Abstract

A diffractive optical element, based on Fourier optics techniques, for use in extreme ultraviolet/soft x-ray experiments has been fabricated and demonstrated. This diffractive optical element, when illuminated by a uniform plane wave, will produce two symmetric off-axis first-order foci suitable for interferometric experiments. The efficiency of this optical element and its use in direct interferometric determination of optical constants are also discussed. Its use in direct interferometric determination of optical constants is also referenced. Its use opens a new era in the use of sophisticated optical techniques at short wavelengths.

© 2002 Optical Society of America

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References

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  1. D. T. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University, Cambridge, U.K., 1999).
  2. C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed., McGraw-Hill, New York, 1996, Chap. 5, Problem 14.
  4. E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
    [CrossRef]
  5. D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, J. H. Underwood, “Tunable coherent radiation in the soft X-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999).
    [CrossRef]

2002 (1)

2000 (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

1999 (1)

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

Anderson, E. H.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Attwood, D.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Attwood, D. T.

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

D. T. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University, Cambridge, U.K., 1999).

Batson, P.

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

Bokor, J.

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

Chang, C.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

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

Chao, W.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Denbeaux, G.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Goldberg, K. A.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., McGraw-Hill, New York, 1996, Chap. 5, Problem 14.

Gullikson, E. M.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

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

Harteneck, B.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Koike, M.

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

Lucero, A.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Medecki, H.

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

Naulleau, P.

C. Chang, P. Naulleau, E. H. Anderson, E. M. Gullikson, K. A. Goldberg, D. Attwood, “Direct index of refraction measurement at extreme ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
[CrossRef]

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

Olynick, D. L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Tejnil, E.

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

Underwood, J. H.

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

Veklerov, E.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Vac. Sci. Technol. B (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution X-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2985 (2000).
[CrossRef]

Opt. Lett. (1)

Other (2)

D. T. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University, Cambridge, U.K., 1999).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., McGraw-Hill, New York, 1996, Chap. 5, Problem 14.

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Figures (6)

Fig. 1
Fig. 1

Computer simulation of the XOR pattern: The parameters used in this simulation are set equal to the actual fabricated element. The pattern in (a) is obtained by taking the XOR of the binary grating and zoneplate. 4096 × 4096 pixels are used to generated this pattern. This pattern is then Fresnel propagated in a computer by one focal length, and the resulting intensity distribution is shown in (b). A horizontal cross-section through the focal spots is also shown. The two symmetric off-axis first-order foci is clearly visible in this simulation. The other two outer spots are caused by the third orders (m = ±3) of the grating, with nine times lower intensity.

Fig. 2
Fig. 2

Visible experiment is performed to directly verify the intensity distribution at the back focal plane of the XOR pattern. For comparison an OR pattern obtained by taking the bit-wise OR of a grating and a zoneplate is also fabricated. The effect of this OR pattern is equivalent to that of a grating and a zoneplate placed in tandem, which is the conventional setup for interferometric experiments. (a) Shows that the intensity distribution at the back focal plane of the XOR pattern consists of only two symmetric off-axis foci, as predicted by the theory. As a comparison, the focal plane intensity distribution of the OR pattern is shown in (b), which has three foci, with one strong on-axis focus and two weaker off-axis symmetric foci. The grating used by the XOR and OR patterns in this visible experiment has a period of 5 µm, and the diameter and the outermost zone width of the zoneplate is D = 5 mm and 2 µm, respectively. A He-Ne laser (λ = 633 nm) is used for illuminating the XOR and OR patterns.

Fig. 3
Fig. 3

Microscope image of the OR pattern used in the experiment with visible light.

Fig. 4
Fig. 4

Center part of the XOR pattern is shown. This diffractive optical element is obtained by taking the bit-wise XOR of a binary amplitude grating and a binary amplitude zoneplate. The functionality of this XOR pattern is equivalent to that of a binary phase grating overlapping a binary amplitude zoneplate, as discussed in the text. The grating used here has a 16 µm period and the zoneplate has a 400 µm diameter and a 0.2 µm outermost zone width.

Fig. 5
Fig. 5

Efficiency of this XOR pattern is measured by scanning a knife-like beam stop across the focal plane. Starting with the beam stop placed at the back focal plane such that the entire beam is blocked, as the beam stop slowly moves aside, the total counts on the CCD increases, allowing fractions of light to pass. The constant slope of the two straight sections results from the effect of zeroth order (straight through) light. The two abrupt steps at the center is caused by the two symmetric off-axis first-order foci being released one at a time by the beam stop. Their strength is shown to be around 4.0%, which agrees with the theoretical value.

Fig. 6
Fig. 6

Object wave, which consists of two converging spherical wavefronts, interferes with a reference plane wave, and the resulting intensity interference pattern is usually referred to as a CGH. This CGH is then binarized for nanofabrication by e-beam lithography. (a) Shows its binarized form. When illuminated by a uniform plane wave, this optical element reconstructs the object wave (two converging spherical waves) as shown in (b). Note that the two spots are symmetrically off-axis.

Equations (8)

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Gx, y=121+sgncos νx,
ZPx, y=121+sgncos γr2,
Gx, y=m=-sinmπ/2mπexp-jmνx,
ZPx, y=n=-sinnπ/2nπexp-jnγr2.
XORx, y=Gx, y+ZPx, y-2Gx, yZPx, y =m=-sinmπ/2mπexp-jmνx+n=-sinnπ/2nπexp-jnγr2-212+m=-m0sinmπ/2mπexp-jmνx ×12+n=-n0sinnπ/2nπexp-jnγr2 =12-2m=-m0sinmπ/2mπexp-jmνx×n=-n0sinnπ/2nπexp-jnγr2.
ηm,n= 4m2n2π4if m, n are both odd,0if m or n is even,
ηm=4m2π2for m=±1, ±3, ,0for m is even.
ηn=1n2π2for n=±1, ±3, ,0for n is even.

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