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Nanophotonics

Femius Koenderink Center 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

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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 ħω

Range around and just below the wavelength of light Well above the length scales of atomic & solid state physics

Nanoscopy

Nobel chemistry 2014

Blue LED Nobel Physics

2014

Information processing THz bandwidth & no loss Lighting & photovoltaics Efficiency Nanoscopy, spectroscopy Fast & noninvasive Quantum information Low loss & decoherence …

This course

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1. Tuesdays 13-17: Lecture course (2h), 2h exercises 2. Thursdays 13-17: Lecture 2h, exercises (2h) 3. Labtour AMOLF: provisional April 14th

Presentations & homework exercises count for final mark Me: f.koenderink@amolf.nl Exercise help: TA indicated per week (rotates) Course slides & information available at: http://www.amolf.nl/research/resonant-nanophotonics/ http://tinyurl.com/p3eep65

mailto:f.koenderink@amolf.nlhttp://www.amolf.nl/research/resonant-nanophotonics/http://www.amolf.nl/research/resonant-nanophotonics/http://www.amolf.nl/research/resonant-nanophotonics/

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

What do you know about light, matter & 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

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 vector

Subtracting 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

Photonics

Dispersion relation:

Refractive index: I use only relative and

Homogeneous media

Photonics Use spatial distribution of to - create confined modes in 0D, 1D and 2D - control dispersion & propagation - control emission & absorption of light

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 )

Refraction

Archetypical problem Fresnel 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 amplitudes Step 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 µ)

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

How could you engineer stuff ?

Break translation invariance: - random stuff creates a diffuse impression (paint) - periodicity creates diffraction orders (gratings) Confine light by internal reflection Boundary conditions control local field strength…

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: transparent Metals: reflective

Insulators

0.4 0.7 1.0 1.3 1.6 1.9-101

2

3

4

Metamaterial(Nature (2008))

GaAsSi

TiO2 (pigment)

glass SiO2 Silicon nitride Si3N4

Refra

ctive

inde

x

Wavelength (micron)

B

Water

Density raises Semiconductors help All ’s between 1 and 4 Vacuum = 1 Spoof (later class)

How comes about

The wave is slowed down by polarization induced in the matter

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)

Wave in a medium

In vacuum , so

In a medium consider response of electrons bound to atom nuclei:

Atomic polarization

Equation of motion of electron:

: damping coefficient for given material : restoring-force constant resonance frequency Assume is varying harmonically, and also

Back to waves

Inserting in wave equation gives

solution: with complex propagation constant with :

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)

Transparent media refractive index Scattering Confining, guiding,...

…Waves Can Scatter

here: a little circular speck of silicon

scattering by spheres: solved by Gustav Mie (1908)

small particles: Lord Rayleigh (1871) why the sky is blue

checkerboard pattern: interference of waves traveling in different directions

Multiple Scattering is Just Messier?

here: scattering off three specks of silicon

Not so messy, very different

the light seems to form several coherent beams that propagate without scattering (or diffraction)

Shrink λ by 20%

light cannot penetrate the structure at this wavelength! all of the scattering destructively interferes

3µm

Photonic Crystals in Nature

wing scale:

Morpho rhetenor butterfly

[ P. Vukosic et al., Proc. Roy. Soc:

Bio. Sci. 266, 1403 (1999) ]

Peacock feather

[J. Zi et al, Proc. Nat. Acad. Sci. USA, 100, 12576 (2003) ]

[figs: Blau, Physics Today 57, 18 (2004)]

http://www.bugguy012002.com/MORPHIDAE.html

[ also: B. Gralak et al., Opt. Express 9, 567 (2001) ]

Example

Periodically perforated Si confines light to within λ/4 or so How strong is the ‘potential’ set by ? (Si: =3.5) How slow or fast does the wave travel ?

Snell’s law with negative index

Does ‘negative index’ mean negative refraction of rays ?

S1 S2

Povray raytrace of Snell’s law

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Squeezing plasmons in a nanowire

Mode width 150 nm SPP-λ < 1 µm At λ = 1.550 µm

Verhagen et al. 2008

Microcavity examples • Whispering gallery mode resonators (e.g. Vahala, Caltech) • Silica microspheres Q ≈ 109

• Silica microtoroids on Si chip Q ≈ 108, V ≈ 10-11 - 10-10 cm3 fabricated by CO2 laser

melting of silica disk

30 µm

Cheating the diffraction limit

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)

Measurement of guiding & bending

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Sample: AIST Japan Meas: AMOLF

Single photons from single emitters

Single emitter Quantum dot, molecule

photon photon

Challenges: (1) Surely catching each photon in a single beam (2) Surely absorbing each photon from a beam

Addressing and seeing single molecules with unit efficiency

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Motivation

Single photon sources: Quantum information in 1 photon can not be eavesdropped

Microscopy: Single molecules at a time can circumvent the diffraction limit Information from fluctuations

Information processing THz bandwidth & no loss Lighting & photovoltaics Efficiency Nanoscopy, spectroscopy Fast & noninvasive Quantum information Low loss & decoherence …

Controlling single molecules

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 λ/20 to , and even smaller

Slide Number 1About length scalesSlide Number 3Slide Number 4This courseTopicsSlide Number 7Slide Number 8Maxwell equations I – divergenceMaxwell equations II – curlMaxwell togetherOptical materialsWave equationSimple matterSimple matterPlane waveEnergy density and Poynting vectorPoynting’s theoremPlane wavePhotonicsSlide Number 21Boundary conditionsBoundary conditionsRefractionSnell’s lawSketch of k|| conservationAmplitudesAmplitude s-polarizationAmplitude s-polarizationAmplitude p-polarizationFresnel reflectionWhat you see from this problemHow could you engineer stuff ?Slide Number 34Optical materialsInsulatorsHow comes aboutDielectricsWave in a mediumAtomic polarizationBack to wavesSlide Number 42Typical solidsTypical solidsQuartz prismSlide Number 46…Waves Can ScatterMultiple Scattering is Just Messier?Not so messy, very differentShrink l by 20% Photonic Crystals in NatureExampleSnell’s law with negative indexSqueezing plasmons in a nanowireMicrocavity examplesCheating the diffraction limitMeasurement of guiding & bendingSingle photons from single emittersSlide Number 59Slide Number 60Controlling single moleculesWhat it is all about