Workshop on "X-ray Science with Coherent Radiation"

F. Pfeiffer^a, Yugang Sun^b, Younan Xia^b, and I.K. Robinson^c

^aSwiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland.

^bDepartment of Chemistry, University of Washington, Seattle, WA 98195-1700, USA.

^cDepartment of Physics, University of Illinois, Urbana, Illinois, 61801, USA.
X-ray crystallography has been proven to be an extremely efficient investigation method to solve the structure of matter at the atomic scale. Although several methods have been employed to circumvent the intrinsic phase problem, other limitations do exist for classical x-ray crystallographic methods. In particular, disordered materials, single nanostructures, or noncrystalline and/or nonrepetitive biological structures (e.g. some important viruses or proteins) cannot be accessed by this approach.

As first considered by Sayre et al. [1], a combination of coherent x-ray diffraction with a so-called oversampling phasing method can overcome these limitations. In a first demonstration experiment, Miao et al. used that method to invert the soft x-ray forward-scattering pattern measured from a fabricated object [2]. More recently, the reconstruction of 2D and 3D crystalline and non-crystalline (!) structures has been reported [3, 4]. Particularly the latest results from Williams et al. [5], where the complete 3D phase and shape information of a micrometer-sized gold crystal could be retrieved, impressively demonstrate the high potential of this nondestructive method. With the work presented in this poster we particularly focus on the feasibility of pushing the limits of imaging small crystals by using coherent x-ray diffraction into the nanometer range.

As demonstration samples we have used chemically synthesized, single crystalline silver nanocubes with an average typical size of 175 nm [6]. The coherent x-ray diffraction experiments have been carried out at the ID34/UNICAT beamline at the Advanced Photon Source (Argonne) using monochromatic x-rays with an energy of 8.5 keV.

In order to have both sufficient flux and the opportunity to select single nanocrystals a Kirk Patrick-Baez (KB) mirror system has been used to focus the x-ray beam to typically 1.0 x 1.5 at the position of the sample. The diffraction data was recorded using a CCD placed at a position corresponding to the 111 Bragg reflection of the silver crystal lattice.

The following major conclusions could be drawn from the experimental results: Firstly and most importantly, the high-resolution reciprocal diffraction patterns clearly demonstrate the feasibility of carrying out such measurements on single nanocrystals with a size in the nanometer range. Depending on the orientation of the individual nanocrystals the measured diffraction patterns showed a nice three- and fourfold symmetry and up to typically 5-10 high contrast interference fringes in directions corresponding to the facets of the cubic structure. Furthermore we have not found any negative effects on the trasverse coherence by using the experimentally crucially important KB focusing optics. Finally, the obtained results agree well with model calculations based on a simple Fourier transform of two-dimensionally projected single silver nanocube.

Encouraged by this successful first demonstration experiment of coherent x-ray diffraction on sub-micrometer single crystalline nano-objects we are currently working on the direct reconstruction of a full 3D diffraction data by using the oversampling phasing method.

Poster Abstracts
[1] D. SAYRE, Imaging Processes and Coherence in Physics, Springer Lecture Notes in Physics Vol. 112, 229 (1980).

[2] J. MIAO, P. CHARALAMBOUS, J. KIRZ, and D. SAYRE, Extending the Methodology of X-ray Crystallography to allow Imaging of Micrometer-sized Non-crystalline Specimens, Nature 4000, 342 (1999).

[3] J. MIAO, T. ISHIKAWA, B. JOHNSON, E.H. ANDERSON, B. LAI, and K.O. HODGSON, High Resolution 3D X-ray Diffraction Microscopy, Phys. Rev. Lett. 89 (2002).

[4] I.K. ROBINSON, I.A. VARTANYANTS, G.J. WILLIAMS, M.A. PFEIFER, and J.A. PITNEY, Reconstruction of the Shapes of Gold Nanocrystals using Coherent X-ray Diffraction, Phys. Rec. Lett. 87, 19 (2001).

[5] G.J. WILLIAMS, M.A. PFEIFER, I.A. VARTANYANTS, and I.K. ROBINSON, Three-dimensional Imaging of Microstructure in Gold Nanocrystals, Phys. Rev. Lett. 90, 17 (2003).

[6] YUGANG SUN and YOUNAN XIA, Shape-Controlled Synthesis of Gold and Silver Nanoparticles, Science 298, 2176 (2002).

Coherent Soft X-ray Branchline at the Advanced Light Source
Kristine Rosfjord^1,2, Charles Kemp¹, Paul Denham¹, Eric Gullikson¹, Phillip Batson¹,

Senajith Rekawa¹, David Attwood<sup>1,2

1</sup>Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

²Electrical Engineering & Computer Science Department, UC Berkeley, Berkeley, CA 94720
A new coherent soft X-ray branchline at the advanced light source has begun operation. Using the third harmonic from an 8cm period undulator, this branch delivers coherent soft x-rays ranging from 200eV to 1000eV. There are two sub-branches, one with 8x demagnification and optimized for 800eV and the other with 14x demagnification and optimized for 500eV. The monochromator consists of a variable-line-spacing grating and an exit slit, enabling a bandwidth of 0.1%. Soft X-rays have been propagated through the exit slit of the monochromator, matching spectral features of nitrogen (410eV) and titanium (454eV). We are currently working to characterize the spatial coherence properties of this radiation. We have shown single pinhole Airy patterns, and by the time of the workshop we expect to have performed two-pinhole interference measurements of the transverse coherence length.

