Abstract

An optical coupler for integrated photonic circuits is presented and analyzed. The coupler is based on frustrated total internal reflection (FTIR) and offers high efficiency in a compact footprint. Analytic expressions for the transmission and reflection coefficients of the coupler are obtained using a plane-wave theory and experimentally verified. Finite-difference time-domain modeling of FTIR is discussed and modeling results of the coupler are presented. A parametric discussion of the FTIR coupler provides design tools for making 3dB couplers.

© 2008 Optical Society of America

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  2. M. Kuznetsov, “Radiation loss in dielectric waveguide Y-branch structures,” J. Lightwave Technol. 3, 674-677 (1985).
    [CrossRef]
  3. M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
    [CrossRef]
  4. T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
    [CrossRef]
  5. A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Technol. 3, 1135-1146 (1985).
    [CrossRef]
  6. J. P. Donnelly, H. Haus, and L. Molter, “Cross power and crosstalk in waveguide couplers,” J. Lightwave Technol. 6, 257-268(1988).
    [CrossRef]
  7. M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
    [CrossRef]
  8. S. W. Ahn and S. Y. Shin, “Grating assisted codirectional coupler filter using electro-optic and passive polymer waveguides,” IEEE J. Sel. Top. Quantum Electron. 7, 819-825(2001).
    [CrossRef]
  9. W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating assisted couplers,” J. Lightwave Technol. 9, 721-727 (1991).
    [CrossRef]
  10. N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
    [CrossRef]
  11. J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
    [CrossRef]
  12. S. Akiyama, M. A. Popovic, P. T. Rakich, K. Wada, J. Michel, H. A. Haus, E. P. Ippen, and L. C. Kimerling, “Air trench bends and splitters for dense optical integration in low index contrast,” J. Lightwave Technol. 23, 2271-2277 (2005).
    [CrossRef]
  13. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54 , 601-607 (1986).
    [CrossRef]
  14. R. H. Renard, “Total reflection: a new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am. 54, 1190-1197 (1964).
  15. G. E. Musset, O. Boquilloin, and J. P. Forth, “High performance, diode pumped, Q-switched Er:Yb:glass laser with FTIR shutter,” in Proceedings of the IEEE Conference on Lasers and Electro-Optics in Europe (IEEE, 2000), p. 1.
  16. I. N. Court and F. K. von Willisen, “Frustrated total internal reflection and applications of its principles to laser cavity design,” Appl. Opt. 3, 719-726 (1964).
  17. D. Axelrod, “Cell-substrate illuminated by total internal reflection fluorescence,” J. Cell Biol. 89, 141-145 (1981).
    [CrossRef]
  18. D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
    [CrossRef]
  19. E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
    [CrossRef]
  20. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef]
  21. K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propagat. Mag. 37, 39-56 (1995).
    [CrossRef]
  22. A. Taflove and S. C. Hagness, Computational Electrodynamics, The Finite-Difference Time-Domain Method (Artech House, 2005).
  23. E. A. Navarro, T. M. Bordallo, and J. Navasquillo-Miralles, “FDTD characterization of evanescent modes--multimode analysis of waveguide discontinuities,” IEEE Trans. Microwave Theory Technol. 48, 606-610 (2000).
    [CrossRef]
  24. L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
    [CrossRef]
  25. H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
    [CrossRef]

2007 (1)

L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

2005 (1)

2004 (1)

H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

2002 (1)

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

2001 (2)

S. W. Ahn and S. Y. Shin, “Grating assisted codirectional coupler filter using electro-optic and passive polymer waveguides,” IEEE J. Sel. Top. Quantum Electron. 7, 819-825(2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

2000 (1)

E. A. Navarro, T. M. Bordallo, and J. Navasquillo-Miralles, “FDTD characterization of evanescent modes--multimode analysis of waveguide discontinuities,” IEEE Trans. Microwave Theory Technol. 48, 606-610 (2000).
[CrossRef]

1998 (1)

1997 (1)

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

1995 (2)

