Abstract

We describe the theoretical and experimental analysis of light propagation in tapered, air-core waveguides with omnidirectional reflector claddings. For light within the omnidirectional band, nearly vertical out-ofplane radiation at wavelength-dependent positions along the length of the taper was observed. The coupling positions correspond to the core sizes at which individual modes approach cutoff. The leaky nature and low scattering loss of the waveguides enabled the direct imaging of modal interference and standing waves. The out-coupling experiments were corroborated by in-coupling experiments and by a theoretical analysis. The mechanism described might find application to three-dimensional optical integration, on-chip spectroscopy, and wavelength division multiplexing.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
    [CrossRef]
  2. M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
    [CrossRef]
  3. Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 5828-5831 (2004).
    [CrossRef]
  4. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
    [CrossRef]
  5. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
    [CrossRef] [PubMed]
  6. S.-S. Lo, M.-S. Wang, and C.-C. Chen, " Semiconductor hollow optical waveguides formed by omni-directional reflectors," Opt. Express 12, 6589-6593 (2004).
    [CrossRef] [PubMed]
  7. Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
    [CrossRef]
  8. R. G. DeCorby, N. Ponnampalam, H. T. Nguyen, M. M. Pai, and T. J. Clement, "Guided self-assembly of integrated hollow Bragg waveguides," Opt. Express 15, 3902-3915 (2007).
    [CrossRef] [PubMed]
  9. N. Ponnampalam and R. G. DeCorby, "Self-assembled hollow waveguides with hybrid metal-dielectric Bragg claddings," Opt. Express 15, 12595-12604 (2007).
    [CrossRef] [PubMed]
  10. G. Roelkens, D. Van Thourhout, and R. Baets, "High efficiency silicon-on-insulator grating coupler based on a poly-silicon overlay," Opt. Express 14, 11622-11630 (2006).
    [CrossRef] [PubMed]
  11. B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
    [CrossRef]
  12. P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
    [CrossRef]
  13. J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
    [CrossRef]
  14. A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
    [CrossRef]
  15. F. Lederer, U. Trutschel, and C. Waechter, "Prismless excitation of guided waves," J. Opt. Soc. Am. A 8, 1536-1540 (1991).
    [CrossRef]
  16. T. Miura, Y. Yokota, and F. Koyama, "Proposal of tunable demultiplexer based on tapered hollow waveguides with highly reflective multilayer mirrors," Proc. of LEOS 2005, 272-273 (2005).
  17. N. Ponnampalam and R. G. DeCorby, "Analysis and fabrication of hybrid metal-dielectric omnidirectional Bragg reflectors," Appl. Opt. 47, 30-37 (2008).
    [CrossRef]
  18. M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
    [CrossRef]
  19. J. Colin, C. Coupeau, and J. Grilhe, "Plastic folding of buckling structures," Phys. Rev. Lett. 99, 046101-1-4 (2007).
    [CrossRef] [PubMed]
  20. T. J. Clement, N. Ponnampalam, H. T. Nguyen, and R. G. DeCorby, "Improved omnidirectional reflectors in chalcogenide glass and polymer by using the silver doping technique," Opt. Express 14, 1789-1796 (2006).
    [CrossRef] [PubMed]
  21. R. G. DeCorby, N. Ponnampalam, H. T. Nguyen, and T. J. Clement, "Robust and flexible free-standing all-dielectric omnidirectional reflectors," Adv. Mater. 19, 193-196 (2007).
    [CrossRef]
  22. A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
    [CrossRef]
  23. B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
    [CrossRef]
  24. W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
    [CrossRef]
  25. T. Tamir, "Leaky waves in planar optical waveguides," Nouv. Rev. Opt. 6, 273-284 (1975).
    [CrossRef]
  26. A. Yariv and P. Yeh, Optical Waves in Crystals, (John Wiley and Sons, New York, 1984), Chap. 11.
  27. D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
    [CrossRef]
  28. D. I. Babic and S. W. Corzine, "Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors," IEEE J. Quantum Electron. 28, 514-524 (1992).
    [CrossRef]
  29. C. H. Tang, "Delay equalization by tapered cutoff waveguides," IEEE Trans. Microwave Theory Tech. 12, 608-615 (1964).
    [CrossRef]
  30. O. Schmidt, P. Kiesel, and M. Bassler, "Performance of chip-size wavelength detectors," Opt. Express 15, 9701-9706 (2007).
    [CrossRef] [PubMed]
  31. M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
    [CrossRef]

2008 (1)

2007 (5)

2006 (4)

T. J. Clement, N. Ponnampalam, H. T. Nguyen, and R. G. DeCorby, "Improved omnidirectional reflectors in chalcogenide glass and polymer by using the silver doping technique," Opt. Express 14, 1789-1796 (2006).
[CrossRef] [PubMed]

