Radiation-matter interaction · 2019-08-13 · Radiation-matter interaction Spontaneous emission control •Drexhage’sexperiment •The Purcell effect Optical antennas •Radiation

Radiation-matter interaction

Spontaneous emission control

• Drexhage’s experiment

• The Purcell effect

Optical antennas

• Radiation reaction in dipolar scatterers

• Decay-rate engineering with optical antennas

• Directionality control with optical antennas

• Overview: sub-wavelength vs. super-wavelength “antennas”

• Overview: optical antennas vs. RF antennas

The limits of our classical theory – from weak to strong coupling

The limits of our classical theory – single photon emission

www.photonics.ethz.ch 1

EmitterTransition dipole moment:Wave function engineering by synthesizing molecules, and quantum dots

Chemistry, material science

EnvironmentLDOS: Electromagnetic mode engineering by shaping boundary conditions for Maxwell’s equations

Physics, electrical engineering

www.photonics.ethz.chantennaking.com, Wikimedia, emory.edu

2

Decay-rate engineering

Clean-up: LDOS and absorption

• The LDOS offers a handle to control spontaneous emission rate

• Does it offer a handle to control light absorption?

• Well, maybe under very special circumstance but in general:Don’t use LDOS when arguing about absorption.

• Get absorption rate via absorption cross section and intensity at absorber


Yagi-Uda antenna (1926)

• Single active element

• Field of active element polarizes passive elements

• Passive elements generate fields and polarize each other (self-consistent solution)

4

Feed element

Passive directors

Passive reflectors

p=aE

Yagi-Uda antenna

5

Taminiau et al., 2008

Optical antennas for directional photon emission

• Optical antennas allow control of directionality of light emission for quantum emitters

• Antenna is photonic environment that offers a large density of states with specific k-vector


Driven elementPassive scatterers

emission

Scale down size, scale up frequency

106

Yagi and Uda (1920s) Curto et al., Science 329, 930 (2010)

emission

Quantum emitter

Metal nanoparticles

Rad

io-e

lect

ron

ics.

com

Antennas – resonators with engineered radiation loss


In the µwave-regime:

Total internal reflection Metallic reflection

From resonators to antennas


Vah

ala,

Nat

ure

42

4,

83

9

Kü

hn

et a

l., P

RL

97

, 01

74

02

(2

00

6)

Mu

nsc

het

al.,

PR

L 2

01

3

Curto et al., Science 329, 930 (2010)

Rad

io-e

lect

ron

ics.

com

Near-field antennas• Sub-l-sized resonators• Naturally high radiation loss

Cavity-based antennas:• l-sized resonators• Deliberately introduced

radiation loss

Is this an antenna?

From resonators to antennas


Vah

ala,

Nat

ure

42

4,

83

9

Kü

hn

et a

l., P

RL

97

, 01

74

02

(2

00

6)

Mu

nsc

het

al.,

PR

L 2

01

3


Rad

io-e

lect

ron

ics.

com

Is this an antenna?

Antennas are devices which mediate between far-field (=propagating) radiation and localized fields.Antennas boost light-matter interaction.Discuss antennas using LDOS.Do not discuss antennas in terms of Purcell factors (mode volume V not well defined).

Near-field antennas• Sub-l-sized resonators• Naturally high radiation loss

Cavity-based antennas:• l-sized resonators• Deliberately introduced

radiation loss

Antennas – radio vs. optical



Rad

io-e

lect

ron

ics.

com

Radio-antennas Optical antennas

Antenna theory: Maxwell Maxwell

Resonance mechanisms: Geometric resonances Geometric resonancesMaterial resonances

Sources: Classical current source Quantum emitter




Rad

io-e

lect

ron

ics.

com








Rad

io-e

lect

ron

ics.

com

• Nano-optics with optical antennas relies on classical antenna theory due to the scale invariance of Maxwell’s equations.

• Difference 1: Frequency dependence of the material constants.At radio frequencies we have practically perfect metals.At optical frequencies metals are imperfect and show material resonances.

