Metamaterials and negative refraction index Dipl.-Phys. Stefan Griesing Group seminar 05.05.06

Metamaterials and negative
refraction index
Dipl.-Phys. Stefan Griesing
Group seminar 05.05.06
Metamaterials
Artificial structure
Exhibit magnetic and dielectric features not
arising in any natural material
Classes of metamaterials
Pure magnetic metamaterials
• Magnetic resonances at high frequencies (ω
>>1GHz)
• Magnetic permeability µ < 0
Optical metamaterials
• Magnetic permeability µ < 0 and dielectric
permittivity ε < 0 in the same frequency range
Relation between µ, ε and n
n = εµ
µ>0, ε >0 n>0
µ<0, ε <0 n=?
o.B.d.A.
µ = ε = −1 ≡ exp(iπ )
n = exp(2iπ ) = exp(iπ ) ≡ −1 ≡ − (−1) ⋅ (−1)
Optical metamaterials exhibit a negative index of
refraction!!!
Meaning of n <0
(first introduced by V. Veselago in 1967)
Snell‘s law:
sin α 1 n2
=
sin α 2 n1
Consequences of negative refraction I
k × E = ωµµ0 E
k × H = −ωεε 0 E
µ > 0, ε > 0
µ < 0, ε < 0
E,H, k right-handed system
S
E,H, k left-handed
system
„Left-handed materials“
Consequences of negative refraction II
Poyntingvector S ∝ E × H antiparallel to
wavevector
Inverse Doppler effect
Consequences of negative refraction III
„Perfect lens“
• Focusing by a flat slab of metamaterial
• No aberrations
Types of metamaterials
Photonic crystals (opt.)
Metamaterials consisting of conducting
elements (magn./opt.)
Photonic crystals I
consist of dielectric
material
Optical bandgap
Size of structural
elements is
comparable to the
wavelength
Can not be described
by macroscopic
parameters µ and ε
Photonic crystals II
Effective refractive
index can be deduced
by Snell‘s law
experiments and can
become negative
Conducting elements metamaterials
„artificial atoms“
Structural elements small against wavelength
Description by macroscopic parameters µ and ε
Realization of left-handed materials I: ε< 0
Metals: negative permittivity for frequencies below plasma
frequency ωp
Ne 2
ωp =
≈ 1015 Hz
ε 0 meff
(N: electron density, meff: effective mass)
But: natural magnetic resonances occur below 109Hz
Matching problem
Realization of left-handed materials II: ε< 0
Decrease N, increase
meff !
Arrays of metal slabs
with radius r and
periodicity a (Pendry,
1996)
R~10µm, a~2000µm
ωp~109 Hz
Magnetic resonances
Highest resonance frequency in natural
materials: ~1 GHz
Need for high-frequency magnetic response
split-ring resonators
Split-ring resonators I
Open metal loop forms
LC oscillating circuit
Incident elm. Wave
induces spin current
Magnetic moments
„artificial magnetic atoms“
Split-ring resonators II
Magnetic response of split-ring structures
Magnetic metamaterials
• Two-dimensional
arrays of split-ringresonators, (Pendry,
1999)
• Three-dimensional
design also possible
Realization of the first optical metamaterial
Combination of slabs and split-ring resonators
(Shelby et al., 2000)
Negative refraction index in the microwave regime
Experimental verification of negative
refraction index (2001)
Snells‘s law experiments at prisms (Teflon vs. LHM)
Magnetic resonances: towards to higher
frequencies I
• Jan. 2005: negative permeability in mid-infrared
at 60THz~5µm (Zhang et al.)
• New structural design: array of gold staples
• LC-circuit is formed by the structure and its
image
Magnetic resonances: towards to higher
frequencies II
Nov. 2005:
neg. permeability at the
telecommunication band
around 200 THz~1.5µm
(Enkrich et al.)
Use of simplified split-ring
resonators
Breakthrough to optical frequencies
(Grigorenko et al., Nov. 2005)
• Simplified split-ring
structures, consisting
of a pair of gold pillars
• Excitation of
antisymmetric surface
plasmons
Breakthrough to optical frequencies
(Grigorenko e al., Nov. 2005)
• Real parts of µ and ε negative for λ=500nm
• Big imaginary parts
• No negative refraction detectable due to extreme
losses
Perfect lens I
Pendrys predictions (2000)
Lenses of metamaterial enhance near-field intensities
sub-diffraction limit resolution possible
Quasistatic limit: no radiative effects decoupling of el.
And magn. fields
„poor man‘s perfect lens“: ε < 0
Perfect lens II
Sub-diffraction limit resolution due to surface
plasmon resonance
(Zhang et al., Science 308, 534, 2005)
Perfect lens III
Magnetic imaging of a
subwavelength
antenna at 20 MHz
Thank you for your attention!!
(Let‘s have some coffee and cake!)