Abstract

A 2500 lines/mm Multilayer Blazed Grating (MBG) optimized for the soft x-ray wavelength range was fabricated and tested. The grating coated with a W/B4C multilayer demonstrated a record diffraction efficiency in the 2nd blazed diffraction order in the energy range from 500 to 1200 eV. Detailed investigation of the diffraction properties of the grating demonstrated that the diffraction efficiency of high groove density MBGs is not limited by the normal shadowing effects that limits grazing incidence x-ray grating performance. Refraction effects inherent in asymmetrical Bragg diffraction were experimentally confirmed for MBGs. The refraction affects the blazing properties of the MBGs and results in a shift of the resonance wavelength of the gratings and broadening or narrowing of the grating bandwidth depending on diffraction geometry. The true blaze angle of the MBGs is defined by both the real structure of the multilayer stack and by asymmetrical refraction effects. Refraction effects can be used as a powerful tool in providing highly efficient suppression of high order harmonics.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. J. H. Underwood, C. Kh. Malek, E. M. Gullikson, and M. Krumrey, “Multilayer-coated echelle gratings for soft x-rays and extreme ultraviolet,” Rev. Sci. Instrum. 66(2), 2147–2150 (1995).
    [Crossref]
  4. T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A multiplexed high-resolution imaging spectrometer for resonant inelastic soft X-ray scattering spectroscopy,” J. Synchrotron Radiat. 21(4), 736–743 (2014).
    [Crossref] [PubMed]
  5. D. L. Voronov, L. I. Goray, T. Warwick, V. V. Yashchuk, and H. A. Padmore, “High-order multilayer coated blazed gratings for high resolution soft x-ray spectroscopy,” Opt. Express 23(4), 4771–4790 (2015).
    [Crossref] [PubMed]
  6. D. L. Voronov, T. Warwick, and H. A. Padmore, “Multilayer-coated blazed grating with variable line spacing and a variable blaze angle,” Opt. Lett. 39(21), 6134–6137 (2014).
    [Crossref] [PubMed]
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    [Crossref]
  8. D. Maystre and R. Petit, “Some recent theoretical results for gratings: application for their use in the very far ultraviolet region,” Nouv. Rev. Opt. 7(3), 165–180 (1976).
    [Crossref]
  9. A. P. Lukirskii and E. P. Savinov, “Use of diffraction gratings and echelettes in the ultrasoft x-ray region,” Opt. Spectrosc. 14, 147–151 (1963).
  10. A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).
  11. M. Nevière and F. Montiel, “Soft x-ray multilayer coated echelle gratings: electromagnetic and phenomenological study,” J. Opt. Soc. Am. A 13(4), 811–818 (1996).
    [Crossref]
  12. Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
    [Crossref]
  13. P. Philippe, S. Valette, O. M. Mendez, and D. Maystre, “Wavelength demultiplexer: using echelette gratings on silicon substrate,” Appl. Opt. 24(7), 1006–1011 (1985).
    [Crossref] [PubMed]
  14. D. L. Voronov, E. M. Gullikson, F. Salmassi, T. Warwick, and H. A. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39(11), 3157–3160 (2014).
    [Crossref] [PubMed]
  15. http://henke.lbl.gov/multilayer/survey.htmlhttp://henke.lbl.gov/
  16. http://henke.lbl.gov/optical_constants/multi2.html
  17. http://www.pcgrate.com/
  18. D. L. Voronov, E. H. Anderson, R. Cambie, S. Cabrini, S. D. Dhuey, L. I. Goray, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, “A 10,000 groove/mm multilayer coated grating for EUV spectroscopy,” Opt. Express 19(7), 6320–6325 (2011).
    [Crossref] [PubMed]
  19. See, for example, Yu. Shvyd’ko, See, for example, Yu. Shvyd’ko, X-Ray Optics. High-Resolution Applications, (Springer, 2004).
  20. V. V. Martynov and Yu. Platonov, “Deep multilayer gratings with adjustable bandpass for XRF spectroscopy,” Adv. X-ray Anal. 45, 402–408 (2002).
  21. F. Choueikani, B. Lagarde, F. Delmotte, M. Krumrey, F. Bridou, M. Thomasset, E. Meltchakov, and F. Polack, “High-efficiency B₄C/Mo₂C alternate multilayer grating for monochromators in the photon energy range from 0.7 to 3.4 keV,” Opt. Lett. 39(7), 2141–2144 (2014).
    [Crossref] [PubMed]

2015 (2)

2014 (4)

2011 (1)

2002 (1)

V. V. Martynov and Yu. Platonov, “Deep multilayer gratings with adjustable bandpass for XRF spectroscopy,” Adv. X-ray Anal. 45, 402–408 (2002).

