Abstract

An interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries, and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular, and elliptical scatterers which are arranged in parallelogram, triangular, and square lattices (with different lattice constants) can be obtained. The photonic bandgaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency (ωa/2πc) of photonic bandgap structures with an equal filling factor are very similar regardless of the interference angle. The results are helpful in designing the forbidden frequency when the lattice constant and the scatterer shape can be controlled by the interferometric lithographic technique.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).
  2. S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," J. Vac. Sci. Technol. B 11, 658-666 (1993).
    [CrossRef]
  3. N. D. Lai, W. P. Liang, J. H. Lin, and C. C. Hsu, "Rapid fabrication of large-area periodic structures containing well-defined defects by combining holography and mask techniques," Opt. Express 13, 5331-5337 (2005).
    [CrossRef] [PubMed]
  4. E. J. Yablonovitch, "Photonic bandgap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  5. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
    [CrossRef] [PubMed]
  6. K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
    [CrossRef]
  7. K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
    [CrossRef]
  8. R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
    [CrossRef] [PubMed]
  9. R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
    [CrossRef]
  10. W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
    [CrossRef]
  11. C. C. Cheng and A. Scherer, "Fabrication of photonic bandgap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
    [CrossRef]
  12. E. Chow, S. Y. Lin, and J. R. Wendt, "Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ = 1.55 μm wavelengths," Opt. Lett. 26, 286-288 (2001).
    [CrossRef]
  13. L. Pang, W. Nakagawa, and Y. Fainman, "Fabrication of two-dimensional photonic crystals with controlled defects by use of multiple exposures and direct write," Appl. Opt. 42, 5450-5456 (2003).
    [CrossRef] [PubMed]
  14. F. Quiñónez, J. W. Menezes, L. Cescato, V. F. Rodriguez-Esquerre, H. Hernandez-Figueroa, and R. D. Mansano, "Bandgap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Express 14, 8578-8583 (2006).
    [CrossRef]
  15. J. W. Menezes, L. Cescato, E. J. de Carvalho, and E. S. Braga, "Recording different geometries of 2D hexagonal photonic crystals by choosing the phase between two-beam interference exposures," Opt. Express 14, 4873-4879 (2006).
    [CrossRef] [PubMed]
  16. A. Fernandez and D. W. Phillion, "Effects of phase shifts on four-beam interference patterns," Appl. Opt. 37, 473-478 (1998).
    [CrossRef]
  17. I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
    [CrossRef]
  18. H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
    [CrossRef]
  19. C. W. Chien, J. C. Chen, and J. Y. Lee, "Applying an interferometric exposure model to analyze the influences of process parameters on the linewidth," Appl. Opt. 45, 8278-8287 (2006).
    [CrossRef] [PubMed]
  20. K. M. Leung and Y. F. Liu, "Large complete bandgap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610-10612 (1990).
  21. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  22. S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  23. X. L. Yang, L. Z. Cai, and Q. Liu, "Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three noncoplanar beams," Opt. Express 11, 1050-1055 (2003).
    [CrossRef] [PubMed]
  24. B. A. Mello, I. F. Costa, L. Cescato, and C. R. A. Lima, "Developed profile of holographically exposed photoresist gratings," Appl. Opt. 34, 597-603 (1995).
    [CrossRef]
  25. A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
    [CrossRef]
  26. J. D. Joannopouls, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).
  27. O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
    [CrossRef]

2006

2005

2004

W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
[CrossRef]

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
[CrossRef]

2003

X. L. Yang, L. Z. Cai, and Q. Liu, "Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three noncoplanar beams," Opt. Express 11, 1050-1055 (2003).
[CrossRef] [PubMed]

L. Pang, W. Nakagawa, and Y. Fainman, "Fabrication of two-dimensional photonic crystals with controlled defects by use of multiple exposures and direct write," Appl. Opt. 42, 5450-5456 (2003).
[CrossRef] [PubMed]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

2002

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

2001

2000

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

1998

1997

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

1995

1993

S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," J. Vac. Sci. Technol. B 11, 658-666 (1993).
[CrossRef]

E. J. Yablonovitch, "Photonic bandgap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
[CrossRef]

1990

K. M. Leung and Y. F. Liu, "Large complete bandgap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610-10612 (1990).

M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Barclay, P. E.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Barthlott, W.

R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
[CrossRef] [PubMed]

Braga, E. S.

Brueck, S. R. J.

