zoom lecture live at 13:30 light sources at the nanoscale
TRANSCRIPT
![Page 1: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/1.jpg)
ZOOM Lecture live at 13:30 – light sources at the nanoscaleTAs live at 15:30 [ photonic crystals ]
Till 13:30- Download slides www.koenderink.info/teaching- Q & A
Next session - May 6 – minisymposionFor input: talk to the TA’s. Ilan is your main contact
On May 6: start at 13:00 sharp.
![Page 2: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/2.jpg)
Quantum emittersFermi’s Golden RuleDensity of states
Nanophotonics class UvAFemius Koenderink – [email protected]
![Page 3: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/3.jpg)
Motivation - LEDs
SemiconductorsChallenge 1: extraction
TIR limits extractionto ~ 2%
Challenge 2: avoidnon-radiative decay
Osram (2000)
![Page 4: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/4.jpg)
4
Motivation – quantum optics
Suppose Alice has a secret message to communicate to Bob..
Quantum information in 1 photoncan not be eavesdropped
Also: suppose you have two localized qubits. How do you transfer a quantum state from A to B
Possible solution: spin A photon spin B
![Page 5: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/5.jpg)
Single molecules [Moerner & Orrit, ’89]
100 micron
1018 molecules
Keep on diluting
1 molecule can emit about 107 photons per second (1 pW)Observable with a standard [6k€] CCD camera + NA=1.4 objective
![Page 6: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/6.jpg)
Fluorescence from quantum sources
Space• Whereto does the photon go ?• With what polarization ?
Time• How long does it take for the photon to appear ?
Matter• Selection rules – what color comes out?
![Page 7: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/7.jpg)
Light from electron transitions in a quantum object
Energy scale for light 1 to 3 eV
Compare: kBT ~ 25 meV
Vibrations in molecules: 0.1 eV
e- transitions in hydrogen: 13.6 eV [1/n12-1/n2
2]
Band gap in Si: 1.1 eV
![Page 8: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/8.jpg)
Interaction of an atom with light
Consider two states of an atom, with energies and states
Suppose I shine light at frequency w on the system.This gives rise to a time-varying perturbation
Just the first term gives a potential energy
![Page 9: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/9.jpg)
Transition dipole moment
Dipole approximation – a small object k.r<<1
potential
Perturbation theory: transitions are governed by
‘Transition dipole moment’
Matrix element means: selection rules
![Page 10: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/10.jpg)
Typical moleculesLarge conjugated carbon chains
Rhodamines
Pentacene, perylene, teryllene
DBATT
Electronic levels explained by particle in a 1D boxN bond chain: about 2N electrons in a 1D box of length ~ NaGround state: first N levels are completely filledExcited state: one electron goes from level N to level N+1
![Page 11: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/11.jpg)
Quantum dot nanocrystals
TEM/you see single atoms
CdSe (CdTe, PbS, PbSe, CdS)Semiconductor nano-crystalsElectron & hole confined as particlesin a box
II-VI quantum dots in solution: Bawendi & Norris (early ‘90s)
![Page 12: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/12.jpg)
Molecules are not just electronic systems
Thermally populated vibrations, rotations ….
energy scales < electronic transition
![Page 13: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/13.jpg)
Jablonski diagram
S0
S1
Electronic ground state
Electronic excited state
T1Triplet
1. Fluorescence is spin-allowed, nanosecond time scales2. Phosphorescence is spin-forbidden, so very slow
![Page 14: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/14.jpg)
Jablonski diagram
S0
S1
Electronic excited state
Franck-Condon principleElectronic transition is instantaneous compared to the nucleiNuclei rearrange in picoseconds after the e- transitionTransition requires large vibrational wave function overlap
![Page 15: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/15.jpg)
Franck Condon
Absorption & fluorescence probabilities are proportionalto vibrational overlap ‘Franck-Condon factor’
Expect mirror-symmetricemission vs absorptionspectra
Sharp peaks obscured by(1) Ensemble(2) Rotations & collisions
![Page 16: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/16.jpg)
If this is all wavefunctions,.....
why care about nanophotonics?