• Difference 2: Emitters in the optical regime show quantum behavior.





EmitterTransition dipole moment:Wave function engineering by synthesizing molecules, and quantum dots

Chemistry, material science

EnvironmentLDOS: Electromagnetic mode engineering by shaping boundary conditions for Maxwell’s equations

Physics, electrical engineering

www.photonics.ethz.chantennaking.com, Wikimedia, emory.edu

13

Decay-rate engineering

Where is the limit to this theory?

Where is the limit of our formalism?

• Emitter decay rate

• Cavity decay rate

• Emitter-cavity coupling rate:


holds in the limit:

The weak-coupling limit


holds in the limit:

• This limit is called “weak-coupling regime”

• Classical model assumes monochromatic source

• Fermi’s Golden Rule assumes weak coupling (perturbation theory)

• Strong-coupling regime: deviation from exponential decay, cyclic energy exchange between emitter and cavity (Rabi oscillations)

See lecture on Quantum Optics

The second-order correlation function

• Beam of light impinging on a 50/50 beamsplitter (BS)

• Record intensity I(t) in each arm after BS

• Calculate normalized cross correlation between signals I1 and I2


50/50 beamsplitterI1(t)

I2(t)

The classical case



• For a classical field I1(t) = I2(t), so g(2) is intensity autocorrelation



I2(t)

Intensity autocorrelation - the classical case



• For a classical field I1(t) = I2(t), so g(2) is intensity autocorrelation

• For long delay times

• correlation at zero delay

• global maximum at zero delay



I2(t)1

t

HW2

Intensity autocorrelation - the coherent case

• Perfectly monochromatic field

• Intensity is therefore



I2(t)1

t

laser

Intensity autocorrelation - the chaotic case

• Collection of sources

• Random phase

• Gaussian distribution of emission frequencies



I2(t)1

t

Intensity autocorrelation – counting photons

• ni(t) is the number of photons on detector i at time t

• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0.



I2(t)

Counting photons – coherent case


• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0

• g(2)(t) = 1 means that photons arrive with Poissonian distribution



I2(t)1

t

laser

Counting photons – chaotic case


• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0

• g(2)(t=0) > 0 means that photons tend to arrive in bunches



I2(t)1

t

Counting photons – a single quantum emitter

• Assume source is a single emitter

• Single emitter can only emit one photon at a time

• If there is a photon on D1 there cannot be a photon on D2 antibunching

• Photon antibunching is at odds with classical electromagnetism

• g(2)(t=0) = 0 is the signature of a single photon source

• What determines the rise time of g(2)(t)?


50/50 beamsplitter

1

I1(t)

I2(t)

t

Intensity correlation – counting single photons

• How do you know your emitter is a single photon source? For n emitters:

• How does the lifetime show up in the correlation function?Rise time is lifetime in the case of weak pumping.



I2(t)

Beveratos, PhD thesis, Univ. Paris Sud (2002)

Intensity correlation – summary

• Second-order correlation function measures temporal intensity correlation

• Bunching: photons tend to “arrive together”, classically allowed/expected

• Antibunching: photons tend to “arrive alone”, classically forbidden



I2(t)

t

Summary – light matter interaction

Quantum emitters are probes for their electromagnetic environment.



Kühn et al., PRL 97, 017402 (2006)

Vah

ala,

Nat

ure

42

4,

83

9

Quantum emission can be tailored via the emitter’s electromagnetic environment.

Radiation carries information about• The emitter• The emitter’s environment• The emitter-environment interaction

Summary – light matter interaction

Quantum emitters are probes for their electromagnetic environment.



Kühn et al., PRL 97, 017402 (2006)

Vah

ala,

Nat

ure

42

4,

83

9

Quantum emission can be tailored via the emitter’s electromagnetic environment.

10 eV1 eV100 meV

kT Ry

Rad

io-e

lect

ron

ics.

com

Documents

Radiation-matter interaction · 2019-08-13 · Radiation-matter interaction Spontaneous emission control •Drexhage’sexperiment •The Purcell effect Optical antennas •Radiation