Abstract

Grating beam splitters have been fabricated for soft X-ray Mach-Zehnder interferometer using holographic interference lithography. The grating beam splitter consists of two gratings, one works at X-ray laser wavelength of 13.9 nm with the spatial frequency of 1000 lines/mm as the operation grating, the other works at visible wavelength of 632.8 nm for pre-aligning the X-ray interferometer with the spatial frequency of 22 lines/mm as the pre-alignment grating. The two gratings lie vertically on the same substrate. The main feature of the beam splitter is the use of lowspatial-frequency beat grating of a holographic double frequency grating as the pre-alignment grating of the X-ray interferometer. The grating line parallelism between the two gratings can be judged by observing the diffraction patterns of the pre-alignment grating directly.

© 2008 Optical Society of America

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  1. L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
    [CrossRef] [PubMed]
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2006

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

2004

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, "Picosecond-resolution soft-x-ray laser plasma interferometry," Appl. Opt. 43, 3938-3946 (2004).
[CrossRef] [PubMed]

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi and J. J. Rocca, "Soft X-ray laser diagnostics of exploding aluminum wire plasmas," Appl. Phys. B 78, 933-937 (2004).
[CrossRef]

2003

J. J. Rocca, E. C. Hammarsten, E. Jankowska J. Filevich, M. C. Marconid, S. Moon, V. N. Shlyaptsev, "Application of extremely compact capillary discharge soft x-ray lasers to dense plasma diagnostics," Phys. Plasmas 10, 2031-2038 (2003).
[CrossRef]

R. F. Smith, J. Dunn, J. Nilsen, J. R. Hunter, V. N. Shlyaptsev, J. J. Rocca, J. Filevich, and M. C. Marconi, "Refraction effects on x-ray and ultraviolet interferometric probing of laser-produced plasmas," J. Opt. Soc. Am. B 20, 254-259 (2003).
[CrossRef]

2000

1996

1995

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

1994

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

1992

F. Shaojun, H. Yilin, T. Xiaoming, and S. Yonggang, "Experimental Research of Double Frequency Grating with Ion Beam Etching Technique," Chin. J. Quant. Electron. 9, 186-190 (1992).

1975

1974

1973

Barbee, T. W.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Bryngdahl, O.

Cauble, R.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Celliers, P.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Changfen, L.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Chengang, Z.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Chilla, J. L. A.

Ciarlo, D.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Da Silva, L. B.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Dunn, J.

Dunnb, J.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Filevich, J.

Filevicha, J.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Hai, M.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Hammarsten, E. C.

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi and J. J. Rocca, "Soft X-ray laser diagnostics of exploding aluminum wire plasmas," Appl. Phys. B 78, 933-937 (2004).
[CrossRef]

J. J. Rocca, E. C. Hammarsten, E. Jankowska J. Filevich, M. C. Marconid, S. Moon, V. N. Shlyaptsev, "Application of extremely compact capillary discharge soft x-ray lasers to dense plasma diagnostics," Phys. Plasmas 10, 2031-2038 (2003).
[CrossRef]

Hunter, J. R.

Hunterb, J. R.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Jankowska, E.

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi and J. J. Rocca, "Soft X-ray laser diagnostics of exploding aluminum wire plasmas," Appl. Phys. B 78, 933-937 (2004).
[CrossRef]

Jianping, X.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Kanizay, K.

Keenan, R.

Keenanb, R.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Libby, S.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

London, R. A.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Marconi, M. C.

Marconia, M. C.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Martinez, O. E.

Matthews, D.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Moon, S. J.

Moonb, S. J.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Moreno, J. C.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Mrowka, S.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Ng, A.

Nilsen, J.

Nilsenb, J.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Ran, H.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Ress, D.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Rocca, J. J.

Roccaa, J. J.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Scofieldb, J. H.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Shaojun, F.

F. Shaojun, H. Yilin, T. Xiaoming, and S. Yonggang, "Experimental Research of Double Frequency Grating with Ion Beam Etching Technique," Chin. J. Quant. Electron. 9, 186-190 (1992).

Shlyaptsev, V. N.

Shlyaptsevc, V. N.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Smith, R. F.

Smithb, R. F.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
[CrossRef]

Szapiro, B.

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi and J. J. Rocca, "Soft X-ray laser diagnostics of exploding aluminum wire plasmas," Appl. Phys. B 78, 933-937 (2004).
[CrossRef]

Trebes, J. E.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Wan, A. S.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Weber, F.

L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, "Electron density Measurements of hign density plasmas using soft X-ray laser interferometry," Phys. Rev. Lett. 74, 3991-3994 (1995).
[CrossRef] [PubMed]

Wyant, J. C.