1996 (1)

1995 (1)

J. H. Underwood, C. Kh. Malek, E. M. Gullikson, and M. Krumrey, “Multilayer-coated echelle gratings for soft x-rays and extreme ultraviolet,” Rev. Sci. Instrum. 66(2), 2147–2150 (1995).
[Crossref]

1989 (1)

1986 (1)

W. Jark, “Enhancement of diffraction grating efficiencies in the soft x-ray region by a multilayer coating,” Opt. Commun. 60(4), 201–205 (1986).
[Crossref]

1985 (1)

1980 (1)

Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
[Crossref]

1976 (1)

D. Maystre and R. Petit, “Some recent theoretical results for gratings: application for their use in the very far ultraviolet region,” Nouv. Rev. Opt. 7(3), 165–180 (1976).
[Crossref]

1963 (2)

A. P. Lukirskii and E. P. Savinov, “Use of diffraction gratings and echelettes in the ultrasoft x-ray region,” Opt. Spectrosc. 14, 147–151 (1963).

A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).

Anderson, E. H.

Aoyama, K. I.

Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
[Crossref]

Barbee, T. W.

Bridou, F.

Cabrini, S.

Cambie, R.

Choueikani, F.

Chuang, Y.-D.

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A multiplexed high-resolution imaging spectrometer for resonant inelastic soft X-ray scattering spectroscopy,” J. Synchrotron Radiat. 21(4), 736–743 (2014).
[Crossref] [PubMed]

Cruddace, R. G.

Delmotte, F.

Dhuey, S. D.

Fujii, Y.

Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
[Crossref]

Goray, L. I.

Gullikson, E. M.

Huang, Q.

Hunter, W. R.

Jark, W.

W. Jark, “Enhancement of diffraction grating efficiencies in the soft x-ray region by a multilayer coating,” Opt. Commun. 60(4), 201–205 (1986).
[Crossref]

Kozhevnikov, I. V.

Krumrey, M.

Lagarde, B.

Lukirskii, A. P.

A. P. Lukirskii and E. P. Savinov, “Use of diffraction gratings and echelettes in the ultrasoft x-ray region,” Opt. Spectrosc. 14, 147–151 (1963).

A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).

Malek, C. Kh.

J. H. Underwood, C. Kh. Malek, E. M. Gullikson, and M. Krumrey, “Multilayer-coated echelle gratings for soft x-rays and extreme ultraviolet,” Rev. Sci. Instrum. 66(2), 2147–2150 (1995).
[Crossref]

Martynov, V. V.

V. V. Martynov and Yu. Platonov, “Deep multilayer gratings with adjustable bandpass for XRF spectroscopy,” Adv. X-ray Anal. 45, 402–408 (2002).

Maystre, D.

P. Philippe, S. Valette, O. M. Mendez, and D. Maystre, “Wavelength demultiplexer: using echelette gratings on silicon substrate,” Appl. Opt. 24(7), 1006–1011 (1985).
[Crossref] [PubMed]

D. Maystre and R. Petit, “Some recent theoretical results for gratings: application for their use in the very far ultraviolet region,” Nouv. Rev. Opt. 7(3), 165–180 (1976).
[Crossref]

Meltchakov, E.

Mendez, O. M.

Minowa, J. I.

Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
[Crossref]

Montiel, F.

Nevière, M.

Padmore, H. A.

Petit, R.

D. Maystre and R. Petit, “Some recent theoretical results for gratings: application for their use in the very far ultraviolet region,” Nouv. Rev. Opt. 7(3), 165–180 (1976).
[Crossref]

Philippe, P.

Platonov, Yu.

V. V. Martynov and Yu. Platonov, “Deep multilayer gratings with adjustable bandpass for XRF spectroscopy,” Adv. X-ray Anal. 45, 402–408 (2002).

Polack, F.

Rife, J. C.

Salmassi, F.

Savinov, E. P.

A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).

A. P. Lukirskii and E. P. Savinov, “Use of diffraction gratings and echelettes in the ultrasoft x-ray region,” Opt. Spectrosc. 14, 147–151 (1963).

Shepelev, Y. P.

A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).

Thomasset, M.

Underwood, J. H.

J. H. Underwood, C. Kh. Malek, E. M. Gullikson, and M. Krumrey, “Multilayer-coated echelle gratings for soft x-rays and extreme ultraviolet,” Rev. Sci. Instrum. 66(2), 2147–2150 (1995).
[Crossref]

Valette, S.

Voronov, D. L.

Wang, Z.

Warwick, T.

Yang, X.

Yashchuk, V. V.

Adv. X-ray Anal. (1)

V. V. Martynov and Yu. Platonov, “Deep multilayer gratings with adjustable bandpass for XRF spectroscopy,” Adv. X-ray Anal. 45, 402–408 (2002).

