Abstract

In this paper, we experimentally demonstrate and compare single-exposure multiple-beam interference lithography based on conventional laser interference, evanescent wave interference, and surface plasmon interference. The proposed two-beam and four-beam interference approaches are carried out theoretically and verified experimentally, employing the proposed configurations so as to realize the patterning of one- and two-dimensional periodic features on photoresists. A custom-fabricated grating is employed in the configuration in order to achieve two- and four-beam interference.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
    [CrossRef]
  2. H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
    [CrossRef]
  3. M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
    [CrossRef]
  4. J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
    [CrossRef]
  5. N. Feth, C. Enkrich, M. Wegener, S. Linden, “Large-area magnetic metamaterials via compact interference lithography,” Opt. Express 15, 501–507 (2007).
    [CrossRef] [PubMed]
  6. R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
    [CrossRef]
  7. Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
    [CrossRef]
  8. N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
    [CrossRef]
  9. A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
    [CrossRef]
  10. W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
    [CrossRef] [PubMed]
  11. J. de Boor, N. Geyer, U. Gosele, and V. Schmidt, “Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning,” Opt. Lett. 34, 1783–1785 (2009).
    [CrossRef] [PubMed]
  12. C. Lu, X. K. Hu, S. S. Dimov, and R. H. Lipson, “Controlling large-scale film morphology by phase manipulation in interference lithography,” Appl. Opt. 46, 7202–7206 (2007).
    [CrossRef] [PubMed]
  13. J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80, 015401 (2009).
    [CrossRef]
  14. S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
    [CrossRef]
  15. P. S. Ramanujam, “Evanescent polarization holographic recording of sub-200nm gratings in an azobenzene polyester,” Opt. Lett. 28, 2375–2377 (2003).
    [CrossRef] [PubMed]
  16. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
    [CrossRef]
  17. R. J. Blaikie and S. J. McNab, “Evanescent interferometric lithography,” Appl. Opt. 40, 1692–1698 (2001).
    [CrossRef]
  18. J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A: Pure Appl. Opt. 8, S213–S218(2006).
    [CrossRef]
  19. J. K. Chua and V. M. Murukeshan, “UV laser-assisted multiple evanescent waves lithography for near-field nanopatterning,” Micro Nano Lett. 4, 210–214 (2009).
    [CrossRef]
  20. K. V. Sreekanth and V. M. Murukeshan, “Large-area maskless surface plasmon interference for one-and two-dimensional periodic nanoscale feature patterning,” J. Opt. Soc. Am. A 27, 95–99 (2010).
    [CrossRef]
  21. K. V. Sreekanth and V. M. Murukeshan, “Four beams surface plasmon interference nanoscale lithography for patterning of two-dimensional periodic features,” J. Vac. Sci. Technol. B 28, 128–130 (2010).
    [CrossRef]
  22. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–4782 (2004).
    [CrossRef]
  23. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
    [CrossRef]
  24. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
    [CrossRef] [PubMed]
  25. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
    [CrossRef]
  26. D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86, 253107 (2005).
    [CrossRef]
  27. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  28. A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
    [CrossRef] [PubMed]

2010 (2)

K. V. Sreekanth and V. M. Murukeshan, “Four beams surface plasmon interference nanoscale lithography for patterning of two-dimensional periodic features,” J. Vac. Sci. Technol. B 28, 128–130 (2010).
[CrossRef]

K. V. Sreekanth and V. M. Murukeshan, “Large-area maskless surface plasmon interference for one-and two-dimensional periodic nanoscale feature patterning,” J. Opt. Soc. Am. A 27, 95–99 (2010).
[CrossRef]

2009 (3)

J. de Boor, N. Geyer, U. Gosele, and V. Schmidt, “Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning,” Opt. Lett. 34, 1783–1785 (2009).
[CrossRef] [PubMed]

