Sub-meV optics for medium energy X-ray spectroscopy: Principles and preliminary studies

XianRong Huang

Advanced Photon Source, Argonne National Laboratoryxrhuang@aps.anl.gov

I. Angular dispersion optics using grazing backscattering

II. Multi-cavity Fabry-Perot interferometry

Thanks to Yuri Shvyd’ko (APS) and D. Peter Siddions (NSLS) …

Sub-meV-resolution optics at medium energy (5-10 keV)

Inelastic X-ray Scattering (IXS):

• Higher energy transfer resolution

• Higher momentum transfer resolution, filling the gap between high and low frequency probes

• Higher brightness at medium energy for many synchrotrons, particularly for NSLS-II

For ~1 nm focusing, may also need narrow energy bandwidths Coherent imaging (coherent length = 2/) High resolution X-ray diffraction…

Backscattering has the highest resolution:

Even ~1 meV mono/analyzer for E <10 keV not realized yet!

• FWHM 1meV for E 20 keV• but FWHM > 30 meV for E < 10 keV• Overall, FWHM when E

High energy resolution optics:a) Monochromator b) Analyzer c) …

based on single-crystal diffraction

Toellner et al, APL 71, 2112 (1997). E = 14.4 keV, E = 0.8 meV Acceptance 8.6 rad

E = 14.4 keV, E ~ 0.1meV!!! Acceptance 6.4 rad Yabashi et al, Rev. Sci. Instrum. 72, 4080 (2001) How about <10 keV???

For E >10 keV, 1 0.1 meV possible using multi-crystal diffraction, but small angular acceptance, a few rad, so NOT for analyzers!

Goals: Sub-meV at E < 10 keV with wide angular acceptance Applicable for both Mono and Analyzer

I. Angular dispersion optics using grazing back diffraction

Backward CDS geometry

Shvyd’ko’s designsPRL 97, 235502 (2006); NSLS-II

In-line (forward) CDDS geometry

Optics does not depend on Darwin Curve Width

In asymmetric x-ray diffraction,the crystal is a natural “prism”.

Dispersion of light by prism:

Incident white light decomposed into component colors. Red light refracted less than violet, so propagating in different directions.

White incidence

Polychromatic

Refraction-based

Diffraction-basedX-ray dispersion

0 0

0 0

, h hx x x

x x hx hx

k k h

K k K k

k k h 0hx x xK K h

Conservation of tangential momentum

2 2 2cos cos sine d

sincos cose d

Relationship between wavelength and incident/exit angles

Bragg law: Kh K0 + h

Angular dispersion in asymmetric diffraction

sincos cose d

sin

sine

ed

= const

No dispersion in symmetric reflection ( = 0 e )

Dispersion coefficient increases with e 0, grazing-exit geometry

DuMond diagramS. Brauer et al. JSR 2, 163 (1995)

sin tan

sin(90 )e

d d

2 tane

H

E

E

2H

hcE

dwhere

A geometry effectIndependent of the Structure Factors and Darwin curve, so also applicable to higher energy optics!

sin

sine

ed

To maximize resolution: 90°, e 0

Grazing backscattering

e

2 tane

H

E

E

For Si 008 reflection: EH 9.1 KeV

If angular acceptance of selector e = 5106 rad

= 88.5 E = 0.6 meV = 89.6 E = 0.16 meV

for a single dispersing crystal

90°

We can use (1) two dispersing crystals (described later) or (2) reduce e or (3) further increase (but must not exceed the critical angle ~89.8°) to achieve 0.1 meV!

CDS scheme

DuMond DiagramShvyd’ko et al., PRL 97, 235502 (2006)

C S

D

Transmission through the thin crystal due to

Bormann effect

Si 220, B = 20.7Asymmetric factor |b| 20

Acceptance ~100 rad 5rad divergence of diffracted

Si 008

Angular acceptance~ 5 rad

0.6 meV 2

CDS scheme

Si 220, B = 20.7

R(E, 1)

sincos cos

d

Full calculation using dynamical theory

R(E, 1) = R1(E, 1) T2(E, 2) R3(E, 3) R4(E, 4)

Totalreflectivity

= 88.5 E = 0.6 meV = 89.6 E = 0.16 meV

Predicted

Calculated with 1 = const

Back diffraction reflectivity ~ 90% for 89.79º, close to the critical angle!!!Because b -1.

1

Angular acceptance~ 87 rad

> 100 rad for = 88.5°

= 89.6°

Energy Tuning

Selectorfixed

Energy tuning

Tuning rate 0.07 meV/rad

2 tanH

E

E

for a single dispersion crystal

In-line (forward) CDDS scheme

4 tanH

E

E

Resolution doubledfor two D-crystals

Full dynamical theory calculations

Inline forward CDDS

steep wingone side

Backward CDS

Horizontal divergence?

