nanophotonics - amolf1 nanophotonics femius koenderink center for nanophotonics amolf, amsterdam...
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1
Nanophotonics
Femius KoenderinkCenter for Nanophotonics
AMOLF, Amsterdam
Nanoscale: 10-9 meter
Photonics: science of controlling
propagation, absorption &
emission of light
(beyond mirrors & lenses)
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About length scales
2
1 m you and your labtable
100 µm thickness of a hair
10 µm smallest you can see
1 µm size of a cell
300 nm smallest you can see with microscope
0.3 nm Si lattice spacing
small molecules
0.05 nm Hydrogen atom 1s orbital
Geometrical
optics
Domain of
e-, not ħw
Nano: Range around and just below the wavelength of light
well above the length scales of atoms & solid state physics
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Dreams 1: signal transport
Lossless, high-bandwidth transport of information
- Ohmic loss limits copper wires
- Glass-fiber: < 1 decibel per kilometer
- Up to 80 colors = up to 80 “wires” in one fiber
- From fiber to chip….?
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Dreams 2: computing
1939
1 Classroom full
1 addition/sec
2015
109 flops/sec
Shrunk (108 ) .. Moore’s law ends where?
Single molecule
Transistor?
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Dream 3: quantum computing
TU Delft – Bell test on 2 spins, entangled by single photons
1. Spins are a controllable quantum degree of freedom
2. Photons are transportable and coherent
How do you interface with unit efficiency light, and a single spin?
Light interfaces with spin, charge, atoms, quantum motion,…
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Dream 4: seeing small stuff
PALM, STORM: beat Abbe limit by seeing a single molecule at a time
Using a stochastic on/off switch to keep most molecules dark
Resolution: how discernible are two objects ?If you have a single object, you can fit the center of a Gaussian with arbitrary precision (depends on noise)
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Dream 4: seeing small stuff
Detecting single molecules
[Detuning of a resonance
by a single molecule]
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Dream 5: better lighting
Blue LED - Nobel Physics – 2014
Nanoscale materials that emit light
How to extract the most light from a single nano-object
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Dream 6: making light work
30 minutes of sunlight contains
enough energy for 1 year
How do you make a solar cell
absorb the most light?
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Controlling photons with nano-
antennas
Femius Koenderink
Center for NanophotonicsFOM Institute AMOLF, Amsterdamwww.amolf.nl
Resonant Nanophotonics AMOLF
My own fascination with nanophotonics
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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
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Spontaneous emission
Matter• Selection rules – which colors & transitions
Time• How long does it take for ħω to appear ?
Space• Whereto does the photon go ?• With what polarization ?
Quantummechanics
Maxwell equations
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High Q Ultrasmall V
micrometers
na
no
meters
Ultimate control over light
Interference-based Material-basedfree-electrons
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This course
15
1. Tuesdays 13-17: Lecture course (2h), 2h exercises
2. Thursdays 13-17: Lecture 2h, exercises (2h)
3. Labtour AMOLF: April 26
Presentations & homework exercises count for final mark
Exercise help: TA indicated per week (rotates)
Course slides & information available at:
https://amolf.nl/research-groups/resonant-nanophotonics/uva-mastercourse
http://tinyurl.com/maaq5gm
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Course calendar
1. What is nano, Maxwell, a first optical scattering problem Apr 3
2. Extreme confinement and dispersion with metals Apr 10
3. Pulses and dispersion, causality, and invisibility cloaks Apr 12
4. Photonic crystals 1 – perfect mirrors from transparent stuff Apr 17
5. Photonic crystals 2 – semiconductors for light Apr 19
6. Antennas on the nanoscale Apr 24
Labtour [ April 26 ]
7. Quantum lightsources at the nanoscale May 1
8. Microscopy & nanoscopy May 3
9. Microcavity resonators May 8
10.Hybrid light-matter systems May 15
Extra exercise class [May 17 ] , final exam session [May 24]
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Provisional exercise calendar
Topic Assistant Handout Handin date Contact time
Exercise 1 Maxwell, Fresnel Hugo, Sylvianne 3-Apr 12-Apr 1.5 session
Exercise 2 Plasmons, causality Annemarie, Ruslan 10-Apr 17-Apr 1.5 session
Exercise 3 Photonic crystals Sachin, Christiaan 17-Apr 24-Apr 2 sessions
Exercise 4 Nanoscale antennas David, Said 24-Apr 3-May 1.5 session
Exercise 5 LDOS & microscopes Isabelle, Ilse 1-May 8-May 2 sessions
Exercise 6 Microcavities Amy, Robin 8-May 20-May 2 sessions
Exercise 7Hybrid light-matter systems Zhou, Radoslaw 15-May 20-May 2 sessions
Exercises count heavily for your final grade [70%] and involve time & effort
Plan carefully – but realize you have always at least a week & 2 Q &A opportunities
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Geometrical optics:
- Light travels as rays in straight lines
- To first order: mirrors, lenses, prisms
- Matter enters as refractive index
- Phase is irrelevant for tracing rays
Nano-optics
- Light is a wave
- Diffraction & interference – wavelength-sized distances
- Full Maxwell equations are needed
- Matter & quantum mechanics - molecules & atoms as sources
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20
Maxwell equations I – divergence
Electric field lines emanate from
charge
Gauss’s law
If you stick bound charges in a new
field D, D-field lines emanate from
free charge
Also
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Maxwell equations II – curl
Ampere’s law
Current generates magnetic field
Separate free current, and bound current in D
Faraday’s law (and Lenz’s law)
A time-changing magnetic flux induces E-field
across enclosing curve (electromotively induced voltage).
