nm science enabled by waveguides

Christian Fuhse, Christoph Ollinger and Tim Salditt

Institute of X-ray Physics, University of Göttingen (Germany)

Outline

Theoretical background● propagation of x-rays in waveguides● waveguide-based lensless imaging / holography

Imaging experiments● in-line phase-contrast imaging and in-line holography● off-axis holography

Outlook● Can we achieve 1 nm resolution by means of x-ray

waveguides?

dc≈2=

2e r e

2

X-ray waveguides

[Spiller & Segmüller, Appl. Phys.Lett. 24 (1974) 60]

θ n1

Re(n2) < Re (n

1)

n2

n2

Guided modes of a planar waveguide

standing waves → guided modes

n

n

n2

n2

z

xdd

(x)

(x)if

if

if

n1

n

n

n2

n2

n1

n

n

n2

n2

n1

Phase-contrast imaging

waveguide

sample

CCD camera

[Lagomarsino et al., Appl. Phys. Lett. 71 (1997) 2557]

12 µm

planar waveguide→ 140 nm spatial resolution in one direction

130 nm C

Cr

Cr

nylon fiber

≈ 500 µm

Two-dimensionally confining waveguides

[Pfeiffer et al., Science 297 (2002) 231]

„Resonant beam coupling“→ flux: 2 x 104 ph/s

beam dimensions 69 x 33 nm2

θr

PMMA Cr

waveguide

Probe

focusing device(Kirkpatrick-Baez mirrors, ID22)

1 – 3 µm

typical flux: 106-107 ph/s from 2D waveguides[Jarre, Fuhse, Ollinger, Seeger, Tucoulou, Salditt, Phys. Rev. Lett. 94 (2005), 074891]

synchrotron

beaml

Direct coupling of a focused beam

sample

CCD detector

30 – 100 nm

Direct coupling into 2D waveguides

E=8 keV[Fuhse & Salditt, Appl. Opt. (2006), in print]

0 0,5 1 z [mm]

x [n

m]

0 0,5 1 z [mm]

100

50

0

-50

-100

d = 40 nm

0 0,5 1 z [mm]

finite-difference field calculationsbased on the parabolic wave equation:

● strong absorption in the cladding● excitement of multiple guided modes● stronger damping of higher-order modes

→ field is dominated by the fundamental mode

d = 60 nm d = 100 nmx

[nm

]100

50

0

-50

-100

x [n

m]

100

50

0

-50

-100

0 2 4 I / I

0

PMMA

Si

d

d

Far-field pattern

● Far-field intensity (Fraunhofer approximation):

● guiding-core cross-sectional dimensions determine numerical aperture and

spatial resolution → spatial resolution ≈ diameter of the guiding core

2θ [deg]

2ω [deg]z

x

y

xy yxE(x,y)

Coherent imaging

point source

sampleplanewave

z1

z2 z

eff

sample

z

E1(x

1,y

1)

E2(x

2,y

2)

S1

S2

x x

y y

Kirchhoff's diffraction formula(Fresnel approximation):

zeff=z1 z2

z1 z2M =

z1 z2

z1

A PAbsorption Phase

edge enhancement

Imaging regimes

absorption & phase in “direct imaging”

A PAbsorption Phase

Imaging regimes

edge enhancement

absorption & phase in “direct imaging”

A PAbsorption Phase

hologram

Imaging regimes

edge enhancement

absorption & phase in “direct imaging”

“Direct” imaging of large objects

SEM

50 µm

gold structures (d=150 nm) → phase-shifting sample @E=10.4 keVtungsten wires ( ø 4.5 µm) → absorbing sample @E=10.4 keV

recorded image (E=10.4 keV)SEM

gold structures (d=150 nm) → phase contrast (edge enhancement)tungsten wires ( ø 4.5 µm) → absorption contrast

“Direct” imaging of large objects

50 µm

(SEM)

sample (Au, d=150 nm)hologram (11 individual exposures)

Imaging of smaller features

Imaging of smaller features

(SEM)

sample (Au, d=150 nm)hologram (11 individual exposures)

