Abstract

Femtosecond laser direct writing is employed for the fabrication of buried tubular waveguides in bulk poly(methyl methacrylate). A novel technique using selective chemical etching is presented to resolve the two-dimensional refractive-index profile of the fabrication structures. End-to-end coupling in the waveguides reveals a near-field intensity distribution that results from the superimposition of several propagating modes with different azimuthal symmetries. Mode analysis of the tubular waveguides is performed using the finite-difference method, and the possible propagating mode profiles are compared with the experimental data.

© 2004 Optical Society of America

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References

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  1. D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.
  2. A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
    [CrossRef] [PubMed]
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  4. A. M. Streltsov and N. F. Borrelli, Opt. Lett. 26, 42 (2001).
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  6. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, J. Opt. Soc. Am. B 20, 1559 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. K. I. White, Opt. Quantum Electron. 11, 185 (1979).
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    [CrossRef] [PubMed]
  11. K. P. Chen, P. R. Herman, R. Taylor, and C. Hnatovsky, J. Lightwave Technol. 21, 1969 (2003).
    [CrossRef]
  12. R. S. Taylor and C. Hnatovsky, Opt. Express 11, 2775 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
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    [CrossRef]

2004 (1)

2003 (5)

2002 (1)

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

2001 (2)

B. C. Sarkar, P. K. Choudhury, and T. Yoshino, Microwave Opt. Technol. Lett. 31, 435 (2001).
[CrossRef]

A. M. Streltsov and N. F. Borrelli, Opt. Lett. 26, 42 (2001).
[CrossRef]

1999 (1)

1979 (1)

K. I. White, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

Bhardwaj, R.

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

Bhardwaj, V. R.

Borrelli, N. F.

Cerullo, G.

Chen, K. P.

Choudhury, P. K.

B. C. Sarkar, P. K. Choudhury, and T. Yoshino, Microwave Opt. Technol. Lett. 31, 435 (2001).
[CrossRef]

Coric, D.

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

Corkum, P. B.

R. S. Taylor, C. Hnatovsky, E. Simova, D. M. Rayner, M. Mehandale, V. R. Bhardwaj, and P. B. Corkum, Opt. Express 11, 775 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

De Silvestri, S.

Gaeta, A. L.

Herman, P. R.

K. P. Chen, P. R. Herman, R. Taylor, and C. Hnatovsky, J. Lightwave Technol. 21, 1969 (2003).
[CrossRef]

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

Hirao, K.

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

Hnatovsky, C.

Hô, N.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Homoelle, D.

Jaroszynski, D. A.

P. J. Scully, D. Jones, and D. A. Jaroszynski, J. Opt. A Pure Appl. Opt. 5, S92 (2003).
[CrossRef]

Jones, D.

P. J. Scully, D. Jones, and D. A. Jaroszynski, J. Opt. A Pure Appl. Opt. 5, S92 (2003).
[CrossRef]

Laporta, P.

Lopez, C.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Marangoni, M.

Mehandale, M.

Osellame, R.

Polli, D.

Qiu, J.

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

Ramponi, R.

Rayner, D. M.

R. S. Taylor, C. Hnatovsky, E. Simova, D. M. Rayner, M. Mehandale, V. R. Bhardwaj, and P. B. Corkum, Opt. Express 11, 775 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

Richardson, K.

Richardson, K. A.

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Richardson, M.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Rivero, C.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Sarkar, B. C.

B. C. Sarkar, P. K. Choudhury, and T. Yoshino, Microwave Opt. Technol. Lett. 31, 435 (2001).
[CrossRef]

Schulte, A.

Scully, P. J.

P. J. Scully, D. Jones, and D. A. Jaroszynski, J. Opt. A Pure Appl. Opt. 5, S92 (2003).
[CrossRef]

Shen, Y.

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

Si, J.

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

Simova, E.

Smith, C.

Streltsov, A. M.

Taccheo, S.

Taylor, R.

Taylor, R. S.

Vallée, R.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Wei, M.

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

White, K. I.

K. I. White, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

Wielandy, S.

Yoshino, T.

B. C. Sarkar, P. K. Choudhury, and T. Yoshino, Microwave Opt. Technol. Lett. 31, 435 (2001).
[CrossRef]

Zhai, J.

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

Zoubir, A.

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Hô, and R. Vallée, Opt. Lett. 29, 748 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

Appl. Phys. Lett. (1)

J. Si, J. Qiu, J. Zhai, Y. Shen, and K. Hirao, Appl. Phys. Lett. 80, 359 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A Pure Appl. Opt. (1)

P. J. Scully, D. Jones, and D. A. Jaroszynski, J. Opt. A Pure Appl. Opt. 5, S92 (2003).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

B. C. Sarkar, P. K. Choudhury, and T. Yoshino, Microwave Opt. Technol. Lett. 31, 435 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

K. I. White, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

Other (2)

D. Coric, M. Wei, P. R. Herman, R. Bhardwaj, P. B. Corkum, and D. M. Rayner, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 128–129.

A. Zoubir, M. Richardson, C. Rivero, C. Lopez, N. Hô, R. Vallée, and K. A. Richardson, in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 125–126.

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Figures (3)

Fig. 1
Fig. 1

(a) Difference interference contrast microscope image of the waveguide cross section. (b) Near-field intensity distribution at the waveguide output λ=632.8 nm.

Fig. 2
Fig. 2

(a) Three-dimensional cross-sectional surface profile after selective chemical etching, (b) corresponding refractive-index profile of a laser-written waveguide in bulk PMMA. The profile is centered on the waveguide core (Region II).

Fig. 3
Fig. 3

(a) Numerical simulation of the intensity distribution for the possible modes. (b) Measured near-field intensity distribution at the waveguide output λ=632.8 nm. (c) Calculated intensity distribution of the mode superimposition.

Equations (3)

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2ψ+n2c22ψt2=0,
ψ=vavJvuvr+bvYvuvrexpjvθ,
uv2=n22k2-βv2;

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