Abstract

For the fabrication of large-area, spatially coherent gratings with periods of 100 nm or less, a grating interferometer is preferred over a conventional holographic configuration because of the limited coherence of available sources. Using a configuration that employs two matched fused silica phase gratings and an ArF excimer laser, we obtain high-quality 100-nm gratings in polymethyl methacrylate. We analyze the conditions for achieving high-contrast fringes with such an achromatic holographic configuration and show that the depth of focus depends only on the spatial coherence of the source. We also describe a highly accurate method for calculating the diffraction efficiency of the phase gratings as a function of polarization, incidence angle, and grating structure.

© 1992 Optical Society of America

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References

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  1. K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
    [CrossRef]
  2. M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).
  3. M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
    [CrossRef]
  4. U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
    [CrossRef]
  5. A. Yen, “Fabrication of large-area 100-nm-period gratings using achromatic holographic lithography,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1991).
  6. E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
    [CrossRef]
  7. E. H. Anderson, “Fabrication and electromagnetic applications of periodic nanostructures,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1988).
  8. A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
    [CrossRef]
  9. A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
    [CrossRef]
  10. F. J. Weinberg, N. B. Wood, “Interferometer based on four diffraction gratings,” J. Sci. Instrum. 36, 227–230 (1959).
    [CrossRef]
  11. E. N. Leith, B. J. Chang, “Space-invariant holography with quasi-coherent light,” Appl. Opt. 12, 1957–1963 (1973).
    [CrossRef] [PubMed]
  12. B. J. Chang, “Holography with non-coherent light,” Opt. Commun. 9, 357–359 (1973).
    [CrossRef]
  13. C. C. Iemmi, J. M. Simon, J. O. Ratto, “Synthesis of asymmetric profiles from a double grating interferometer: an experimental demonstration,” Appl. Opt. 26, 1822–1824 (1987).
    [CrossRef]
  14. H. Chen, R. R. Hershey, E. N. Leith, “Sawtooth profile fringes with a two-grating interferometer,” Appl. Opt. 27, 1193–1198 (1988).
    [CrossRef] [PubMed]
  15. R. R. Hershey, E. N. Leith, “Grating interferometers for producing large holographic gratings,” Appl. Opt. 29, 937–943 (1990).
    [CrossRef] [PubMed]
  16. A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
    [CrossRef]
  17. B. J. Chang, R. Alferness, E. N. Leith, “Space-invariant achromatic grating interferometer: theory,” Appl. Opt. 14, 1592–1600 (1975).
    [CrossRef] [PubMed]
  18. Y.-S. Cheng, “Fringe formation in incoherent light with a two-grating interferometer,” Appl. Opt. 23, 3057–3059 (1984).
    [CrossRef] [PubMed]
  19. G. J. Swanson, “Broad-source fringes in grating and conventional interferometers,” J. Opt. Soc. Am. A 1, 1147–1153 (1984).
    [CrossRef]
  20. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. Inst. Electr. Eng. 73, 894–937 (1985).
  21. R. Magnusson, T. K. Gaylord, “Equivalence of multiwave coupled-wave theory and modal theory for periodic-media diffraction,” J. Opt. Soc. Am. 68, 1777–1779 (1978).
    [CrossRef]
  22. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]
  23. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

1992 (1)

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

1991 (3)

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

1990 (4)

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
[CrossRef]

R. R. Hershey, E. N. Leith, “Grating interferometers for producing large holographic gratings,” Appl. Opt. 29, 937–943 (1990).
[CrossRef] [PubMed]

1988 (2)

E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
[CrossRef]

H. Chen, R. R. Hershey, E. N. Leith, “Sawtooth profile fringes with a two-grating interferometer,” Appl. Opt. 27, 1193–1198 (1988).
[CrossRef] [PubMed]

1987 (1)

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. Inst. Electr. Eng. 73, 894–937 (1985).

1984 (2)

1978 (2)

1975 (1)

1973 (2)

1959 (1)

F. J. Weinberg, N. B. Wood, “Interferometer based on four diffraction gratings,” J. Sci. Instrum. 36, 227–230 (1959).
[CrossRef]

Alferness, R.

Anderson, E. H.

M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
[CrossRef]

E. H. Anderson, “Fabrication and electromagnetic applications of periodic nanostructures,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1988).

Arai, S.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

Bagwell, P. F.

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

Cao, M.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Carter, J. M.

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

Chang, B. J.

Chen, H.

Cheng, Y.-S.

Chu, W.

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. Inst. Electr. Eng. 73, 894–937 (1985).

R. Magnusson, T. K. Gaylord, “Equivalence of multiwave coupled-wave theory and modal theory for periodic-media diffraction,” J. Opt. Soc. Am. 68, 1777–1779 (1978).
[CrossRef]

Ghanbari, R. A.