J. K. Chua and V. M. Murukeshan, “UV laser-assisted multiple evanescent waves lithography for near-field nanopatterning,” Micro Nano Lett. 4, 210–214 (2009).
[CrossRef]

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80, 015401 (2009).
[CrossRef]

2008 (3)

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
[CrossRef]

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

2007 (3)

2006 (3)

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A: Pure Appl. Opt. 8, S213–S218(2006).
[CrossRef]

2005 (2)

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
[CrossRef] [PubMed]

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86, 253107 (2005).
[CrossRef]

2004 (3)

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–4782 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

2003 (2)

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

P. S. Ramanujam, “Evanescent polarization holographic recording of sub-200nm gratings in an azobenzene polyester,” Opt. Lett. 28, 2375–2377 (2003).
[CrossRef] [PubMed]

2001 (2)

R. J. Blaikie and S. J. McNab, “Evanescent interferometric lithography,” Appl. Opt. 40, 1692–1698 (2001).
[CrossRef]

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

1999 (2)

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

1995 (2)

J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
[CrossRef]

N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
[CrossRef]

Acevedo, D. F.

A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
[CrossRef]

Anne, E.

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

Barbero, C. A.

A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
[CrossRef]

Blaikie, R. J.

Carole, E.

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

Carter, J.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Chen, G. X.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Chen, S. C.

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86, 253107 (2005).
[CrossRef]

Chen, X.

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Chong, T. C.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Chua, J. K.

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80, 015401 (2009).
[CrossRef]

J. K. Chua and V. M. Murukeshan, “UV laser-assisted multiple evanescent waves lithography for near-field nanopatterning,” Micro Nano Lett. 4, 210–214 (2009).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
[CrossRef]

Crozier, K. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

de Boor, J.

Dimov, S. S.

Divliansky, I. B.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Du, C.

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Elings, V. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Enkrich, C.

Evans, P. G.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Farhoud, M.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Ferrell, T. L.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Ferrera, J.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Feth, N.

Fu, Y.

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Geyer, N.

Ghislain, L. P.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Gosele, U.

J. de Boor, N. Geyer, U. Gosele, and V. Schmidt, “Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning,” Opt. Lett. 34, 1783–1785 (2009).
[CrossRef] [PubMed]

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

Harwryluk, A. M.

J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
[CrossRef]

Hong, M. H.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Hu, X. K.

Ishihara, T.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–4782 (2004).
[CrossRef]

Ji, R.

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

Kania, D. R.

J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
[CrossRef]

Keating, C. D.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Khoo, I. C.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Kino, G. S.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Kramer, N.

N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
[CrossRef]

Lasagni, A. F.

A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
[CrossRef]

Lee, W.

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

Lereu, L.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Li, H.

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Linden, S.

Lipson, R. H.

Liu, Z. W.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
[CrossRef] [PubMed]

Lochtenburg, A. J.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Lougnot, D. J.

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

Lu, C.

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Luo, X.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–4782 (2004).
[CrossRef]

Mallouk, T. E.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Manalis, S. R.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Martinez-Anton, J. C.

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A: Pure Appl. Opt. 8, S213–S218(2006).
[CrossRef]

Mayer, T. S.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

McNab, S. J.

Meriaudeau, F.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Minne, S. C.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Mucklich, F.

A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
[CrossRef]

Murphy, T. E.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Murukeshan, V. M.

K. V. Sreekanth and V. M. Murukeshan, “Large-area maskless surface plasmon interference for one-and two-dimensional periodic nanoscale feature patterning,” J. Opt. Soc. Am. A 27, 95–99 (2010).
[CrossRef]

K. V. Sreekanth and V. M. Murukeshan, “Four beams surface plasmon interference nanoscale lithography for patterning of two-dimensional periodic features,” J. Vac. Sci. Technol. B 28, 128–130 (2010).
[CrossRef]

J. K. Chua and V. M. Murukeshan, “UV laser-assisted multiple evanescent waves lithography for near-field nanopatterning,” Micro Nano Lett. 4, 210–214 (2009).
[CrossRef]

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80, 015401 (2009).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
[CrossRef]

Nielsch, K.