0hx x xK K h Conservation of tangential momentum

2 2 2cos cos sine d

sincos cose d

To treat incidence deviated by a small angle in the horizontal plane, replace 2/ with

(2/)cos = (2/)(1 2/2...) Modification negligible when < 1 mrad

Experimental verification

Shvyd’ko et al., PRL 97, 235502 (2006)Shvyd’ko et al., SRI 2007

= 88.5°

X-ray transmission topographs of selector (thin crystal)

on peak

off peak

X. R. Huang et al., to be published

Technical issues

1. Long dispersion crystal (segmented)

0.1 meV, E/E ~ 10-8 d/d ~ 10-8

temperature stability and homogeneity ~1 mK

Thermal coefficient of Si: 2.5610-6 K-1

No bending of the entire long crystal, < 1rad How to mount? (gravity)

Surface roughness of long crystals?

No strict requirement for the stability of the undulator beam

2. Thin crystal

Alternative designs?

sin

sine

ed

sin80o = 0.985sin89.6o =0.99997563

General CDS

Spectrum of General CDSfor collimated incidence

compared with 0.18 meV (59%) for CDS

compared with 87 rad for CDS

Unfortunately!

How to increase acceptance?

Add another collimator C to increase acceptance by a factor b, say 30

But also increases

crystal lengths by b !!!

The long crystals not shortened (for mono, could be shortened) Efficiency less than CDDS.

Acceptance > 100 rad

More flexible, many variants Avoid multi-beam diffraction Arbitrary energy Scan in wide energy range More suitable for monos!

Pros:

Cons:

More work is undergoing to optimize and to shorten the crystals

Yabashi et al, E = 14.4 keV, E ~ 0.1meV!!!

C1

C2 D

S

Conclusion of Angular Dispersion Optics

Sub-meV resolution optics ~ 0.1 meV with angular acceptance ~ 100 rad is feasible based on the Angular Dispersion Principle in asymmetric x-ray diffraction, no doubt in principles.

Backward CDS In-line forward CDDS

o Both using grazing back diffraction: E/E independent of E or Bragg reflection.

o The smaller the photon energy E the smaller is the bandpass E.o For a fixed E, E can be varied by changing (crystal lengths change

though).o Efficiency R and the Acceptance almost constant (while changing ).

Multiple-crystal CCDS For both monos and analyzer (combined with mirrors) Long crystals, strain free, temperature, no bending, mounting

II. Multi-cavity Fabry-Perot Interferometer

In optics, a Fabry-Pérot interferometer typically made of two parallel highly reflecting mirrors:

For normal incidence = 90º

Free spectral range Ed 0.5hc/tc

Finesse F = Ed /E R1/2/(1 R)

Spectrum

No large-angle X-ray mirrors!

Using diffraction reflectivity, particularly back diffraction

X-ray interferometer

Dynamical theory

Dynamical theory simulation

Chang SL et al., PRL 94, 174801 (2005)Shvyd’ko et al., PRL 90, 013904 (2003).

Experiments:

Si (12 4 0), t = 70 m, tc = 520 m

Tough requirement of pre-monochromator

Solution: Increase Ed. Ed 0.5hc/tc

by shrinking the cavity distance tc

5 meV pre-monochromator is practical,but spectrum is not clean (and E increased).

tc decreased to 80 m from 520 m

Solution: to increase Finesse? F = Ed /E R1/2/(1 R)

i.e. to increase R, but this is difficult

True solution: using two cavities

(a) Two-cavity resonaotor.

(b) t1 = 45 m

t2 = 90 m

tc = 81 m.

(c) t1 = 60 m (R increased)

t2 = 120 m

tc = 81 m

Si (660), E = 9.69 keV

How to further increase the energy resolution?

Three-cavity interferometer

Compact, single-component,tiny yet powerful

Si (12 4 0) E = 14.4 keV

~ eV

Angular acceptance

t1 = 60 m

t2 = 120 m

tc = 81 m

Physical size limited

Substantial undercut on the outside wallis largely corrected this time, withoutmessing up the verticality of the inside wall.

Note that we etched deeper than 100 microns.

There is still some bowing near the corner of the structure, but there is a way to address that.

How to avoid Absorption & Multi-Diffraction?

Multi-cavity interferometers suffer absorption

Diamond

Low absorption

High reflectivity (very close to unity)

High Debye-Waller temperature

Hard, resistance to bending, strains

Fabrication???

Sapphire: avoid multiple diffraction

more energy choices

quality concern

Thank you!