G. Roelkens, D. Van Thourhout, and R. Baets, "High efficiency silicon-on-insulator grating coupler based on a poly-silicon overlay," Opt. Express 14, 11622-11630 (2006).
[CrossRef] [PubMed]

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

2004 (4)

S.-S. Lo, M.-S. Wang, and C.-C. Chen, " Semiconductor hollow optical waveguides formed by omni-directional reflectors," Opt. Express 12, 6589-6593 (2004).
[CrossRef] [PubMed]

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 5828-5831 (2004).
[CrossRef]

2003 (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

2002 (3)

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

1999 (1)

1994 (1)

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

1992 (2)

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

D. I. Babic and S. W. Corzine, "Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors," IEEE J. Quantum Electron. 28, 514-524 (1992).
[CrossRef]

1991 (1)

1987 (1)

A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
[CrossRef]

1984 (1)

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

1975 (2)

P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
[CrossRef]

T. Tamir, "Leaky waves in planar optical waveguides," Nouv. Rev. Opt. 6, 273-284 (1975).
[CrossRef]

1964 (1)

C. H. Tang, "Delay equalization by tapered cutoff waveguides," IEEE Trans. Microwave Theory Tech. 12, 608-615 (1964).
[CrossRef]

Akiyama, S.

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

Babic, D. I.

D. I. Babic and S. W. Corzine, "Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors," IEEE J. Quantum Electron. 28, 514-524 (1992).
[CrossRef]

Baets, R.

G. Roelkens, D. Van Thourhout, and R. Baets, "High efficiency silicon-on-insulator grating coupler based on a poly-silicon overlay," Opt. Express 14, 11622-11630 (2006).
[CrossRef] [PubMed]

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Bassler, M.

Benisty, H.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Bermel, P.

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

Bienstman, P.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Bockstaele, R.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Cheben, P.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Chen, C.-C.

Chigrin, D. N.

Chow, Y. L.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Clement, T. J.

Colin, J.

J. Colin, C. Coupeau, and J. Grilhe, "Plastic folding of buckling structures," Phys. Rev. Lett. 99, 046101-1-4 (2007).
[CrossRef] [PubMed]

Corzine, S. W.

D. I. Babic and S. W. Corzine, "Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors," IEEE J. Quantum Electron. 28, 514-524 (1992).
[CrossRef]

Coupeau, C.

J. Colin, C. Coupeau, and J. Grilhe, "Plastic folding of buckling structures," Phys. Rev. Lett. 99, 046101-1-4 (2007).
[CrossRef] [PubMed]

DeCorby, R. G.

Delage, A.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Delbeke, D.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Duan, X.

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

Fink, Y.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Gaponenko, S. V.

Gaylord, T. K.

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

Ghatak, A. K.

A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
[CrossRef]

Glytsis, E. N.

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

Grilhe, J.

J. Colin, C. Coupeau, and J. Grilhe, "Plastic folding of buckling structures," Phys. Rev. Lett. 99, 046101-1-4 (2007).
[CrossRef] [PubMed]

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Huang, W.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Hutchinson, J. W.

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

Ibanescu, M.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

Janz, S.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Joannopoulos, J. D.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Johnson, S. G.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

Kash, J. A.

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

Kiesel, P.

Kimerling, L. C.

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

Kisker, D. W.

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

Koyama, F.

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 5828-5831 (2004).
[CrossRef]

Krauss, T. F.

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
[CrossRef]

Kung, S.-Y.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

Lamontagne, B.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Lavrinenko, A. V.

Lederer, F.

Lee, K.-R.

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

Lo, S.-S.

Martin, R. J.

P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
[CrossRef]

Meindl, J. D.

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

Moon, M.-W.

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

Mule, A. V.

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

Nathan, A.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Nguyen, H. T.

Oh, K.H.

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

Pai, M. M.

Pezeshki, B.

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

Ponnampalam, N.

Post, E.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

Roelkens, G.

Sakurai, Y.

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 5828-5831 (2004).
[CrossRef]

Schmidt, O.

Shenoy, M. R.

A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
[CrossRef]

Shubair, R. M.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Smolinsky, G.

P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
[CrossRef]

Soljacic, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

Tamir, T.

T. Tamir, "Leaky waves in planar optical waveguides," Nouv. Rev. Opt. 6, 273-284 (1975).
[CrossRef]

Tang, C. H.

C. H. Tang, "Delay equalization by tapered cutoff waveguides," IEEE Trans. Microwave Theory Tech. 12, 608-615 (1964).
[CrossRef]

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Thyagarajan, K.

A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
[CrossRef]

Tien, P. K.

P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
[CrossRef]

Tong, F. F.

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

Trutschel, U.

Van Thourhout, D.

Waechter, C.

Wang, M.-S.

Xu, D.-X.

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Yarotsky, D. A.