T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propagat. Mag. 37, 39-56 (1995).
[CrossRef]

1992 (1)

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

1991 (2)

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating assisted couplers,” J. Lightwave Technol. 9, 721-727 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
[CrossRef]

1990 (1)

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

1988 (1)

J. P. Donnelly, H. Haus, and L. Molter, “Cross power and crosstalk in waveguide couplers,” J. Lightwave Technol. 6, 257-268(1988).
[CrossRef]

1986 (1)

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54 , 601-607 (1986).
[CrossRef]

1985 (2)

M. Kuznetsov, “Radiation loss in dielectric waveguide Y-branch structures,” J. Lightwave Technol. 3, 674-677 (1985).
[CrossRef]

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

1981 (1)

D. Axelrod, “Cell-substrate illuminated by total internal reflection fluorescence,” J. Cell Biol. 89, 141-145 (1981).
[CrossRef]

1980 (1)

1964 (2)

Ahn, S. W.

S. W. Ahn and S. Y. Shin, “Grating assisted codirectional coupler filter using electro-optic and passive polymer waveguides,” IEEE J. Sel. Top. Quantum Electron. 7, 819-825(2001).
[CrossRef]

Akiyama, S.

Axelrod, D.

D. Axelrod, “Cell-substrate illuminated by total internal reflection fluorescence,” J. Cell Biol. 89, 141-145 (1981).
[CrossRef]

Boquilloin, O.

G. E. Musset, O. Boquilloin, and J. P. Forth, “High performance, diode pumped, Q-switched Er:Yb:glass laser with FTIR shutter,” in Proceedings of the IEEE Conference on Lasers and Electro-Optics in Europe (IEEE, 2000), p. 1.

Bordallo, T. M.

E. A. Navarro, T. M. Bordallo, and J. Navasquillo-Miralles, “FDTD characterization of evanescent modes--multimode analysis of waveguide discontinuities,” IEEE Trans. Microwave Theory Technol. 48, 606-610 (2000).
[CrossRef]

Bossert, D. J.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Bour, D. P.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Bowers, J. E.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

Bulmer, C. H.

Burns, W. K.

Butler, J. K.

J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

Carlson, N. W.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Chaudhuri, S. K.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating assisted couplers,” J. Lightwave Technol. 9, 721-727 (1991).
[CrossRef]

Congdon, P.

J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

Court, I. N.

Dagli, N.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

DeFreez, R. K.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Donnelly, J. P.

J. P. Donnelly, H. Haus, and L. Molter, “Cross power and crosstalk in waveguide couplers,” J. Lightwave Technol. 6, 257-268(1988).
[CrossRef]

Elliot, R. A.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Evans, G. A.

J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Forth, J. P.

G. E. Musset, O. Boquilloin, and J. P. Forth, “High performance, diode pumped, Q-switched Er:Yb:glass laser with FTIR shutter,” in Proceedings of the IEEE Conference on Lasers and Electro-Optics in Europe (IEEE, 2000), p. 1.

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics, The Finite-Difference Time-Domain Method (Artech House, 2005).

Hammer, J. M.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Hardy, A.

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

Haus, H.

J. P. Donnelly, H. Haus, and L. Molter, “Cross power and crosstalk in waveguide couplers,” J. Lightwave Technol. 6, 257-268(1988).
[CrossRef]

Haus, H. A.

Hawley, D.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54 , 601-607 (1986).
[CrossRef]

Hihara, M.

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

Hirata, T.

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

Hosomatsu, H.

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

Huang, W.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating assisted couplers,” J. Lightwave Technol. 9, 721-727 (1991).
[CrossRef]

Hunt, M. M.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Ippen, E. P.

Jeong, D.

H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

Kim, J.

H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

Kimerling, L. C.

Kotlyar, M. V.

L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

Krauss, T. F.

L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

Kuznetsov, M.

M. Kuznetsov, “Radiation loss in dielectric waveguide Y-branch structures,” J. Lightwave Technol. 3, 674-677 (1985).
[CrossRef]

Lee, J.

