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Microparticles
• Particles with dimensions on the order of l or bigger
• Insulators…Rayleigh Scattering (blue sky)
• Semiconductors....Resonance absorption at ħw ³ EGAP , size dependent fluorescence…)
• Metals…Resonance absorption at surface plasmon frequency, no light emission)
Nanoparticles
• Light scattering due to harmonically driven dipole oscillator
Enhanced forward scattering
Applications: resonators, lasers, etc…
Intuitive ray-picture useful
Rainbows due to dispersion H20
Lecture 4: Light Interaction with Small StructuresMolecules
Light Interaction with a Small ObjectElectric field drives harmonic motion of electrons
• Consider the Lorentz model
Nucleus
e-
+
0 ,w g
2
2 20
1L
em iw w gw
=- -
p E
~ Atomic polarizability
Oscillating charges radiates • This radiation is the scattered light intensity
• What does this process look like?
+
-E
H
Oscillating charges Emits EM Waves
+-
E-field lines start at positive charge
E and H fields from oscillating charges
E-field lines end at negative charge
E-field lines close upon themselves(field lines cannot cross)
The start of an EM wave After several periods
Radiation mainly ^ to oscillation direction
Oscillating charges Emit EM WavesRadiation is angle dependent
• Radiated intensity:2 4
22 3 20
sin32pIc r
w qp e
=
p0
• Radiated pattern:
• Total scattered radiation:2 40
30
'12S
A
pP IdAc
wpe
= =òClosed surface around the dipole
Derivation: Feynman lectures on physics (or Ramo, et al)
Radiation Emitted by a Lorentz OscillatorScattered intensity from a Lorentz Oscillator
2
2 20
1L
em iw w gw
=- -
p E
• Scattered intensity by a dipole:2 4
22 3 20
sin32pIc r
w qp e
=
• Lorentz model:
• Lorentz model: 24 4
2 22 2 3 2 2 2
0 0
1 sin32S L
eI Em c r iw q
p e w w gwæ ö
= ç ÷- -è ø
• Strongest scattering near a resonance
• Strongest scattering for higher w or shorter l
• Scattering occurs both in the forward and backward directions
Conclusions Incoming intensity
The Blue Sky
• l two times shorter Scattering 24 = 16 times stronger
4 42 2
2 2 3 2 2 20 0
1 sin32S
eI Em c r iw q
p e w w gw=
- -
• In the visible: O2, and N2 molecules have : w0 >> w
Incoming sun lightcontaining a range of l’s
Long l hardly get scattered
• Similar situation for insulating nanoparticles,
Non-resonant scattering
0 1 2 3 4 50.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
EB
Band
gap
(eV)
Diameter (nm)
EC
EV
Ehn=EG
h
e
D: 1-5 nm
C.Delerue et al. Phys Rev. B 48, 11024 (1993)
Example: Si nanocrystals
Semiconductor Nanoparticles
Photoluminescence
SiO2 Si50 keV Si High resolution TEM
image
� Implantation: 5x1016 Si @ 50 keV ® 100 nm SiO2
� Anneal: 1100 °C/10 min in vacuum
� Hydrogen passivation to 1) quench defect luminescence
2) increase fraction of optically active nanocrystals
Ion Beam Synthesis of Si nanocrystals
Synthesis of Si nanocrystals
600 700 800 900 1000 1100 12000.0
0.2
0.4
0.6
0.8
1.0
EGAP Bulk Si
0 min 3 min 10 min 15 min 20 min 25 min 30 min
PL S
igna
l (a.
u.)
Wavelength (nm)
Tuning of the lEmission of Si Nanocrystals by Oxidation
Si + O2 Si + SiO2
� Oxidation of Si nanocrystals at T = 1000 °C
� Peak wavelength tunable over more than 300 nm
Experimental parameters
P = 10 mW/mm2
lEXC= 458 nm
T = 293 K
M.Bruchez et al. (Alivisatos group), Science, 2013, 281 (2014)
Size and Material Dependent Optical Properties
• Blue series: CdSe nanocrystals with diameters of 2.1, 2.4,3.1, 3.6, and 4.6 nm• Green series: InP nanocrystals with diameters of 3.0, 3.5,and 4.6 nm.• Red series: InAs nanocrystals with diameters of 2.8, 3.6, 4.6, and 6.0 nm
Wavelength (nm)
Fluo
resc
ence
sig
nal (
a.u.