Yi, Y.

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

Acta Mater. (1)

M.-W. Moon, K.-R. Lee, K.H. Oh, and J. W. Hutchinson, "Buckle delamination on patterned substrates," Acta Mater. 52, 3151-3159 (2004).
[CrossRef]

Adv. Mater. (1)

R. G. DeCorby, N. Ponnampalam, H. T. Nguyen, and T. J. Clement, "Robust and flexible free-standing all-dielectric omnidirectional reflectors," Adv. Mater. 19, 193-196 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide," Appl. Phys. Lett. 85, 1466-1468 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. I. Babic and S. W. Corzine, "Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors," IEEE J. Quantum Electron. 28, 514-524 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, "High-efficiency semiconductor resonant-cavity light-emitting diodes: a review," IEEE J. Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, "Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials," IEEE J. Sel. Top. Quantum Electron. 12, 1345-1348 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

P. K. Tien, G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech. 23, 79-85 (1975).
[CrossRef]

C. H. Tang, "Delay equalization by tapered cutoff waveguides," IEEE Trans. Microwave Theory Tech. 12, 608-615 (1964).
[CrossRef]

IEEE Trans. VLSI Systems (1)

A. V. Mule, E. N. Glytsis, T. K. Gaylord, and J. D. Meindl, "Electrical and optical clock distribution networks for gigascale microprocessors," IEEE Trans. VLSI Systems 10, 582-594 (2002).
[CrossRef]

J. Lightwave Technol. (4)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
[CrossRef]

A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, "Numerical analysis of planar optical waveguides using transfer matrix approach," J. Lightwave Technol. 5, 660-667 (1987).
[CrossRef]

B. Pezeshki, F. F. Tong, J. A. Kash, and D. W. Kisker, "Vertical cavity devices as wavelength selective waveguides," J. Lightwave Technol. 12, 1791-1801 (1994).
[CrossRef]

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

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

J. Phys. D. (1)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
[CrossRef]

J. Vac. Sci. Technol. A (1)

B. Lamontagne, P. Cheben, E. Post, S. Janz, D.-X. Xu, and A. Delage, "Fabrication of out-of-plane micromirrors in silicon-on-insulator planar waveguides," J. Vac. Sci. Technol. A 24, 718-722 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 5828-5831 (2004).
[CrossRef]

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Nouv. Rev. Opt. (1)

T. Tamir, "Leaky waves in planar optical waveguides," Nouv. Rev. Opt. 6, 273-284 (1975).
[CrossRef]

Opt. Express (6)

Phys. Rev. E (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, and Y. Fink, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 0466081-8 (2003).
[CrossRef]

Proc. of IEEE (1)

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. of IEEE 72, 850-866 (1984).
[CrossRef]

Other (3)

T. Miura, Y. Yokota, and F. Koyama, "Proposal of tunable demultiplexer based on tapered hollow waveguides with highly reflective multilayer mirrors," Proc. of LEOS 2005, 272-273 (2005).

J. Colin, C. Coupeau, and J. Grilhe, "Plastic folding of buckling structures," Phys. Rev. Lett. 99, 046101-1-4 (2007).
[CrossRef] [PubMed]

A. Yariv and P. Yeh, Optical Waves in Crystals, (John Wiley and Sons, New York, 1984), Chap. 11.

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 (12)

Fig. 1.
Fig. 1.

(a). Microscope photograph showing portions of 3 adjacent hollow waveguides, with base width tapered from 80 to 20 µm. (b). Schematic of the mask layout used to define the region of delamination for the tapers. For light-guiding experiments, the samples were cleaved part way along the tapers as indicated. (c) Schematic cross-section (end view) of a buckled hollow channel with upper (curved) and lower cladding mirrors. Layer details are provided in the main text. (d) Peak buckle height versus base width as determined from AFM scans at several points along a typical taper. The red line is a linear fit.

Fig. 2.
Fig. 2.

(a). Angle-averaged reflectance versus wavelength, as predicted by a planar transfermatrix model, for the top and bottom cladding mirrors of the as-fabricated waveguides. (b) Reflectance versus incident angle at a wavelength of 1550 nm.

Fig. 3.
Fig. 3.

(a). Schematic of a quasi-symmetric air-core slab waveguide with quarter-wavelength Bragg cladding mirrors and high index layers adjacent to the core. In general, N period mirrors comprising IG2 glass (n~2.55) and PAI polymer (n~1.65) were assumed. Forward and backward propagating plane-waves in the external medium and the core (both air) are indicated. (b). Schematic of the slab model representing the as-fabricated, asymmetric waveguides. The 5.5 period bottom mirror has a low index layer adjacent to the core. In the 4 period top mirror, all the IG2 glass layers are Ag-doped (n~2.95) and the layer adjacent to the core is approximately twice as thick as the other Ag:IG2 layers. Both top and bottom mirrors were terminated by a gold layer. The ray bouncing at angle ϕm represents a low loss, leaky mode.