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," J. Vac. Sci. Technol. B 11, 658-666 (1993).
[CrossRef]

Cabuz, A. I.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Cai, L. Z.

Carpio, R. A.

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

Cassagne, D.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Centeno, E.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Cerrina, F.

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

Cescato, L.

Chan, C. T.

M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chan, T. Y. M.

O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
[CrossRef]

Chen, J.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Chen, J. C.

Chen, X.

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

Cheng, C. C.

C. C. Cheng and A. Scherer, "Fabrication of photonic bandgap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

Chien, C. W.

Cho, A. Y.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Chow, E.

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Costa, I. F.

David, C.

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

de Carvalho, E. J.

Fainman, Y.

Fernandez, A.

Furstner, R.

R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
[CrossRef] [PubMed]

Gareth, H. M.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Gehan, A. J. A.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Gmachl, C.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Gobrecht, J.

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

Grigaliunas, V.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Gu, B. Y.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Hernandez-Figueroa, H.

Ho, M.

M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Hou, Z. L.

W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
[CrossRef]

Hsu, C. C.

Joannopoulos, J.

Joannopouls, J. D.

J. D. Joannopouls, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

John, S.

O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
[CrossRef]

Johnson, S.

Jose, B.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Karen, K. G.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Kenneth, B. K. T.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Kenneth, K. S. L.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Kopustinskas, V.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Kuang, W. M.

W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
[CrossRef]

Lai, N. D.

Lee, J. Y.

Leung, K. M.

K. M. Leung and Y. F. Liu, "Large complete bandgap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610-10612 (1990).

Liang, W. P.

Lima, C. R. A.

Lin, J. H.

Lin, S. Y.

Liu, Q.

Liu, Y. F.

K. M. Leung and Y. F. Liu, "Large complete bandgap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610-10612 (1990).

Liu, Y. Y.

W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
[CrossRef]

Manish, C.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Mansano, R. D.

Mead, R. D.

J. D. Joannopouls, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

Mello, B. A.

Menezes, J. W.

Meskinis, S.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Mickervicius, J.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Mikulskas, I.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Nakagawa, W.

Neinhuis, C.

R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
[CrossRef] [PubMed]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Painter, O.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Pang, L.

Petersen, J. S.

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

Phillion, D. W.

Quiñónez, F.

Rodriguez-Esquerre, V. F.

Scherer, A.

C. C. Cheng and A. Scherer, "Fabrication of photonic bandgap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

Solak, H. H.

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

Soukoulis, C. M.

M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Srinivasan, K.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Toader, O.

O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
[CrossRef]

Tomasiunas, R.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Vaitkus, J.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

Walzel, P.

R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
[CrossRef] [PubMed]

Wang, L.

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

Wang, R. Z.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Wang, X. H.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Wendt, J. R.

William, I. M.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Winn, J. N.

J. D. Joannopouls, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

Yablonovitch, E. J.

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Yang, G. Z.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Yang, X. L.

Zaidi, S. H.

S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," J. Vac. Sci. Technol. B 11, 658-666 (1993).
[CrossRef]

Zhang, Z.

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

Appl. Opt.

Appl. Phys. Lett.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystal," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Appl. Surf. Sci.

I. Mikulskas, J. Mickervicius, J. Vaitkus, R. Tomasiunas, V. Grigaliunas, V. Kopustinskas, and S. Meskinis, "Fabrication of photonic structures by means of interference lithography and reactive ion etching," Appl. Surf. Sci. 186, 599-603 (2002).
[CrossRef]

J. Appl. Phys.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Vac. Sci. Technol. B

S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," J. Vac. Sci. Technol. B 11, 658-666 (1993).
[CrossRef]

C. C. Cheng and A. Scherer, "Fabrication of photonic bandgap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, "Multiple-beam interference lithography with electron beam written gratings," J. Vac. Sci. Technol. B 20, 2844-2848 (2002).
[CrossRef]

Langmuir

R. Furstner, W. Barthlott, C. Neinhuis, and P. Walzel, "Wetting and self-cleaning properties of artificial superhydrophobic surfaces," Langmuir 21, 956-961 (2005).
[CrossRef] [PubMed]

Nano Lett.

