1

Nanophotonics

Femius KoenderinkCenter for Nanophotonics

AMOLF, Amsterdam

f.koenderink@amolf.nl

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

Me: f.koenderink@amolf.nl

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:f.koenderink@amolf.nlhttps://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

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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

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

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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

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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

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 ?

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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