nanophotonics - amolf€¦ · about length scales 4 1 m you and your labtable 100 µm thickness of...
TRANSCRIPT
-
1
Nanophotonics
Femius KoenderinkCenter for Nanophotonics
AMOLF, Amsterdam
Nanoscale: 10-9 meter
Photonics: science of controlling
propagation, absorption &
emission of light
(beyond mirrors & lenses)
-
This course
2
1. Mondays 9-13: Lecture course (2h), 2h exercises
2. Thursdays 9-13: Lecture 2h, exercises (2h)
3. Labtour AMOLF: provisional: April 24
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
mailto:[email protected]://amolf.nl/research-groups/resonant-nanophotonics/uva-mastercourse
-
This course
1. Mondays 9-13: Lecture course (2h), 2h exercises
2. Thursdays 9-13: Lecture 2h, exercises (2h)
3. Labtour AMOLF: provisional May 1st
Exercise sets caveat:
A. Some exercises can be a lot of work [no exam]
B. Exercises & classes bunch in May
Reserve time & use the extra wrap-up exercise class
-
About length scales
4
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?
-
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
-
Motivation
Optical microscopybelow l/2 limit
Single moleculesinformation fromfluctuations
Spectroscopy
Distance ruler,vibrationsTHz, IR and VIS
Liu & AlivisatosBates & Zhuang [PALM, STORM]
Single photon sourcesQuantum information
Quantum informationin 1 photon can not be eavesdropped
-
High Q Ultrasmall V
micrometers
na
no
meters
Ultimate control over light
Interference-based Material-basedfree-electrons
-
Topics
1. What do you know about light, matter & optics ?
2. Plasmonics & guiding light
3. Scattering by small particles
4. Metamaterials
5. Microcavities
6. Photonic crystals
7. Emission of light, LDOS
8. Microscopy and Near field optics
-
- Light is a wave
- Light travels as rays in straight lines
- Wavelengths from 450 to 750 nm are recorded by your eye
- Optics: Light as characterized by color, refraction & reflection
- To first order: mirrors, lenses, prisms
- Matter enters as refractive index, scattering & absorption
-Molecules & atoms as sources
-Complicated stuff: interference, diffraction
-
19
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
-
Plane wave
righthanded, perpendicular set
Transverse wave
Propagation speed , with the refractive index
-
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
-
31
Ray optics
Rays in bulk media
- Refract - refractive index
- Reflect - metals reject light
Nano-optics
Waves, controlle by matter
scattering, interference,
diffraction, confinement
-
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
33
Sample: AIST JapanMeas: AMOLF
-
34
Squeezing light into a metal
Mode width 150 nm
SPP-l < 1 µm
At l = 1.550 µm
-
What ’s does nature give us ?
Why ?
What happens with fields at interfaces ?
-
Boundary conditions
Take a very thin loop
-
Boundary conditions
for a thin pillbox
(so jumps by )
Take a very thin pilbox
-
Refraction
Archetypical problemFresnel reflection & refraction
Let’s see if we can retrace how to solve this problem
-
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
-
Amplitudes
Symmetry does not specify amplitudesStep 2: Once you have identified the solutions per domain
Tie them together via boundary conditions
-
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
-
What you see from this problem
Scattering: incident field (plane wave) is split by object
Reflections: are specular whenever translation invariance rules
Refraction: Snell’s law is just wave vector conservation
Total internal reflection: if wave vector is too long to
be conserved across the interface
Boundary conditions determine everything to do with amplitude
-
What ’s does nature give us ?
Why ?
What happens with fields at interfaces ?
-
49
Optical materials
Optics deal with plane waves of speed
with
Insulators: transparentMetals: reflective
-
Insulators
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)
-
What it is all about
- Guiding light on scales of a integrated circuit
- Seeing ultrasmall things efficiently, such as a single
molecule
- Controlling transitions in matter by confining light around it
emission, absorption, lasing, switching of light
Our tools
- Light is not a ray
- Light is a wave
- Control interference by clever placing of materials is to
control light at a scale of l/20 to , and even smaller
-
Dielectrics
Dielectric materials:
All charges are attached to specific atoms or molecules
Response to an electric field :
Microscopic displacement of charges
Macroscopic material properties: electric susceptibility ,
dielectric constant (or relative dielectric permittivity)
-
Atomic polarization
Equation of motion of electron:
: damping coefficient for given material
: restoring-force constant
resonance frequency
Assume is varying harmonically, and also
-
Wave in a medium
In vacuum , so
In a medium consider response of electrons bound to
atom nuclei:
-
So that we find the refractive index of the dielectric:
- Number density helps
- Number of bound electron resonances per atom helps
- Free electrons ?
-
Typical solids
multiple resonances for electrons per molecule:
Where is the
oscillator strength or
(quantum mechanically)
the transition probability
is a complex number:
-
Typical solids
Absorption bands close to
intrinsic resonances
Real n to the red
also outside absorption
Most materials have ’normal
dispersion’, i.e.,
goes up with energy
is higher towards the blue
is higher towards short
Until you go through an absorption resonance
-
Quartz prism
goes up with energy
is higher towards the blue
is higher towards short
Stronger refraction towards the blue
(bad news for microscopy, photography, people with glasses)
-
What it is all about
- Guiding light on scales of a integrated circuit
- Seeing ultrasmall things efficiently, such as a single
molecule
- Controlling transitions in matter by confining light around it
emission, absorption, lasing, switching of light
Our tools
- Light is not a ray
- Light is a wave
- Control interference by clever placing of materials is to
control light at a scale of l/20 to , and even smaller