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

Plan for today

1. Overview of the course

2. EM radiation

3. Optical cavities

Overview of the course

IPhysics of the light- matter interaction

Overview of the course: I. Physics of the light- matter interaction

E

t

1

1/e

0

Overview of the course

IPhysics of the light-

matter coupling

IISemiconductor

Quantum Dot as a source of the light

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

Overview of the course

IPhysics of the light- matter interaction

IIIQuantum Dot in

Optical microcavity

IISemiconductor

Quantum Dot as a source of the light

Overview of the course: III. Quantum Dot in Optical microcavity

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

+ QDs and plasmonics

Overview of the course: IV. Practical implementations and outlook

© Evident Technologies

X. Gao et al.,Nature Biotechnology’ 2004

1988: Wolfram Mathematica

- symbolic language for algorithmic computation

2009:

- web computational engine accepting free form input

Exercises©

Wol

fram

Alp

ha

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

A trendy subject of the course

1970 1980 1990 2000 20100

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Publication Year

"Quantum Dot" or QD

1970 1980 1990 2000 20100

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Publication Year

photonic

source: ISI Web of Knowledge

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

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1250

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Publication Year

"Quantum Dot" or QD "Quantum Well" or QW

• 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• 1926 - “un-creatable and indestructible” photons by Gilbert N. Lewis• 1977 - unambiguous confirmation – single photon correlation

experiment, Kimble et al.

Nature (1926)

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)

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….

Electromagnetic wave

2

2

002

2

t

B

x

B

tkxBB

tkxEE

cos

cos

max

max

Speed:

1.

o o

v

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

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

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

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...)

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

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

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

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.

The Casimir effect: a „particle” viewElectron-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 standing-wave pattern.

Ring resonators: the light circulates in two different directions. A ring resonator has no end mirrors

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

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

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:

Summary

• General properties of EM radiation• Basics of optical microcavities

Next lecture:• Spontaneous emission and its control(Prucell effect, strong light matter-coupling)