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

Hershey, R. R.

Hirayama, H.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Iemmi, C. C.

Ismail, K.

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

Knop, K.

Komatsu, K.

E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
[CrossRef]

Ku, Y.-C.

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

Leith, E. N.

Magnusson, R.

Marti, U.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Martin, D.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

Miyake, Y.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Miyamoto, Y.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. Inst. Electr. Eng. 73, 894–937 (1985).

Morier-Genoud, F.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Orlando, T. P.

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

Proctor, M.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Ratto, J. O.

Reinhart, F. K.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Schattenburg, M. L.

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
[CrossRef]

Senior, B.

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Simon, J. M.

Smith, H. I.

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
[CrossRef]

E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
[CrossRef]

Suematsu, Y.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Swanson, G. J.

Tamura, S.

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Taylor, G. N.

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

Weinberg, F. J.

F. J. Weinberg, N. B. Wood, “Interferometer based on four diffraction gratings,” J. Sci. Instrum. 36, 227–230 (1959).
[CrossRef]

Wood, N. B.

F. J. Weinberg, N. B. Wood, “Interferometer based on four diffraction gratings,” J. Sci. Instrum. 36, 227–230 (1959).
[CrossRef]

Yen, A.

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

A. Yen, “Fabrication of large-area 100-nm-period gratings using achromatic holographic lithography,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

Appl. Opt. (6)

J. Electrochem. Soc. (1)

A. Yen, M. L. Schattenburg, H. I. Smith, G. N. Taylor, “An anti-reflective coating for use with PMMA at 193 nm,” J. Electrochem. Soc. 139, 616–619 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Sci. Instrum. (1)

F. J. Weinberg, N. B. Wood, “Interferometer based on four diffraction gratings,” J. Sci. Instrum. 36, 227–230 (1959).
[CrossRef]

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

E. H. Anderson, K. Komatsu, H. I. Smith, “Achromatic holographic lithography in the deep ultraviolet,” J. Vac. Sci. Technol. B 6, 216–218 (1988).
[CrossRef]

Microelectron. Eng. (3)

A. Yen, R. A. Ghanbari, E. H. Anderson, H. I. Smith, “Fabrication of 100nm-period gratings using achromatic holographic lithography,” Microelectron. Eng. 11, 201–205 (1990).
[CrossRef]

A. Yen, R. A. Ghanbari, Y.-C. Ku, W. Chu, M. L. Schattenburg, J. M. Carter, H. I. Smith, “X-ray masks with large-area 100nm-period gratings for quantum-effect device applications,” Microelectron. Eng. 13, 271–274 (1991).
[CrossRef]

U. Marti, M. Proctor, D. Martin, F. Morier-Genoud, B. Senior, F. K. Reinhart, “Fabrication of buried GaAlAs NM-structures by deep UV holographic lithography and MBE growth on finely channeled substrates,” Microelectron. Eng. 13, 391–394 (1991).
[CrossRef]

Opt. Commun. (1)

B. J. Chang, “Holography with non-coherent light,” Opt. Commun. 9, 357–359 (1973).
[CrossRef]

Phys. Scr. (1)

M. L. Schattenburg, E. H. Anderson, H. I. Smith, “X-ray/VUV transmission gratings for astrophysical and laboratory applications,” Phys. Scr. 41, 13–20 (1990); “Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF),” Opt. Eng. 30, 1590 (1991).
[CrossRef]

Proc. IEEE (1)

K. Ismail, P. F. Bagwell, T. P. Orlando, H. I. Smith, “Quantum phenomena in field-effect-controlled semiconductor nanostructures,” Proc. IEEE 19, 1106–1116 (1991).
[CrossRef]

Proc. Inst. Electr. Eng. (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. Inst. Electr. Eng. 73, 894–937 (1985).

Trans. Inst. Electron. Inform. Commun. Eng. E (1)

M. Cao, Y. Miyake, S. Tamura, H. Hirayama, S. Arai, Y. Suematsu, Y. Miyamoto, “Lasing action in GaInAs/GaInAsP quantum-wire structure,” Trans. Inst. Electron. Inform. Commun. Eng. E 73, 63–70 (1990).

Other (3)

A. Yen, “Fabrication of large-area 100-nm-period gratings using achromatic holographic lithography,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

E. H. Anderson, “Fabrication and electromagnetic applications of periodic nanostructures,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1988).

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

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Figures (5)

Fig. 1
Fig. 1

Achromatic holographic configuration for generating 100-nm-period gratings.

Fig. 2
Fig. 2

A 100-nm-period grating in polymethyl methacrylate (PMMA) on top of an antireflective coating (ARC).

Fig. 3
Fig. 3

Diagram for calculating the optical paths of two arms of a grating interferometer.

