Abstract

A design method for fully adiabatic waveguide branches is developed for the first time. Mode conversion between local normal modes is entirely suppressed through the explicit decoupling of the modes, where novel parametric and graphical representations of the self-consistent orthogonal coupled-mode theory are utilized to describe the strongly coupled part of the waveguide branches. A closed-form expression for an adiabatic condition is derived, and the significance of degenerated waveguide patterns with nonuniform waveguide widths is clarified. Validity of the method is tested by numerical simulations, and L<sup>-2</sup> dependence of the converted power to a circuit length is found. These results raise a fundamental question about the meaning of the adiabaticity in the waveguide branches.

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  1. H. Yajima, "Dielectric thin film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).
  2. W. Burns, A. F. Milton, "Mode conversion in planar-dielectric separating waveguides," IEEE J. Quantum Electron. QE-11, 32-39 (1975).
  3. H. Yajima, "Coupled mode analysis of dielectric planar branching waveguides," IEEE J. Quantum Electron. QE-14, 749-755 (1978).
  4. W. Burns, A. F. Milton, "An analytic solution for mode coupling in optical waveguide branches," IEEE J. Quantum Electron. QE-16, 446-454 (1980).
  5. M. Izutsu, A. Enokihara, T. Sueta, "Optical-waveguide hybrid coupler," Opt. Lett. 7, 549-551 (1982).
  6. Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, K. J. Orlowsky, "Integrated optic adiabatic devices on silicon," IEEE J. Quantum Electron. 27, 556-566 (1991).
  7. R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, G. R. Weber, "Adiabatic 3 dB couplers, filters, and multiplexers made with silica waveguides on silicon ," J. Lightw. Technol. 10, 46-50 (1992).
  8. N. J. P. Frenette, J. C. Cartledge, "Towards the optimization of dielectric waveguide: The effect of longitudinal variations in the branching angle," IEEE J. Quantum Electron. 24, 2491-2499 (1988).
  9. N. J. P. Frenette, J. C. Cartledge, "The effect of wavefront tilt on mode conversion in asymmetric Y-branch waveguides," IEEE J. Quantum Electron. 25, 742-748 (1989).
  10. J. D. Love, R. W. C. Vance, A. Joblin, "Asymmetric, adiabatic multipronged planar splitters," Opt. Quantum Electron. 28, 353-369 (1996).
  11. T. A. Ramadan, R. Scarmozzino, R. M. Osgood, Jr."Adiabatic couplers: Design rules and optimization," J. Lightw. Technol. 16, 277-283 (1998).
  12. K. Jinguji, N. Takato, A. Sugita, M. Kawachi, "Mach–Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio," Electron. Lett. 26, 1326-1327 (1990).
  13. A. Messiah, Quantum Mechanics (Dover, 2000).
  14. A. W. Schnyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  15. W. H. Louisell, "Analysis of the single tapered mode coupler," Bell Syst. Tech. J. 34, 853-870 (1955).
  16. R. R. A. Syms, "The digital directional coupler: Improved design," IEEE Photon. Technol. Lett. 4, 1135-1138 (1992).
  17. A. Syahriah, V. M. Schneider, S. Al-Bader, "The design of mode evolution couplers," J. Lightw. Technol. 16, 1907-1914 (1998).
  18. G. T. Paloczi, A. Eyal, A. Yariv, "Wavelength-insensitive nonadiabatic mode evolution couplers," IEEE Photon. Technol. Lett. 16, 515-517 (2004).
  19. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightw. Technol. LT-5, 16-23 (1987).
  20. W. P. Huang, H. A. Haus, "Self-consistent vector coupled-mode theory for tapered optical waveguides," J. Lightw. Technol. 8, 922-926 (1990).
  21. R. G. Peall, R. R. A. Syms, "Scalar strong coupled mode theory for slowly varying waveguide arrays," Opt. Commun. 67, 421-424 (1988).
  22. W. P. Huang, S. Lessard, "Wavefront-tilt effect in nonparallel optical waveguides," J. Lightw. Technol. 10, 316-322 (1992).
  23. J. P. Davis, P. Pechukas, "Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case," J. Chem. Phys. 64, 3129-3137 (1976).
  24. M. Berry, "Histories of adiabatic quantum transitions," Proc. R. Soc. Lond. A, Math. Phys. Sci. 429, 61-72 (1990).
  25. H. Nakamura, Nonadiabatic Transition: Concepts, Basic Theories and Applications (World Scientific, 2002).
  26. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2005).
  27. D. B. Mortimore, "Wavelength-flattened fused couplers," Electron. Lett. 21, 742-743 (1990).
  28. M. Berry, "Quantal phase factor accompanying adiabatic changes," Proc. R. Soc. Lond. A, Math. Phys. Sci. 392, 45-57 (1984).
  29. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