Xiaoming, T.

F. Shaojun, H. Yilin, T. Xiaoming, and S. Yonggang, "Experimental Research of Double Frequency Grating with Ion Beam Etching Technique," Chin. J. Quant. Electron. 9, 186-190 (1992).

Yilin, H.

F. Shaojun, H. Yilin, T. Xiaoming, and S. Yonggang, "Experimental Research of Double Frequency Grating with Ion Beam Etching Technique," Chin. J. Quant. Electron. 9, 186-190 (1992).

Yonggang, S.

F. Shaojun, H. Yilin, T. Xiaoming, and S. Yonggang, "Experimental Research of Double Frequency Grating with Ion Beam Etching Technique," Chin. J. Quant. Electron. 9, 186-190 (1992).

Yu, L.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Acta Opt. Sin.

M. Hai, Z. Chengang, L. Yu, X. Jianping, H. Ran, and L. Changfen, "Measurement of Temperature Field with schlieren shearing interferometry of double frequency gratings," Acta Opt. Sin. 14, 214-218 (1994).

Appl. Opt.

Appl. Phys. B

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi and J. J. Rocca, "Soft X-ray laser diagnostics of exploding aluminum wire plasmas," Appl. Phys. B 78, 933-937 (2004).
[CrossRef]

Chin. J. Quant. Electron.

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J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Quant. Spectrosc. Radiat. Transf.

J. Filevicha, J. J. Roccaa, M. C. Marconia, S. J. Moonb, J. Nilsenb, J. H. Scofieldb, J. Dunnb, R. F. Smithb, R. Keenanb, J. R. Hunterb and V. N. Shlyaptsevc, "Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction," J. Quant. Spectrosc. Radiat. Transf. 99, 165-174 (2006).
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J. J. Rocca, E. C. Hammarsten, E. Jankowska J. Filevich, M. C. Marconid, S. Moon, V. N. Shlyaptsev, "Application of extremely compact capillary discharge soft x-ray lasers to dense plasma diagnostics," Phys. Plasmas 10, 2031-2038 (2003).
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R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S . Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., "Picosecond X-Ray Laser Interferometry of Dense Plasmas," Phys. Rev. Lett.  89, 065004-1-4 (2002).
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[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

3D sketch map of the soft X-ray diffraction grating interferometer.

Fig. 2.
Fig. 2.

Schematic diagram of laser interference lithography for grating fabrication.

Fig. 3.
Fig. 3.

Intensity spatial distribution in the photoresist (a) I 1(x) and I 2(x), (b) I after two exposures.

Fig. 4.
Fig. 4.

Micrograph images of the two HDFGs (a) grating lines of the two component gratings are parallel; (b) grating lines of the two component gratings are not parallel during two exposures.

Fig. 5.
Fig. 5.

Schematic diffraction patterns of the gratings illuminated by a He-Ne laser (a) a general grating with the spatial frequency of ν 1 ; (b) a HDFG which is fabricated by the two component gratings with parallel grating lines during two exposures; (c) a HDFG in which the grating lines of the two component gratings are not parallel during two exposures.

Fig. 6.
Fig. 6.

Schematic diagram of an X-ray holographic grating beam splitter.

Fig. 7.
Fig. 7.

Digital camera photo of an X-ray grating beam splitter fabricated by holographic method (a) AFM image of groove profile of the operation grating with 1000 lines/mm.

Equations (7)

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I 1 = I 0 [ 1 + cos ( 2 π x d 1 ) ] = I 0 [ 1 + cos ( 2 π ν 1 x ) ]
I = I 1 + I 2 = I 0 [ 2 + cos ( 2 π x d 1 ) + cos ( 2 π x d 2 ) ]
h ( x ) = h 0 [ 2 + cos ( 2 π x d 1 ) + cos ( 2 π x d 2 ) ] = h 0 [ 2 + cos ( 2 π ν 1 x ) + cos ( 2 π ν 2 x ) ]
r ( x ) = e x p { j 2 π λ 2 n i h 0 [ 2 + cos ( 2 π x d 1 ) + cos ( 2 π x d 2 ) ] } · rect ( x ι )
sin β ( p , q ) = sin α + λ ( p d 1 + q d 2 ) = sin α + λ ( p ν 1 + q ν 2 )
sin β 0 ( 1 ) = sin α + λ ( ν 0 )
sin β a ( 1 , 1 ) = sin α + λ ( ν 0 + ( 1 ) · ν 2 ) = sin α + λ ( ν a )

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