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Introduction to Nanooptics, Abbe School of Photonics, FSU Jena, Prof. T. Pertsch, 08.06.2012 1

Introduction to Nanooptics Prof. Thomas Pertsch

Abbe School of Photonics Friedrich-Schiller-Universität Jena

1. Introduction and Motivation ..................................................................... 2 1.1 What makes Nanooptics unique ....................................................................... 2 1.2 Optical properties of matter ............................................................................... 3 1.2.1 Dielectric materials ........................................................................................... 3 1.2.2 Noble metals (Au, Ag) ....................................................................................... 4 1.3 Homogeneous waves ....................................................................................... 8

2. Plasmon polaritons ................................................................................ 10 2.1 Surface Plasmon polariton at planar metal-dielectric interfaces ..................... 10 2.1.1 Properties of surface plasmon polaritons ........................................................ 11 2.1.2 Excitation of surface plasmon polaritons......................................................... 13 2.2 Plasmon polaritons at nanowires .................................................................... 16

3. Photonic crystals – Band gap materials ................................................. 18 3.1 Periodic layer structures = 1D photonic crystal ............................................... 19 3.2 Scale invariance ............................................................................................. 22 3.3 Dimensionality: 1D, 2D, 3D ............................................................................. 24 3.3.1 1D Photonic crystals ....................................................................................... 25 3.3.2 2D Photonic crystals ....................................................................................... 26 3.4 Control of dispersion, refraction, diffraction ..................................................... 28 3.5 Lattice and reciprocal lattice ........................................................................... 30 3.6 Inhomogeneities ............................................................................................. 32

4. Sources ................................................................................................. 34


1. Introduction and Motivation 1.1 What makes Nanooptics unique Even though Maxwell’s equations are scale invariant, the physics of nanooptics is unique, since material parameters change with frequency, e.g. plasma frequency of metals is in the optical spectral range. Plasmons volume charge density oscillations at surfaces: plasmon polaritons results in strongly enhanced optical near-fields

Nanooptics

Classical optics

Light-matter interaction

nano particle

wavelength of light

macro object

atom


1.2 Optical properties of matter 1.2.1 Dielectric materials Light in some medium different from vacuum can’t be considered just as an electromagnet wave, it always includes some component of matter excitation forming a mixed or hybrid state, resulting in a specific dispersion relation. • Optical properties are represented by the frequency dependent (i.e.

dispersive) complex dielectric function, the permittivity ( )ε ω . • Magnetic effects can be neglected for optical frequencies ( 1µ = ).

• Governs the properties of electromagnetic waves

0( , ) exp( )t i i t cc= − ω +E r E kr according to dispersion relation

2 2

2 22 2n

c cω ω

= εµ =k

with n refractive index n = ± εµ since optics 1µ = it simplifies to n = ± ε

• Electric permittivity of a dielectric medium:

Remark: It is a important characteristic of optics that material properties are highly dispersive since the energy of light quanta lies in the Energy range of electronic and vibrational transitions of matter. Otherwise our visual perception of our surrounding would not contain that rich information.

µ

ε

1

1


• Ultra Violet (UV): polarizability of electrons Incident electric field forces the bound electrons to oscillate relative to the immobile atomic core. For small amplitudes: harmonic potential.

• Infrared (IR): polarization of lattice

Incident electric field forces the sub lattices to oscillate relative to each other.

• Microwave (MW):

Orientation polarization of permanent electric dipoles Can be only found in solids containing permanent electric dipoles external E-field aligns the permanent dipoles

1.2.2 Noble metals (Au, Ag) Properties are determined by • main contribution: conduction electrons can move freely within the bulk • secondary contribution: interband transitions (excitation for which the

photon energy exceeds the bandgap energy of the metal)

Simple physics based model • electric field leads to displacement r of unbounded electrons • results in dipole moment

e=p r • cumulative effect of all individual dipole moments of free electrons results

in macroscopic polarization per unit volume n=P p with n number of electrons per unit volume


• P is connected to the dielectric function at a fixed frequency by

0

( )( ) 1( )ω

ε ω = +ε ωPE

• Existence of oscillating excitations of electron gas: Plasmons = short form for quantized plasma oscillation more exactly = quantized density fluctuations of free charges in metals and semiconductors in quantum theory quasi particle semi-classic picture electron cloud which oscillates relative to the stationary positive ions with the plasma frequency Pω

