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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)

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

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

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

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

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