A. A bare molecule radiates as a dipole
How do you create directivity
B. The rate of emission controls brightness
How do you control rate
![Page 17: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/17.jpg)
Controlling brightness
Radiation resistance – environment sets power to current ratio
The work you need to do keep current j going depends on environment
![Page 18: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/18.jpg)
Radiation resistance
1) Dipole antenna2) Ground plane
(Balanis Antenna Handbook)
![Page 19: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/19.jpg)
RF antenna in front of a mirror
- +
-+
-
+
-
+
The same current radiates a different far field power“Method of image charge”’ - Interference with its mirror image
![Page 20: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/20.jpg)
Single quantum emitter
20
• After one excitation, emits just one quantum of light
• Probabilistic timing of when emission occurs
Laser pulses
Hits ondetector
Hits onAPD 2
Time
S0
S1
Time (ns)
Lounis & Orrit, Single photon sources, Rep. Prog. Phys (2005)
![Page 21: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/21.jpg)
Scanning mirror ‘Drexhage experiment’
• 25mm PS bead covered with 400nm Ag as mirror
• PS bead glued to cleaved fiber, mounted in AFM
• Sideways scanning varies vertical emitter-mirror distance
Experiment first done by B. C. Buchler (2005)
![Page 22: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/22.jpg)
Drexhage experiment
22
Note how: the power is may be always one photon per laser pulsebut the decay rate varies with mirror-geometry
K.H. Drexhage first did this, with ensembles of molecules (1966)
0 40 80t (ns)
10
100
1000
Even
ts
slope
NV-color center in diamond
![Page 23: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/23.jpg)
Understanding Fermi’s Golden Rule
2
2all finalstates
2( )f i f i
f
V E E
Energy conservationMatrix elements:Transition strengthSelection rules
Spontaneous emission of a two-level atom:
Initial state: excited atom + 0 photons.Final state: ground state atom + 1 photon in some photon state
Question: how many states are there for the photon ???
![Page 24: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/24.jpg)
Understanding Fermi’s Golden Rule
2
2all finalstates
2( )f i f i
f
V E E
Energy conservationMatrix elements:Transition strengthSelection rules
Quantum: rates are proportional to number of available final photon states “DOS”
Classical: Density of States = radiation resistance for a source
2
2
0
| | ( )3
if
m w w
![Page 25: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/25.jpg)
How many photon in a L x L x L box of vacuum ?
( , ) sin( ) with ( , , )i tE x t Ae l m nL
w k r kStates in an LxLxL box:
l,m,n positive integers
Number of states with |k|between k and k+dk:
3
24( ) 2
8
LN k dk k dk
l,m,n > 0fill one octant
fudge 2 for polarization
2 23 3
2 2 2 3( )
dkN d L d L d
c d c
w ww w w w
w
k
dk
![Page 26: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/26.jpg)
26
Fluorescence decay rates
Fermi’s Rule: Fluorescence rate number of photon states
0 2 4 60
50000
100000
150000
Photo
n s
tate
s p
er
m3, per
Hz
Frequency w (1015
s-1)
Visible light: ~105 photon states per Hz, per m3 of vacuum
Loudon, The Quantum Theory of Light
![Page 27: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/27.jpg)
Example: 3D photonic crystal
27
Air-sphere / Sifcc photonic crystal
1st inverse opal photonic crystal: Wijnhoven & WLV, Science 281 (1998) 802LDOS calculations: Nikolaev, Vos & Koenderink, JOSA-B 5 (2009) 987
![Page 28: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/28.jpg)
Dispersion relation
Stop gap
wave vector k0 π/a
standing wave in n1
standing wave in n2
Freq
ue
ncy
Density of States
Redistribution of states: - photonic band gap - flat bands imply high DOS
Busch & John, Phys. Rev. E (1998)
![Page 29: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/29.jpg)
Observations -2D quantum well
Fujita et al., Science (2005)Two-dimensional: Kyoto [Noda], Stanford [Vuckovic], DTU [ Lodahl], WSI [Finley] ...Three dimension: Lodahl et al. (Nature 2004), Leistikow et al. (PRL ’11)
![Page 30: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/30.jpg)
30
Cavity
Fluorescence in a cavity
0 2 4 60
50000
100000
150000
Photo
n s
tate
s p
er
m3, per
Hz
Frequency w (1015
s-1)
Fermi’s Rule: Fluorescence rate number of photon states
