Abstract

Marcatili's famous approximate analytical description of light propagating through rectangular dielectric waveguides, published in 1969, gives accurate results for low-index-contrast waveguides. However, photonic-integrated circuit technology has advanced to high-index-contrast (HIC) waveguides. In this paper, we improve Marcatili's model by adjusting the amplitudes of the components of the electromagnetic fields in his description. We find that Marcatili's eigenvalue equation for the propagation constant is also valid for HIC waveguides. Our improved method shows much better agreement with rigorous numerical simulations, in particular for the case of HIC waveguides. We also derive explicit expressions for the effective group index and the effects of external forces on the propagation constant. Furthermore, with our method, the phenomenon of avoided crossing of modes is observed and studied.

© 2012 IEEE

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  1. E. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2121 (1969).
  2. D. Marcuse, Theory of Dielectrically Optical Waveguides (Academic, 1991).
  3. C. Yeh, F. I. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008).
  4. C. Pollock, M. Lipson, Integrated Photonics (Kluwer, 2003).
  5. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, 2002).
  6. P. Dumon, W. Bogaerts, A. Tchelnokov, J.-M. Fedeli, R. Baets, "Silicon nanophotonics," Future Fab Int. 25, 29-36 (2008).
  7. A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).
  8. M. Smit, "New focusing and dispersive planar component based on an optical phased array," Electron. Lett. 24, 385-386 (1988).
  9. J. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133-2160 (1969).
  10. A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in delectric waveguides," Pure Appl. Opt.: J. Eur. Opt. Soc. A 3, 381-388 (1994).
  11. O. Ivanova, M. Hammer, R. Stoffer, E. van Groesen, "A variational mode expansion mode solver," Opt. Quantum Electron. 39, 849-864 (2007).
  12. Fimmwave-Numerical Waveguide Mode Solver OxfordU.K. (2011) Photon Design Ltd..
  13. A. Melloni, D. Roncelli, F. Morichetti, A. Canciamilla, A. Bakker, "Statistical design in integrated optics," presented at the Eur. Quantum Electron. Conf. MunichGermany (2009) JSI1-4.
  14. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delage, B. Lamontagne, J. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).
  15. K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator forsensitive and label-free biosensing," Opt. Exp. 15, 7610-7615 (2007).
  16. Material Database and Material Models OxfordU.K. (2011) Photon Design Ltd. distributed with FimmWave software package.
  17. Matlab—The Language of Technical Computing NatickMA The MathWorks Inc. (2010).
  18. Y. Okada, Y. Tokumaru, "Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 k," J. Appl. Phys. 56, 314-320 (1984).
  19. L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, 1977).

2008 (1)

P. Dumon, W. Bogaerts, A. Tchelnokov, J.-M. Fedeli, R. Baets, "Silicon nanophotonics," Future Fab Int. 25, 29-36 (2008).

2007 (2)

O. Ivanova, M. Hammer, R. Stoffer, E. van Groesen, "A variational mode expansion mode solver," Opt. Quantum Electron. 39, 849-864 (2007).

K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator forsensitive and label-free biosensing," Opt. Exp. 15, 7610-7615 (2007).

2006 (1)

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delage, B. Lamontagne, J. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).

2000 (1)

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).

1994 (1)

A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in delectric waveguides," Pure Appl. Opt.: J. Eur. Opt. Soc. A 3, 381-388 (1994).

1988 (1)

M. Smit, "New focusing and dispersive planar component based on an optical phased array," Electron. Lett. 24, 385-386 (1988).

1984 (1)

Y. Okada, Y. Tokumaru, "Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 k," J. Appl. Phys. 56, 314-320 (1984).

1969 (2)

J. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133-2160 (1969).

E. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2121 (1969).

Bell Syst. Tech. J. (2)

E. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2121 (1969).

J. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133-2160 (1969).

Electron. Lett. (1)

M. Smit, "New focusing and dispersive planar component based on an optical phased array," Electron. Lett. 24, 385-386 (1988).

Electron. Lett. (1)

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).

Future Fab Int. (1)

P. Dumon, W. Bogaerts, A. Tchelnokov, J.-M. Fedeli, R. Baets, "Silicon nanophotonics," Future Fab Int. 25, 29-36 (2008).

IEEE Photon. Technol. Lett. (1)

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delage, B. Lamontagne, J. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).

J. Appl. Phys. (1)

Y. Okada, Y. Tokumaru, "Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 k," J. Appl. Phys. 56, 314-320 (1984).

Opt. Exp. (1)

K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator forsensitive and label-free biosensing," Opt. Exp. 15, 7610-7615 (2007).

Opt. Quantum Electron. (1)

O. Ivanova, M. Hammer, R. Stoffer, E. van Groesen, "A variational mode expansion mode solver," Opt. Quantum Electron. 39, 849-864 (2007).

Pure Appl. Opt.: J. Eur. Opt. Soc. A (1)

A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in delectric waveguides," Pure Appl. Opt.: J. Eur. Opt. Soc. A 3, 381-388 (1994).

Other (9)

D. Marcuse, Theory of Dielectrically Optical Waveguides (Academic, 1991).

C. Yeh, F. I. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008).

C. Pollock, M. Lipson, Integrated Photonics (Kluwer, 2003).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, 2002).

Fimmwave-Numerical Waveguide Mode Solver OxfordU.K. (2011) Photon Design Ltd..

A. Melloni, D. Roncelli, F. Morichetti, A. Canciamilla, A. Bakker, "Statistical design in integrated optics," presented at the Eur. Quantum Electron. Conf. MunichGermany (2009) JSI1-4.

L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, 1977).

Material Database and Material Models OxfordU.K. (2011) Photon Design Ltd. distributed with FimmWave software package.

Matlab—The Language of Technical Computing NatickMA The MathWorks Inc. (2010).

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