Nanophotonics. Nanoscale: propagation, absorption & emission of light (beyond mirrors & lenses)

Transcription

1 Nanophotonics Nanoscale: Photonics: 10-9 meter science of controlling propagation, absorption & emission of light (beyond mirrors & lenses) Femius Koenderink Center for Nanophotonics AMOLF, Amsterdam

2 About length scales Geometrical optics Domain of e-, not ħw 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 Nano: Range around and just below the wavelength of light well above the length scales of atoms & solid state physics

3 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.?

4 Dreams 2: computing Classroom full 1 addition/sec flops/sec Single molecule Transistor? Shrunk (10 8 ).. Moore s law ends where?

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6 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,

7 Dream 4: seeing small stuff 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) PALM, STORM: beat Abbe limit by seeing a single molecule at a time Using a stochastic on/off switch to keep most molecules dark

8 Dream 4: seeing small stuff Detecting single molecules [Detuning of a resonance by a single molecule]

9 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

10 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?

11 My own fascination with nanophotonics Resonant Nanophotonics AMOLF Controlling photons with nanoantennas Femius Koenderink Center for Nanophotonics FOM Institute AMOLF, Amsterdam

12 Single molecules [Moerner & Orrit, 89] Keep on diluting molecules 100 micron 1 molecule can emit about 10 7 photons per second (1 pw) Observable with a standard [6k ] CCD camera + NA=1.4 objective

13 Spontaneous emission Matter Selection rules which colors & transitions Quantum mechanics Time How long does it take for ħω to appear? Space Whereto does the photon go? With what polarization? Maxwell equations

14 Ultimate control over light micrometers High Q nanometers Ultrasmall V Interference-based Material-based free-electrons

15 This course 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: Exercise help: TA indicated per week (rotates) Course slides & information available at:

16 Course calendar 1. What is nano, Maxwell, a first optical scattering problem Apr 3 2. Extreme confinement and dispersion with metals Apr Pulses and dispersion, causality, and invisibility cloaks Apr Photonic crystals 1 perfect mirrors from transparent stuff Apr Photonic crystals 2 semiconductors for light Apr 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]

17 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 Hybrid light-matter Exercise 7 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

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19 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

20 Maxwell equations I divergence Gauss s law Electric field lines emanate from charge If you stick bound charges in a new field D, D-field lines emanate from free charge Also

21 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).

22 Maxwell together Optics is charge-neutral Current: only used to describe light sources

23 Optical materials Maxwell s equations Material properties + Matter enters only via the constitutive relation Nanophotonics controls light via matter

24 Wave equation Source free Maxwell - curl one of the curl equations

25 Simple matter Plane waves solve Maxwell in free infinite space Obviously divergence free if Means that Transverse wave, with righthanded set perpendicular,

26 Simple matter Plane waves solve Maxwell in free infinite space Means that Dispersion relation: Refractive index:

27 Plane wave righthanded, perpendicular set Transverse wave Propagation speed, with the refractive index

28 Energy density and Poynting vector Subtracting Maxwell curl equations after dotting with complement Integrate over volume, use Gauss theorem

29 Poynting s theorem Poynting vector flux integral Energy density in the field Charge x velocity x force/charge Work done, or work delivered by a source or sink

30 Plane wave E k B Poynting vector S = E x H along k

31 Working definition of nano-optics Optics means w = 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)

32 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?

33 Measurement of guiding & bending Sample: AIST Japan Meas: AMOLF 33

34 Squeezing light into a metal Mode width 150 nm SPP-l < 1 µm At l = µm

35 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?

36 Boundary conditions Take a very thin loop

37 Boundary conditions Take a very thin pilbox for a thin pillbox (so jumps by )

38 Optical materials Optics deal with plane waves of speed with Metals: reflective Insulators: transparent

39 What e does nature give us Refractive index B Water Si GaAs TiO 2 (pigment) Silicon nitride Si 3 N 4 glass SiO 2 Metamaterial (Nature (2008)) Wavelength (micron) Density raises Semiconductors help All s between 1 and 4 Vacuum = 1 Spoof (later class)

40 Solving our first problem This class: Refraction at a single interface Next class: Guiding light by interfaces

41 Refraction Archetypical problem: Fresnel reflection & refraction 1. Monochromatic solution means one chosen w 2. Note that the wavelength is different in medium 1 and 2 3. Incident angle translates into parallel momentum k

42 Snell s law Generic solution steps: Step 1: Whenever translation invariance: Use to find allowed refracted wave vectors conservation

43 Sketch of k conservation k conservation: The only way for the Phase fronts to match everywhere, any time on the interface

44 Sketch of k conservation k conservation: The only way for the Phase fronts to match everywhere, any time on the interface

45 Amplitudes Symmetry does not specify amplitudes Step 2: Once you have identified the solutions per domain Tie them together via boundary conditions

46 Amplitudes 1. Causality excludes non-physical solution parts 2. Solid algebra solves amplitudes

47 Amplitude s-polarization Remember Now eliminate t to obtain reflection coefficient r (equal m)

48 Shorthand Amplitude s-polarization

49 Amplitude p-polarization Suppose now that is coming out of the screen. The rules are the same: is conserved, and are continuous exercise

50 Fresnel reflection From air to glass From glass to air

51 Fresnel implications Fiber guides light Reflective Transmissive Miles Morgan photography Evanescent-tail microscopy

52 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

53 Take home messages Nano-optics is about controlling light [w~10 15 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