Drude-Sommerfeld model • to describe the displacement r depending on the electric field an equation

of motion of free electrons can be employed according to Drude-Sommerfeld theory

2

e e 02 exp( )m m e i tt t

∂ ∂+ Γ = − ω

∂ ∂r r E (1)

with e charge of electron em effective mass of free electron in periodic potential (takes into account interaction effects with lattice) 0E amplitude of applied electric field ω frequency of applied electric field Γ damping term F /v lΓ = Fv Fermi velocity l electron’s mean free path between scattering events

• equation of motion contains no restoring force since electrons are unbounded

• ansatz for the solution of Eq. (1) 0( ) exp( )t i t= − ωr r (2)

yields

2P

Drude 2( ) 1i

ωε ω = −

ω + Γω (3)


with Pω volume plasma frequency 2P e 0/ ( )ne mω = ε

• Eq. (3) can be decomposed into real and imaginary component

2 2P P

Drude 2 2 2 2( ) 1( )

iω Γωε ω = − +

ω + Γ ω ω + Γ (4)

Example: gold (Au) has 15 1P 13.8 10 s−ω = × and 14 11.075 10 s−Γ = ×

• Since the real part of ( )ε ω is negative the light field can’t penetrate deeply

into the metal (due to the resulting imaginary part of the refractive index ( ) ( )n ω = ε ω the associated exponential decay).

• The non-zero imaginary part of ( )ε ω results in dissipation of energy associated with the damped motion of electrons in metal

• Remark: exponential decay and dissipative loss are generally two different phenomena

Interband transitions • The Drude-Sommerfeld model is sufficient to describe noble metals in the

near infrared (NIR) spectral range. • However in the visible (VIS) spectral range the response of bound

electrons to the high energy photons becomes important. Example: gold at 550nmλ = has a larger imaginary part of ε than predicted by Drude model since electrons of lower-lying bands are excited into conduction band by photons.

• Improvement of our classical model: oscillating bound electrons, which correspond to electrons in lower-lying shells of metal atoms

• Equation of motion of bound electrons according to Lorentz oscillator model (equivalent to the model for dielectrics)

2

I I I 02 exp( )m m e i tt t

∂ ∂+ Γ + α = − ω

∂ ∂r r r E (5)

2 2Pω − Γ


with Im effective mass of bound electron IΓ (radiative) damping of bound electrons α spring constant restoring position of bound electrons

• With ansatz Eq. (2) we obtain contribution of bound electrons to dielectric function

2PI

Interband 2 20 I

( ) 1( ) i

ωε ω = +

ω − ω − Γ ω (6)

with PIω interband plasma frequency 2PI I I 0/ ( )n e mω = ε

0Iω eigen oscillation frequency of bound electrons 0I I/ mω = α

• Eq. (6) can be decomposed into real and imaginary component

2 2 2 2PI 0I I PI

Interband 2 2 2 2 2 2 2 20 I 0 I

( )( ) 1( ) ( ) ( ) ( )

iω ω − ω Γ ω ωε ω = + +

ω − ω − Γ ω ω − ω − Γ ω (7)

Example: gold has 14 1PI 45 10 s−ω = × , 14 1

I 9 10 s−Γ = × , and 0I I2 /cω = π λ with I 450 nmλ =

Comparison with measured data Example: gold


• 650 nmλ > Drude-Sommerfeld is correct

Drude( ) ( )ε ω = ε ω • 500nm 650 nm< λ < interband transitions significant

Drude-Lorentz model Drude Interband( ) ( ) ( ) ∞ε ω = ε ω + ε ω + ε with ∞ε integrated effect of all higher-energy interband transitions, not considered in the model ( 6∞ε = for gold)

• 500 nmλ < model fails reason: higher-order transitions are not included

1.3 Homogeneous waves • homogeneous solution = eigenmode = solution which exists without

external excitation • wave equation for homogeneous space

2

2( , ) ( ) ( , ) 0cω

∇ × ∇ × ω − ε ω ω =E r E r (8)

• plane wave ansatz


( , ) exp( )x

y

z

EE i i tE

ω = − ω

E r kr (9)

dispersion relation (relation between wavevector and frequency ω )

2

2 2 2 202 ( ) ( ) x y zk k k k

cω

ε ω = ε ω = + + (10)