Microcavity: Exactly one extra state per Dw=w/Q in a volume V
Gérard & Gayral, J. Lightw. Technol. (1999)
![Page 31: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/31.jpg)
31
Cavity
Fluorescence in a cavity
0 2 4 60
50000
100000
150000
Photo
n s
tate
s p
er
m3, per
Hz
Frequency w (1015
s-1)
Fermi’s Rule: Fluorescence rate number of photon states
Microcavity: Exactly one extra state per Dw=w/Q in a volume V
Purcell factor
3
2
3
4
QF
V
Gérard & Gayral, J. Lightw. Technol. (1999)
![Page 32: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/32.jpg)
Record high Purcell factor
Akselrod et al.Nat. PhotonicsVol 8, 835 (2014)
Single-crystalAg-cube on Au
8 nm gap (PVP spacer)
Claim:up to 1000-foldEnhancement
50% lost in metal50% appears as light
![Page 33: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/33.jpg)
Local density of states
Consider a molecule / quantum dot / ... - as located at a fixed position- as oriented along a fixed direction
The available modes have to be weighted by how well the dipole orientation and position match to them
DOS: just count
LDOS: local strength
Sprik, v. Tiggelen & Lagendijk, Eur. Phys. Lett. (1996)
![Page 34: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/34.jpg)
State of the art number summary
Microcavities Photonic crystals Plasmonics
Narrowband Dw/w=10-5
Local (mode profile)
Theory: F =103
Data: F=20Single |E|2 dominates
Broadband Dw/w=0.2Global
Theory: F=0 to 20Data: F=0.1 to 10 Many modes count
Broadband Dw/w=0.3Local
Theory: F=104
Data: F=500 to 1000 Problem: loss
Picture: Verhagen Picture: Moerner
F = LDOS / vacuum LDOS - L mean “local”
![Page 35: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/35.jpg)
Why relevant?
![Page 36: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/36.jpg)
1. Outpacing non-radiative decay channels
2. Less timing jitter in a single photon source
3. Brighter source by faster cycling through transition
4. Extracting light via the mode that dominates the LDOS
![Page 37: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/37.jpg)
Why relevant?
1) Nanophotonics to measure quantum efficiency
2) Nanophotonics to improve quantum efficiency
heat/...
![Page 38: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/38.jpg)
Calibration example – single NV center
38
For a mirror the LDOS is exactly knownThe contrast of the oscillation tells you the quantum efficiency
Single emitter quantum-efficiency measurement
Drexhage / Buchler & Sandoghdar/ Barnes / Polman / Frimmer
0 40 80t (ns)
10
100
1000
Eve
nts
slope
![Page 39: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/39.jpg)
AC current - radio, WIFI, GSM… up to 100 GHz frequenciesOptics (200 THz) - no classical AC electronics available
![Page 40: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/40.jpg)
Funneling light into a single beam
Sample: perforated Au film - hexagons of 440 nm pitchSources: dilute fluorophores Atto 640 dye diffusing in H2O
Molecules in the central hole pumped in a confocal microscope
![Page 41: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/41.jpg)
Emission strongly redirected in a narrow beam
Single aperture: 10x brightness enhancement (full NA), pump |E|2
Array: 40x enhancement in forward direction
L. Langguth et al. ACS Nano
Single hole One shell Two shells Three shells
Fourier image kx (up to NA=1.2)
ky
Funneling light into a single beam
![Page 42: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/42.jpg)
Route to quantum
Fermi’s Golden Rule: irreversible decay
Strong coupling QED: regime of reversible interaction“Strong coupling cavity QED” [Haroche, Wineland, 2012]
![Page 43: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/43.jpg)
Conclusions
Absorption <-> stimulated emission Induced by external E
Spontaneous emission without any driving‘stimulated by vacuum fluctuations’
Fermi’s Golden rule
Nanophotonics controls the DOS/LDOS (w)
- How fast and whereto quantum sources emit light- Black body emitters- Any force mediated by ‘vacuum fluctuations’
2
2
0
| | ( )3
if
m w w
![Page 44: ZOOM Lecture live at 13:30 light sources at the nanoscale](https://reader031.vdocuments.net/reader031/viewer/2022013001/61cba210d9bf2079b07aa97e/html5/thumbnails/44.jpg)
44
Fluorescence decay rates
Fermi’s Rule: Fluorescence rate number of photon states
0 2 4 60
50000
100000
150000
Photo
n s
tate
s p
er
m3, per
Hz
Frequency w (1015
s-1)
Visible light: ~105 photon states per Hz, per m3 of vacuum