H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

Little, B. E.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating assisted couplers,” J. Lightwave Technol. 9, 721-727 (1991).
[CrossRef]

Liu, B.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

Lurie, M.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Maeda, M.

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

Michel, J.

Moeller, R. P.

Molter, L.

J. P. Donnelly, H. Haus, and L. Molter, “Cross power and crosstalk in waveguide couplers,” J. Lightwave Technol. 6, 257-268(1988).
[CrossRef]

Musset, G. E.

G. E. Musset, O. Boquilloin, and J. P. Forth, “High performance, diode pumped, Q-switched Er:Yb:glass laser with FTIR shutter,” in Proceedings of the IEEE Conference on Lasers and Electro-Optics in Europe (IEEE, 2000), p. 1.

Navarro, E. A.

E. A. Navarro, T. M. Bordallo, and J. Navasquillo-Miralles, “FDTD characterization of evanescent modes--multimode analysis of waveguide discontinuities,” IEEE Trans. Microwave Theory Technol. 48, 606-610 (2000).
[CrossRef]

Navasquillo-Miralles, J.

E. A. Navarro, T. M. Bordallo, and J. Navasquillo-Miralles, “FDTD characterization of evanescent modes--multimode analysis of waveguide discontinuities,” IEEE Trans. Microwave Theory Technol. 48, 606-610 (2000).
[CrossRef]

Ni, T. D.

T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

O'Faolain, L.

L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

Okuno, T.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

Orloff, J.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Palfrey, S. L.

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

Pang, L.

J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

Paolella, A.

T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

Perlman, B.

T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

Popovic, M. A.

Raburn, M.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

Rakich, P. T.

Rauscher, K.

M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

Renard, R. H.

Roy, R.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54 , 601-607 (1986).
[CrossRef]

Schneider, J. B.

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propagat. Mag. 37, 39-56 (1995).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

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H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

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S. W. Ahn and S. Y. Shin, “Grating assisted codirectional coupler filter using electro-optic and passive polymer waveguides,” IEEE J. Sel. Top. Quantum Electron. 7, 819-825(2001).
[CrossRef]

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K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propagat. Mag. 37, 39-56 (1995).
[CrossRef]

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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

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A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

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T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

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J. K. Butler, N. H. Sun, G. A. Evans, L. Pang, and P. Congdon, “Grating assisted coupling of light between semiconductor and glass waveguides,” J. Lightwave Technol. 16, 1038-1048(1998).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

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H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
[CrossRef]

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M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
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[CrossRef]

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[CrossRef]

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L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

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D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
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E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
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M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

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E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
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Adv. Mater. (1)

H. Shin, D. Jeong, J. Lee, M. M. Sung, and J. Kim, “Formation of TiO2 and ZrO2 nanotubes using atomic layer deposition with ultraprecise control of the wall thickness,” Adv. Mater. 16, 1197-1200 (2004).
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S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54 , 601-607 (1986).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. J. Bossert, R. K. DeFreez, H. Ximen, R. A. Elliot, M. M. Hunt, G. A. Wilson, J. Orloff, G. A. Evans, N. W. Carlson, M. Lurie, J. M. Hammer, D. P. Bour, and S. L. Palfrey, “Grating-surface-emitting lasers in a ring configuration,” Appl. Phys. Lett. 56, 2068-2070 (1990).
[CrossRef]

IEEE Antennas Propagat. Mag. (1)

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propagat. Mag. 37, 39-56 (1995).
[CrossRef]

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M. Raburn, B. Liu, K. Rauscher, T. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron. 8, 935-942 (2002).
[CrossRef]

S. W. Ahn and S. Y. Shin, “Grating assisted codirectional coupler filter using electro-optic and passive polymer waveguides,” IEEE J. Sel. Top. Quantum Electron. 7, 819-825(2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. D. Ni, D. Sturzebecher, A. Paolella, and B. Perlman, “Novel polymer optical couplers based on symmetry mode mixing,” IEEE Photon. Technol. Lett. 7, 1186-1188 (1995).
[CrossRef]

