Title slide

Light-matter interaction

from: dielectric catastrophe

to: localization

dielectric response there is a wavevector there is dispersion density of states

Content

dielectric response there is a wavevector there is dispersion density of states

Dielectric response ...

Restriction to dielectrics

dielectric response no magnetic response no combined response

Restriction to linear response all amplitude-like observables scale with

a single, overall amplitude factor

all intensity-like observables scale with this factor squared

Light-matter interaction

Light sees variation in speed of light

Spatial variation in index of refraction

Describing wave propagation

Why not solving the wave equation

Problems:

1.often not possible

2.does not give necessarily insight

3.each case has to be done all over again

Non-stationary interaction

all our standard approaches fail unless:

• fully adiabatic

or

• fully diabatic

varying with time: very complicated

Stationary interaction from nowinteraction is time-independent

measurements might be time-dependent

Use symmetry

time reversal

Translational symmetry

If there is no translational symmetry

there is no wavevector

there is no dispersion relation

you only have eigenfunctions, and you have many of them

When is there a wavevector?

effective medium average over disorder lattice asymptotically free space

There is a wave vector

From now on:

there is a wavevector

dielectric response there is a wavevector there is dispersion density of states

There is a wave vector ...

We have translational symmetry Translational symmetry

full translational symmetry full translational symmetry after averaging lattice

Stationary

Unless I state explicitly otherwise:

stationary potential

stationary measurement

DC, no pulse, no frequency change, ...

Dielectric constant to first order Objects that can be polarized

polarizability density

Conclusion: is a measure for the interaction

Dielectric constant: local field effect

Lorentz-LorenzClausius-Mossotti (zero frequency)

Interaction in photonic crystals

volume fraction

photonic strength

Localization

Why not use larger wave length?

Strength in terms of refractive index

Assume no absorption: extinction = scattering

Assumption there is no background with index

Is this localization?

Where is the dispersion?

dielectric response there is a wavevector there is dispersion density of states

There is dispersion ...

Driven harmonically bound charge (2)

Force:

Equation of motion:

Long-time solution:

Everything known of HO's

Driven harmonic oscillators

frequencydampingchargemassdensity

We will lump them into 2 independent parameters

Minimize index of refraction

Overdamped system

Is this localization?

Delay plays no role

The delay time, or slowness, plays no direct role

Background is dispersive

real part of index of refractiondetermined by host

imaginary part of index of refractiondetermined by impurities

host scatterers

Photonic crystal waveguide

If there is a dispersion relation

Wavevector in the localization criterion is no problem

You give me a frequencyand I will look the wavevector up in the graph

waveguide, slab, sphere

single scatterer in waveguide, slab, sphere

Cross-section?

Is this localization?

Where is the density of states?

introducing groupthere is a wavevectorthere is dispersion density of states

Density of states ...

Local density of states

LDOS is real part of refractive index

You very often see:in localization criteria: Einstein relation

Misleading as dynamical effectscancel

For single scatterer S with T-matrix:

One should calculate

Criterion

introducing groupthere is a wavevectorthere is dispersion density of states

The end