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Sergey Gaponenko
Institute of Molecular and Atomic Physics
National Academy of Sciences, Minsk, Belarus
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Electrons vs photons and EM-waves
E –
energy,
ω
–
frequency,
k –
wavenumber,
c –
speed of light in vacuum
parameter
electrons
photons
rest mass
m
0
= 9,109534
⋅
10
−
31
kg
zero
charge
å
= 1,602189
⋅
10
−
19
C
zero
spin
1/2
1
dispersion law (in free space)
E = h
2
k
2
/2m
0
h
ω
= c k
density of states
(in 3 dimensions)
D E
m
E
(
)
/
/
/
/
=
3 2 1 2
1 2 1 2 3
2
π
h
D(
ω
) =
ω
2
/2
π
2
c
3
statistic
Fermi–Dirac
Bose–Einstein
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Properties of electrons which have no
analog for EM waves
•
e-e interactions (excitons, e-h plasma, Coulomb blockade…)
•
spin effects
•
Fermi-liquid in metals
•
superconductivity
•
etc…
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Isomorphism of Schroedinger and Helmholtz equations
Steady-state single-particle Schroedinger equation with U(x) potential
h
2
2
2
0
m
x
E
U x
x
∇
+
−
=
Ψ
Ψ
( )
( )
( )
[
]
Helmholtz equation for a EM-wave in
ε
(x) medium
∇
+
=
2
2
2
0
E x
x
c
E x
(
)
(
)
(
)
ε
ω
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Electron and EM-wave in a complex medium
→
∧∧∧∧∧
→
∧∧∧∧∧
A B
→ x
→
∧∧∧∧
↑
U(x)
electron
→
∧∧∧∧
↑
n(x)
EM-wave
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•
•
Textbook analogies of quantum particles
and EM-waves
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Textbook example 1: Reflection from a barrier
h
λ
2
=
h
[2m(E-U)]
1/2
(2mE)
1/2
E
U
x
Ψ
(x)
x
EM -wave
electron
λ
1
=
A
n
1
λ
2
=
λ
1
n
1
/n
2
λ
1
n
2
< n
1
x
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Tunneling: A quantum phenomenon?
Ψ
( x )
c o o r d i n a t e
E
U
0
E n e r g y
0
Leontovich and Mandelshtam, 1928
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Tunneling in optics
Transparency of thin metal films
p r o p a g a tio n a x is
m e ta l la y e r
tr a n s m i tte d
w a v e
r e f le c t e d
in c id e n t
0
E ( x )
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Electron in a well between two barriers:
resonant tunneling
transmittance
Energy
0
1
U
1
U
0
E
2
E
1
ψ
2
ψ
1
Energy
coordinate
A cornerstone phenomenon for nanoelectronics:
“Resonant tunneling in semiconductors: Physics and applications”. Kluwer 1991.
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Fabry-Perot resonator
(with metal mirrors)
0,0
0,5
1,0
λ
0
/2
λ
0
coordinate
metal mirror
metal mirror
tr
an
sm
it
ta
n
ce
wavelength
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1D-periodic structures
reflection
reflection
reflection
transmission
ω
=ck/n
wavenumber
fr
eq
u
en
cy
EM-w ave
g ap
Kr onig, Penney 1931
Elec tr on
coordinate
Energy
Wavenumber
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Photonic band structure in 1D
Brilloun zones for em-waves
E=pc/n
E=pc
E
n
er
g
y
Wavenumber
(c)
(b)
Wavenumber
forbidden
gap
π
/a
Wavenumber
+
π
/a
-
π
/a
forbidden
gap
(a)
1D continuous medium
Periodic medium
Reduced diagram
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0.5
1
1.5
2
0.2
0.4
0.6
0.8
1
0.5
1
1.5
2
0.2
0.4
0.6
0.8
1
Frequency [arb.units]
Frequency [arb.units]
Finite periodic structure
Bragg reflector
Periodic structure with defect
Planar Microcavity
Interference filter
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Photonic solids
•
Photonic band gap in optical
range can be performed in 1-,
2-, and 3 dimensions
•
Only a single group reported
on light localisation in a 3 d-
structure
•
Coherent backscattering is well
reproducible
Electrons 1982-83
Albada, Lagendijk (1985)
Wolf, Maret (1985)
Anderson 1958
John 1984 - theory
Lagendijk 1999 - expts
Yablonovitch 1987
Quantum theory of solids
1930-40
Coherent backscaterring
Random scaterrers
Localisation of light?
