Abstract

For traditional microprism-type bent waveguides one must take into consideration only the two outer optical paths to compensate for the phase difference between phase fronts in front of and behind the bent region. We propose a systematic design rule to achieve an optimal phase matching condition by taking account of the whole optical paths for full phase compensation. The simulated results obtained with the fast Fourier transform beam propagation method indicate that the normalized transmitted powers are greater than 95% even though the bent angle is as large as 10°.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. K. Hirayama, M. Koshiba, “A new low-loss structure of abrupt bend in dielectric waveguides,” IEEE J. Lightwave Technol. 10, 563–569 (1992).
    [CrossRef]
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    [CrossRef]
  9. H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
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1997 (1)

M. L. Wu, P. L. Fan, C. T. Lee, “Completely adiabatic S-shaped bent tapers in optical waveguides,” IEEE Photon. Technol. Lett. 9, 212–214 (1997).
[CrossRef]

1996 (1)

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

1995 (1)

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

1994 (1)

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

1992 (1)

K. Hirayama, M. Koshiba, “A new low-loss structure of abrupt bend in dielectric waveguides,” IEEE J. Lightwave Technol. 10, 563–569 (1992).
[CrossRef]

1986 (2)

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

T. Shiina, K. Shiraishi, S. Kawakami, “Waveguide-bend configuration with low-loss characteristics,” Opt. Lett. 11, 736–738 (1986).
[CrossRef] [PubMed]

1983 (1)

1980 (1)

Bosworth, R. H.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

Fan, P. L.

M. L. Wu, P. L. Fan, C. T. Lee, “Completely adiabatic S-shaped bent tapers in optical waveguides,” IEEE Photon. Technol. Lett. 9, 212–214 (1997).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Hirayama, K.

K. Hirayama, M. Koshiba, “A new low-loss structure of abrupt bend in dielectric waveguides,” IEEE J. Lightwave Technol. 10, 563–569 (1992).
[CrossRef]

Hsu, J. M.

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Johnson, L. M.

Kawakami, S.

Korotky, S. K.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

Koshiba, M.

K. Hirayama, M. Koshiba, “A new low-loss structure of abrupt bend in dielectric waveguides,” IEEE J. Lightwave Technol. 10, 563–569 (1992).
[CrossRef]

Lee, C. T.

M. L. Wu, P. L. Fan, C. T. Lee, “Completely adiabatic S-shaped bent tapers in optical waveguides,” IEEE Photon. Technol. Lett. 9, 212–214 (1997).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Leonberger, F. J.

Liao, Y. P.

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

Lin, H. B.

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

Marcatili, E. A. J.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

Shiina, T.

Shiraishi, K.

Su, J. Y.

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

Tamir, T.

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1989).

Veselka, J. J.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

Wang, W. S.

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

Wei, P. K.

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

Wu, M. L.

M. L. Wu, P. L. Fan, C. T. Lee, “Completely adiabatic S-shaped bent tapers in optical waveguides,” IEEE Photon. Technol. Lett. 9, 212–214 (1997).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Bosworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 8, 92–94 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (2)

K. Hirayama, M. Koshiba, “A new low-loss structure of abrupt bend in dielectric waveguides,” IEEE J. Lightwave Technol. 10, 563–569 (1992).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” IEEE J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. B. Lin, J. Y. Su, P. K. Wei, W. S. Wang, “Design and application of very low-loss abrupt bends in optical waveguides,” IEEE J. Quantum Electron. 30, 2827–2835 (1994).
[CrossRef]

H. B. Lin, J. Y. Su, Y. P. Liao, W. S. Wang, “Study and design of step-index channel waveguide bends with large-angle and low-loss characteristics,” IEEE J. Quantum Electron. 31, 1131–1138 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. L. Wu, P. L. Fan, C. T. Lee, “Completely adiabatic S-shaped bent tapers in optical waveguides,” IEEE Photon. Technol. Lett. 9, 212–214 (1997).
[CrossRef]

Opt. Lett. (2)

Other (1)

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1989).

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Figures (3)

Fig. 1
Fig. 1

Full phase compensation microprism-type bent waveguide: (a) top view and (b) three-dimensional structure.

Fig. 2
Fig. 2

Field intensity distributions for the full phase compensation microprism-type bent waveguide with a bent angle of θ = 10°.

Fig. 3
Fig. 3

Dependence of normalized transmitted power efficiency η on bent angle θ for a full phase compensation microprism-type bent waveguide.

Equations (13)

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OPL τ = n p ξ τ + 2 n g η τ       for   arbitrary   τ ,
OPL 0 = n p ξ 0 = n p θ W A - W eff 2     for   τ = 0 ,
W eff = W g + 1 α 1 x + 1 α 2 x ,
n p ξ τ + 2 n g η τ = n p θ W A - W eff 2 .
ξ τ + 2 η τ = θ W A - W eff 2 + τ .
η τ = θ n p 2 n p - n g   τ = κ θ τ ,
α = η τ W τ = κ θ W τ   τ ,
κ θ = θ n p 2 n p - n g ,     W τ = W A - W eff 2 + τ .
x 1 τ = W A - W eff 2 + xp 1 - W τ cos   α , z 1 τ = zp 1 + W τ sin   α .
x 2 τ = W A - W eff 2 cos   θ + xp 2 - W τ cos θ - α , z 2 τ = zp 1 + W τ sin θ - α .
Δ ϕ b = β ξ W eff + 2 η W eff - ξ 0 = k 0 n eff θ W eff .
Δ ϕ p = n p - n s k 0 θ   W A - W eff 2 × cos θ / 2 - m   cos 2 θ / 2 1 - m   cos 2 θ / 2 ,
n p - n s W A - W eff 2 cos θ / 2 - m   cos 2 θ / 2 1 - m   cos 2 θ / 2 = n eff W eff .

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