Fig. 4
Fig. 4

Diagram of a phase grating showing the various parameters that are needed in diffraction efficiency calculations.

Fig. 5
Fig. 5

Diffraction efficiencies of 200-nm-period fused silica phase gratings at 193 nm, as a function of groove depth d and fractional linewidth b, as defined in Fig. 4. Each contour represents a 10% increase in efficiency. Matrix size, 10 × 10. (a) First-order diffraction efficiency for TE polarization at normal incidence. (b) First-order diffraction efficiency for TM polarization at normal incidence. (c) Second-order diffraction efficiency for TE polarization at 74.8% angle of incidence. (d) Second-order diffraction efficiency for TM polarization at 74.8° angle of incidence.

Equations (27)

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

p = λ 2 sin θ ,
E 1 = A e ^ 1 cos ( Φ 1 - ω t ) ,
E 2 = B e ^ 2 cos ( Φ 2 - ω t ) ,
I ( E 1 + E 2 ) · ( E 1 + E 2 )
= A 2 + B 2 2 + A B ( e ^ 1 · e ^ 2 ) cos ( Φ 1 - Φ 2 ) ,
I = λ 0 - Δ λ / 2 λ 0 + Δ λ / 2 θ 0 - Δ θ / 2 θ 0 + Δ θ / 2 ( 1 + cos Δ Φ ) d λ d θ ,
β = sin - 1 1 n ( λ / p + sin θ ) ,
γ = sin - 1 1 n ( λ / p - sin θ ) .
T 1 ( x ) = m A m exp ( i 2 π m p x ) ,
T 2 ( x ) = m B m exp ( i 2 π m p x ) .
E 1 = A 1 exp ( i 2 π p x ) exp ( i 2 π n λ d cos γ ) × exp ( i 2 π λ g cos γ ) B - 2 exp ( - i 2 π 2 p x ) × exp [ i 2 π n λ ( d - δ ) cos β ] exp [ i 2 π λ ( g + δ ) cos β ] ,
E 2 = A - 1 exp ( - i 2 π p x ) exp ( i 2 π n λ d cos β ) × exp ( i 2 π λ g cos β ) B 2 exp ( i 2 π 2 p x ) × exp [ i 2 π n λ ( d - δ ) cos γ ] exp [ i 2 π λ ( g + δ ) cos γ ] .
Δ Φ = - 4 π p x - 2 π n λ δ ( cos β - cos γ ) + 2 π λ δ ( cos β - cos γ ) = - 4 π p x - 2 π λ δ { [ n 2 - ( λ / p + θ ) 2 ] 1 / 2 - [ n 2 - ( λ / p - θ ) 2 ] 1 / 2 } + 2 π λ δ { [ 1 - ( λ / p + θ ) 2 ] 1 / 2 - [ 1 - ( λ / p - θ ) 2 ] 1 / 2 } .
2 π δ [ 2 λ 0 θ 0 ( n 2 p 2 - λ 0 2 ) 3 / 2 d λ + 2 ( n 2 p 2 - λ 0 2 ) 1 / 2 d θ ] - 2 π δ [ 2 λ 0 θ 0 ( p 2 - λ 0 2 ) 3 / 2 d λ + 2 ( p 2 - λ 0 2 ) 1 / 2 d θ ] .
- π 2 4 π d θ [ δ ( n 2 p 2 - λ 0 2 ) 1 / 2 - δ ( p 2 - λ 0 2 ) 1 / 2 ] π 2 .
- ( p 2 - λ 0 2 ) 1 / 2 4 Δ θ + δ ( p 2 - λ 0 2 n 2 p 2 - λ 0 2 ) 1 / 2 δ ( p 2 - λ 0 2 ) 1 / 2 4 Δ θ + δ ( p 2 - λ 0 2 n 2 p 2 - λ 0 2 ) 1 / 2 .
( p 2 - λ 0 2 ) 1 / 2 2 Δ θ .
2 E II x 2 + 2 E II z 2 + k 0 2 ( x ) E II = 0 ,
B ( z ) = B exp ( i κ z ) ,
d 2 A ( x ) d x 2 + [ k 0 2 ( x ) - κ 2 ] A ( x ) = 0.
A ( x ) = U ( x ) exp ( i ϕ x ) .
U ( x ) = m = - a m exp ( i 2 π m p x ) .
M · a = κ 2 a ,
E II = m , q a m q exp [ i ( 2 π m p + ϕ ) x ] × [ b q exp ( i κ q z ) + c q exp ( - i κ q z ) ] .
E I = exp ( i k 0 · r ) + m = - R m exp ( i k 1 m · r ) ,
E III = m = - T m exp [ i k 3 m · ( r - d z ^ ) ] ,
S 3 m · z ^ S inc · z ^ ,

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