3D-periodicity
Photonic crystal
n
2
n
1
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1-dimensional
:
iridescent coating
of fly’s wings
2-dimensional:
surface of moth’s eye,
human eye cornea
3-dimensional:
gem opals
Isaac Newton 1730 Interference in peacock feathers
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:
:
•
•
Thin-film vacuum deposition
(routine technique in laser production)
•
•
Thin film multilayer heterostructures
(MBE, MOCVD – Bragg
reflector in
semiconductor VCSEL lasers)
•
•
S
S
i
i
l
l
i
i
c
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o
o
n
n
:
:
porous structures with periodic porosity
•
•
S
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n
:
:
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g
g
V. Tolmachev et al. Proceeding SPIE 2003
Si/air:
Largest Refraction index gradient!
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The field of 1D multilayer structures is rather old.
?
?
Is it possible to find smth novel in design and application
•
•
Propagation of em-wave in
non-periodic
structures (e. g. fractal-like) and application to
filter design:
Zhukovsky, Lavrinenko, Sandomirskii, Gaponenko, Phys. Rev. E 65, 036621 (2002)
•
•
Optical data coding:
Gaponenko et al. Opt. Communications 49, 205 (2002)
•
•
Omnidirectional reflector:
Chigrin, Gaponenko, et al. Appl. Phys. B 68, 25 (1999)
Joannopoulos, Fink et al. Patent US 6130780 (2000)
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2
2
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D
S
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g
•
•
Idea:
V.Lehmann and H.Foll, J.Electrochem. Soc. 137, 653 (1990)
•
•
Realisation:
many groups over the world, pore size from 0.3 to 10
µm
•
•
Pre-patterning:
holographic techniques, electron beam lithography and other.
Honey-comb structures on Si substrate Calculated band structure
Van Driel et al. MRS Proc. V.722 (2002) Meade et al, APL 1992
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Porous anodic alumina:
a 2D photonic crystal for the visible
Masuda et al – Appl. Phys. Lett. 71, 2770 (1997)
•
•
High transmission along pore axis (98% in our measurements)
•
•
High reflectance in the plane ortogonal to pore axis
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3
3
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2 approaches
•
•
Self-organization: Solid state colloidal crystals
•
•
Combination of photolithography + selective etching
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Petrov, Bogomolov, Gaponenko et al.
Phys. Rev. Lett. 81, 77 (1998)
Bogomolov, Gaponenko et al.
Phys. Rev. E 81, 7619 (1997)
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First publications
Astratov, V. N., Bogomolov, V. N. et al., Il Nuovo Cimento 17, 1349 (1995)
Bogomolov, V.N., Gaponenko, S.V. et al. Applied Physics A 63, 613 (1996)
Opals can be impregnated with highly refractive materials:
•
•
Polymers
Petrov,…, Gaponenko et al, PRL 1998
•
•
TiO
2
Kapitonov, Gaponenko et al. Phys. Stat. Sol. B 1998, Vos et al. Science 1998
•
•
Q-dots
Astratov et al, Phys. Lett. 1996, Romanov et al, Phys. Stat. Sol. 1997, Gaponenko
et al. JETP Lett. 1998, Norris et al. 1998, Meseguer et al. J. Cryst. Growth 1997
•
•
Fullerenes
Zakhidov et al. Science 1998
•
•
Poly-Si
Vlasov, Norris Nature 2001
•
•
V
2
O
5
Golubev et al. Appl. Phys. Lett. 2001
•
•
Liquid crystals
Kitzerow et al. Appl. Phys. Lett. 2002
Then SiO
2
can be removed by etching. These structures are called
“
inverse opals”
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Band sturcture of inverse opal
photonic crystal with n=3.45
John and Busch, Opt. Expr. 2002
Inverse opal structure of poly-Si on
Si substrate
Vlasov et al. Nature 4141 (2001) 289
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3D PC:
Woodpile structures
Realizations: selective etching +wafer bonding: A masterpiece made by man
InP, GaAs:
Noda et al. Science 289 (2000) 604
Poly-Si:
Dood, PhD Thesis Amsterdam 2002
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Optical characteristics of a 4-layer woodpile InP photonic crystal
Omnidirectional 3D photonic band gap has been reported by the Kyoto Uni group!
