1
Nanophotonics
Femius KoenderinkCenter for Nanophotonics
AMOLF, Amsterdam
Nanoscale: 10-9 meter
Photonics: science of controlling
propagation, absorption &
emission of light
(beyond mirrors & lenses)
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
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….?
Dreams 2: computing
1939
1 Classroom full
1 addition/sec
2015
109 flops/sec
Shrunk (108 ) .. Moore’s law ends where?
Single molecule
Transistor?
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,…
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)
Dream 4: seeing small stuff
Detecting single molecules
[Detuning of a resonance
by a single molecule]
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
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?
Controlling photons with nano-
antennas
Femius Koenderink
Center for NanophotonicsFOM Institute AMOLF, Amsterdamwww.amolf.nl
Resonant Nanophotonics AMOLF
My own fascination with nanophotonics
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
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
High Q Ultrasmall V
micrometers
na
no
meters
Ultimate control over light
Interference-based Material-basedfree-electrons
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
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]
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
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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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
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).
Maxwell together
Optics is charge-neutral
Current: only used to
describe light sources
Optical materials
Maxwell’s equations Material properties
+
Matter enters only via the constitutive relation
Nanophotonics controls light via matter
Wave equation
Source free Maxwell - curl one of the curl equations
Simple matter
Plane waves solve Maxwell in free infinite space
Obviously divergence free if
Means that
Transverse wave, with perpendicular,
righthanded set
Simple matter
Plane waves solve Maxwell in free infinite space
Means that
Dispersion relation:
Refractive index:
Plane wave
righthanded, perpendicular set
Transverse wave
Propagation speed , with the refractive index
Energy density and Poynting
vectorSubtracting Maxwell curl equations after dotting with
complement
Integrate over volume, use Gauss theorem
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
Plane wave
k
B
E
Poynting vector S = E x H along k
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)
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 ?
Measurement of guiding &
bending
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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
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?
Boundary conditions
Take a very thin loop
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
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)
Solving our first problem
This class:
Refraction at a single interface
Next class:
Guiding light by interfaces
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||
Snell’s law
Generic solution steps:Step 1: Whenever translation invariance: Use conservation
to find allowed refracted wave vectors
Sketch of k|| conservation
k|| conservation:
The only way for the
Phase fronts to match
everywhere, any time
on the interface
Sketch of k|| conservation
k|| conservation:
The only way for the
Phase fronts to match
everywhere, any time
on the interface
Amplitudes
Symmetry does not specify amplitudesStep 2: Once you have identified the solutions per domain
Tie them together via boundary conditions
Amplitudes
1. Causality excludes non-physical solution parts2. Solid algebra solves amplitudes
Amplitude s-polarization
Remember
Now eliminate t to obtain reflection coefficient r (equal m)
Amplitude s-polarization
Shorthand
Amplitude p-polarization
Suppose now that is coming out
of the screen.
The rules are the same:
is conserved,
and are continuous
exercise
Fresnel reflection
From air to glass From glass to air
Fresnel implications
Miles Morgan photography
Reflective
Transmissive
Fiber –
guides light
Evanescent-tail microscopy
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
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