Artificial Magnetic Resonators and Potential Applications in Nonlinear Field Yongmin Liu Applied...
-
Upload
norah-dickerson -
Category
Documents
-
view
218 -
download
1
Transcript of Artificial Magnetic Resonators and Potential Applications in Nonlinear Field Yongmin Liu Applied...
Artificial Magnetic Resonators and
Potential Applications in Nonlinear Field
Yongmin Liu
Applied Science & Technology
Physics 208A Presentation
Oct. 18th, 2004
Outline
I. Background of Metamaterials
II. Artificial Magnetic Resonators at THz
III. Potential Application in Nonlinearity
IV. Summary
What are Metamaterials?What are Metamaterials?
Artificially fabricated structures or media that exhibit electrodynamic properties not found in naturally occurring materials.
* Dimension of the unit cell is less than the wavelength of excitation EM wave, thus the effective-media theorem can be applied.
Why Metamaterials are Interesting?Why Metamaterials are Interesting?
* We can design and control the properties of materials. Some novel properties, such as negative electric permittivity, negative magnetic permeability, negative refractive index etc. have been explored.
Negative PermittivityNegative Permittivity
The permittivity of metal is given by
)(1)(
2
i
ep
eep m
ne
0
22
Plasma frequency:
where n is the electron density, and me is the electron mass
Damping factor: 0
where is the electric conductivity
In the visible region, is negative for most metals. At lower frequencies, permittivity is imaginary.
(typically in the UV region)
Negative with small loss in low frequencies can be achieved by metallic wire lattice
Pendry J.B. et al., Phys. Rev. Lett. 76, 4773 (1996)
Negative PermittivityNegative Permittivity (cont’d) (cont’d)
,2
2
a
rnneff
)/ln(
2
20 rane
meff
eff
effep m
en
0
22
,100.1 6 mr
,100.5 3 ma
31710675.5 mn
!!2.8 GHzep
)1.0(1
2
ep
epeff i
lattice constant:
radius of wire:
Negative can be achieved by split-ring resonator (SRR)
Negative PermeabilityNegative Permeability
Magnetism originates from
1) orbital motion of electrons
2) unpaired electron spins
The magnetic response of most nature materials fades away in GHz region.
Artificial magnetism can be realized by conducting, nonmagnetic split-ring resonators. The magnetic response is able to extend to THz, even higher frequency with lar
ge positive or negative permeability.
Will discuss in detail later !
Left-handed Materials (LHM) with Left-handed Materials (LHM) with Negative Refractive Index (NIR)Negative Refractive Index (NIR)
2n
n
When andsimultaneously, we have to choose
Refractive index:
E
H
k
S
Right handed materials (RHM)
E
H
k S
Left handed materials (LHM)
n > 0
n < 0
,HEk
EHk
Maxwell’s equation:
LHM with NRI (cont’d)LHM with NRI (cont’d)
1. Snell’s law: n sin
sin
2
1
Exotic properties of LHM:
Negative refraction !
2. Flat superlens
Diffraction-limit (min) free !
Veselago V.G. Sov. Phys.10, 509 (1968); Pendry J. B. PRL 85, 3966 (2000)
S kLHM
RHM
Fourier Expansion of 2D object:
, ,
, , exp
x y
x y z x yk k
t k k ik z ik x ik y i t
E r E
2 2 2 2 2 2 2 2, ,z x y x yk c k k c k k
2 2 2 2 2 2 2 2, .z x y x yk i k k c c k k
Propagating waves:
Evanescent waves:
Z
LHM with NRI (cont’d)LHM with NRI (cont’d)
Artificially engineered metamaterials implements the concept of LHM!
Photograph of LHM
Shelby R. A. et al., Science 292, 77 (2001); Smith D. R. et al., Science 305, 788 (2004)
Negative refraction by LHM prism
LHM with NRI (cont’d)LHM with NRI (cont’d)Imaging properties of LHM
Houck A. A. et al. PRL 90, 137401 (2003); Kolinko P. et al. Opt Exp 11, 640 (2003)
Simulation of subwavelength imging by FDTD
Imaging experiment in microwave region
Electric field of a point source focused by a LHM slab
http://physics.ucsd.edu/~drs/ Prof. Smith D.R. in UCSD
LHM with NRI (cont’d)LHM with NRI (cont’d)
Metamaterials open a new field in physics, engineering material science and optics!
Negative refraction is among the Top 10 highlights of 2003 by Physicsweb
Outline
I. Background of Metamaterials
II. Artificial Magnetic Resonators at THz
III. Potential Application in Nonlinearity
IV. Summary
Concept:
1. The magnetic-flux induced current loop to form magnetic dipole.
2. The intrinsic conductance and inductance will cause strong paramagnetic or diamagnetic activity around the resonance frequency.