Fig. 4.
Fig. 4.

Modal analysis results for the symmetric QWS slab waveguide [Fig. 3(a)], with 8 period top and bottom mirrors and at the resonant wavelength (1600 nm) of the mirrors. (a). The core transmittance parameter TC versus incidence angle, for several core thicknesses (in µm) as indicated. The Lorentzian lines correspond to the m=0 mode in this case. (b) The predicted effective index and attenuation versus core thickness, for the 3 lowest order modes. The vertical dotted lines indicate the cutoff thicknesses of these modes.

Fig. 5.
Fig. 5.

Results from an analysis of radiation at cutoff in a tapered, ODR-clad slab waveguide. (a) Schematic illustration showing a guided ray approaching normal incidence as the core is tapered to the cutoff thickness of the associated mode. The length of the arrows in the external medium indicates the increased leakage of the mode with decreasing core thickness. Radiation through the bottom mirror also occurs. (b)-(d) Results from the ray optics model applied to the asymmetric slab structure, representative of the as-fabricated waveguides: (b) Transverse intensity profiles (in the air core) of the 3 lowest order modes, for a core thickness of 3 µm and a wavelength of 1600 nm. (c) The predicted effective index and attenuation versus core thickness, for the 5 lowest order modes at 1600 nm. (d) As in part (c), but for the 6 lowest order modes at 1520 nm. The vertical dotted lines indicate the cutoff thicknesses in each case.

Fig. 6.
Fig. 6.

Selected low-order mode field profiles predicted by a commercial, two-dimensional finite difference mode solver are shown (not to scale), for a buckled waveguide with 67 µm base width and 3.5 µm peak core height. The wavelength was set to 1600 nm. (a) TE00, TE01, and TE02 modes. (b) TE10, TE11, and TE12 modes. (c) TE20, TE21, and TE22 modes.

Fig. 7.
Fig. 7.

Selected results from the finite difference mode solver are shown, for a wavelength of 1600 nm. In each figure, the dashed vertical lines are the cutoff thicknesses predicted by the ray optics model for an equivalent thickness slab waveguide. (a) Predicted modal effective indices versus peak core height. (b) Predicted modal attenuation versus peak core height.

Fig. 8.
Fig. 8.

Outcoupling results for a hollow Bragg waveguide with base width tapered from ~67 µm to ~10 µm. Light from a tunable laser was coupled into the large end of the taper, at the left of each image. Outcoupling streaks are attributed to radiation of 4 or 5 (depending on wavelength) vertical mode families, as indicated. Scale bar: 1 mm.

Fig. 9.
Fig. 9.

High magnification images of the radiation streaks from Fig. 8 are shown, for a wavelength of 1600 nm. The images appear in order of position along the taper. (a) TE4n radiation streak. (b) TE3n radiation streak. (c) TE2n radiation streak. (d) TE1n radiation streak.

Fig. 10.
Fig. 10.

Typical far-field profiles of the light radiated at cutoff, as picked up by a MMF probe scanned at various fixed heights above the sample surface. The case shown is for the TE2n radiation streak of an 80–10 µm taper. (a) Intensity profile along the y -axis (normal to the axis of the waveguide). (b) Intensity profile along the z-axis (parallel to the axis of the waveguide).

Fig. 11.
Fig. 11.

Plot of power measured at the input facet (large end) of a tapered (80–20 µm) hollow waveguide, versus position of a MMF used to normally illuminate the surface of the taper. The wavelength was fixed to 1560 nm for the case shown.

Fig. 12.
Fig. 12.

Plot of power at the input facet versus wavelength, for normal incidence illumination by a SMF at a fixed position overtop a taper (80–10). (a) Typical result when the SMF is centered with respect to the taper axis, near the TE4n cutoff point. (b) Typical result when the SMF was offset relative to the taper axis, near the TE2n cutoff point. Note that the position of the SMF along the taper is different in the two cases, so that the n=0 peaks are not coincident in wavelength.

Equations (8)

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

δ ( y ) = δ max 2 ( 1 + cos ( π y b ) ) ,
δ max = h 4 3 ( ( b b min ) 2 1 ) ,
2 · k x · d Φ T Φ B = m · 2 π ,
r T r B exp ( j · 2 · k x · d ) = 1 ,
k z = k 0 2 k x 2 = β m j · α m 2 ,
α m = ln ( R T R B ) 2 · d eff · tan ϕ m ,
T C = E C + E I 2 .
d eff = d + L T + L B = d + λ 0 4 π ( ( arg ( r T ) ) ( cos ϕ ) ) + λ 0 4 π ( ( arg ( r B ) ) ( cos ϕ ) ) ,

Metrics