Abstract

We report the initial three-dimensional finite-difference time-domain modeling of a vertically coupled photonic racetrack. The modeling reveals details of the full suite of space–time behavior of electromagnetic-wave phenomena involved in guiding, coupling, multimoding, dispersion, and radiation. This behavior is not easily obtainable by analytical or full-vector frequency-domain methods, measurements of terminal properties, or near-field scanning optical microscopy.

© 2003 Optical Society of America

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References

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  1. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).
  2. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
    [CrossRef]
  3. A. Sakai and T. Baba, J. Lightwave Technol. 17, 1493 (1999).
    [CrossRef]
  4. W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
    [CrossRef]
  5. B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
    [CrossRef]
  6. G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
    [CrossRef]

2000 (4)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
[CrossRef]

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

1999 (1)

1997 (1)

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

Baba, T.

Chu, S. T.

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

Chu, S.-T.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Goldberg, B. B.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Guo, W.-H.

W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

Ho, S. T.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

Huang, Y.-Z.

W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
[CrossRef]

Little, B. E.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

Rafizadeh, D.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

Sakai, A.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

Unlu, M. S.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Vander Rhodes, G. H.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Wang, Q.-M.

W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. H. Vander Rhodes, B. B. Goldberg, M. S. Unlu, S.-T. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W.-H. Guo, Y.-Z. Huang, and Q.-M. Wang, IEEE Photon. Technol. Lett. 12, 813 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

J. Lightwave Technol. (2)

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, J. Lightwave Technol. 15, 2154 (1997).
[CrossRef]

A. Sakai and T. Baba, J. Lightwave Technol. 17, 1493 (1999).
[CrossRef]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

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Figures (8)

Fig. 1
Fig. 1

Horizontal (xy) cuts through the 3-D FDTD modeling geometry: (a) through the bus waveguide beneath the racetrack, (b) through the racetrack. Vertical transverse field observation cut planes P1, P2, P3, and P4 are also shown.

Fig. 2
Fig. 2

Vertical (yz) cross section through the 3-D FDTD modeling geometry at P2 in the center of the coupling region.

Fig. 3
Fig. 3

FDTD-calculated absolute value of the y component of the electric field of the optical pulse within the racetrack: (a) +x-directed propagation immediately after the initial coupling from the bus waveguide; (b) counter-clockwise propagation upon entering the first curved section, showing modal distortion; (c) -x-directed propagation after exiting the first curved section, showing residual modal-distortion effects.

Fig. 4
Fig. 4

FDTD-calculated transverse field vectors in the vertical (yz) cross section at P2 at the instant of peak excitation within the bus waveguide: (a) electric field E, (b) magnetic field H. The bus and racetrack waveguides are shown as shaded rectangles.

Fig. 5
Fig. 5

FDTD-calculated transverse field vectors in the vertical (xz) cross section at P4 at the instant of peak excitation within the racetrack waveguide: (a) electric field E, (b) magnetic field H. The racetrack waveguide is shown as a shaded rectangle.

Fig. 6
Fig. 6

Relative FDTD-calculated Poynting vector in the direction of propagation. The magnitudes are normalized by the maximum magnitude in each plot, and the boundaries of the bus and racetrack waveguides are shown as solid rectangles. (a) x component of the Poynting vector along the vertical (yz) cross section at P2 at the instant of peak excitation within the bus waveguide, (b) y component of the Poynting vector along the vertical (xz) cross section at P4 at the instant of peak excitation within the racetrack waveguide.

Fig. 7
Fig. 7

FDTD-calculated ratio of the coupled racetrack power at P4 to the incident bus waveguide power as a function of wavelength (left axis) and FDTD-calculated ratio of the transmitted bus waveguide power to the incident bus waveguide power as a function of wavelength (right axis). Subsequent backcouplings from the racetrack to the bus waveguide are excluded.

Fig. 8
Fig. 8

FDTD-calculated power retention within the racetrack as a function of wavelength. A single complete propagation around the racetrack from P4 back to P4 is considered.

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