)
1771 1033 729 564 460
• Confocal microscopy image of Mouse fibroblasts • Labeling with semiconductor nanoparticles• 363-nm excitation, observation in the visible
Tagging Biomaterials with Semiconductor Nanocrystals
Excitation of a Metal Nanoparticle
( ) ( )( ) ( )
'3/ 2'
0 2 2, ' ,,9
2M
ext H
M H M
Vc
e wws w ee w e e w
=é ù+ +ë û
2 Hn
eM = e’M + ie’’M
eH = e’H =
Volume = V0
Particle
Host matrix
E-field+++++
-- - --
300 400 500 600 700 800 9000
100
200
300
400
500
n=3.3n=1.5
1
R = 5 nm
sex
t (nm
2 )
l (nm)
4 3.5 3 2.5 2 1.5
Energy (eV)
Ag clusterD = 10 nm
Homework problem
• Engraved Czechoslovakian glass vase• Ag nanoparticles cause yellow coloration• Au nanoparticles cause red coloration• Molten glass readily dissolves 0.1 % Au• Slow cooling results in nucleation and growth of nanoparticles
Applications Metallic Nanoparticles
Light scattering by particles with d » l
• Red circle intensity from polarization out of the plane
Scattering from a driven dipole d << l
• Black curve show total scattering pattern for a random incident polarization
1+ sin2q
Scattering from a particle with size d » l
• More forward scattering
sin2q
1
Light interaction with particles d » l
1+ sin2q
sin2
q
1Particle d << l
Particle d » l
Particle d » 2l
• Very strong forward scattering
• Scattering intensities similar for different colors (white clouds!)
• Scattering maxima occur in different directions for different colors
• Scattering is more forward
Light interaction with particles d >> l
Ray pictures of light become appropriate
• Example: explanation of rainbows
SunlightRain
Anti solar point
42o
Sunlight
Violet
Red
430
410
Coupling Light into a SiO2 Microsphere
� Coupling light into a whispering gallery mode using a tapered fiber
* Ming Cai, Oskar Painter, and Kerry Vahala, Phys Rev. Lett. 85, 74 (2000)
Pump, n
few µmPT
n
Q = Dn/n
Whispering Gallery
Mode
Symmetryaxis
Taper-sphere Coupling region
Fiber output
Control rod“Stem”
h = 99.8%
(n,l,m)
Microsphere Doped with Er ions
• Similarity with electron orbits• Er doped sphere lases ! (Consider roundtrip loss and gain)
� Determined by quality factor Q =
� Q-values of 103 - 104 are considered excellent
� Measured Q-value of a SiO2 microsphere resonator: ~ 1010.! *
Photon storage time ~ µs
Photon comes around 106 times for D = 100 µm
� Ultimate Q of 1010 is limited by intrinsic material properties
Microsphere can act as a MicroresonatorPerformance
Photon lifetimeOptical period
* M.L. Gorodetsky, A.A. Savchenkov, and V.S. Ilchenko, Opt. Lett. 21, 453 (1996)
� Low threshold micro-lasers
� Narrow linewidth optical filters
� Sensors with submonolayer sensitivity
� Wavelength Division Multiplexing devices for telecommunications
� Non-linear optics
� Quantum electrodynamics experiments
MicrOspheres: Devices and Applications
Comparison with more conventional resonators
Devices and applications
� Examples: or or
� Characteristic dimensions: l - 100l
Summary
Microparticles
• Particles with dimensions on the order of l
• Insulators…Rayleigh Scattering (blue sky)
• Semiconductors....Resonance absorption at ħw ³ EGAP , size dependent fluorescence…)
• Metals…Resonance absorption at surface plasmon frequency, no light emission)
Nanoparticles
• Microspheres with diameters much larger than l
Light interaction with small objects (d < l)• Light scattering due to harmonically driven dipole oscillator
l-independent (white clouds)Enhanced forward scattering
Applications: resonators, lasers, etc…
Intuitive ray-picture useful
Rainbows due to dispersion H20
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