Abstract

It is shown that the bandwidth of a traveling-wave electro-optical modulator can be greatly increased by matching of the group velocities of the optical and rf waves in the waveguides with cascaded Bragg gratings. A LiNbO3 Mach–Zehnder modulator with 1-V half-wave voltage and a bandwidth in excess of 100 GHz is proposed and its performance evaluated.

© 2000 Optical Society of America

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References

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  1. R. C. Walker, IEEE J. Quantum Electron. 27, 654 (1991).
    [CrossRef]
  2. G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
    [CrossRef]
  3. W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
    [CrossRef]
  4. I. P. Kaminow and J. Liu, Proc. IEEE 51, 132 (1963).
    [CrossRef]
  5. R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
    [CrossRef]
  6. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997), pp. 251–253.
  7. P. St. J. Russell, J. Mod. Opt. 38, 1559 (1991).
    [CrossRef]
  8. N. M. Litchinitser, B. J. Eggleton, and G. P. Agrawal, J. Lightwave Technol. 16, 1523 (1998).
    [CrossRef]
  9. S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
    [CrossRef]
  10. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
    [CrossRef]
  11. M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
    [CrossRef]
  12. L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
    [CrossRef]
  13. H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
    [CrossRef]

1998 (5)

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
[CrossRef]

L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, and G. P. Agrawal, J. Lightwave Technol. 16, 1523 (1998).
[CrossRef]

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

1994 (1)

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

1993 (1)

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

1991 (2)

R. C. Walker, IEEE J. Quantum Electron. 27, 654 (1991).
[CrossRef]

P. St. J. Russell, J. Mod. Opt. 38, 1559 (1991).
[CrossRef]

1984 (1)

R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
[CrossRef]

1963 (1)

I. P. Kaminow and J. Liu, Proc. IEEE 51, 132 (1963).
[CrossRef]

Agrawal, G. P.

Alferness, R. C.

R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
[CrossRef]

Bulmer, C. H.

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

Burns, W. K.

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

Chen, L. R.

L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
[CrossRef]

Cooper, D. J. F.

L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
[CrossRef]

Eggleton, B. J.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Erlig, H.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Feinberg, J.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Fetterman, H. R.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Gopalakrishnan, G. K.

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

Greenblatt, A. S.

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

Grubsky, V.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Howerton, M. M.

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

Ibsen, M.

M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
[CrossRef]

Ishii, H.

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow and J. Liu, Proc. IEEE 51, 132 (1963).
[CrossRef]

Korotky, S. K.

R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
[CrossRef]

Laming, R. I.

M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
[CrossRef]

Litchinitser, N. M.

Liu, J.

I. P. Kaminow and J. Liu, Proc. IEEE 51, 132 (1963).
[CrossRef]

Marcatili, E. A. J.

R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
[CrossRef]

McElhanon, R. M.

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

Moeller, R. P.

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, J. Mod. Opt. 38, 1559 (1991).
[CrossRef]

Smith, P. W. E.

L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
[CrossRef]

Starodubov, D. S.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Tamamura, T.

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

Tohmori, Y.

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

Walker, R. C.

R. C. Walker, IEEE J. Quantum Electron. 27, 654 (1991).
[CrossRef]

Wang, S.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Yablonovich, E.

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997), pp. 251–253.

Yoshikuni, Y.

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. C. Walker, IEEE J. Quantum Electron. 27, 654 (1991).
[CrossRef]

R. C. Alferness, S. K. Korotky, and E. A. J. Marcatili, IEEE J. Quantum Electron. QE-20, 301 (1984).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovich, V. Grubsky, D. S. Starodubov, and J. Feinberg, IEEE Microwave Guided Wave Lett. 8, 327 (1998).
[CrossRef]

IEEE Photon Technol. Lett. (1)

H. Ishii, Y. Tohmori, T. Tamamura, and Y. Yoshikuni, IEEE Photon Technol. Lett. 4, 393 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Ibsen, M. K. Durkin, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 84 (1998).
[CrossRef]

L. R. Chen, D. J. F. Cooper, and P. W. E. Smith, IEEE Photon. Technol. Lett. 10, 1283 (1998).
[CrossRef]

W. K. Burns, M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. M. McElhanon, IEEE Photon. Technol. Lett. 10, 805 (1998).
[CrossRef]

J. Lightwave Technol. (3)

G. K. Gopalakrishnan, W. K. Burns, R. M. McElhanon, C. H. Bulmer, and A. S. Greenblatt, J. Lightwave Technol. 12, 1807 (1994).
[CrossRef]

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, and G. P. Agrawal, J. Lightwave Technol. 16, 1523 (1998).
[CrossRef]

J. Mod. Opt. (1)

P. St. J. Russell, J. Mod. Opt. 38, 1559 (1991).
[CrossRef]

Proc. IEEE (1)

I. P. Kaminow and J. Liu, Proc. IEEE 51, 132 (1963).
[CrossRef]

Other (1)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997), pp. 251–253.

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Figures (4)

Fig. 1
Fig. 1

Proposed Mach–Zehnder modulator with cascaded Bragg gratings.

Fig. 2
Fig. 2

Group index dispersion in the LiNbO3 waveguide with cascaded Bragg gratings with periods of 0.355 and 0.365 µm.

Fig. 3
Fig. 3

Transmission of the 3-cm-long Mach–Zehnder EOM’s with 0.25-V sinusoidal voltage applied: a, modulator with or without a cascaded grating at 1 GHz; b, modulator without cascaded gratings at 5 GHz; c modulator with cascaded gratings at 25 GHz; d, modulator with cascaded gratings at 100 GHz.

Fig. 4
Fig. 4

Frequency response of a Mach–Zehnder EOM: a, without a grating and b, with a cascaded grating.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

2z2E-n2c22t2E=1c2n4r2t2ErfE,
2z2Erf-nrf2c22t2Erf=1c2n4rE,
Erf=12iΩ=0ΩmEΩ expiΩt-krfΩz-c.c.
Ez,t=12N=-Ω=0ΩmENzexpiω+NΩt-kω+NΩz+c.c.,
dENdz=14ω+NΩcn3rEΩEN-1 expiδk+Ωz-EN+1 expiδk-Ωz,
δk±NΩ=kω+NΩ-kω+N±1ΩkrfΩ.
δk+N-δk-N=dkdωω-dkrfdΩ0Ω+122N-1d2kdω2ω-12d2krfdΩ20Ω2.
δkmΩc=|[(vg-1ω-vg,rf-10]Ωc+vg-1ω+NmΩc-vg-1ωΩc|.
δkm=nω-nrf0Ωcc,
Ωc=πcL1ngω-ngω+NmΩc-ngω-nrf0,

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