• considering wave-evolution along z different cases must be distinguished − 2 2 2

0 ( ) x yk k kε ω > + zk is real valued propagating plane wave

− 2 2 20 ( ) x yk k kε ω < + zk is imaginary valued exponentially

growing/decaying wave which cannot exist in homogeneous space


2. Plasmon polaritons Terms related to plasmon polaritons • Surface plasmons

− exact: quanta of surface-charge-density oscillations − more general: collective oscillations of electron density in metals close

to surface − Very often the term is used equivalent to the term surface plasmon

polaritons. • Plasmon polaritons

− exact: quanta of surface-charge-density oscillations coupled to electromagnetic waves outside the metal (hence polariton)

− more general: collective oscillations of electron density in metals close to surface coupled to electromagnetic waves outside the metal

• Surface plasmon polariton (SPP) − exact: plasmon polariton at any metal-dielectric interface − here: plasmon polariton at infinite planar metal-dielectric interface

2.1 Surface Plasmon polariton at planar metal-dielectric interfaces

• configuration: planar interface at 0z = between 2 half-spaces filled with 2 materials with

− 0z < material 1j = : complex frequency-dependent 1( )ε ω − 0z > material 2j = : real-valued 2 ( )ε ω

• looking for homogeneous solution of wave equation (8) which are p-

polarized (=TM polarization)in both half-spaces (s-polarized waves cannot exist, as can be easily shown) with plane wave ansatz

,

, ,

,

0 exp( )exp( ), 1,2j x

j j x j z

j z

Eik x i t ik z j

E

= − ω =

E (11)

• wavevector continuity in x-direction requires


2 2 2, 0 , 1,2x j z jk k k j+ = ε = (12)

• divergence equation div( ) 0=D without sources requires , , , 0, 1,2x j x j z j zk E k E j+ = = (13)

• inserting (13) into (11) and considering (12) gives

, ,

,

10 exp( )exp( ), 1,2/

j j x x j z

x j z

E ik x i t ik z jk k

= − ω = −

E (14)

• boundary condition at the planar interface: continuity of parallel components of E and normal components of D

1, 2,

1 1, 2 2,

00

x x

z z

E EE E

− =

ε − ε = (15)

Eqs. (13) for 1,2j = and Eqs. (15) form a system of 4 equations for 4 unknowns

• existence of solution requires vanishing of determinant 1 2, 2 1, 0z zk kε − ε = (16)

• using Eq. (12) one can formulate the dispersion relation (relation between wavevector along propagation direction and angular frequency ω )

2

2 21 2 1 20 2

1 2 1 2xk k

cε ε ε ε ω

= =ε + ε ε + ε

(17)

• and derive an expression for the normal wavevector-component

2

2 2, 0

1 2

, 1,2jj zk k j

ε= =

ε + ε (18)

conditions for existence of localized interface mode 1 2( ) ( ) 0ε ω ⋅ ε ω < (19) 1 2( ) ( ) 0ε ω + ε ω < (20) in words: One dielectric function must be negative with an absolute value larger than the other one

2.1.1 Properties of surface plasmon polaritons We consider a planar interface between: 1j = , metal: 1 1 1i′ ′′ε = ε + ε including ohmic losses but assuming 1 1′′ ′ε << ε 2j = , dielectric: 2 2′ε = ε neglecting absorptive losses • calculating real and imaginary part of longitudinal xk from (17):

real part 1 2

1 2xk

c′ω ε ε′ ≈

′ε + ε determines phase velocity of SPP


imag. part 1 2 1 2

1 2 1 1 22 ( )xkc

′ ′′ω ε ε ε ε′′ ≈′ ′ ′ε + ε ε ε + ε

damping of SPP along x

• calculating transverse ,j zk from (18) to first order in 1 1/′′ ′ε ε :

inside metal 2

1 11,

1 2 1

12zk i

c ′ ′′ω ε ε

≈ + ′ ′ε + ε ε

inside dielectric 22 1

2,1 2 1 2

12( )zk i

c ′′ω ε ε

≈ + ′ ′ε + ε ε + ε

• field distribution of SPP

SPP

− wave which is localized at the metal dielectric interface with an exponential decay of intensity having a 1/ e decay length of field

fieldtransvers ,1 / j zL k=

− exponentially decaying along propagation direction parallel to interface with a 1/ e decay length of intensity intensity

longitudinal 1 / (2 )xL k′′= which is caused by ohmic losses of electrons in metal resulting in heating of metal