Noda et al. Science 289 (2000) 604
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:
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:
:
Total reflection in high-refractive material
Drawbacks: finite absorption increase losses
bending results in leakage
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2D PC based waveguides for light bending
(Caltech–Corning)
Loncar et al. Appl. Phys. Lett. 77 (2000) 1937
Note:
Macroporous Si or porous Al
2
O
3
properly impregnated with other
materials can be used to fabricate planar “printed circuits”
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Waveguide inside a 3D photonic crystal
Materials: GaAs, InP
S. Noda et al. Science 289 (2000) 605; Appl. Phys. Lett. 75 (1999) 3741
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Hollow fiber:
no absorption losses!
Filled fiber:
polarization control
Team headed by Prof. Philip Russel (Bath Uni, England + Blaze Photonics)
Publications: Physics World 5, No. 8 p. 37 (1992), SCIENCE 285, 1537 (1999)
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Problem: Frenel reflection at Silicon/air boundary exceeds
30%
Solution: AR coating has been proposed using the moth eye design.
Lalanne et al. Nanotechnology 8, 53 (1997)
For a silicon surface patterned
with
an
800-nm-period
reflectance is reduced to below
2% over the 1.5–5.5-µm
band.
Motheye surfaces are capable of
maintaining low reflectance,
even as the incident angle is
increase to 50°.
Laser Focus World , August 1999
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Spontaneous emission of photons
a result of interaction with EM-vacuum
E
G
hk
|G, 1
k
>
|E, 0
k
>
W
∝
D(k)
<E,0|H
int
|G,1>
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Density of states
: Definition
L
x
U
∆k =
π
/L
Universal function
in 3d-space
D(k)
=
k
2
2
2
π
D(E)= D k
dk
dE
( )
N E E
V
D E dE
E
E
(
)
(
)
,
1
2
1
2
=
∫
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DOS for photons in 3d-space
0
1
2
3
0
25
50
D(E) = 4
π
E
2
/(hc)
3
D(E),
µ
-3
eV
-1
E = h
ν
, eV
photon
D(
ω
)=
1
2
2
2
3
π
ω
⋅
c
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E. Pursell 1947
– first prediction of modified spontaneous
emission in mesoscopic structures
Model mesoscopic structures in which the effect is being studied:
•
Media with n > 1
•
Microcavities
•
Thin layers
•
Photonic crystals (3d and 2d)
•
Cell membranes
•
Metal–dielectric interfaces
•
Nuclear reactions
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V.P.Bykov JETP 1972
E.Yablonovitch PRL 1987 –
The PC concept
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1
1
D
D
-
-
P
P
C
C
:
:
Quantum confined Si
nanocrystals in porous Si
microcavity
L
L
.
.
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s
.
.
R
R
e
e
v
v
.
.
B
B
1
1
9
9
9
9
5
5
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Anisotropic light emission from porous alumina structures
PL enhancement of ions embedded in porous Al
2
O
3
N.V. Gaponenko et al.
Appl. Phys. Letters 76, 1006 (2000)
J. Electrochem. Soc. 148, H13 (2001)
149, H49 (2002)
z
y
x
S.Gaponenko, N.Gaponenko, A.Lutich, I.Molchan, J. Appl. Spectr. 2003
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Light emitting device utilizing a periodic dielectric structure
Efficient extraction of light: A combination of antireflection coating and spontaneous emission control
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Decay of Eu
3+
complexes in opal-based structures
Decay time distributions in bulk polystyrol and in a opal-based photonic crystal
Ksenzov, Pavich, Petrov, Gaponenko, in press
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1D photonic crystals are being used in VCSEL as
Bragg mirrors
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2D photonic crystals are involved in semiconductor laser
design in 3 ways:
•
Semiconductor laser mirrors
Forchel et al. Semicond. Sci. Tech. 16 (2001) 227;
Appl. Phys. Lett. 79 (2001) 4091
•
Distributed feedback structures
•
Formation of high-Q microcavities
via defects in PC lattice
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In DFB lasers wavelength-selective feedback is formed by means of
coupling of active medium with grating.
