Transcript Prezentacja programu PowerPoint

Quantum Dots in Photonic Structures
(Nanophotonics with Quantum Dots)
Jan Suffczyński
Wednesdays, 17.00, SDT
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
Plan for today
1. Overview
of the course
2. EM radiation
3. Optical cavities
Overview of the course
I
Physics of the lightmatter interaction
Overview of the course:
I. Physics of the light- matter interaction
E
1
1/e
0
t
Overview of the course
I
Physics of the lightmatter coupling
II
Semiconductor
Quantum Dot as a
source of the light
Overview of the course: II. Semiconductor
Quantum Dot as a source of the light
CdTe/ZnTe Quantum Dot emission
-PL Intensity [arb. units]
InAs/AlAs Quantum Dot
T=2K
CX
XX
Correlated counts
2210
Transmission Electron Microscope
cross-sectional image,
Offermans et al., Phys. Rev. B 2005
X
2215
2220
2225
Photon Energy [m eV]
Overview of the course
I
Physics of the lightmatter interaction
III
Quantum Dot in
Optical
microcavity
II
Semiconductor
Quantum Dot as a
source of the light
Overview of the course:
III. Quantum Dot in Optical microcavity
Overview of the course
IV
Implementations,
challenges, …
III
Quantum Dot in
Optical
microcavity
I
Physics of the lightmatter interaction
II
Semiconductor
Quantum Dot as a
source of the light
Overview of the course:
IV. Practical implementations and outlook
© Evident
Technologies
X. Gao et al.,
Nature Biotechnology’ 2004
+ QDs and plasmonics
© Wolfram Alpha
Exercises
1988: Wolfram Mathematica
-
symbolic language for algorithmic computation
2009:
-
web computational engine accepting free form input
© Wolfram Alpha
Exercises
• Downloadable .nb files at
www.fuw.edu.pl/~jass/wyklad.html
on the evening before the lecture
• Calculations and interactive data
plotting during the lecture
1988: Wolfram Mathematica
-
symbolic language for algorithmic computation
2009:
-
web computational engine accepting free form input
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"Quantum Dot" or QD
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Publication Year
2010
Published Items in Each Year
Published Items in Each Year
A trendy subject of the course
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source: ISI Web of Knowledge
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"Quantum Dot" or QD
"Quantum Well" or QW
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Published Items in Each Year
Published Items in Each Year
A trendy subject of the course
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Publication Year
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source: ISI Web of Knowledge
• Development of the technology of the sample production
• Nanoscale control of the structure parameters
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
• 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
• 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
A brief history of the photon
• Ancient Greek φῶς (phōs) = “light”
• Particle vs wave models of the light
• 1850 – Young experiment
A brief history of the photon
• Ancient Greek φῶς (phōs) = “light”
• Particle vs wave models of the light
• 1850 – Young’s experiment
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.
Interference Pattern for three slits?
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
Nature (1926)
1926 - “un-creatable and indestructible” photons by Gilbert N. Lewis
1977 - unambiguous confirmation – single photon correlation
experiment, Kimble et al.
The light
Classical picture
The light
Classical picture
Quantum picture
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
Maxwell’s Equation’s
(in Differential Form)
 
Gauss’s Law
 D  
James Clerk Maxwell
 
 B  0
Gauss’s Law for Magnetism

 
B
 E  
Faraday’s Law
t 
   D
 H  J 
t
Ampere’s Law (in full extent)
Changing E-field results in changing H-field
resulting in changing E-field….
Electromagnetic wave
2B
2B
 0 0 2
2
x
t
Speed:
1
v
o o
.
E  Emax coskx  t 
B  Bmax coskx  t 
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.
Some Important Quantities
E  Emax coskx  t 
B  Bmax coskx  t 
1
c
0 0

c
f
Wavelength
  2f
k
k
k
Speed of Light
2

 c
Angular Frequency
Wavenumber
Dispersion relation
Electromagnetic spectrum
λ ≈ 700 - 420 nm
λ ≈ 10-4 - 10-6 m
λ≈
λ ≈ 10-1 - 103 m
10-2
-
10-3
m
λ ≈ 10-9 - 10-11 m
λ ≈ 10-12 - 10-14 m
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...)
Cavity quantum electrodynamics
(CQED)
What happens to a photon confined in a box?
5
(10*10-9 m)3
10
10
10
Energy density emitted by the Sun
Optical cavity mode (lat. modus)
mirror
mirror
d
Condition for resonance in a cavity:
2d = N
N = 1, 2, 3, ...
(round trip distance 2d equal to an integral number of wavelengths)
Surprising cavity effects at the
nanoscale: the Casimir effect
Hendrik Casimir
(1909-2000)
• A net pressure
from the excluded
wavelengths
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).
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 the
cantilever and photodiodes to monitors the effect.
The Casimir effect: a „particle” view
Electron-positron production
Quantum fluctuations of the
vacuum create virtual particles
(real for an instant) that produce
mechanical force
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 standingwave pattern.
Ring resonators: the light circulates
in two different directions. A ring
resonator has no end mirrors
Cavities: important parameters
Intrinsic ones:
• Cavity mode (= elecromagnetic field distribution)
• Quality factor (= temporal time)
• Mode volume (= spatial confinement)
• Free spectral range (= spectral mode separation)
Some others:
• Ease of fabrication
• Connectivity to waveguides
• Integration in larger circuits
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
Quality factor Q
Consider leak-out of the photon from a cavity:
E = Electric field at a
E
certain position
1
 t
1
u = Energy density
2
E t   cos 0 t e
2
1/e
0
t
2/ = photon decay time
Optical period T = 1/f0 = 2/0
1. Definition of Q via energy storage:
  1 t 
u t    e 2   e t




Energy density decay:

dut 
 e t
dt
0
StoredEnergy
u t 
2
Q  2
 2


dut 
EnergyLostPerOptCycle


T  T
dt
Summary
• General properties of EM radiation
• Basics of optical microcavities
Next lecture:
• Spontaneous emission and its control
(Prucell effect, strong light matter-coupling)