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

Y. Fujii, K. I. Aoyama, and J. I. Minowa, “Optical demultiplexer using a silicon echelette grating,” IEEE J. Quantum Electron. 16(2), 165–169 (1980).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Synchrotron Radiat. (1)

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A multiplexed high-resolution imaging spectrometer for resonant inelastic soft X-ray scattering spectroscopy,” J. Synchrotron Radiat. 21(4), 736–743 (2014).
[Crossref] [PubMed]

Nouv. Rev. Opt. (1)

D. Maystre and R. Petit, “Some recent theoretical results for gratings: application for their use in the very far ultraviolet region,” Nouv. Rev. Opt. 7(3), 165–180 (1976).
[Crossref]

Opt. Commun. (1)

W. Jark, “Enhancement of diffraction grating efficiencies in the soft x-ray region by a multilayer coating,” Opt. Commun. 60(4), 201–205 (1986).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Opt. Spectrosc. (2)

A. P. Lukirskii and E. P. Savinov, “Use of diffraction gratings and echelettes in the ultrasoft x-ray region,” Opt. Spectrosc. 14, 147–151 (1963).

A. P. Lukirskii, E. P. Savinov, and Y. P. Shepelev, “Behaviour of gold and titanium coated echelettes in the 23.6-113 A region,” Opt. Spectrosc. 15, 290–293 (1963).

Rev. Sci. Instrum. (1)

J. H. Underwood, C. Kh. Malek, E. M. Gullikson, and M. Krumrey, “Multilayer-coated echelle gratings for soft x-rays and extreme ultraviolet,” Rev. Sci. Instrum. 66(2), 2147–2150 (1995).
[Crossref]

Other (4)

http://henke.lbl.gov/multilayer/survey.htmlhttp://henke.lbl.gov/

http://henke.lbl.gov/optical_constants/multi2.html

http://www.pcgrate.com/

See, for example, Yu. Shvyd’ko, See, for example, Yu. Shvyd’ko, X-Ray Optics. High-Resolution Applications, (Springer, 2004).

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Figures (8)

Fig. 1
Fig. 1 An AFM image (left) and profile (right) of the 2,500 lines/mm soft x-ray multilayer blazed grating.
Fig. 2
Fig. 2 Efficiency of the soft x-ray MBG versus wavelength measured (symbols) and calculated (curves) for different incidence angles (a). Experimental (curve with circles) and theoretical peak diffraction efficiency calculated for anti-blaze angles of 20° (curve with triangles) and 80° (curve with star symbols) (b).
Fig. 3
Fig. 3 Reflectance of the W/B4C plane multilayer witness versus wavelength measured (circles) and calculated (curves) for different grazing angles of incidence (a). Experimental and theoretical peak ML reflectance calculated for interface roughness of 0, 0.46, and 0.58 nm rms (b).
Fig. 4
Fig. 4 Relative efficiency versus the asymmetry factor: calculated by formula (1), experimental, and calculated by PCGrate 6.5 code for an ideal grating with the anti-blaze angle 80° and a grating with realistic groove profile measured by AFM (see Fig. 1).
Fig. 5
Fig. 5 Efficiency of the fabricated multilayer grating measured for the direct (α = 79.96°) and reciprocal (αr = 76.88°) geometry (a). Dependence of the bandwidth for a plane multilayer witness (circles) and the grating in direct (triangles) and reciprocal (squares) geometry (b). Experimental (symbols) and calculated by formula (3) (curve) ratio of the bandwidths for direct and reciprocal geometry (c)
Fig. 6
Fig. 6 Detector scan for the incidence angle of 82.2° and the wavelength of 1.77 nm (a). The same for a range of the wavelengths (b).
Fig. 7
Fig. 7 A structure of a MBG with slight deviation from the ideal blazing condition (formula (5)). Staggered layers define a new periodical structure with an effective blaze angle, ϕ, different from the substrate blaze angle, ϕ0.
Fig. 8
Fig. 8 Diffraction efficiency of the 2nd, 4th, and 6th blazed orders of the MBG measured at an incidence angle of 75.7° (a). Normalized efficiency of the 2nd, 4th, and 6th orders versus a product of the wavelength and diffraction order (b).

Equations (7)

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E Maystre =R×min[ cosα/cosβ,cosβ/cosα ],
FWH M a =FWH M S / | b |
FWH M a direct /FWH M a reciprocal =| b |=cosβ/cosα
ϕ=(αβ)/2
d grating sin ϕ 0 D ML = m n ,
tgϕ= D ML m d grating cos ϕ 0 ,
2Dsinθ=nλ(1+ ω S ),

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