Examples: 633nmλ = , dielectric is air 2 1ε = • Silver (Ag) @: 1 18.2 0.5iε = − + intensity

longitudinal 60µmL ≈ , fieldtransvers, Ag 23nmL ≈ , field

transvers, Air 421nmL ≈

• Gold (Au) @ 633nmλ = : 1 11.6 1.2iε = − + intensity

longitudinal 10µmL ≈ , fieldtransvers, Au 28nmL ≈ , field

transvers, Air 328nmL ≈

Comment: decay length into metal is larger than electron’s mean free path and go beyond many atomic layers from the surface into the bulk bulk parameters of ε can be safely assumed

Hy, Ex Ez

z z


2.1.2 Excitation of surface plasmon polaritons Excitation requires matching of some excitation field to SPP time and space averaged overlap of fields should be maximized energy ω and momentum xk must be matched, which are related by dispersion relation (17)

Solid: Drude-Lorentz metal; dashed: Drude metal; dashed dotted: light line; the lower braches correspond to SPP, the upper branches are the delocalized Brewster modes leaking into the metal (not considered here) All lines are calculated neglecting the imaginary part of metalε , otherwise a back-bending of the branched would be observed which connects the upper and lower branch and leads to a maximum of xk of the diverging k-vector close to the plasma frequency.

• xk of SPP is always larger than wavevector in free space (SPP is to the right of the light line) due to the strong coupling of photons to surface charges (light has to drag electrons behind) excitation from free space is impossible


Top: matching of the SPP wavevector to free-space waves can be achieved by shifting the light-line to the right using high index material; Bottom left: Otto configuration; Bottom right: Kretschmann configuration

Excitation of SPP by Otto configuration for different widths of the air gap (Au film)


Excitation of SPP by Kretschmann configuration for different thicknesses of the Au film; note: for Ag the peak is much sharper due to the lower propagation damping of the SPP

Other methods for SPP excitation: (a) illumination through tip of scanning nearfield microscope; (b) local inhomogeneity of the metal film; (c) nano-sized emitters like dyes. Grating represent another possible method.

SPP can be used as sensors since their resonance position depends critically on the optical properties of the dielectric close to the metal surface.


2.2 Plasmon polaritons at nanowires

close to a sub-wavelength object the electric field can be assumed to oscillate spatially homogeneous in time with exp( )i tω quasi-static limit electric field can be represented by scalar potential as

= −∇ΦE which satisfys Laplace equation 2 0∇ Φ = (21) and some boundary conditions at the interfaces of different materials for concentric wires oriented along z we use cylindrical coordinates

cos( )sin( )

xyz z

= ρ ϕ= ρ ϕ=

(22)

Laplace equation in cylindrical coordinates without any z-dependence

2

2 2

1 1 0 ∂ ∂Φ ∂ Φ

ρ + = ρ ∂ρ ∂ρ ρ ∂ϕ (23)

looking for solutions by separation ansatz ( , ) ( ) ( )RΦ ρ ϕ = ρ Θ ϕ gives

2

22

1 1R mR

∂ ∂ ∂ Θρ ρ = − = ∂ρ ∂ρ Θ ∂ϕ

(24)

with m being some constant angular part has solution: 1 2( ) cos( ) sin( )c m c mΘ ρ = ϕ + ϕ (25) m must be integer to assure continuity at 2pi periodicity because of symmetry of excitation field only cos-terms must be considered radial part has solution:

3 4

5 6

( ) , 0( ) ln , 0

m mR c c mR c c m

−ρ = ρ + ρ >

ρ = ρ + = (26)

solution for m=0 diverges at the origin to infinity and is hence unphysical

y

x

ε2

ε1

E0


The complete solution is represented by the following expansion:

1

1

2 scatter 0 01

( ) cos( )

( ) cos( ) cos( )

nn

n

nn

n

a n

a n E

∞

=

∞−

=

Φ ρ < = Φ = α ρ ϕ

Φ ρ > = Φ = Φ + Φ = β ρ ϕ − ρ ϕ

∑

∑ (27)

with nα and nβ being constants to be determined by boundary conditions and 0Φ being the potential of the excitation field