2004 (1)

G. T. Paloczi, A. Eyal, A. Yariv, "Wavelength-insensitive nonadiabatic mode evolution couplers," IEEE Photon. Technol. Lett. 16, 515-517 (2004).

1998 (2)

A. Syahriah, V. M. Schneider, S. Al-Bader, "The design of mode evolution couplers," J. Lightw. Technol. 16, 1907-1914 (1998).

T. A. Ramadan, R. Scarmozzino, R. M. Osgood, Jr."Adiabatic couplers: Design rules and optimization," J. Lightw. Technol. 16, 277-283 (1998).

1996 (1)

J. D. Love, R. W. C. Vance, A. Joblin, "Asymmetric, adiabatic multipronged planar splitters," Opt. Quantum Electron. 28, 353-369 (1996).

1992 (3)

R. R. A. Syms, "The digital directional coupler: Improved design," IEEE Photon. Technol. Lett. 4, 1135-1138 (1992).

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, G. R. Weber, "Adiabatic 3 dB couplers, filters, and multiplexers made with silica waveguides on silicon ," J. Lightw. Technol. 10, 46-50 (1992).

W. P. Huang, S. Lessard, "Wavefront-tilt effect in nonparallel optical waveguides," J. Lightw. Technol. 10, 316-322 (1992).

1991 (1)

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, K. J. Orlowsky, "Integrated optic adiabatic devices on silicon," IEEE J. Quantum Electron. 27, 556-566 (1991).

1990 (4)

K. Jinguji, N. Takato, A. Sugita, M. Kawachi, "Mach–Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio," Electron. Lett. 26, 1326-1327 (1990).

W. P. Huang, H. A. Haus, "Self-consistent vector coupled-mode theory for tapered optical waveguides," J. Lightw. Technol. 8, 922-926 (1990).

M. Berry, "Histories of adiabatic quantum transitions," Proc. R. Soc. Lond. A, Math. Phys. Sci. 429, 61-72 (1990).

D. B. Mortimore, "Wavelength-flattened fused couplers," Electron. Lett. 21, 742-743 (1990).

1989 (1)

N. J. P. Frenette, J. C. Cartledge, "The effect of wavefront tilt on mode conversion in asymmetric Y-branch waveguides," IEEE J. Quantum Electron. 25, 742-748 (1989).

1988 (2)

N. J. P. Frenette, J. C. Cartledge, "Towards the optimization of dielectric waveguide: The effect of longitudinal variations in the branching angle," IEEE J. Quantum Electron. 24, 2491-2499 (1988).

R. G. Peall, R. R. A. Syms, "Scalar strong coupled mode theory for slowly varying waveguide arrays," Opt. Commun. 67, 421-424 (1988).

1987 (1)

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightw. Technol. LT-5, 16-23 (1987).

1984 (1)

M. Berry, "Quantal phase factor accompanying adiabatic changes," Proc. R. Soc. Lond. A, Math. Phys. Sci. 392, 45-57 (1984).

1982 (1)

1980 (1)

W. Burns, A. F. Milton, "An analytic solution for mode coupling in optical waveguide branches," IEEE J. Quantum Electron. QE-16, 446-454 (1980).

1978 (1)

H. Yajima, "Coupled mode analysis of dielectric planar branching waveguides," IEEE J. Quantum Electron. QE-14, 749-755 (1978).

1976 (1)

J. P. Davis, P. Pechukas, "Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case," J. Chem. Phys. 64, 3129-3137 (1976).

1975 (1)

W. Burns, A. F. Milton, "Mode conversion in planar-dielectric separating waveguides," IEEE J. Quantum Electron. QE-11, 32-39 (1975).

