Abstract

Unusual x-ray focusing effect is reported for parabolic curved multi-plate x-ray crystal cavities of silicon consisting of compound refractive lenses (CRL). The transmitted beam of the (12 4 0) back reflection near 14.4388 keV from these monolithic silicon crystal devices exhibits extraordinary focusing enhancement, such that the focal length is reduced by as much as 18% for 2-beam and 56% for 24-beam diffraction from the curved crystal cavity. This effect is attributed to the presence of the involved Bragg diffractions, in which the wavevector of the transmitted beam is bent further when traversing several curved crystal surfaces.

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    [CrossRef]
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    [CrossRef]
  4. B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
    [CrossRef]
  5. A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
    [CrossRef] [PubMed]
  6. K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
    [CrossRef] [PubMed]
  7. K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (1)

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

2008 (1)

M.-S. Chiu, Y. P. Stetsko, and S.-L. Chang, “Dynamical calculation for X-ray 24-beam diffraction in a two-plate crystal cavity of silicon,” Acta Crystallogr. A 64(3), 394–403 (2008).
[CrossRef] [PubMed]

2007 (1)

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

2006 (1)

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

2005 (3)

C. G. Schroer and B. Lengeler, “Focusing hard x rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94(5), 054802 (2005).
[CrossRef] [PubMed]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

2003 (1)

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

2002 (1)

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

2001 (3)

C. David, B. Nöhammer, and E. Ziegler, “Wavelength tunable diffractive transmission lens for hard x rays,” Appl. Phys. Lett. 79(8), 1088–1090 (2001).
[CrossRef]

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

1999 (1)

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

1996 (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

1971 (1)

M. Hart, “Bragg reflection x ray optics,” Rep. Prog. Phys. 34(2), 435–490 (1971).
[CrossRef]

Ablett, J. M.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Alp, E. E.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Benner, B.

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

Bortel, G.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Bozovic, N.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Caine, E.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Chang, S.-L.

M.-S. Chiu, Y. P. Stetsko, and S.-L. Chang, “Dynamical calculation for X-ray 24-beam diffraction in a two-plate crystal cavity of silicon,” Acta Crystallogr. A 64(3), 394–403 (2008).
[CrossRef] [PubMed]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Chang, Y.-Y.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Chen, S.-Y.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Chiu, M.-S.

M.-S. Chiu, Y. P. Stetsko, and S.-L. Chang, “Dynamical calculation for X-ray 24-beam diffraction in a two-plate crystal cavity of silicon,” Acta Crystallogr. A 64(3), 394–403 (2008).
[CrossRef] [PubMed]

Colella, R.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

David, C.

C. David, B. Nöhammer, and E. Ziegler, “Wavelength tunable diffractive transmission lens for hard x rays,” Appl. Phys. Lett. 79(8), 1088–1090 (2001).
[CrossRef]

Detlefs, C.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Drakopoulos, M.

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

Evans-Lutterodt, K.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Fernandez, P.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Fuhse, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Grigoriev, M. B.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Hart, M.

M. Hart, “Bragg reflection x ray optics,” Rep. Prog. Phys. 34(2), 435–490 (1971).
[CrossRef]

Hu, E. E.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Hy, M. Y.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Ishikawa, T.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

Jarre, A.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Kikuta, S.

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

Kuo, T.-T.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Lee, P. L.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Lee, Y.-R.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Lengeler, B.

C. G. Schroer and B. Lengeler, “Focusing hard x rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94(5), 054802 (2005).
[CrossRef] [PubMed]

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

Li, Y.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Lin, Y.-H.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Mimura, H.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Miwa, D.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Mori, Y.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Nöhammer, B.

C. David, B. Nöhammer, and E. Ziegler, “Wavelength tunable diffractive transmission lens for hard x rays,” Appl. Phys. Lett. 79(8), 1088–1090 (2001).
[CrossRef]

Ollinger, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Pelletier, O.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Richwin, M.

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

Roth, T.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Safinya, C. R.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Saito, A.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Salditt, T.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Sano, Y.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Schroer, C.

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

Schroer, C. G.

C. G. Schroer and B. Lengeler, “Focusing hard x rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94(5), 054802 (2005).
[CrossRef] [PubMed]

Seeger, J.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Shew, B.-Y.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Shy, J.-T.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Sinn, H.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

Souvorov, A.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Stein, A.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Stetsko, Y. P.

M.-S. Chiu, Y. P. Stetsko, and S.-L. Chang, “Dynamical calculation for X-ray 24-beam diffraction in a two-plate crystal cavity of silicon,” Acta Crystallogr. A 64(3), 394–403 (2008).
[CrossRef] [PubMed]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Sturhahn, W.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Sun, W.-H.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Sutter, J. P.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Tamasaku, K.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

Tang, M.-T.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Taylor, A.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Tennant, D. M.

