quantum dots in photonic structures (nanophotonics with quantum dots) wednesdays, 17.00, sdt jan...
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Quantum Dots in Photonic Structures(Nanophotonics with Quantum Dots)
Wednesdays, 17.00, SDT
Jan Suffczyński
Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki
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Plan for today
1. Overview of the course
2. EM radiation
3. Optical cavities
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Overview of the course
IPhysics of the light- matter interaction
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Overview of the course: I. Physics of the light- matter interaction
E
t
1
1/e
0
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Overview of the course
IPhysics of the light-
matter coupling
IISemiconductor
Quantum Dot as a source of the light
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Overview of the course: II. Semiconductor Quantum Dot as a source of the light
Transmission Electron Microscope cross-sectional image,Offermans et al., Phys. Rev. B 2005
2210 2215 2220 2225
XX
CX
-P
L I
nte
ns
ity
[a
rb.
un
its
]
Photon Energy [meV]
X
CdTe/ZnTe Quantum Dot emission InAs/AlAs Quantum Dot
Corr
elat
ed c
ount
s
T = 2 K
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Overview of the course
IPhysics of the light- matter interaction
IIIQuantum Dot in
Optical microcavity
IISemiconductor
Quantum Dot as a source of the light
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Overview of the course: III. Quantum Dot in Optical microcavity
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Overview of the course
IPhysics of the light- matter interaction
IVImplementations,
challenges, …
IIIQuantum Dot in
Optical microcavity
IISemiconductor
Quantum Dot as a source of the light
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+ QDs and plasmonics
Overview of the course: IV. Practical implementations and outlook
© Evident Technologies
X. Gao et al.,Nature Biotechnology’ 2004
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1988: Wolfram Mathematica
- symbolic language for algorithmic computation
2009:
- web computational engine accepting free form input
Exercises©
Wol
fram
Alp
ha
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1988: Wolfram Mathematica
- symbolic language for algorithmic computation
2009:
- web computational engine accepting free form input
Exercises©
Wol
fram
Alp
ha
• Downloadable .nb files atwww.fuw.edu.pl/~jass/wyklad.html on the evening before the lecture
• Calculations and interactive data plotting during the lecture
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A trendy subject of the course
1970 1980 1990 2000 20100
500
1000
1500
Pub
lishe
d Item
s in
Eac
h Y
ear
Publication Year
"Quantum Dot" or QD
1970 1980 1990 2000 20100
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3000
Pub
lishe
d Item
s in
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photonic
source: ISI Web of Knowledge
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A trendy subject of the course
1970 1980 1990 2000 20100
500
1000
1500
2000
2500
3000
Pub
lishe
d Item
s in
Eac
h Y
ear
Publication Year
photonic
source: ISI Web of Knowledge
1970 1980 1990 2000 20100
250
500
750
1000
1250
Pub
lishe
d Item
s in
Eac
h Y
ear
Publication Year
"Quantum Dot" or QD "Quantum Well" or QW
• Development of the technology of the sample production• Nanoscale control of the structure parameters
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Photonics
• The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com)
• The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation
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Photonics
• The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com)
• The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation
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Photonics
• The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com)
• The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation
• Photonics = electronics using a photons instead of electrons
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A brief history of the photon• Ancient Greek φῶς (phōs) = “light”• Particle vs wave models of the light• 1850 – Young experiment
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A brief history of the photon• Ancient Greek φῶς (phōs) = “light”• Particle vs wave models of the light• 1850 – Young’s experiment
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Interference Pattern Develops
• Stages of two-slit interference pattern. • The pattern of individually exposed grains progresses
from (a) 28 photons to (b) 1000 photons to (c) 10,000 photons.
• As more photons hit the screen, a pattern of interference fringes appears.
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Interference Pattern for three slits?
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A brief history of the photon• Ancient Greek φῶς (phōs) = “light”• Particle vs wave models of the light• 1805 – Young’s experiment – wave!• 1865 – James Clerk Maxwell's prediction that light was an
electromagnetic wave• 1888 – Heinrich Hertz's experimental confirmation by detection of radio
waves• 1905 – Albert Einstein, “light quantum” (das Lichtquant) and
photoelectric effect• 1923 – Compton, particle-like character of the light• 1926 - “un-creatable and indestructible” photons by Gilbert N. Lewis• 1977 - unambiguous confirmation – single photon correlation
experiment, Kimble et al.
Nature (1926)
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The light
Classical picture
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The light
Classical picture Quantum picture
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Maxwell’s Equations
• Electromagnetism - one of the four fundamental
forces (others: gravity and strong & weak nuclear
forces)
• Fundamental quantities: Electric field E, magnetic
field H, and D(E), B(H).
