Sub-15 nm beam confinement by two
crossed x-ray waveguides

doi:10.1364/OE.18.013492

Sub-15 nm beam confinement by two crossed x-ray waveguides

S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt »View Author Affiliations

Optics Express, Vol. 18, Issue 13, pp. 13492-13501 (2010)
http://dx.doi.org/10.1364/OE.18.013492

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Abstract

We have combined two high transmission planar x-ray waveguides glued onto each other in a crossed geometry to form an effective quasi-point source. From measurements of the far-field diffraction pattern, the phase and amplitude of the near-field distribution is retrieved using the error-reduction algorithm. In agreement with finite difference field simulations (forward calculation), the reconstructed exit wave intensity distribution (inverse calculation) exhibits a full width at half maximum (FWHM) below 15 nm in both dimensions. Finally, holographic imaging is successfully demonstrated for the crossed waveguide device by translation of a lithographic test structure through the waveguide beam.

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(340.7440) X-ray optics : X-ray imaging

ToC Category:
X-ray Optics

History
Original Manuscript: January 25, 2010
Revised Manuscript: March 18, 2010
Manuscript Accepted: April 27, 2010
Published: June 8, 2010

Citation
S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, "Sub-15 nm beam confinement by two crossed x-ray waveguides," Opt. Express 18, 13492-13501 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13492

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References

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000). [CrossRef] [PubMed]
S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004). [CrossRef] [PubMed]
C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006). [CrossRef]
H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focused X-ray fields," Nat Phys 2, 101-104 (2006). [CrossRef]
C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003). [CrossRef]
A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010). [CrossRef]
O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003). [CrossRef]
W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005). [CrossRef] [PubMed]
H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010). [CrossRef]
H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008). [CrossRef]
W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, "Demonstration of 12 nm Resolution Fresnel Zone Plate Lens based Soft X-ray Microscopy," Opt. Express 17, 17669-17677 (2009). [CrossRef] [PubMed]
C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005). [CrossRef]
T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008). [CrossRef] [PubMed]
F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002). [CrossRef] [PubMed]
L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008). [CrossRef]
I. A. Vartanyants and A. Singer, "Analysis of Coherence Properties of 3-rd Generation Synchrotron Sources and Free-Electron Lasers," (2009).
Strictly speaking, only a mono-modal waveguide acts as a perfect coherence filter. However, numerical simulations of the coupling process show that even for a waveguide with three modes, coherence is already significantly filtered (M. Osterhoff et al., unpublished).
J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005). [CrossRef]
S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, "X-ray phasecontrast microscopy and microtomography," Opt. Express 11, 2289-2302 (2003). [CrossRef] [PubMed]
C. Fuhse, "X-ray waveguides and waveguide-based lensless imaging," Ph.D. thesis, University of Gottingen (2006).
A minor difference with respect to one of the four parameters was the following: The detector area used for the reconstruction shown in Fig. 4 was 256×241 pixels, for the simulation we have used a square area of 248×248 pixels with the same pixel size as in the experiment.
L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982). [CrossRef]

Anderson, E. H.
Attwood, D. T.
Bahtz, C.
Bergeman, C.
Boye, P.
Burghammer, M.
Burkeeva, I.
Cai, Z.
Cedola, A.
Chao, W.
Cloetens, P.
Conley, R.
David, C.
Davis, T.
De Caro, L.
Di Fonzo, S.
Eberhardt, W.
Eisebitt, S.
Feldkamp, J.
Feldkamp, J. M.
Fienup, J. R.
Fischer, P.
Fuhse, C.
Giannini, C.
Giewekemeyer, K.
Guagliardi, A.
Gulden, J.
Gureyev, T.
Handa, S.
Harteneck, B. D.
Hellwig, O.
Hignette, O.
Holt, M. V.
Hoppe, R.
Inagaki, K.
Ishikawa, T.
Jark, W.
Kang, H. C.
Keymeulen, H.
Kim, J.
Kimura, T.
Kruger, S. P.
Kuchler, M.
Kurapova, O.
Lagomarsino, S.
Lee, W.-K.
Lengeler, B.
Liddle, J. A.
Liu, C.
Lorgen, M.
Ludwig, W.
Luning, J.
Macrander, A. T.
Mancuso, A. P.
Maser, J.
Matsuyama, S.
Mayo, S.
Metzger, T. H.
Miller, P.
Mimura, H.
Mocuta, C.
Muller, M.
Nishino, Y.
Nugent, K. A.
Ollinger, C.
Paganin, D.
Paterson, D.
Patommel, J.
Peele, A. G.
Pelliccia, D.
Pfeiffer, F.
Pogany, A.
Quiney, H. M.
Rekawa, S.
Riekel, C.
Rostaing, G.
Salditt, T.
Samberg, D.
Sano, Y.
Sch¨oder, S.
Schlotter, W. F.
Schroer, C. G.
Schropp, A.
Stephan, S.
Stephenson, G. B.
Stevenson, A.
Stohr, J.
Tamasaku, K.
van der Hart, A.
van der Veen, J. F.
Vartanyants, I. A.
Vincze, L.
Vogt, S.
Weckert, B.
Wilke, R. N.
Wilkins, S.
Winarski, R. P.
Yabashi, M.
Yamakawa, D.
Yamamura, K.
Yamauchi, K.
Yan, H.
Yokoyama, H.
Yumoto, H.