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Maxwell together
Optics is charge-neutral
Current: only used to
describe light sources
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Optical materials
Maxwell’s equations Material properties
+
Matter enters only via the constitutive relation
Nanophotonics controls light via matter
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Wave equation
Source free Maxwell - curl one of the curl equations
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Simple matter
Plane waves solve Maxwell in free infinite space
Obviously divergence free if
Means that
Transverse wave, with perpendicular,
righthanded set
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Simple matter
Plane waves solve Maxwell in free infinite space
Means that
Dispersion relation:
Refractive index:
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Plane wave
righthanded, perpendicular set
Transverse wave
Propagation speed , with the refractive index
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Energy density and Poynting
vectorSubtracting Maxwell curl equations after dotting with
complement
Integrate over volume, use Gauss theorem
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Poynting’s theorem
Charge x velocity x force/charge
Work done, or work delivered
by a source or sink
Poynting vector – flux integral Energy density in the field
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Plane wave
k
B
E
Poynting vector S = E x H along k
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Working definition of nano-optics
“Optics” means
w = 1013- 1015 rad/s
“Nano” optics often means:
controlling light to be very different from a plane wave
by arranging n(r) on length scales << 2pc/w (vacuum wavelength)
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Geometry matters
Periodically perforated Si confines light to within l/4 or so
How strong is the ‘potential’ set by ? (Si: =3.5)
How slow or fast does the wave travel ?
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Measurement of guiding &
bending
33
Sample: AIST JapanMeas: AMOLF
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Squeezing light into a metal
Mode width 150 nm
SPP-l < 1 µm
At l = 1.550 µm
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Controlling light by controlling material (e,m) in space
is like
controlling wave functions by engineering potential landscapes
Question 1: what does light do at boundaries of material?
Question 2: what values of n, e,m are available?
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Boundary conditions
Take a very thin loop
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Boundary conditions
for a thin pillbox
(so jumps by )
Take a very thin pilbox
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Optical materials
Optics deal with plane waves of speed
with
Insulators: transparentMetals: reflective
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What e does nature give us
0.4 0.7 1.0 1.3 1.6 1.9
-1
01
2
3
4
Metamaterial
(Nature (2008))
GaAs
Si
TiO2 (pigment)
glass SiO2
Silicon nitride Si3N
4
Re
fra
ctive
in
de
x
Wavelength (micron)
B
Water
Density raises
Semiconductors help
All ’s between 1 and 4
Vacuum = 1
Spoof (later class)
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Solving our first problem
This class:
Refraction at a single interface
Next class:
Guiding light by interfaces
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Refraction
Archetypical problem: Fresnel reflection & refraction
1. Monochromatic solution means one chosen w 2. Note that the wavelength is different in medium 1 and 23. Incident angle translates into parallel momentum k||
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Snell’s law
Generic solution steps:Step 1: Whenever translation invariance: Use conservation
to find allowed refracted wave vectors
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Sketch of k|| conservation
k|| conservation:
The only way for the
Phase fronts to match
everywhere, any time
on the interface
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Sketch of k|| conservation
k|| conservation:
The only way for the
Phase fronts to match
everywhere, any time
on the interface
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Amplitudes
Symmetry does not specify amplitudesStep 2: Once you have identified the solutions per domain
Tie them together via boundary conditions
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Amplitudes
1. Causality excludes non-physical solution parts2. Solid algebra solves amplitudes
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Amplitude s-polarization
Remember
Now eliminate t to obtain reflection coefficient r (equal m)
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Amplitude s-polarization
Shorthand
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Amplitude p-polarization
Suppose now that is coming out
of the screen.
The rules are the same:
is conserved,
and are continuous
exercise
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Fresnel reflection
From air to glass From glass to air
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Fresnel implications
Miles Morgan photography
Reflective
Transmissive
Fiber –
guides light
Evanescent-tail microscopy
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What you see from this problem
Scattering: incident field (plane wave) is split by object e(r)
Translation invariance provides parallel momentum conservation
Boundary conditions determine everything to do with amplitude
Total internal reflection: if wave vector is too long to
be conserved across the interface
Exercise: total internal reflection still means evanescent field
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Take home messages
Nano-optics is about controlling light [w~1015 s-1] and matter
at the scale of nanometers [10-9 m]
The spatial distribution of matter e, m controls light fields
Maxwell’s wave equation – not ray optics
Fresnel problem, k|| conservation, causality & E||, H|| match
Next week - what causes e & how to trap light