Abstract

We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the reflection and transmission coefficient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal waveguide band and indicates efficient coupling between the slab waveguide and the photonic crystal waveguide. Other applications of adiabatic mode transformation in photonic crystal waveguides and the coupled-resonator optical waveguides are also discussed.

© 2000 Optical Society of America

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References

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  2. Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  8. D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
    [CrossRef]
  9. J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
    [CrossRef]
  10. A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
  11. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
    [CrossRef] [PubMed]
  12. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
  13. Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 387 (2000).
    [CrossRef]

2000

1999

1998

1996

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

1994

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1989

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

1987

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1980

D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
[CrossRef]

1966

K. S. Yee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Ackerman, D. A.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

Atkin, D. M.

Berenger, J. P.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Birks, T. A.

Chen, J. C.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Fan, S.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Fischer, R.

D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
[CrossRef]

Henry, C. H.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

Joannopoulos, J. D.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Kewitsch, A. S.

Kistler, R. C.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

Knight, J. C.

Kurland, I.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lee, R. K.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

Mekis, A. M.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Merewether, D. E.

D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
[CrossRef]

Orlowsky, K. J.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

Rakuljic, G. A.

Russell, P. St. J.

Scherer, A.

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968).

Shani, Y.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

Smith, F. W.

D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
[CrossRef]

Villeneuve, P. R.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Willems, P. A.

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

Yee, K. S.

K. S. Yee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Appl. Phys. Lett.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, Appl. Phys. Lett. 55, 2389 (1989).
[CrossRef]

IEEE Trans. Antennas Propag.

K. S. Yee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

IEEE Trans. Nucl. Sci.

D. E. Merewether, R. Fischer, and F. W. Smith, IEEE Trans. Nucl. Sci. NS-27, 1829 (1980).
[CrossRef]

J. Comput. Phys.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. Lett.

A. M. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Other

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the two-dimensional computational domain. A tapered slab semiconductor waveguide is connected with a square-lattice photonic crystal waveguide and back into a tapered slab waveguide. For small taper angle, adiabatic mode conversion can be achieved. (b) The dispersion relation of the single TM waveguide mode in a square-lattice photonic crystal waveguide formed by removal of one row of semiconductor rods.

Fig. 2
Fig. 2

Transmission and reflection spectra of the structure shown in Fig. 1(a). The parameter θ corresponds to the different taper angles shown in Fig. 1(a).

Fig. 3
Fig. 3

E field distribution with slab waveguide taper angle θ=6.3°. In (a), the normalized mode frequency is ωa/2π=0.39; in (b), ωa/2π is 0.3.

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