Appl. Opt.

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]

Appl. Phys. Lett.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005). [CrossRef]
A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010). [CrossRef]
H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008). [CrossRef]
L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982). [CrossRef]

J. Phys. IV France

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003). [CrossRef]

Nat Phys

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focused X-ray fields," Nat Phys 2, 101-104 (2006). [CrossRef]
H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010). [CrossRef]

Nature

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000). [CrossRef] [PubMed]
S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004). [CrossRef] [PubMed]
W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005). [CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008). [CrossRef]

Phys. Rev. Lett.

T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008). [CrossRef] [PubMed]
C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006). [CrossRef]
C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003). [CrossRef]

Physica B: Condensed Matter

C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005). [CrossRef]

Science

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002). [CrossRef] [PubMed]

Other

I. A. Vartanyants and A. Singer, "Analysis of Coherence Properties of 3-rd Generation Synchrotron Sources and Free-Electron Lasers," (2009).
Strictly speaking, only a mono-modal waveguide acts as a perfect coherence filter. However, numerical simulations of the coupling process show that even for a waveguide with three modes, coherence is already significantly filtered (M. Osterhoff et al., unpublished).
C. Fuhse, "X-ray waveguides and waveguide-based lensless imaging," Ph.D. thesis, University of Gottingen (2006).
A minor difference with respect to one of the four parameters was the following: The detector area used for the reconstruction shown in Fig. 4 was 256×241 pixels, for the simulation we have used a square area of 248×248 pixels with the same pixel size as in the experiment.

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[1] S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000). [CrossRef] [PubMed]

[2] S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004). [CrossRef] [PubMed]

[3] C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006). [CrossRef]

[4] H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focused X-ray fields," Nat Phys 2, 101-104 (2006). [CrossRef]

[5] C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003). [CrossRef]

[6] A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010). [CrossRef]

[7] O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003). [CrossRef]

[8] W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005). [CrossRef] [PubMed]

[9] H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010). [CrossRef]

[10] H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008). [CrossRef]

[11] W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, "Demonstration of 12 nm Resolution Fresnel Zone Plate Lens based Soft X-ray Microscopy," Opt. Express 17, 17669-17677 (2009). [CrossRef] [PubMed]

[12] C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005). [CrossRef]

[13] T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008). [CrossRef] [PubMed]

[14] F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002). [CrossRef] [PubMed]

[15] L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008). [CrossRef]

[16] I. A. Vartanyants and A. Singer, "Analysis of Coherence Properties of 3-rd Generation Synchrotron Sources and Free-Electron Lasers," (2009).

[17] Strictly speaking, only a mono-modal waveguide acts as a perfect coherence filter. However, numerical simulations of the coupling process show that even for a waveguide with three modes, coherence is already significantly filtered (M. Osterhoff et al., unpublished).

[18] J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]

[19] C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005). [CrossRef]

[20] S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, "X-ray phasecontrast microscopy and microtomography," Opt. Express 11, 2289-2302 (2003). [CrossRef] [PubMed]

[21] C. Fuhse, "X-ray waveguides and waveguide-based lensless imaging," Ph.D. thesis, University of Gottingen (2006).

[22] A minor difference with respect to one of the four parameters was the following: The detector area used for the reconstruction shown in Fig. 4 was 256×241 pixels, for the simulation we have used a square area of 248×248 pixels with the same pixel size as in the experiment.

[23] L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982). [CrossRef]

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