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

Niesten, M.

N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
[CrossRef]

Nishimura, S.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Passian, A.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Pena, D.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Quate, C. F.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Ramanujam, P. S.

Ross, C.

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

Ross, C. A.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Sainov, S.

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

Scahattenburg, M. L.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Schmidt, V.

Scholz, R.

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

Schonenberger, C.

N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
[CrossRef]

Shao, D. B.

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86, 253107 (2005).
[CrossRef]

Shi, L. P.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Shishido, A.

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

Smith, H. I.

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

Spallas, J. P.

J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
[CrossRef]

Sreekanth, K. V.

K. V. Sreekanth and V. M. Murukeshan, “Four beams surface plasmon interference nanoscale lithography for patterning of two-dimensional periodic features,” J. Vac. Sci. Technol. B 28, 128–130 (2010).
[CrossRef]

K. V. Sreekanth and V. M. Murukeshan, “Large-area maskless surface plasmon interference for one-and two-dimensional periodic nanoscale feature patterning,” J. Opt. Soc. Am. A 27, 95–99 (2010).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Tan, H. L.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Thundat, T.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Wegener, M.

Wei, Q. H.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
[CrossRef] [PubMed]

Wie, Q.

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

Wig, A.

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Wilder, K.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Zhang, X.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Adv. Eng. Mater. (1)

A. F. Lasagni, D. F. Acevedo, C. A. Barbero, and F. Mucklich, “One-step production of organized surface architectures on polymeric materials by direct laser interference patterning,” Adv. Eng. Mater. 9, 99–103 (2007).
[CrossRef]

Adv. Mater. (1)

R. Ji, W. Lee, R. Scholz, U. Gosele, and K. Nielsch, “Templated fabrication of nanowire and nanoring arrays based on interference lithography and electrochemical deposition,” Adv. Mater. 18, 2593–2596 (2006).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (6)

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

I. B. Divliansky, A. Shishido, I. C. Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[CrossRef]

N. Kramer, M. Niesten, and C. Schonenberger, “Resistless high resolution optical lithography on silicon,” Appl. Phys. Lett. 67, 2989–2991 (1995).
[CrossRef]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–4782 (2004).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93, 093103 (2008).
[CrossRef]

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86, 253107 (2005).
[CrossRef]

J. Alloys Compd. (1)

Q. Wie, M. H. Hong, H. L. Tan, G. X. Chen, L. P. Shi, and T. C. Chong, “Fabrication of nanostructures with laser interference lithography,” J. Alloys Compd. 449, 261–264(2008).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A: Pure Appl. Opt. 8, S213–S218(2006).
[CrossRef]

S. Sainov, E. Anne, E. Carole, and D. J. Lougnot, “High spatial frequency evanescent wave holographic recording in photopolymers,” J. Opt. A: Pure Appl. Opt. 5, 142–146 (2003).
[CrossRef]

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

J. Vac. Sci. Technol. B (3)

M. Farhoud, J. Ferrera, A. J. Lochtenburg, T. E. Murphy, M. L. Scahattenburg, J. Carter, C. A. Ross, and H. I. Smith, “Fabrication of 200nm period nanomagnet arrays using interference lithography and a negative resist,” J. Vac. Sci. Technol. B 17, 3182–3185 (1999).
[CrossRef]

J. P. Spallas, A. M. Harwryluk, and D. R. Kania, “Field emitter array mask patterning using laser interference lithography,” J. Vac. Sci. Technol. B 13, 1973–1978 (1995).
[CrossRef]

K. V. Sreekanth and V. M. Murukeshan, “Four beams surface plasmon interference nanoscale lithography for patterning of two-dimensional periodic features,” J. Vac. Sci. Technol. B 28, 128–130 (2010).
[CrossRef]