→ holographic reconstruction required

In-line holography

z z z

S

R

S S*

R

~ ~

reference beam signal wavephase-conjugate wave

”twin image“

recording: reconstruction:

sample

hologram hologram

Holographic reconstruction

phase of the reconstructed wave

(SEM)

sample (Au, d=150 nm)hologram (11 individual exposures)

Holographic reconstruction

resolution ≈ 360 nm→ but: d

WL < 100 nm

1,8

µm

phase of the reconstructed wave

(SEM)

sample (Au, d=150 nm)hologram (11 individual exposures)

sample

hologram

z z z

referencebeam

hologram

directimage

S S*

R

twinimage

Off-axis holography

→ direct image and twin image are spatially separated!

z1

z2

synchrotron

beam

Kirkpatrick-Baez mirrors

DoutD

in

Din≈ 100 nm < transversal coherence length

Dout ≈ 5 µm

M =z1 z2

z1

.

magnified off-axis hologram

2 waveguides

CCD camera

sample

Waveguide-based off-axis holography

Off-axis holography

off-axishologram

(E=10.4 keV)

phase of the reconstructed wave

(from 25 holograms)

tungsten tip(SEM)

Quantitative analysis

→ Phase of the reconstructed wave in quantitative agreement with the simulation!

100 nm

Quantitative analysis

→ Phase of the reconstructed wave in quantitative agreement with the simulation!

Summary: State of the art

● off-axis holography with two waveguides– better image quality– better spatial resolution ( ≈ 100 nm)– quantitative determination of the phase

(→ projected electron density)

● lensless imaging with a single waveguide:– “direct” imaging of large objects

(phase & absorption)– holographic reconstruction of smaller features

resolution ≈ 360 nm but: severe artifacts (“twin image”)

1,8

µm

20 µm

Perspectives

● 3D imaging: tomography:small numerical aperture → large focal depthlarge penetration depth (in particular in the hard-X-ray regime)

ERL seems to be a well-suited source!

● temporal resolution: single-shot experiments with highly-brilliant pulsed sourcesXFEL seems well-suited

● increase spatial resolution:cross-sectional dimensions of the guiding core

fundamental limit: ~ 10 nm

depending on the electron density of the utilized materials[C. Bergemann,H. Keymeulen and J. F. van der Veen, Phys. Rev. Lett. 91, 204801 (2003)]

● waveguide core dimensions determine NA of the waveguide beamspatial resolution ≈ core dimensions

● higher spatial resolution requires the evaluation of radiation scattered outside the waveguide beam

● measure coherent scattering dataproblem: loss of phase information

Can we achieve 1 nm resolution?

sample

waveguide

● waveguide core dimensions determine NA of the waveguide beamspatial resolution ≈ core dimensions

● higher spatial resolution requires the evaluation of radiation scattered outside the waveguide beam

● measure coherent scattering dataproblem: loss of phase information

use an additional bent waveguide beam as a referenceto measure the phase!→ solution of the phase problem ?→ How far can we bend the waveguides ?

Can we achieve 1 nm resolution?

waveguide

sample

Can we achieve 1 nm resolution?

NA = 2° → spatial resolution ≈ λ / 2NA ≈ 1.5 nm

bent to 1°losses: a factor of about 3

bent to 2°losses: a factor of about 15

beams from bent waveguides (Si/calixarene, d ≈ 60 nm, E=12 keV)(ROBL beamline, ESRF)

Acknowledgments

● Ansgar Jarre, Jens Seeger, Sebastian Kalbfleisch,(Insitute of X-ray Physics, Göttingen)

● ESRF:- ID22 (Remi Tucoulou) → imaging experiments- ROBL (Norbert Schell) → curved waveguides

● Institute of Material Physics, Göttingen:Talaat Al-Kassab (tungsten tips)

● German Federal Ministry of Education and Research (BMBF, grant no. 05 KS4MGA/9)

Comparison off-axis / in-line

Comparison of phase and intensity

intensity phase

far-fieldwithout sample

hologram ofthe sample

reconstruction(intensity)

reconstruction(phase)

Off-axis holography

Beam damage

Fabrication of x-ray waveguides

substrate

resist

e-beamexposure

development

evaporation of thetop cladding layer

lead tapesilver dag

incidentbeam

200 nm

beam

incident

4 mm