Boundary conditions on the wire surface aρ = :

1 2 1 21 2,

a a a aρ= ρ= ρ= ρ=

∂Φ ∂Φ ∂Φ ∂Φ= ε = ε ∂ϕ ∂ϕ ∂ρ ∂ρ

(28)

inserting (27) into (28) it follows that nα and nβ vanish for 1n > hence for 1n =

22 1 21 0 1 0

1 2 1 2

2 ,E a Eε ε − εα = − β =

ε + ε ε + ε (29)

and for the electric field

21 0

1 22 2

21 2 1 22 0 0 02 2

1 2 1 2

2 ,

(1 2sin ) 2 sin cos

x

x x y

E

a aE E E

ε=

ε + ε

ε − ε ε − ε= + − ϕ + ϕ ϕ

ε + ε ρ ε + ε ρ

E n

E n n n (30)

a resonance occurs if the denominator 1 2ε + ε is zero and consequently the fields diverge for 1 2Re( ( ))ε λ = −ε For metal nano spheres in an analogous way a similar formula can be derived:

3 1 21 0

1 2

42

a ε − εα = πε

ε + ε (31)


3. Photonic crystals – Band gap materials Characteristic lengths scale: wavelength λ / lattice constant a

Photonic crystals = Semiconductors of light

Visionary applications of photonic crystals • Custom designed electromagnetic vacuum


• Control of spontaneous emission • Zero threshold lasers • Ultrasmall optical components • Ultrafast all-optical switching • Integration optoelectronics

3.1 Periodic layer structures = 1D photonic crystal Concept remember what you have learned about periodic layer systems (Bragg-mirrors) in Fundamentals Modern Optics and generalize to multidimensional periodic systems

System infinite periodic layer system here 2 layers of width 1d and 2d repeated periodically

( ) ( )x xε = ε + Λ with period 1 2d dΛ = +

Bloch-theorem generalized normal modes (Bloch modes or Bloch waves) of a periodic system must have the following form

( ){ },( , ; ) exp ( )kE x z x k zk k E xω = + ωxzx zi

with Bloch vector xk K= which has to fulfill a dispersion relation ( ),k k ωx z

and periodic function ( ) ( )k kE x E x+ Λ =x x

Solution compare Bloch-theorem with matrix method relation between E and E’ when we advance by one period (from period N to period 1N + )


Bloch-theorem:

( )( )' 'exp .

E EK

E E+ Λ Λ

= Λ

N 1 N

i

matrix method:

( )

' 'ˆE E

E E+ Λ Λ

=

M

N 1 N

with ( ) ( )2 1ˆ ˆ ˆd d=M m m → (2) (1)

kij ik kjM m m= ∑

Both method must have the same solution, hence

( ){ } 'ˆ exp 0

EK

EΛ

Λ =

M I

N

i−

eigen problem { } 'ˆ 0

EE

Λ

µ =

M I

N

− with eigenvalue ( )exp Kµ = Λi (32)

solution based on solvability condition { }ˆdet 0µ =M I− using { }ˆdet 1=M , for

lossless dielectrics gives

( ) ( ) ( ) 211 22 11 22exp 1.

2 2M M M M

K± ±

+ + µ = Λ = ± −

i

Two principle cases

A) ( )11 22 12

M M+≥ µ=real

evanescent decay/growth of Bloch modes no propagating states = so-called band gap total reflection at interface to homogeneous outside medium Bragg condition /K = π Λ

B) ( )11 22 12

M M+< µ=imaginary

infinitely extended Bloch modes propagating states = so-called band partial transmission/reflection through

dispersion relation ( ){ } ( )11 22cos ,2

M MK k

+ω Λ =z


Example: for normal incidence ( )0k =z

• band structure diagram can be reduced to Brillouin zone K−π ≤ Λ ≤ π

or

even 0.5KG

≤ because of periodicity

Spatial intensity profile in a finite periodic multilayer structure for transmission bands in the close vicinity to band gap edges (a) 1ω and (b) 2ω . Dashed lines show the refractive index profile.


The spatial intensity profile in a finite periodic multilayer structure for the frequency value in the center of the gap 0ω . The dashed line shows the refractive index profile.