Micro Nano Lett. (1)

J. K. Chua and V. M. Murukeshan, “UV laser-assisted multiple evanescent waves lithography for near-field nanopatterning,” Micro Nano Lett. 4, 210–214 (2009).
[CrossRef]

Nano Lett. (2)

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085–1088 (2004).
[CrossRef]

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5, 957–961 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Scr. (1)

J. K. Chua and V. M. Murukeshan, “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr. 80, 015401 (2009).
[CrossRef]

Sens. Actuators B (1)

H. Li, C. Du, X. Chen, and Y. Fu, “Ag dots array fabricated using laser interference technique for biosensing,” Sens. Actuators B 134, 940–944 (2008).
[CrossRef]

Small (1)

W. Lee, R. Ji, C. Ross, U. Gosele, and K. Nielsch, “Wafer-scale Ni imprint stamps for porous alumina membranes based on interference lithography,” Small 2, 978–982 (2006).
[CrossRef] [PubMed]

Ultramicroscopy (1)

A. Passian, A. Wig, L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area SP interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004).
[CrossRef] [PubMed]

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Interference between a pair of s-polarized incident plane waves.

Fig. 2
Fig. 2

Schematic illustration of setup to realize TIR-generated EWIL.

Fig. 3
Fig. 3

Schematic illustration of prism-coupling-based SPIL configuration.

Fig. 4
Fig. 4

Periodic grating lines with period 253 nm and linewidth 136 nm patterned in photoresist from two-beam LIL, exposure time 400 ms and development time 1 min . (a) 2D AFM image and (b) 3D AFM image.

Fig. 5
Fig. 5

Two-dimensional square array features patterned using four-beam LIL. The periodicity is 246 ± 11 nm , and pillars have a diameter of 128 ± 11 nm , exposure time of 400 ms , and development time of 1 min . (a) 2D AFM image and (b) 3D AFM image.

Fig. 6
Fig. 6

AFM image of one-dimensional grating lines patterned from two-beam EWIL. The obtained period is 187 nm , linewidth 97 nm , height 100 nm , exposure time 300 ms , and development time 1 min .

Fig. 7
Fig. 7

AFM images of features resulting from four-beam EWIL. Square array patterns with period 164 ± 11 nm , resolution 82 ± 11 nm , and height 100 nm is obtained; the exposure time is 300 ms , and the development time is 1 min .

Fig. 8
Fig. 8

AFM image of one-dimensional grating lines patterned from two-beam SPIL using Ag film. The obtained period is 175 nm , linewidth 93 nm , height 180 nm , exposure time 3 s , and development time 1 min .

Fig. 9
Fig. 9

AFM images of features resulting from four-beam SPIL using Ag film. Square array patterns with period 164 ± 11 nm , resolution 82 ± 11 nm , and height 160 nm are obtained with exposure time of 3 s and development time of 1 min .

Fig. 10
Fig. 10

AFM image of one-dimensional grating lines patterned from two-beam SPIL using Al film with the obtained period of 175 nm , linewidth 93 nm , height 200 nm , exposure time 25 s , and development time 2 min .

Fig. 11
Fig. 11

AFM images of features resulting from four-beam SPIL using Al film. Square array patterns with period of 164 ± 11 nm , resolution 82 ± 11 nm , height 180 nm , exposure time 25 s , and development time 2 min .