For example in dye DFB lasers grating is formed inside active medium
using 2 interfering pump beam forming a standing wave and a periodic
alteration of gain coefficient and refraction index.
In a semiconductor DFB laser a grating is attached to active layer so
that difracted light multiply comes back to gain region
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Recently
Susumu Noda et al. (Kyoto Uni, Japan)
have demonstrated a 2D
PC based InP DFB laser
Imada et al. Appl. Phys. Lett. 75 (1999) 316
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6 equivalent directions exist which provide
multiple reflection of emitted light
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The spectrum of outcoming radiation is the same in all directions
Imada et al. Phys. Rev. B 65 (2002) 195306
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Comment:
Gain medium and PC are separated.
Does PC actually plays a role of a feedback structure or
only helps to extract efficiently outcoming light?
Theory of 2D PC-based DFB laser
with gain medium inside PC
S. Nojima (NTT Basic Res. Lab. Japan)
Phys. Rev. B 65 (2002) 073103
J. Appl. Phys. 90 (2001) 545
Loop-like reccurent-photon feedback is predicted for 2d DFB laser
contrary to straight-forward feedback in a 1D DFB-laser
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Two-dimensional photonic band-gap defect mode laser
Caltech group (Painter, Scherer, Yariv, Dapkus et al)
Science 284 (1999) 1819
Material:
InGaAsP
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Spectral and power features
λ
= 1.504
µ
m,
∆λ
= 0.2 nm, T = 143 K
optical pumping by a 830 nm semiconductor laser
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Two-dimensional photonic band-gap defect mode laser
(Korean Adv. Inst. Technol.)
InGaAsP on InP, room temperature operation,
pump by 980 nm 1 MHz semiconductor laser
Hwang et al Appl. Phys. Lett. 76 (2000) 2982
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3D
structures based on opals with laser dyes
Frolov, …, Zakhidov et al. Opt. Comm. 162 (1999) 241
610
615
620
0
100
200
300
400
500
Эксперимент
Лоренц
И
н
те
нс
ив
н
ос
ть
,
от
н.
е
д
.
Длина волны, нм
Gaponenko et al. 1999, unpublished
Drawbacks:
Block domain structure of macro-opal samples. + photobleaching of dye.
Plans:
To use smaller monoblock samples, to apply picosecond pumping
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Shkunov, …, Zakhidov, … Adv. Funct. Mat. 12, 21 (2002)
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One more PC application:
Heat isolators and heat conductors.
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y
s
s
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l
:
:
A blue dream or a bright future?
Figure courtesy to S. Noda
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Books
1. P. Yeh “Optical Waves in Layered Media” (Wiley, NY 1988).
2. J. Joannopoulos, R. Meade, J. Winn
“Photonic Crystals: Molding the Flow of Light” Princeton, 1995
3. Kazuaki Sakoda “Optical Properties of Photonic Crystals “ 2001
Springer
Review
Krauss T F, De la Rue R M, PROG QUANT ELECTRON 23: 51-96 1999.
Special issues:
JOSA B 1993,
J. Mod. Opt. 1994,
J. Lightwave Techn. 1999, MRS Bull. 2001
Web-site
supported by Yuri Vlasov
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s
k
k
1
1
D
D
:
:
Theory (IMAPh—BSU)
Zn/ZnSe-multilayer structures (with IRE, Russia)
Optical properties of multilayer fractal structures
2
2
D
D
:
:
Theory
Synthesis: porous alumina (BSUIR)
Anisotropic optical properties of porous alumina incl. PL
Impregnation with dyes, lanthanides, polymers
Lasing
???
3
3
D
D
:
:
Theory
Light emission in opal-based PC
Impregnation with dyes, lanthanides, polymers
Lasing
???
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