• In free space: D=0E, B=0H.
• Electric and Magnetic fields produce forces on
charges
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Maxwell’s Equation’s(in Differential Form)
D B 0
Gauss’s Law
Gauss’s Law for Magnetism
EB
t
H JD
t
Faraday’s Law
Ampere’s Law (in full extent)
James Clerk Maxwell
Changing E-field results in changing H-field resulting in changing E-field….
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Electromagnetic wave
2
2
002
2
t
B
x
B
tkxBB
tkxEE
cos
cos
max
max
Speed:
1.
o o
v
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Properties of EM Waves• The solutions to Maxwell’s equations in free space
are wavelike• Electromagnetic waves travel through free space at
the speed of light.• The electric and magnetic fields of a plane wave are
perpendicular to each other and the direction of propagation (they are transverse).
• The ratio of the magnitudes of the electric and magnetic fields is c.
• EM waves obey the superposition principle.
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Some Important Quantities
2
k Wavenumber
00
1
c Speed of Light
f 2 Angular Frequency
f
c Wavelength
ck =
w(k)
tkxBB
tkxEE
cos
cos
max
max
Dispersion relation
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Electromagnetic spectrum
λ ≈ 700 - 420 nm
λ ≈ 10-9 - 10-11 m
λ ≈ 10-12 - 10-14 m
λ ≈ 10-4 - 10-6 m
λ ≈ 10-2 - 10-3 m
λ ≈ 10-1 - 103 m
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Cavity quantum electrodynamics (CQED)
• Developed from the 50s of XX cent.• CQED deals with modications of the
electromagnetic field properties that are induced by the presence of boundaries for the field (mirrors, interfaces...)
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Energy density emitted by the Sun
Cavity quantum electrodynamics (CQED)
What happens to a photon confined in a box?
(10*10-9 m)3
10
10
10
5
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Optical cavity mode (lat. modus)
Condition for resonance in a cavity:
d
2d = Nl N = 1, 2, 3, ...
(round trip distance 2d equal to an integral number of wavelengths)
mirror mirror
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Surprising cavity effects at the nanoscale: the Casimir effect
Hendrik Casimir(1909-2000)
H. B. G. Casimir, On the attraction between two perfectly conducting plates, Proceedings of the Royal Netherlands Academy
of Arts and Sciences, Vol. 51, pp. 793–795 (1948).
• A net pressure from the excluded wavelengths
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The Casimir effect – how to measure it and how strong is it?
Example: two mirrors with an area of 1 cm2 separated by a distance of 1 μm have an attractive Casimir force of about 10–
7 N
When the sphere is brought near to the plate, an attractive Casimir force causes the cantilever to bend. Bouncing a laser off the top of thecantilever and photodiodes to monitors the effect.
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The Casimir effect: a „particle” viewElectron-positron production
Quantum fluctuations of the vacuum create virtual particles (real for an instant) that produce mechanical force
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Optical resonator
Two basic types:
Linear resonators: the light bounces back and forth between two end mirrors. There are counter propagating waves, which interfere with each other to form a standing-wave pattern.
Ring resonators: the light circulates in two different directions. A ring resonator has no end mirrors
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Some others:• Ease of fabrication• Connectivity to waveguides• Integration in larger circuits
Intrinsic ones:• Cavity mode (= elecromagnetic field distribution)• Quality factor (= temporal time)• Mode volume (= spatial confinement)• Free spectral range (= spectral mode separation)
Cavities: important parameters
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Quality factor of the optical cavity
• Ideal cavity: the photon preserved infinitely long
• In real: the photon escapes from the cavity within the finite time
Quality factor Q:
• Describes ability of the cavity to preserve a photon
• Compares the frequency at which a system oscillates to the
rate at which it dissipates its energy
A resonant cavity analogue: resonant LC curquit
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Quality factor Q
E
t
1
1/e
2/ = photon decay time
tettE
2
1
0cos
Consider leak-out of the photon from a cavity:
Optical period T = 1/f0 = 2/0
tteetu
2
2
1
tedt
tdu
0
E =Electric field at acertain position
u =Energy density
0222
TT
dt
tdutu
ePerOptCyclEnergyLost
gyStoredEnerQ
1. Definition of Q via energy storage:
Energy density decay:
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Summary
• General properties of EM radiation• Basics of optical microcavities
Next lecture:• Spontaneous emission and its control(Prucell effect, strong light matter-coupling)