Inside the band gap, we find damped solutions:

3.2 Scale invariance The solution at one scale is equivalent to the solution at a different scale when the dispersion of the material properties is neglected

Justification If for a dielectric configuration ( )ε r a magnetic field ( )H r is the solution of Maxwell’s Equations


21 ( ) ( )

( ) cω ∇ × ∇ × = ε

H r H rr

It follows that for a dielectric configuration ( )′ ′ε r being a scaled version of ( )ε r according to ( ) ( / )s′ ′ ′ε = εr r , we can show a corresponding to an equivalently scaled solution. Using s′ =r r , ( / ) ( )s′ ′ ′=H r H r , and / s′∇ = ∇

21 ( ) ( )

( ) csω ′ ′ ′ ′ ′ ′∇ × ∇ × = ′ ′ε

H r H rr

Hence. after changing the length scale by s the original solution and its frequency is scaled by the same factor

Hence all parameters are normalized to the lattice constant a and the unites of the physical quantities become: frequency: /c a angular frequency 2 /c aπ wavevector 2 / aπ wavelength a Consequently a normalized result must be scaled to the particular problem, which is illustrated in the following band diagram: • gap extends from 0.2837 c/a to 0.4183 c/a with a mid-gap frequency of

0.3510 c/a • a crystal with a mid-gap frequency corresponding to a wavelength of 1.55

micron would then have: c/(1.55 micron)=0.3519 c/a a=0.3510*1.55 micron=0.5440 micron


3.3 Dimensionality: 1D, 2D, 3D

2D homogeneous space first we try to visualize the dispersion relation of homogeneous space in 2D

2 2x yc k kω = + light cone

different ways to visualize this dispersion relation (band structure)


3.3.1 1D Photonic crystals


3.3.2 2D Photonic crystals

(left) dispersion relation of Bloch waves; (right) projection of frequency along borders of irreducible Brillouin zone on pathways between high-symmetry points (assuming monotonous dependence in between these borders – high symmetry)

Constant frequency contours (here for the first band)

• At low frequencies the constant frequency diagram approaches a circle since the photonic crystal behaves as a uniform dielectric with properties determined by the averaging of the different material domains.

• With increasing frequencies the constant frequency contour becomes more complicated

• period close to half the wavelength strong effects on propagation leading to effects like superprism, slow light, negative refraction/diffraction, and self-collimation

• period equal to half the wavelength no light propagation / gap

Γ

M

X

frequ

ency

λ-1

X

planar Bloch vector kplan

Γ Μ Κ Γ0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Γ XM Γ

frequ

ency

λ-1


• in general: large index contrast & small period control of large angular spectrum

3.3.2.1 2D photonic crystals as slab waveguides

For 2D photonic crystal slabs the confinement of light in the slab is provided by total internal reflection in the high index slab. The 2D photonic band gap provides in plane confinement.

Photonic band diagram for photonic crystal slabs

• Radiation modes above the light line • Lossless guided modes below the light line • band gap in the spectrum of guided modes


3.3.2.2 Photonic crystal fibers

• propagation perpendicular to the periodic plane • infinite homogeneous extension in the propagation direction • confinement in air is possible

3.4 Control of dispersion, refraction, diffraction The dielectric mode and the air mode have zero group velocity at the boundary of the 1. Brillouin zone strongly enhanced light matter interaction for nonlinear optics or quantum optics


Refraction at interfaces


3.5 Lattice and reciprocal lattice Photonic crystals are constructed from periodically arranged inhomogeneities of material properties

( ) ( )x x Rε = ε + with R ma= and { }0, 1, 2,...m∈ ± ±

( ) ( )ε = ε +r r R with x x y y z zm m m= + +R a a a and { }, , 0, 1, 2,...x y zm m m ∈ ± ±


Example: 2D square lattice

Example: triangular lattice

Additional symmetry properties of the Photonic Crystal alow for the restriction of analysis to the irreducible Brillouin zone.


3.6 Inhomogeneities Point defects


Line defects


4. Sources • L. Novotny and B. Hecht, “Principles of Nano-Optics,” Cambridge

University Press (2006). • S. V. Gaponenko, “Introduction to Nanophotonics,” Cambridge University

Press (2010). • M. Wegener and S. Linden, “Photonic crystals, plasmonics, and

metamaterials,” Lecture materials given at Karlsruhe Institute of Technology and University Bonn.

• V. Shalaev, “Nanophotonics and Metamaterials,” Lecture materials given at Purdue University.

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