one lens (9 metallic stacked layers) @ 940 GHzDiameter decreases along the radius from 62 to 52 µm (parabolic function)(yellow arrow)
Hk
E
E field magnitude Real Poynting vector
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
Conclusions
• Stacked subwavelength hole arrays as THz NIMR & T measurements:
-3 dB @ 0.5 THz Zero index working capabilities
Angular measurementsNegative refraction with a significant level near the Zero angle
• ApplicationsEnvironment sensing
FOM > 500 by means of an asymmetric pattern (~1 THz)
Polarization rotationRotary power > 1000 / λ
FocusingDesign of a NIM GRIN lens for 1 THz operation
GDR THz - International Workshop, 29 March - 1 April 20 11, Tignes, France
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