Universal optimal transmission

of light through disordered materials

Allard MoskMESA+ Institute for NanotechnologyUniversiteit Twente

Literature

• Reviews:J.B. Pendry, Physics 1, 20 (September 2008) , “Light finds a way through the maze”J. Miller, Phys. Today 61, 20 (September 2008), “Shaped light waves can pass through opaque material”

• Experimental work:I.M. Vellekoop and A.P. Mosk,Universal optimal transmission of light through disordered materialsPhys. Rev. Lett. 101, 120601: 1-4 (2008).

I. M. Vellekoop, E.G. van Putten, A. Lagendijk and A. P. Mosk,Demixing light paths in disordered metamaterialsOpt. Express 16, 67-80 (2008).

I. M. Vellekoop and A. P. Mosk,Focusing coherent light through opaque strongly scattering mediaOpt. Lett. 32, 2309-2311 (2007).

• All references can be found onhttp://cops.tnw.utwente.nl

CoworkersIvo Vellekoop - Ph.D. Student (FOM-PR)

Elbert van Putten - Ph.D. Student (NWO-Vidi)

Ad Lagendijk - AMOLF & Twente

Willem Vos - AMOLF & Twente

Complex Photonic Systems (COPS)MESA+ Institute for Nanotechnology, University of Twente

Some preliminary context

What makes white materials opaque

glass is clear glass is opaque

Nanostructure changes optical properties

Scattering is nasty problem

Focus lighthere

Start here

impossible because of scattering

Outline

• How interference can bring light to a focus

• Focusing through opaque materials

–Contrast

–Resolution

–Conservation of energy

• Focusing inside opaque materials

• Conclusion

Speckle

Sample: 10 µm layer of titanium dioxide paint.Transmitted light has random phaseRandom interference pattern: laser speckle

Low intensity, no resolution.

Guide light by interference

sample

target

Divide incomingwavefront in N segments

total field in target

N~8A/λ2

Electric field in target

Linear problem

field at targetfield from phase

modulator segment a

random, uncorrelated

scattering coefficients

N independent parameters φa

Graphical representation

Re E

Im E

contribution of

segment 1contribution of

segment 2

contribution of

segment N

Maximize Eb

Guide light by interference

samplephase modulatorwith N segments

target

total field in target

Algorithm

Adjust phase of individual segments

until contribution is in phase with total field

Global maximumbefore after

all the same phase

global maximum

Experimental results

measured transmission (normalized by average diffuse intensity)

Opaque objects focus light: Opaque lens

Vellekoop & Mosk. Optics Letters 32, 2309 (2007)

Intensity of focus

Saturation:Sample changesin time

Works for all white solids

teeth (ex vivo)

daisy petals(fresh)

Scotchtape

eggshell

poroussemi-conductor

paint(dry)

chicken breast(prepared)

next step:human skin?

Successfully focused light through:

Conservation of Energy

If we optimize and make a focus:

a. Background transmission reduced?• (energy removed from other transmitted channels)

b. Background transmission same?• (true if all elements of tab uncorrelated)

c. Background transmission grows?• (no intuitive reason why this should happen)

Option (a) seems likely

samplephase modulator

target

Are these two situations equivalent?

Setup for perfect wavefront control

We need as much control over the incident wave as possible:

– 2 polarizations

– High NA

– Small sample area

Before and after

before

after

The counter-intuitive case (c) is correct

Mesoscopic desription of diffusion

The random sample ismodeled as a waveguidewith disorder

Transmission matrix tab : coupling between 8 (HW)/2

channels, on left and right sides of the waveguide.

Strong parallels exist between transport of photons and electrons (Pendry, Beenakker, van Houten)

Transparency eigenvalues

t: symmetric and complex NxN matrixnot a normal matrix -> eigensystem not complete

The matrix tt † is Hermitian:Has N eigenvalues, “channel transparencies” t2.

Interpretation: t2 is integrated transmissionfor an incoming eigen-wavefront.

Energy conservation: 0< t2 <1

Bimodal transparency distribution- Dorokhov (1984) calculated

transparency distribution

for quasi-1D

- Pendry (1990):

“Maximal Fluctuationprinciple”

MANY closed channelsTransparency eigenvalues 0 FEW open channels

VERY FEW modes withaverage transmission

0.0 0.5 1.0 P

robabili

ty d

ensity

Transmission eigenvalue t

Almost maximum fluctuations• Optimization selects transparent channels-> Transmission increases to 1 in ideal case.

But:- Channels not all completely transparent- We control phase but not amplitude

->Expect 2/3 transmission when we control the incident phases for 100%.

– Vellekoop & Mosk, arXiv:0804.2412

More control, more transmission

Line extrapolates

to T=0.64

We find a similar value

0.67(17)

for thicker samples

Direct evidence for

bimodal distribution of

transmission coefficients

Numerical simulation tovisualize optimized transport

Simulated using MEEP software; Fardapour et al. Optics Letters 31 (20), 2972–2974 (2006).

Focusing inside

Focus lighthere

Start here

Need feedback!

Focusing inside

• Guiding light through opaque objects is impossible without feedback

• Use fluorescent probe particle (150 nm)

shapedwavefront

Focusing inside!

Fluorescence from embedded 300 nm sphere

size of sphere (same scale)

plane wave shaped wave

Deep focussing

Ballistic intensity(assuming all geometricaberrationsare corrected)

wavefront shaping

Vellekoop, van Putten, Lagendijk & Mosk. Opt. Expr. 16, 67 (2008)

Depth of sphere (mean free path)

Conclusion

• New method for bringing light to a focus– Focus light through variety of materials– Scattering can improve resolution– Focus light inside opaque objects

• Possible applications– Mesoscopic physics– Tissue optics– Microscopy– Nonlinear optics

Vacancies for Ph.D. students!

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