Abstract

We report on the fabrication of a grating-based add–drop filter in SiON planar waveguide technology. We achieved apodization of the Bragg grating by concatenating subgratings with various duty cycles. We present the theoretical and experimental dependence of the coupling coefficient on the duty cycle, which leads to a minimum coupling coefficient of 30%. With a breeder genetic algorithm we were able to find optimal apodization profiles within this limited coupling coefficient range. The final device is compatible with a 100-GHz channel spacing and has a bandwidth utilization factor of 36%.

© 2003 Optical Society of America

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  1. D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
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  2. C. R. Giles and V. Mizrahi, “Low-loss add/drop multiplexers for WDM lightwave networks,” in Technical Digest of Tenth International Conference on Integrated Optics and Optical Fiber Communication (Chinese University Press, Hong Kong, 1995), paper ThC2–1, pp. 66–67.
  3. B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
    [CrossRef]
  4. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
    [CrossRef]
  5. A. Talneau, C. Ougier, and S. Slempkes, “Multiwavelength grating reflectors for widely tunable laser,” IEEE Photon. Technol. Lett. 8, 497–499 (1996).
    [CrossRef]
  6. Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
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  7. H. Sakata, “Sidelobe suppression in grating-assisted wavelength-selective couplers,” Opt. Lett. 17, 463–465 (1992).
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  8. A. Lupu, A. Carenco, P. Win, H. Sik, P. Boulet, M. Carre, and S. Slempkes, “Spectral response apodization of Bragg-like optical filters,” in Optical Fiber Communication Conference (OFC)/International Conference on Integrated Optics and Optical Fiber Communications (IOOC), Postconference Digest (Optical Society of America, Washington, D.C., 1999), paper WM26–7, pp. 271–273.
  9. C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
    [CrossRef]
  10. D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
    [CrossRef]
  11. R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
    [CrossRef]
  12. C. David and D. Hambach, “Line width control using a defocused low voltage electron beam,” Microelectron. Eng. 46, 219–222 (1999).
    [CrossRef]
  13. G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
  14. W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
    [CrossRef]
  15. Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. QE-14, 245–258 (1978).
    [CrossRef]
  16. P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
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  17. M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987).
    [CrossRef] [PubMed]
  18. N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
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  21. H. Mühlenbein and D. Schlierkamp-Voosen, “The science of breeding and its application to the breeder genetic algorithm BGA,” Evol. Comput. 1, 335–360 (1993).
    [CrossRef]
  22. D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

2001 (1)

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

2000 (4)

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

1999 (1)

C. David and D. Hambach, “Line width control using a defocused low voltage electron beam,” Microelectron. Eng. 46, 219–222 (1999).
[CrossRef]

1996 (1)

A. Talneau, C. Ougier, and S. Slempkes, “Multiwavelength grating reflectors for widely tunable laser,” IEEE Photon. Technol. Lett. 8, 497–499 (1996).
[CrossRef]

1994 (2)

Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
[CrossRef]

P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
[CrossRef]

1993 (1)

H. Mühlenbein and D. Schlierkamp-Voosen, “The science of breeding and its application to the breeder genetic algorithm BGA,” Evol. Comput. 1, 335–360 (1993).
[CrossRef]

1992 (1)

1987 (3)

M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987).
[CrossRef] [PubMed]

N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
[CrossRef]

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

1978 (1)

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. QE-14, 245–258 (1978).
[CrossRef]

1976 (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
[CrossRef]

1975 (1)

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
[CrossRef]

Beyeler, R.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

Bilodeau, F.

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

Bona, G. L.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

Burnham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
[CrossRef]

David, C.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

C. David and D. Hambach, “Line width control using a defocused low voltage electron beam,” Microelectron. Eng. 46, 219–222 (1999).
[CrossRef]

Erni, D.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

Faucher, S.

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

Fröhlich, J.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Germann, R.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

Hafner, Ch.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Hambach, D.

C. David and D. Hambach, “Line width control using a defocused low voltage electron beam,” Microelectron. Eng. 46, 219–222 (1999).
[CrossRef]

Hill, K. O.

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

Horst, F.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

Hunziker, S.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Johnson, D. C.

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

Kamiya, T.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. QE-14, 245–258 (1978).
[CrossRef]

Kärtner, F. X.

N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
[CrossRef]

Keller, U.

N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
[CrossRef]

Kondo, Y.

Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
[CrossRef]

Lüsse, P.

P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
[CrossRef]

Massarek, I.

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

Matuschek, N.

N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
[CrossRef]

Moreno, E.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Mühlenbein, H.

H. Mühlenbein and D. Schlierkamp-Voosen, “The science of breeding and its application to the breeder genetic algorithm BGA,” Evol. Comput. 1, 335–360 (1993).
[CrossRef]

Offrein, B. J.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

Oku, S.

Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
[CrossRef]

Oswald, B.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Ougier, C.

A. Talneau, C. Ougier, and S. Slempkes, “Multiwavelength grating reflectors for widely tunable laser,” IEEE Photon. Technol. Lett. 8, 497–499 (1996).
[CrossRef]

Sakata, H.

Sakuda, K.

Salemink, H. W. M.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, “Adaptive gain equalizer in high-index-contrast SiON technology,” IEEE Photon. Technol. Lett. 12, 504–506 (2000).
[CrossRef]

R. Germann, H. W. M. Salemink, R. Beyeler, G. L. Bona, F. Horst, I. Massarek, and B. J. Offrein, “Silicon oxynitride layers for optical waveguide applications,” J. Electrochem. Soc. 147, 2237–2241 (2000).
[CrossRef]

Schlierkamp-Voosen, D.