Artificial Magnetic Resonators at THzArtificial Magnetic Resonators at THz
+ + +
+ + +
_ _ _
_ _ _
Ha
2r
Pendry J.B. et al, IEEE MTT 47, 2075 (1999)
Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)
Current distribution of SRR simulated by Microwave Studio
Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)
H-field of SRR simulated by Microwave Studio
320
20
2
2
321
1
Crri
ar
eff
30
20
3
Cr
)/1(
3223
02 arCrmp
Resonance frequency:
Magnetic plasma frequency:
mr 3100.2
GHzfGHzf mp 17.4,94.20
Typical value:
mdma 43 100.1,100.5
Artificial Magnetic Resonators at THzArtificial Magnetic Resonators at THz
Pendry J.B. et al, IEEE MTT 47, 2075 (1999)
Dispersion of eff with frequency
50um
Sample
L :
len
gth
G: gap
S: space
W:
wid
th
quartz
Cu
Au/Ti
L:26m, S:10m, W:4m
d=L+S, G: 2m, :1.5x103
Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)
Ye T.J. et al., Science 303, 1494 (2004)
DieSimulation
(THz)Experiment
(THz)
D1 1.22 1.27±0.07
D2 0.88 0.96±0.05
D3 0.91 0.85±0.15
=30o
IRI0
Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)
Experimentally and theoretically ellipsometric results
Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)
k (cm-1) f (THz) λ/a
LSR400 1100 33.00 2.52525
LSR350 1282 38.46 2.47629
LSR300 1490 44.70 2.48571
0 10000 20000 30000 40000 50000 60000-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Re(
Mue
)
Frequency (GHz)
LSR300 LSR350 LSR400
Near-infrared (45THz) magnetic resonance is achieved by novel design. Final goal is visible
region.
Outline
I. Background of Metamaterials
II. Artificial Magnetic Resonators at THz
III. Potential Application in Nonlinearity
IV. Summary
Potential Application in NonlinearityPotential Application in Nonlinearity
Extremely high intensity is the key to nonlinear phenomena!Brabec T et al., Rev. Mod. Phys. 72, 545 (2000)
Potential Application in Nonlinearity (cont’d)Potential Application in Nonlinearity (cont’d)
When resonance takes place, the energy is strongly localized inside the small resonators. Local fields can be many orders higher than that in free space.
For a capacitor of , one single photon can create an electric field about 108V/cm.
nmnmnm 111
Localized E-filed with 103 times larger than the external field.
Potential Application in Nonlinearity (cont’d)Potential Application in Nonlinearity (cont’d)
Embed the magnetic resonator into dielectric matrix whose permittivity is intensity-dependent.
Two aspects of the nonlinear response:
1) The strong localized field changes the dielectric permittivity, since D D (|E|2)
2) Nonlinear eigenfrequency adjusts correspondingly due to the change of capacitance.
External H fieldIntensity of the local E fieldValue of permittivity Capacitance Eigenfrequency
Potential Application in Nonlinearity (cont’d)Potential Application in Nonlinearity (cont’d)
Effect nonlinear permittivity:
)1()|(|)|(|
222
i
EE pDeff
Effective permeability:
i
daH
NLeff 2
02
222 )/(1)(
)|)((|)()(
222
0 HEh
d
a
cH
gD
gNL
where
Consider Kerr nonlinearity:
220
2 /||)|(| cDD EEE
Ec is a characteristic electric field, and corresponds to focusing or defocusing nonlinearity respectively.
1
Zharov A.A. et al., PRL 91, 037401 (2003)
Potential Application in Nonlinearity (cont’d)Potential Application in Nonlinearity (cont’d)
6
222222222 ]))[(1(
||X
XXEAH c
,/,/ 000 NLX is the eigenfrequency in linear limit
Jump of eff due to
external H field Transition of eff from – to +
Outline
I. Background of Metamaterials
II. Artificial Magnetic Resonators at THz
III. Potential Application in Nonlinearity
IV. Summary
SummarySummary
The unprecedented properties associated with metamaterials, such as negative refraction, superlensing etc. are reviewed.
The principle of achieving negative permeability, which is critical in realizing LHM is interpreted. Magnetic resonators with resonance frequency above THz is successfully demonstrated.
The strong localized field inside the resonator can cause nonlinear effect. As one example, the hysteresis-type dependence of the magnetic permeability on the field intensity is theoretically studied.
It is the right time to start the new topic--nonlinear effects in metamaterials. The engineering of nonlinear composite materials will open a number of applications such as swithers, frequnecy multipliers etc.