Abstract

We have demonstrated the use of a high-repetition-rate 46.9-nm tabletop laser to characterize diffraction gratings designed for grazing-incidence operation in the soft-x-ray spectral region. The efficiencies for various diffraction orders were measured as a function of angle of incidence and compared with the results of model simulations. This measurement technique provides benchmarks with which to improve electromagnetic codes used in the design of soft-x-ray diffraction gratings. The results illustrate the potential of compact tabletop soft-x-ray lasers for use as a new tool for characterization of short-wavelength optics at the manufacturer’s site.

© 2001 Optical Society of America

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  1. D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
    [CrossRef]
  2. A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
    [CrossRef]
  3. J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000)
    [CrossRef]
  4. H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
    [CrossRef] [PubMed]
  5. J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).
  6. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993).
    [CrossRef]
  7. B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
    [CrossRef]
  8. C. D. Macchietto, B. R. Benware, J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115–1117 (1999).
    [CrossRef]
  9. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 4.
    [CrossRef]
  10. J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
    [CrossRef] [PubMed]
  11. E. Popov, M. Nevière, “Differential theory for diffraction gratings: a new formulation for TM polarization with rapid convergence,” Opt. Lett. 25, 598–600 (2000).
    [CrossRef]

2000

1999

C. D. Macchietto, B. R. Benware, J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115–1117 (1999).
[CrossRef]

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

1998

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

1996

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
[CrossRef] [PubMed]

1993

1982

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

Attwood, D. T.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Backus, S.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Batson, P.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Beguiristain, R.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Benware, B. R.

C. D. Macchietto, B. R. Benware, J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115–1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

Bokor, J.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
[CrossRef] [PubMed]

Chandezon, J.

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

Chang, C.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Chang, Z.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Chilla, J. L. A.

J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000)
[CrossRef]

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

Clark, D. P.

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

Cornet, G.

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

Dupuis, M. T.

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

Durfee, C. G.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Filevich, J.

Goldberg, K. A.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
[CrossRef] [PubMed]

Gullokson, E.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Herne, C.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Kanizay, K.

Kapteyn, H. C.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Koike, M.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Li, L.

Macchietto, C. D.

C. D. Macchietto, B. R. Benware, J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115–1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

Marconi, M. C.

Maystre, D.

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

Medecki, H.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
[CrossRef] [PubMed]

Moreno, C. H.

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

Murnane, M.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Naulleau, P.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Nevière, M.

Popov, E.

Rocca, J. J.

J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000)
[CrossRef]

C. D. Macchietto, B. R. Benware, J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115–1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

Rudquist, A.

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Shlyaptsev, V. N.

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

Tejnil, E.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

H. Medecki, E. Tejnil, K. A. Goldberg, J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526–1528 (1996)
[CrossRef] [PubMed]

Underwood, J.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

Vincent, P.

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 4.
[CrossRef]

IEEE J. Quantum Electron.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. Gullokson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft x-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A 72, 839–846 (1982).

L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, “Demonstration of a high average power tabletop soft x-ray laser,” Phys. Rev. Lett. 81, 5804–5807 (1998).
[CrossRef]

J. J. Rocca, D. P. Clark, J. L. A. Chilla, V. N. Shlyaptsev, “Energy extraction and achievement of the saturation limit in a discharge pumped table-top soft x-ray amplifier,” Phys. Rev. Lett. 77, 1476–1479 (1996).
[CrossRef] [PubMed]

Science

A. Rudquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef]

Other

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 4.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Atomic-force microscope image of the groove profile corresponding to the 300-line/mm diffraction grating and (top) trace of the image.

Fig. 2
Fig. 2

Experimental setup used to characterize the efficiency of diffraction gratings at 46.9 nm. Vacuum Photodiode B is rotated to measure the intensities of the various diffraction orders. Photodiode A is used to monitor the shot-to-shot variation of the intensity of the incident laser beam.

Fig. 3
Fig. 3

Comparison of measured and computed absolute diffraction efficiencies of a 1800-line/mm gold-coated diffraction grating as a function of grazing-incidence angle. The angles between the facets and the mean surface are A = 10.028 deg and B = 60 deg. (a) Data for first and second diffraction orders; (b) zero-order data.

Fig. 4
Fig. 4

Comparison of measured and computed diffraction efficiencies of the M = 0 and M = -1 diffraction orders of a 300-line/mm gold-coated diffraction grating as a function of incidence angle. The angles between the facets and the mean surface are A = 1.33 deg and B = 80 deg.

Fig. 5
Fig. 5

Comparison of measured and computed diffraction efficiencies of the 300-line/mm gold-coated diffraction grating as a function of incidence angle and for several values of angle B. The blaze angle is 1.33 deg.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

fx, y=fincx, y+n Rn exp iγnx+βny, y>h,fx, y=n Tn exp iγnx+ϕny,  y<0,
2fx, y+αx, yfx, y=0,
fx, y=n fnyexp iγnx,
αx, y=n αnyexp in2πx/d.
fn=αnfn-n αn-mfm.
fn0=-iϕnfn0,
fnh-iβnfnh=-2iβ0 exp-iβ0hδ0n,
Rn=fnhexp-iβnh-exp-2iβnhδ0n,
Tn=fn0.
fny=n Smfnmy.
n Smfnmh-iβnfnmh=-2iβ0×exp-iβ0hδ0n.

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