H. Mühlenbein and D. Schlierkamp-Voosen, “The science of breeding and its application to the breeder genetic algorithm BGA,” Evol. Comput. 1, 335–360 (1993).
[CrossRef]

Schule, J.

P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
[CrossRef]

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
[CrossRef]

Shibata, Y.

Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
[CrossRef]

Slempkes, S.

A. Talneau, C. Ougier, and S. Slempkes, “Multiwavelength grating reflectors for widely tunable laser,” IEEE Photon. Technol. Lett. 8, 497–499 (1996).
[CrossRef]

Spühler, M.

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Streifer, W.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
[CrossRef]

Stuwe, P.

P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
[CrossRef]

Talneau, A.

A. Talneau, C. Ougier, and S. Slempkes, “Multiwavelength grating reflectors for widely tunable laser,” IEEE Photon. Technol. Lett. 8, 497–499 (1996).
[CrossRef]

Tamamura, T.

Y. Shibata, T. Tamamura, S. Oku, and Y. Kondo, “Coupling coefficient modulation of waveguide grating using sampled grating,” IEEE Photon. Technol. Lett. 6, 1222–1224 (1994).
[CrossRef]

Unger, H.-G.

P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–493 (1994).
[CrossRef]

Wiesmann, D.

C. David, D. Wiesmann, R. Germann, F. Horst, B. J. Offrein, R. Beyeler, H. W. M. Salemink, and G. L. Bona, “Apodized Bragg gratings in planar waveguides for add-drop filters,” Microelectron. Eng. 57/58, 713–719 (2001).
[CrossRef]

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12, 639–641 (2000).
[CrossRef]

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Yamada, M.

Yamamoto, Y.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. QE-14, 245–258 (1978).
[CrossRef]

Yanai, H.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. QE-14, 245–258 (1978).
[CrossRef]

Appl. Comput. Electromagn. Soc. J. (1)

D. Ėrni, D. Wiesmann, M. Spühler, S. Hunziker, E. Moreno, B. Oswald, J. Fröhlich, and Ch. Hafner, “Applications of evolutionary optimization algorithms in computational optics,” Appl. Comput. Electromagn. Soc. J. 15, 43–60 (2000).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
[CrossRef]

Electron. Lett. (1)

D. C. Johnson, K. O. Hill, F. Bilodeau, and S. Faucher, “New design concept for a narrowband wavelength-selective optical tap and combiner,” Electron. Lett. 23, 668–669 (1987).
[CrossRef]

Evol. Comput. (1)

H. Mühlenbein and D. Schlierkamp-Voosen, “The science of breeding and its application to the breeder genetic algorithm BGA,” Evol. Comput. 1, 335–360 (1993).
[CrossRef]

IEEE J. Quantum Electron. (3)

N. Matuschek, F. X. Kärtner, and U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1987).
[CrossRef]

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficient for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic of the grating-based add–drop filter.

Fig. 2
Fig. 2

Dependence of the calculated coupling coefficient on the duty cycle for TE-polarized light (open circles) and TM-polarized light (filled squares).

Fig. 3
Fig. 3

Transmission (left) and reflection (right) spectra for a set of uniform gratings with different duty cycles with lengths between 0.2 and 0.7 mm. The spectra were measured with TE-polarized light. For better visibility both spectra have been offset and the transmission spectra for the two smallest duty-cycle gratings have been enlarged by factors of 10 and 20.

Fig. 4
Fig. 4

Simulated (open circles) and experimentally determined (filled squares) coupling coefficients as functions of the grating duty cycle. The measured values are for TE-polarized light. The experimentally determined coupling coefficients for TM-polarized light are identical within the measurement accuracy. The simulation uses grating-teeth dimensions determined from a cross section of a test wafer measured in a secondary electron microscope. Perfectly rectangular grating teeth both on and beside the grating ridge are assumed.

Fig. 5
Fig. 5

Simulated (open circles) and experimentally determined (filled squares) coupling coefficients as functions of the grating duty cycle. Degradation of the grating teeth beside the grating ridge was taken into account for the simulation.

Fig. 6
Fig. 6

Effect of the truncation of the Hamming taper function on sidelobe suppression. The reflection spectra have been calculated with the coupled-mode theory. The minimum coupling coefficients κmin were chosen to be 0%, 14%, and 30% of the maximum value κmax. The latter was adjusted such that all three gratings had the same strength, i.e., κmean was the same.

Fig. 7
Fig. 7

Calculated reflection and transmission spectra of an apodized grating with a coupling strength distribution that was optimized with the breeder genetic algorithm. The coupling strength distribution is shown in the inset.

Fig. 8
Fig. 8

Comparison between measured and simulated transmission and reflection spectra for apodized gratings, based on a concatenation of gratings with different duty cycles. The measurement was performed with TM-polarized light.

Fig. 9
Fig. 9

Spectra measured at the four ports of the add–drop filter with TE-polarized light. The spectra were normalized to the transmission through a noncorrugated waveguide.

Equations (9)

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E+(z)E-(z)=FE+(z)E-(z)=f11f12f21f22 E+(0)E-(0),
f11=iΔβ sinh(γz)+γ cosh(γz)γexpiπzΛ,
f12=iκ sinh(γz)γexpiπzΛ,
f21=-iκ sinh(γz)γexp-iπzΛ,
f22=-iΔβ sinh(γz)+γ cosh(γz)γexp-iπzΛ,
γ2=κ2-Δβ2.
κ=β2neff Δ1(x, y)U2(x, y)dxdyU2(x, y)dxdy,
κ=ncore2-ncladding2neffλsinπ wΛ×corrugationU2(x, y)dxdyU2(x, y)dxdy.
Rresonance=1-Tresonance=tanh2(κL),

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