1973 (1)

H. Yajima, "Dielectric thin film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).

1955 (1)

W. H. Louisell, "Analysis of the single tapered mode coupler," Bell Syst. Tech. J. 34, 853-870 (1955).

Appl. Phys. Lett. (1)

H. Yajima, "Dielectric thin film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).

Bell Syst. Tech. J. (1)

W. H. Louisell, "Analysis of the single tapered mode coupler," Bell Syst. Tech. J. 34, 853-870 (1955).

Electron. Lett. (2)

K. Jinguji, N. Takato, A. Sugita, M. Kawachi, "Mach–Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio," Electron. Lett. 26, 1326-1327 (1990).

D. B. Mortimore, "Wavelength-flattened fused couplers," Electron. Lett. 21, 742-743 (1990).

IEEE J. Quantum Electron. (6)

W. Burns, A. F. Milton, "Mode conversion in planar-dielectric separating waveguides," IEEE J. Quantum Electron. QE-11, 32-39 (1975).

H. Yajima, "Coupled mode analysis of dielectric planar branching waveguides," IEEE J. Quantum Electron. QE-14, 749-755 (1978).

W. Burns, A. F. Milton, "An analytic solution for mode coupling in optical waveguide branches," IEEE J. Quantum Electron. QE-16, 446-454 (1980).

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, K. J. Orlowsky, "Integrated optic adiabatic devices on silicon," IEEE J. Quantum Electron. 27, 556-566 (1991).

N. J. P. Frenette, J. C. Cartledge, "Towards the optimization of dielectric waveguide: The effect of longitudinal variations in the branching angle," IEEE J. Quantum Electron. 24, 2491-2499 (1988).

N. J. P. Frenette, J. C. Cartledge, "The effect of wavefront tilt on mode conversion in asymmetric Y-branch waveguides," IEEE J. Quantum Electron. 25, 742-748 (1989).

IEEE Photon. Technol. Lett. (2)

R. R. A. Syms, "The digital directional coupler: Improved design," IEEE Photon. Technol. Lett. 4, 1135-1138 (1992).

G. T. Paloczi, A. Eyal, A. Yariv, "Wavelength-insensitive nonadiabatic mode evolution couplers," IEEE Photon. Technol. Lett. 16, 515-517 (2004).

J. Chem. Phys. (1)

J. P. Davis, P. Pechukas, "Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case," J. Chem. Phys. 64, 3129-3137 (1976).

J. Lightw. Technol. (6)

T. A. Ramadan, R. Scarmozzino, R. M. Osgood, Jr."Adiabatic couplers: Design rules and optimization," J. Lightw. Technol. 16, 277-283 (1998).

W. P. Huang, S. Lessard, "Wavefront-tilt effect in nonparallel optical waveguides," J. Lightw. Technol. 10, 316-322 (1992).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightw. Technol. LT-5, 16-23 (1987).

W. P. Huang, H. A. Haus, "Self-consistent vector coupled-mode theory for tapered optical waveguides," J. Lightw. Technol. 8, 922-926 (1990).

A. Syahriah, V. M. Schneider, S. Al-Bader, "The design of mode evolution couplers," J. Lightw. Technol. 16, 1907-1914 (1998).

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, G. R. Weber, "Adiabatic 3 dB couplers, filters, and multiplexers made with silica waveguides on silicon ," J. Lightw. Technol. 10, 46-50 (1992).

Opt. Commun. (1)

R. G. Peall, R. R. A. Syms, "Scalar strong coupled mode theory for slowly varying waveguide arrays," Opt. Commun. 67, 421-424 (1988).

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. D. Love, R. W. C. Vance, A. Joblin, "Asymmetric, adiabatic multipronged planar splitters," Opt. Quantum Electron. 28, 353-369 (1996).

Proc. R. Soc. Lond. A, Math. Phys. Sci. (2)

M. Berry, "Quantal phase factor accompanying adiabatic changes," Proc. R. Soc. Lond. A, Math. Phys. Sci. 392, 45-57 (1984).

M. Berry, "Histories of adiabatic quantum transitions," Proc. R. Soc. Lond. A, Math. Phys. Sci. 429, 61-72 (1990).

Other (5)

H. Nakamura, Nonadiabatic Transition: Concepts, Basic Theories and Applications (World Scientific, 2002).

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2005).

A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

A. Messiah, Quantum Mechanics (Dover, 2000).

A. W. Schnyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

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