K. S. L. Kenneth, B. Jose, B. K. T. Kenneth, C. Manish, A. J. A. Gehan, I. M. William, H. M. Gareth, and K. G. Karen, "Superhydrophobic carbon nanotube forests," Nano Lett. 3, 1701-1705 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

W. M. Kuang, Z. L. Hou, and Y. Y. Liu, "The effects of shapes and symmetries of scattererers on the phononic bandgap in 2D phononic crystals," Phys. Lett. A 322, 481-490 (2004).
[CrossRef]

Phys. Rev. B

K. M. Leung and Y. F. Liu, "Large complete bandgap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610-10612 (1990).

Phys. Rev. Lett.

M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

O. Toader, T. Y. M. Chan, and S. John, "Photonic bandgap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905-1-043905-4 (2004).
[CrossRef]

Science

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Other

X. Chen, Z. Zhang, S. R. J. Brueck, R. A. Carpio, and J. S. Petersen, "Process development for 180 nm structures using interferometric lithography and I-line photoresist," in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE 3048, 309-318 (1997).

J. D. Joannopouls, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

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 (10)

Fig. 1
Fig. 1

(Color online) Schematic experimental arrangement of the interferometric lithographic system.

Fig. 2
Fig. 2

(Color online) Normalized isointensity surface of the 2D simulation results superposed by a pair of 1D interference fringes with intensities of I 0 1 = I Φ 2 = I and Φ 2 = ( a ) 15°, (b) 50°, (c) 90°.

Fig. 3
Fig. 3

Two-dimensional periodic structures at rotational angles of Φ 1 = 0 ° and Φ 2 = ( a ) 15 ° , (b) 50°, (c) 90° under the same exposure energy per step and a 10 s development time at room temperature.

Fig. 4
Fig. 4

Two-dimensional periodic structures given the same exposure energy per step at rotational angles of Φ 1 = 0 ° , and (a) Φ 2 = 50 ° and a 13 s development time at room temperature, (b) Φ 2 = 90 ° and a 18 s development time at room temperature.

Fig. 5
Fig. 5

Two-dimensional air rods in photoresist at rotational angles of Φ 1 = 0 ° and Φ 2 = 15 ° , an average exposure energy of 10 mJ / cm 2 for a single beam, and a 10 s development time, at room temperature.

Fig. 6
Fig. 6

(Color online) Normalized long and short side period simulation results at different ΔΦ.

Fig. 7
Fig. 7

(Color online) Scattering lattice at Δ Φ = ( a ) 30° (parallelogram), (b) 60° (triangular), (c) 90° (square).

Fig. 8
Fig. 8

Simulation axial angle results θ L at different Δ Φ angles.

Fig. 9
Fig. 9

(Color online) Photonic band structure of H polarization for triangular rods in air, when Δ Φ = 60 ° and f = 0.024 , at an interference angle of (a) 30° and (b) 10°.

Fig. 10
Fig. 10

(Color online) Gap–midgap ratio ω R as a function of the filling factor f for PCs with different substrate rotational angle in elliptic rods.

Tables (2)

Tables Icon

Table 1 Constant Values of the Parameters in the Normalized Period Equation

Tables Icon

Table 2 Properties of the PBG Structures Under Different Substrate Rotational Angles

Equations (16)

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

E ( x , y , z ) = E 0 × exp [ r 2 w 0 2 ] × exp i ( k r k ) ,
r = x 2 + y 2 ,
I = | E 1 + E 2 | 2 t ,
I = ( I 01 + I 02 ) [ 1 + V cos ( 2 π P x ) ] × exp [ 2 ( x 2 w 0 x 2 sec 2 θ i + y 2 w 0 y 2 ) ] ,
P = λ 2 sin θ i ,
I M E = l I Φ l ,
× [ 1 ε ( r ) × H ] = ω 2 c 2 H ,
H ( r ) = G j = 1 , 2 H G , j e ^ j exp i ( k + G ) r ,
ε ( r ) = G ε ( G ) exp i ( G r ) ,
ε ( G ) = 1 S S ε ( r ) exp [ i ( G r ) ] d r ,
G | k + G | | k + G | ε 1 ( G G ) H G , 1 = ω 2 c 2 H G , 1 .
NP L o n g = L o n g s i d e P e r i o d P ,
NP S h o r t = S h o r t s i d e P e r i o d P .
NP L o n g = P L 1 exp ( Δ Φ F L 1 ) + P L 2 exp ( Δ Φ F L 2 ) + P L 3 exp ( Δ Φ F L 3 ) + P L 0 ,
NP S h o r t = P S 1 exp ( Δ Φ F S 1 ) + P S 0 ,
b = 1 2 a × sec θ L ,

Metrics