Near-diffraction limited coherent X-ray focusing using planar refractive lenses made in epoxy resist SU8.
I. Snigireva*, A. Snigirev*, V. Nazmov**, E. Reznikova**, M. Drakopoulos*, J.Mohr**, V.Saile**, V. Kohn***

* ESRF, BP-220, 38043 Grenoble Cedex, France

** Institut für Mikrostrukturtechnik, FZK, 76021 Karlsruhe, Germany

*** Russian Research Centre “Kurachatov Institute“, 123182 Moscow, Russia.
We present results on optical properties of high resolution planar refractive lenses studied with hard X-ray coherent radiation. Large aperture (up to 1mm) and high aspect ratio planar parabolic lenses were manufactured in epoxy type SU8 resist using deep synchrotron lithography. Resolution of about 250 nm was measured for the Su8 lens consisting of 62

Poster Abstracts
individual lenses at 14 keV in a distance of 58 m from the source. In-line holography of B-fibber was realized in imaging and projection mode with a magnification of 3 and 20 respectively. Submicron features of the fiber were clearly resolved. Coherent properties of the set-up allow to resolve near-focus fine structure in scanning and imaging mode with lens defocusing. This fine structure is determined by the tiny aberrations caused by lens imperfections close to the parabola apex.
Quantum-Deceleration Self-Modulation of High Energy Electron Beam

and the Problem of Optimization of Coherent Photon Collider
Vladimir I. Vysotskii, Mickle V. Vysotskii

Kiev Shevchenko University, Radiophysical Faculty, 01033, Kiev, Ukraine

The problems of creation of a sources of coherent hard radiation and high energy photon colliders optimization were studied. It is well known that low efficiency of gamma-gamma colliders is the result of very low cross-section of laser quanta scattering on relativistic electrons. The method of controlled non-threshold quantum-deceleration self-modulation of high energy electron beam in space (space period of self-modulation equals ) and time (frequency of modulation equals  = 2v/) with effectiveness about 1 for photon-electron scattering is discussed. The result of colliding resonant interaction of this modulated electron beam and optical laser beam with intensity J₀, wave-length  and frequency ₀ is generation of intensive gamma-beam with frequency of gamma-radiation =4²₀ and intensity J=KJ₀.

The method of self-modulation of electron beam is the following. The total wave function of each electron of the nonmodulated beam after passing of this beam through thin periodical diaphragm with thickness L_0­ and period D₀+D₁ (see fig.) has the form of coherent superposition

( r_, z>L₀,t_­)=₀(r_, z, t_­) + ₁(r_, z,t) = ₀(r_) exp[-i2(E₀t-p₀z)/]+₁(r_)exp[-i2(E₁t-p₁z)/].

Here ₀(r_,z,t_­) is the wave function of an electron which has passed through one of microholes (with size D₀) in diaphragm; ₁(r_,z,t_­) is the wave function of an electron which has passed through one of the absorptive parts (size D₁) of this diaphragm and has reduced energy E₁=E­₀-E(L₀). Here E(L₀)=E₀L₀/L^c_rad; L^c_rad<< L_rad is a coherent radiation length of diaphragm crystal; E₁=E­₀-E(L₀) and p₁=p₀-p(L₀) are longitudinal energy and impulse of each electron in the state ₁; E₀=mc², p₀=mv; p(L₀) = p₀ - {[E₀-E(L₀)]² - m²c⁴}^1/2/c  E(L₀)/c(²-1)^1/2.

The phenomenon of non-threshold quantum-deceleration self-modulation of electron beam takes place in the region of mutual coherence L_iz L_coh of electron eigenfunctions _0,1((r_, z,t_­).

Here L_i  (D₀+D₁)/_d = 2mv(D₀+D₁)²_­/; L_coh  ²Q = Q. 

Poster Abstracts
For this region the electron concentration and current density of electron beam have the forms of relativistic electron quasicrystal and n(z,t)=|₀(r_,z,t_­)+₁(r_,z,t)|²;

j_z(r_,z,t)=(ie/4m){d^*/dz-^*d/dz}=j₀{1+gexp[i(t-kz)]+g*exp[-i(t-kz)]}.

Here j₀= (ep₀/2m)[|₀|²+|₁|²]; g =₁₀*/(|₀|²+|₁|²),  = 2E(L₀)/,
k=2^-1=2p(L₀)/, Q=E₀/[<(E₀)²>+<(E₁)²>]^1/2 is the quality of the electron beam,

E_i is a fluctuation of energy E_i.

For the optimal case of symmetric diaphragm (D­₁=D₀, <|₀(r_)|²>_r=<|₁(r_)|²>_r) we have the phenomenon of total electron beam self-modulation and formation of “running electron periodical lattice” n(z,t) = n₀{1+cos (t - kz)}; j_z(z,t) = j₀{1+cos (t - kz)}; n₀  |(z=0)|².

For realization of a requirement of a Bragg interaction (Bragg diffraction) of laser beam with wave lengh ₀=4²=4²/p(L₀) and this electron beam with period of modulation  the condition of Bragg diffraction L₀=4L^ñ_rad/₀mc in back direction = is necessary. For the case of periodical diaphragm made of zeolite-like crystal (L^c_rad<<1 cm, D₀D₁20 A) and at laser wave-length ₀=1m we need L₀10^-5 L^c_rad  cm. The total cross-section  of diffraction of laser beam on this modulated beam and the total coefficient K of reflection (coefficient of diffraction) of laser beam with cross-section S equal K=/S,

_max=(d/do)do=2(e²/mc²)²n₀²S(L_coh-L_i)²2S(e²²n₀Q/mc²)². 

For the laser beam with total cross-section S=10^-4 cm² and wave-lengh ₀=1m and for the case of relativistic electron beam with electron density n₀=10¹⁴ cm^-3 and quality Q=10⁴ we have L_coh   cm, L_i10^-3  cm, _max10^-5 S and K_max=10^-5 that by many order of magnitude more that in the case of usual non Bragg-like gamma-gamma colliders.