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[CrossRef]

S. Akiyama, M. A. Popovic, P. T. Rakich, K. Wada, J. Michel, H. A. Haus, E. P. Ippen, and L. C. Kimerling, “Air trench bends and splitters for dense optical integration in low index contrast,” J. Lightwave Technol. 23, 2271-2277 (2005).
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[CrossRef]

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[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet-Bloch theory,” J. Lightwave Technol. 15, 2301-2315(1997).
[CrossRef]

J. Opt. Soc. Am. (1)

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

L. O'Faolain, M. V. Kotlyar, N. Tripathi, R. Wilson, and T. F. Krauss, “Fabrication of photonic crystals using a spin-coated hydrogen silsesquioxane hard mask,” J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Maeda, T. Hirata, M. Surfiuro, M. Hihara, A. Yamaguchi, and H. Hosomatsu, “Photonic integrated circuit combining two GaAs distributed Bragg reflector laser diodes for generation of the beat signal,” Jpn. J. Appl. Phys. 31, L183 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, and K. M. Yeung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

Other (2)

A. Taflove and S. C. Hagness, Computational Electrodynamics, The Finite-Difference Time-Domain Method (Artech House, 2005).

G. E. Musset, O. Boquilloin, and J. P. Forth, “High performance, diode pumped, Q-switched Er:Yb:glass laser with FTIR shutter,” in Proceedings of the IEEE Conference on Lasers and Electro-Optics in Europe (IEEE, 2000), p. 1.

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Figures (12)

Fig. 1
Fig. 1

Reflection and transmission coefficients for a plane wave as gap width varies from 0 to 300 nm . Waveguide index = 3.22 , trench index = 1 , wavelength = 1.55 μm , angle of incidence = 45 ° . Dashed curves, transverse electric; solid curves, transverse magnetic.

Fig. 2
Fig. 2

Photograph of RF experimental setup verifying coupler design. 3.4 mm radiation is launched into a dielectric waveguide with a 45 ° cut. The gap width is varied to determine the power that evanescently couples across the gap.

Fig. 3
Fig. 3

Experimental and analytical results of RF evanescent coupling experiment. Dots, experimental; solid curve, analytical.

Fig. 4
Fig. 4

Numerical and experimental results of RF evanescent coupling experiment. Dots, experimental; squares, numerical.

Fig. 5
Fig. 5

FDTD model of optical FTIR coupler. The fundamental mode is launched from bottom left leg toward the “T” intersection. Reflected light travels into the bottom right leg while transmitted light travels into the top right leg. The waveguide is InP with a 3.5 μm ridge. The fundamental mode index is n = 3.22 . The trench is at a 45 ° angle to the waveguide direction of propagation.

Fig. 6
Fig. 6

Hy field distribution after FDTD run. The run proceeds long enough for steady state fields to settle. The trench is 25 nm wide filled with air, n = 1 . Note the Goos–Hanchen shift evident in the reflected field distribution.

Fig. 7
Fig. 7

Analytical and numerical results for transmission and reflection coefficients. Wavelength = 1.55 μm , angle of incidence = 45 ° , index of trench n = 1 , trench width 0 200 nm . Solid curves, analytic; squares, numerical.

Fig. 8
Fig. 8

Trench width required for 50% coupling as the index of refraction of the waveguide varies from n = 1.5 to n = 3.5 . Dashed curve, TE; solid curve, TM.

Fig. 9
Fig. 9

Trench width required for 50% coupling as the index of refraction of the trench varies from n = 1 to n = 2.5 . Dashed curve, TE; solid curve, TM.

Fig. 10
Fig. 10

Trench width required for 50% coupling of TE field as waveguide index varies for multiple trench index fills. Air, n = 1 ; PMMA, n = 1.48 ; SU-8, n = 1.57 ; sapphire, n = 1.75 ; Zr 0 2 , n = 2.1 .

