Abstract

We demonstrate the coupling of a 2×2 waveguide array produced by a femtosecond laser in fused silica. The coupling constants of the waveguide array are obtained by measuring the ratio of output power of each waveguide by the coupled-mode theory. The variation of the coupled power between four waveguides as a function of the propagation distance is investigated experimentally and theoretically.

©2007 Optical Society of America

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  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
    [Crossref] [PubMed]
  2. K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
    [Crossref]
  3. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001).
    [Crossref]
  4. D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
    [Crossref]
  5. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
    [Crossref] [PubMed]
  6. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposes to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999).
    [Crossref]
  7. A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26, 42–43 (2001).
    [Crossref]
  8. K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26, 1516–1518 (2001).
    [Crossref]
  9. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
    [Crossref] [PubMed]
  10. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24, 646–648 (1999).
    [Crossref]
  11. E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T.-H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21, 2023 (1996).
    [Crossref] [PubMed]
  12. E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882 (1997).
    [Crossref]
  13. W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
    [Crossref]
  14. W. Watanabe and K. Itoh, “Motion of bubble in solid by femtosecond laser pulses,” Opt. Express. 10, 603 (2002).
    [PubMed]
  15. A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
    [Crossref]
  16. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
    [Crossref] [PubMed]
  17. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13, 459 (1996).
    [Crossref]
  18. M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
    [Crossref]

2006 (3)

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

2002 (1)

W. Watanabe and K. Itoh, “Motion of bubble in solid by femtosecond laser pulses,” Opt. Express. 10, 603 (2002).
[PubMed]

2001 (3)

2000 (1)

1999 (2)

1998 (1)

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

1997 (2)

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882 (1997).
[Crossref]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

1996 (3)

An, R.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Asano, T.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

Blomer, D.

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

Borrelli, N. F.

Brodeur, A.

Burghoff, J.

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

Callan, J. P.

Cheng, Z.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Davis, K. M.

Dou, Y.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Feit, M. D.

Finlay, R. J.

Fujimoto, J. G.

Gaeta, A. L.

Garcia, J. F.

Glezer, E. N.

Gong, Q.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Hartl, I.

Hayashi, K.

Her, T.-H.

Herman, S.

Hirao, K.

Homoelle, D.

Huang, L.

Inouye, H.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

Ippen, E. P.

Itoh, K.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

W. Watanabe and K. Itoh, “Motion of bubble in solid by femtosecond laser pulses,” Opt. Express. 10, 603 (2002).
[PubMed]

W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
[Crossref]

Kautek, W.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Kazansky, P. G.

Kondo, Y.

Kowalevicz, A. M.

Krausz, F.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Krueger, J.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Lederer, F.

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

Lenzner, M.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Li, Y.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Liu, D.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Mazur, E.

Milosavljevic, M.

Minoshima, K.

Mitsuyu, T.

Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24, 646–648 (1999).
[Crossref]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

Miura, K.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[Crossref] [PubMed]

Mourou, G.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Nishii, J.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
[Crossref]

Nolte, S.

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

Nouchi, K.

Perry, M. D.

Pertsch, T.

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

Peschel, U.

Qiu, J.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

Rubenchik, A. M.

Sartania, S.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Schaffer, C. B.

Shore, B. W.

Smith, C.

Spielmann, Ch.

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

Streltsov, A. M.

Stuart, B. C.

Sugimoto, N.

Szameit, A.

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

Toma, T.

Tunnermann, A.

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

Tünnermann, A.

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

Watanabe, M.

Watanabe, W.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

W. Watanabe and K. Itoh, “Motion of bubble in solid by femtosecond laser pulses,” Opt. Express. 10, 603 (2002).
[PubMed]

W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
[Crossref]

Wielandy, S.

Will, M.

Yamada, K.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
[Crossref]

Yang, H.

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Appl. Phys. A. (1)

D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A. 84, 257–260 (2006).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

A. Szameit, D. Blomer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tunnermann, “Hexagonal waveguide arrays written with fs-laser pulses”, Appl. Phys. B: Lasers Opt. 82, 507 (2006).
[Crossref]

Appl. Phys. Lett. (2)

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882 (1997).
[Crossref]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[Crossref]

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

Opt. Express. (2)

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional solitons in cubic fs laser written waveguide arrays in fused silica,” Opt. Express. 14, 6055 (2006).
[Crossref] [PubMed]

W. Watanabe and K. Itoh, “Motion of bubble in solid by femtosecond laser pulses,” Opt. Express. 10, 603 (2002).
[PubMed]

Opt. Lett. (9)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[Crossref] [PubMed]

W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25, 1669 (2000).
[Crossref]

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001).
[Crossref]

Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24, 646–648 (1999).
[Crossref]

E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T.-H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21, 2023 (1996).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29,468 (2004).
[Crossref] [PubMed]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposes to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999).
[Crossref]

A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26, 42–43 (2001).
[Crossref]

K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26, 1516–1518 (2001).
[Crossref]

Opt.Lett. (1)

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt.Lett. 28, 2491–2493 (2003).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Lenzner, J. Krueger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80, 4076 (1998).
[Crossref]

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Figures (5)
Fig. 1.
Fig. 1. Scheme of the writing process in transparent bulk material using fs laser pulses. Inset: Microscopic image of the end facet of the sample of the 2× 2 waveguide array marked in Arabic numerals. The waveguide to waveguide spacing is 20 μm.

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Fig. 2.
Fig. 2. Contour plots of simulated electron density profiles.

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Fig. 3.
Fig. 3. Experiment setup for the investigation of output intensity distribution

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Fig. 4.
Fig. 4. Output intensity distribution for excitation of different waveguides of a 2 × 2 waveguide array

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Fig. 5.
Fig. 5. The coupled powers of waveguide as a function of propagation distance x.

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Equations (8)

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

dρ dt = αI ( t ) ρ ( t ) + σ k I k ( t )
I ( x , y , z , t ) = I 0 ( ω 0 ω ( z ) ) 2 exp [ − 2 ( x 2 + y 2 ) ω ( z ) 2 ] exp [ − ( t τ p ) 2 ] ,
{ i da 1 dx + c h a 2 + c v a 3 + i γ ∣ a 1 ∣ 2 a 1 = 0 i da 2 dx + c h a 1 + c v a 4 + i γ ∣ a 2 ∣ 2 a 2 = 0 i da 3 dx + c h a 4 + c v a 1 + i γ ∣ a 3 ∣ 2 a 3 = 0 i da 4 dx + c h a 3 + c v a 2 + i γ ∣ a 4 ∣ 2 a 4 = 0
{ a 1 = cos ( c h x ) cos ( c v x ) a 2 = i sin ( c h x ) cos ( c v x ) a 3 = i cos ( c h x ) sin ( c v x ) a 4 = − sin ( c h x ) sin ( c v x )
p 1 ( x ) = cos 2 ( c h x ) cos 2 ( c v x ) , p 2 ( x ) = sin 2 ( c h x ) cos 2 ( c v x ) ,
p 3 ( x ) = cos 2 ( c h x ) sin 2 ( c v x ) , p 4 ( x ) = sin 2 ( c h x ) sin 2 ( c v x ) ,
P 3 ( x ) P 1 ( x ) = sin 2 ( c v x ) cos 2 ( c v x ) = 1.448 ,
P 4 ( x ) P 3 ( x ) = sin 2 ( c h x ) cos 2 ( c h x ) = 1.309 ,

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