We demonstrated the Talbot effect using a broadband hard x-ray beam (Δλ/λ ~1). The exit wave-field of the x-ray beam passing through a grating with a sub micro-meter scale period was successfully replicated and recorded at effective Talbot distance, Z_T. The period was reduced to half at Z_T/4 and 3/4Z_T, and the phase reversal was observed at Z_T/2. The propagating wave-field recorded on photoresists was consistent with a simulated result.

© 2010 OSA

1. H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).
2. L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).
3. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995). [CrossRef] [PubMed]
4. L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999). [CrossRef]
5. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002). [CrossRef] [PubMed]
6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).
7. W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009). [CrossRef] [PubMed]
8. W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009). [CrossRef] [PubMed]
9. N. Guérineau, E. Di Mambro, J. Primot, and F. Alves, “Talbot experiment re-examined: study of the chromatic regime and application to spectrometry,” Opt. Express 11(24), 3310–3319 (2003). [CrossRef] [PubMed]
10. P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22(14), 1059–1061 (1997). [CrossRef] [PubMed]
11. C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005). [CrossRef]
12. H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007). [CrossRef] [PubMed]
13. Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html
14. K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003). [CrossRef]
15. J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).
16. K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).
17. X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33

Alves, F.
Arndt, M.
Baruchel, J.
Brezger, B.
Bunk, O.
Case, W. B.
Chapman, M. S.
Clark, C. W.
Cloetens, P.
Conley, R.
David, C.
De Martino, C.
Deachapunya, S.
Deng, L.
Denschlag, J.
Di Mambro, E.
Edwards, M.
Ekstrom, C. R.
Guérineau, N.
Guigay, J. P.
Hackermüller, L.
Hagley, E. W.
Hammond, T. D.
Helmerson, K.
Hiller, J.
Kang, H. C.
Khachatryan, R.
Koritala, R.
Lee, K.
Lee, S. S.
Liu, C.
Macrander, A. T.
Maser, J.
Momose, A.
Petschinka, J.
Pfeiffer, F.
Phillips, W. D.
Primot, J.
Pritchard, D. E.
Rayleigh, L.
Rolston, S. L.
Schlenker, M.
Schmiedmayer, J.
Simsarian, J. E.
Stephenson, G. B.
Suzuki, Y.
Takeda, Y.
Takeuchi, A.
Talbot, H. F.
Tannian, B. E.
Tomandl, M.
Uttenthaler, S.
Wehinger, S.
Weitkamp, T.
Wieczorek, M.
Yan, H.
Yashiro, W.
Zeilinger, A.
Zurbuchen, M. A.

J. Appl. Phys.

• C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005). [CrossRef]

Nature

• F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Opt. Express

• W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009). [CrossRef] [PubMed]
• N. Guérineau, E. Di Mambro, J. Primot, and F. Alves, “Talbot experiment re-examined: study of the chromatic regime and application to spectrometry,” Opt. Express 11(24), 3310–3319 (2003). [CrossRef] [PubMed]

Opt. Lett.

• P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22(14), 1059–1061 (1997). [CrossRef] [PubMed]

Philos. Mag.

• H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).
• L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

Phys. Rev. A

• M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995). [CrossRef] [PubMed]

Phys. Rev. Lett.

• L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999). [CrossRef]
• B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002). [CrossRef] [PubMed]
• W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009). [CrossRef] [PubMed]

Rev. Sci. Instrum.

• H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007). [CrossRef] [PubMed]

Sens. Actuators A Phys.

• K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003). [CrossRef]

Other

• J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).
• K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).
• X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33
• Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html

2009, Yashiro, Phys. Rev. Lett.
2009, Case, Opt. Express
2007, Kang, Rev. Sci. Instrum.
2006, Pfeiffer, Nature
2005, Liu, J. Appl. Phys.
2003, Lee, Sens. Actuators A Phys.
2003, Guérineau, Opt. Express
2002, Brezger, Phys. Rev. Lett.
1999, Deng, Phys. Rev. Lett.
1997, Cloetens, Opt. Lett.
1995, Chapman, Phys. Rev. A
1881, Rayleigh, Philos. Mag.
1836, Talbot, Philos. Mag.

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