Abstract

Various interference pattern formations have been investigated using six countering laser beams that form a six-sided pyramid. Phase shift and amplitude variations among the interfering beams are very useful for designing interference patterns summarized here. The interference patterns are categorized into 32 unit figures, and structural changes with different thresholds are investigated in detail.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  2. C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
    [CrossRef]
  3. B. R. Brown and A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969(1966).
    [CrossRef]
  4. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef]
  5. Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
    [CrossRef]
  6. Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
    [CrossRef]
  7. Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
    [CrossRef]
  8. Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
    [CrossRef]
  9. Y. Nakata, T. Hiromoto, and N. Miyanaga, “Frozen water drops in the nanoworld,” SPIE Newsroom (2009). DOI: 10.1117/2.1200906.1708.
    [CrossRef]
  10. Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
    [CrossRef]
  11. Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
    [CrossRef]
  12. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulse overlap,” Opt. Lett. 23, 1378–1380 (1998).
    [CrossRef]
  13. A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
    [CrossRef]
  14. R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
    [CrossRef]
  15. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
    [CrossRef]

2011 (1)

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

2010 (1)

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
[CrossRef]

2007 (1)

Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
[CrossRef]

2005 (2)

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

2004 (1)

Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
[CrossRef]

2003 (1)

Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
[CrossRef]

2002 (1)

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
[CrossRef]

1998 (1)

1997 (1)

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

1971 (1)

C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
[CrossRef]

1967 (1)

1966 (1)

Bjorkholm, J. E.

C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
[CrossRef]

Brown, B. R.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Crimmins, T. F.

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Grober, R. D.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Hiromoto, T.

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
[CrossRef]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef]

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef]

Kogelnik, H.

C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
[CrossRef]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Lohmann, A. W.

Lohmann, W.

Maeda, M.

Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
[CrossRef]

Maznev, A. A.

Miyanaga, N.

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
[CrossRef]

Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
[CrossRef]

Momoo, K.

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

Nakata, Y.

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
[CrossRef]

Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
[CrossRef]

Nelson, K. A.

Okada, T.

Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
[CrossRef]

Paris, D. P.

Prober, D. E.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Schoelkopf, R. J.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

Shank, C. V.

C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
[CrossRef]

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef]

Wegener, M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (2)

Y. Nakata, T. Okada, and M. Maeda, “Lithographical laser ablation using femtosecond laser,” Appl. Phys. A 79, 1481–1483 (2004).
[CrossRef]

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Mesoscopic nanomaterials generated by interfering femtosecond laser processing,” Appl. Phys. A 101, 471–474 (2010).
[CrossRef]

Appl. Phys. Lett. (4)

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides—application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable distributed-feedback dye laser,” Appl. Phys. Lett. 18, 395–396(1971).
[CrossRef]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81, 4239–4241 (2002).
[CrossRef]

Appl. Surf. Sci. (1)

Y. Nakata, N. Miyanaga, and T. Okada, “Effect of pulse width and fluence of femtosecond laser on the size of nanobump array,” Appl. Surf. Sci. 253, 6555–6557 (2007).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Nakata, T. Okada, and M. Maeda, “Nano-sized hollow bump array generated by single femtosecond laser pulse,” Jpn. J. Appl. Phys. 42, L1452–L1454 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Proc. SPIE (1)

Y. Nakata, K. Momoo, T. Hiromoto, and N. Miyanaga, “Generation of superfine structure smaller than 10 nm by interfering femtosecond laser processing,” Proc. SPIE 7920, 79200B (2011).
[CrossRef]

Other (1)

Y. Nakata, T. Hiromoto, and N. Miyanaga, “Frozen water drops in the nanoworld,” SPIE Newsroom (2009). DOI: 10.1117/2.1200906.1708.
[CrossRef]

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 (4)

Fig. 1.
Fig. 1.

Schematic of six countering interfering beams; (a) Six countering laser beams forming a six-sided pyramid and (b) top view of (a).

Fig. 2.
Fig. 2.

Interference patterns as a function of the phase shift of beam 1: (a) φa=0, (b) φa=1/4π, (c) φa=2/4π, (d) φa=3/4π, and (e) φa=π. The top diagrams are simulated interference patterns. The sets of six diagrams under the corresponding interference patterns are contour plots at different thresholds: (i) 95%, (ii) 90%, (iii) 85%, (iv) 80%, (v) 50%, and (vi) 20%, which are shown in the inset at the bottom right.

Fig. 3.
Fig. 3.

Interference patterns as a function of field intensity of interfering beams.

Fig. 4.
Fig. 4.

Interference patterns as a function of phase and field intensity of interfering beams.

Tables (1)

Tables Icon

Table 1. Shapes of Higher and Lower Fluence Regions (Bold, Lower Fluence Regions; Italic, Higher Fluence Regions)

Equations (2)

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

I(x,y,z)=|n=1,2,NEn(x,y,z,θint,n,,θrot,n,φn,t)|2dt,
En(x,y,z,θint,n,,θrot,n,φn,t)=En0cos(kcosθint,n*z+ksinθint,n*(xcosθrot,nysinθrot,n)ωt+φn),

Metrics