Abstract

The performance of grating-assisted output couplers of finite extent excited by finite ultrafast pulsed modes is characterized numerically by the finite-difference time-domain method. The results for pulsed excitations with extremely long pulse envelopes are compared with those that contain only a few optical cycles for gratings that are both long and short compared with the equivalent pulse length. We demonstrate that the shortest length of either the grating or the pulse dictates the far-field performance of the grating-assisted output couplers.

© 1998 Optical Society of America

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References

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  1. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  2. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, Boston, Mass., 1991).
  3. A. Taflove, Computational Electrodynamics (Artech, Norwood, Mass., 1995).
  4. T. Liang and R. W. Ziolkowski, J. Lightwave Technol. 15, 1966 (1997).
    [CrossRef]
  5. R. W. Ziolkowski and T. Liang, Opt. Lett. 22, 1033 (1997).
    [CrossRef] [PubMed]
  6. K. Kunz and R. Lubbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

1997 (2)

T. Liang and R. W. Ziolkowski, J. Lightwave Technol. 15, 1966 (1997).
[CrossRef]

R. W. Ziolkowski and T. Liang, Opt. Lett. 22, 1033 (1997).
[CrossRef] [PubMed]

Kunz, K.

K. Kunz and R. Lubbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

Liang, T.

R. W. Ziolkowski and T. Liang, Opt. Lett. 22, 1033 (1997).
[CrossRef] [PubMed]

T. Liang and R. W. Ziolkowski, J. Lightwave Technol. 15, 1966 (1997).
[CrossRef]

Lubbers, R.

K. Kunz and R. Lubbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, Boston, Mass., 1991).

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech, Norwood, Mass., 1995).

Ziolkowski, R. W.

T. Liang and R. W. Ziolkowski, J. Lightwave Technol. 15, 1966 (1997).
[CrossRef]

R. W. Ziolkowski and T. Liang, Opt. Lett. 22, 1033 (1997).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

T. Liang and R. W. Ziolkowski, J. Lightwave Technol. 15, 1966 (1997).
[CrossRef]

Opt. Lett. (1)

Other (4)

K. Kunz and R. Lubbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, Boston, Mass., 1991).

A. Taflove, Computational Electrodynamics (Artech, Norwood, Mass., 1995).

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Figures (6)

Fig. 1
Fig. 1

Sampling planes for FDTD modeling of grating-assisted output couplers.

Fig. 2
Fig. 2

Far-field patterns for 5–30–5 pulse excitation when the coupler consists of 2 (dashed curve), 5 (dotted curve), 11 (dotted–dashed curve), or 20 (solid curve) grating unit cells.

Fig. 3
Fig. 3

Solid curve, half-beam widths (HBW) of the far-field patterns excited by a 5–30–5 pulse as a function of the number of grating cells N in the coupler. Dashed curve, a normalized 1/N curve.

Fig. 4
Fig. 4

Effect of the grating duty factor: solid and dashed curves, two 2 grating cells with duty factors of 0.1 and 0.5, respectively; dotted curve, 20 grating cells with a duty factor of 0.5. All curves were obtained by 5–30–5-pulse excitation.

Fig. 5
Fig. 5

Far-field patterns for 2–2–2 pulse excitation when the coupler consists of 2 (dashed curve), 5 (dotted curve), 11 (dotted–dashed curve), and 20 (solid curve) grating unit cells.

Fig. 6
Fig. 6

Half-beam widths (HBW) of the far-field patterns excited by 5–30–5 (dashed curve) and 2–2–2 (solid curve) pulses.

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