Tables (1)

Tables Icon

Table 1 Comparison Chart for Interference Lithography Techniques

Equations (15)

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

E s ( 1 ) = | τ s ( I , r ) | A 1 cos ( k r sin θ r x + k r cos θ r z 2 π T t + δ 1 + χ s ) exp ( k κ r z cos θ r ) e y ,
E s ( 2 ) = | τ s ( I , r ) | A 2 cos ( k r sin θ r x + k r cos θ r z 2 π T t + δ 2 + χ s ) exp ( k κ r z cos θ r ) e y .
I ( E s ( 1 ) + E s ( 2 ) ) ( E s ( 1 ) + E s ( 2 ) ) = | τ s ( I , r ) | 2 { A 1 2 2 + A 2 2 2 A 1 A 2 cos ( 2 k sin θ x δ 1 , 2 ) } exp ( 2 k κ r z cos θ r ) .
E p ( 1 ) = | τ p ( I , r ) | A 1 cos ( k r sin θ r x + k r cos θ r z 2 π T t + δ 1 + χ p ) ( cos θ r x + sin θ r z ) exp ( k κ r z cos θ r ) ,
E p ( 2 ) = | τ p ( I , r ) | A 2 cos ( k r sin θ r x + k r cos θ r z 2 π T t + δ 2 + χ p ) ( cos θ r e x sin θ r e z ) exp ( k κ r z cos θ r ) .
I | τ p ( I , r ) | 2 { A 1 2 2 + A 2 2 2 A 1 A 2 cos ( 2 θ r ) cos ( 2 k sin θ x δ 1 , 2 ) } exp ( 2 k κ r z cos θ r ) .
I 4 s | τ s ( I , r ) | 2 T 0 t exp [ l = 1 4 A l cos ( H s / 2 ) sin ( ϕ l ) ] 2 + [ w = 1 4 A w cos ( H s / 2 ) cos ( ϕ l ) ] 2 t ,
I 4 p | τ p ( I , r ) | 2 2 T 0 t exp { ( 1 + cos ( 2 θ r ) ) [ [ l = 1 4 A l cos ( H p / 2 ) sin ( ϕ w ) ] 2 + [ l = 1 4 A l cos ( H / p 2 ) cos ( ϕ l ) ] 2 ] + ( 1 cos ( 2 θ r ) ) [ l = 1 4 A l cos ( H p / 2 ) ] } t ,
H s , p = 2 ( χ s , p + δ 1 , 2 ) + 2 k r cos θ r z + 2 k r sin θ r sin ϕ l y + 2 k r cos θ r sin ϕ l x 4 π t / T .
I e | 2 s E e 2 | 2 s = 2 A 2 | τ p ( i , r ) | 2 exp ( 2 k Q z ) ( 1 + cos ( 2 k n i sin θ i x ) ) ,
E e 2 | 2 p = 1 2 A 2 | τ p ( i , r ) | 2 exp ( 2 k Q z ) × { 4 G 2 cos ( 2 k n i sin θ i x ) + 2 n i r 2 ( 1 cos 2 θ i ) ( 1 cos ( 2 k n i sin θ i x ) ) } ,
G = κ r 2 ( 1 + q ( θ r ) ) 2 + q 2 ( θ r ) n r 2 q ( θ r ) .
E e 2 | 4 s = 2 A | τ p ( i , r ) | 2 exp ( 2 k Q z ) { cos ( 2 k n i sin θ i x ) + cos ( 2 k n i sin θ i y ) 2 } .
E e 2 | 4 p = 1 2 A | τ p ( i , r ) | 2 exp ( 2 k Q z ) { 4 G 2 [ cos ( 2 k n i sin θ i x ) + cos ( 2 k n i sin θ i y ) ] 4 n i r 2 cos 2 θ i + 8 G 2 + 4 n i r 2 + n i r 2 ( 1 cos 2 θ i ) × [ 4 cos ( 2 k n i sin θ i ( x y ) ) 4 cos ( 2 k n i sin θ i ( x + y ) ) 4 cos ( 2 k n i sin θ i ( x y ) ) 4 cos ( 2 k n i sin θ i ( x + y ) ) ] } ,
| ψ 1 + ψ 2 | 2 = 2 | ψ 0 | 2 [ 1 + cos ( 4 π ε d sin θ S p λ ) x ] ,

Metrics