Fig. 11
Fig. 11

Trench width required for 50% coupling of TM field as waveguide index varies for multiple trench index fills. Air, n = 1 ; PMMA, n = 1.48 ; SU-8, n = 1.57 ; sapphire, n = 1.75 ; Zr 0 2 , n = 2.1 .

Fig. 12
Fig. 12

Trench width required for 50% coupling as angle of incidence changes from 0 ° 90 ° . Waveguide index n = 3.22 , trench index n = 1 , θ crit = 18.09 ° . Dashed curve, TE; solid curve, TM.

Equations (24)

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E transverse I ( x , y , z = 0 , t ) = E transverse II ( x , y , z = 0 + , t ) ,
H normal I ( x , y , z = 0 , t ) = H normal II ( x , y , z = 0 + , t ) ,
E transverse II ( x , y , z = w , t ) = E transverse III ( x , y , z = 0 + , t ) ,
H normal II ( x , y , z = w , t ) = H normal III ( x , y , z = w + , t ) .
H x ( x , y , t ) = x ^ cos ( θ i ) E 0 η 1 exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] ,
H z ( x , y , t ) = z ^ sin ( θ i ) E 0 η 1 exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] ,
E y ( x , y , t ) = y ^ E 0 exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] .
E inc I ( x , y ) + E ref I ( x , y ) = E + II ( x , y ) + E II ( x , y ) ,
E + II exp ( j k 0 n 2 cos ( θ 2 ) w ) + E II exp ( + j k 0 n 2 cos ( θ 2 ) w ) = E tran III exp ( j k 0 n 2 cos ( θ 2 ) w ) ,
n 1 cos ( θ 1 ) ( E inc I E ref I ) = n 2 cos ( θ 2 ) ( E + II E II ) ,
n 2 cos ( θ 2 ) E + I exp ( j k 0 n 2 cos ( θ 2 ) w ) + E II exp ( j k 0 n 2 cos ( θ 2 ) w ) = n 1 cos ( θ 1 ) E tran III exp ( j k 0 n 2 cos ( θ 2 ) w ) ,
E tran III E inc I = 4 α TE β TE exp [ j k 0 w ( n 2 cos ( θ 2 ) n 1 cos ( θ 1 ) ) ] α TE 2 ( exp ( δ ) 1 ) + β TE 2 ( exp ( δ ) 1 ) 2 α TE β TE ( exp ( δ ) + 1 ) ,
E ref I E inc I = α TE 2 ( exp ( δ ) 1 ) + β TE 2 ( 1 exp ( δ ) ) α TE 2 ( exp ( δ ) 1 ) + β TE 2 ( exp ( δ ) 1 ) 2 α TE β TE ( exp ( δ ) + 1 ) ,
α TE = n 1 cos ( θ 1 ) ,
β TE = n 2 cos ( θ 2 ) ,
δ = j k 0 n 2 2 w cos ( θ 2 ) .
H y ( x , y , t ) = y ^ H 0 exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] ,
E x ( x , y , t ) = x ^ cos ( θ i ) H 0 η exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] ,
E x ( x , y , t ) = z ^ sin ( θ i ) H 0 η exp [ j k 0 ( x sin ( θ i ) + z cos ( θ i ) ) ] .
E tran III E inc I = 4 α β ( exp ( δ / 2 ) 1 ) α TM 2 ( exp ( δ ) 1 ) + β TM 2 ( exp ( δ ) 1 ) + 2 α β ( exp ( δ ) + 1 ) ,
E ref I E inc I = ( β TM 2 α TM 2 ) ( exp ( δ / 2 ) + 1 ) α TM 2 ( exp ( δ ) 1 ) + β TM 2 ( exp ( δ ) 1 ) + 2 α TM β TM ( exp ( δ ) + 1 ) ,
α TM = n 1 cos ( θ 2 ) ,
β TM = n 2 cos ( θ 1 ) .
c Δ t = 1 ( Δ x 2 + Δ y 2 + Δ z 2 ) 1 / 2 .

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