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

Toellner, T. S.

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Tucoulou, R.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

Tümmler, J.

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

Vaughan, G.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Wu, H.-H.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

Yabashi, M.

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

Yamamura, K.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Yamauchi, K.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Yasa, M.

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

Yunkin, V.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

Ziegler, E.

C. David, B. Nöhammer, and E. Ziegler, “Wavelength tunable diffractive transmission lens for hard x rays,” Appl. Phys. Lett. 79(8), 1088–1090 (2001).
[CrossRef]

Acta Crystallogr. A (1)

M.-S. Chiu, Y. P. Stetsko, and S.-L. Chang, “Dynamical calculation for X-ray 24-beam diffraction in a two-plate crystal cavity of silicon,” Acta Crystallogr. A 64(3), 394–403 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

C. David, B. Nöhammer, and E. Ziegler, “Wavelength tunable diffractive transmission lens for hard x rays,” Appl. Phys. Lett. 79(8), 1088–1090 (2001).
[CrossRef]

Y. Li, M. Yasa, O. Pelletier, C. R. Safinya, E. Caine, E. E. Hu, and P. Fernandez, “Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays,” Appl. Phys. Lett. 82(15), 2538–2540 (2003).
[CrossRef]

J. Synchrotron Radiat. (2)

B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
[CrossRef]

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror,” J. Synchrotron Radiat. 9(5), 313–316 (2002).
[CrossRef] [PubMed]

Nature (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384(6604), 49–51 (1996).
[CrossRef]

Phys. Rev. B (2)

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, “Crystal cavity resonance for hard x rays: A diffraction experiment,” Phys. Rev. B 74(13), 134111 (2006).
[CrossRef]

J. P. Sutter, E. E. Alp, M. Y. Hy, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, “Multiple-beam x-ray diffraction near exact backscattering in silicon,” Phys. Rev. B 63(9), 094111 (2001).
[CrossRef]

Phys. Rev. Lett. (5)

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[CrossRef] [PubMed]

K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, “Using compound kinoform hard-x-ray lenses to exceed the critical angle limit,” Phys. Rev. Lett. 99(13), 134801 (2007).
[CrossRef] [PubMed]

C. G. Schroer and B. Lengeler, “Focusing hard x rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94(5), 054802 (2005).
[CrossRef] [PubMed]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, “Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics,” Phys. Rev. Lett. 94(7), 074801 (2005).
[CrossRef] [PubMed]

S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, “X-ray resonance in crystal cavities: realization of Fabry-Perot resonator for hard x rays,” Phys. Rev. Lett. 94(17), 174801 (2005).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

M. Hart, “Bragg reflection x ray optics,” Rep. Prog. Phys. 34(2), 435–490 (1971).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, “X-ray monochromator with an energy resolution of 8×10−9 at 14.41 keV,” Rev. Sci. Instrum. 72(11), 4080–4083 (2001).
[CrossRef]

Other (3)

A. Authier, Dynamical Theory of X-Ray Diffraction (Oxford University Press, Oxford, 2001) p.149.

S.-L. Chang, X-ray Multiple-Wave Diffraction: Theory and Application (Springer-Verlag, Berlin, 2004).

M. Born, and M. Wolf, Principles of Optics (Pergamon Press, Oxford, 1964).

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Figures (4)

Fig. 1
Fig. 1

Schematic of compound refractive lenses with the (12 4 0) satisfying back reflection for E=14.4388 keV: Each hole serves as a crystal cavity of a Fabry-Perot type. The crystal between two adjacent holes serves as an x-ray lens. The total length along [12,4 0] is 1.2 mm.

Fig. 2
Fig. 2

(a) Angular Δθ scans of the transmitted (000) beam of the (12 4 0) back diffraction (A, B, and C correspond to Δθ=−0,053°, 0.02°, and 0°);(b) Horizontal transmitted beam sizes through the cavity crystal measured at the exact position for the 2-beam back reflection, Δθ=−0,053° (open circles), at the 24-beam diffraction position Δθ=0° (curve with solid squares), and for refractive focusing (triangles) as the distance from the exit end of the cavity crystal along the transmitted-beam direction (errors in beam-size~1.0 μm).

Fig. 3
Fig. 3

Schematic of the focusing of the transmitted beams: (a) Ray-tracing in a single crystal lens under back diffraction condition with Δθ ~0 in real space; (b) Projection of the dispersion surface of the 2-beam case on the plane of incidence of (12 4 0) in reciprocal space; (c) Projected dispersion surface of the 24-beam case on the plane of incidence of (12 4 0).

Fig. 4
Fig. 4

(a) In the reciprocal space, the projection of the dispersion surface of the 2-beam case on the plane of incidence of (12 4 0) with Δθ>0; (b) Ray tracing of focusing for the incident beam with Δθ~0, Δθ>0, and Δθ<0.

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