Abstract

A new criterion for the optimum design of curved dielectric waveguides is proposed. The bends designed according to this model are named matched bends. In the matched bend, the suitable choice of both bending radius and bending angle reduces the total losses of the bend and avoids the leaky-mode excitation at the end of the bend. For a given angle, a discrete number of bending radii that satisfy the matched bend criterion can be analytically determined. With respect to the lateral offset, matched bends are more robust to both fabrication tolerances and wavelength and can be realized in every technology. The reduction of the leaky-mode excitation at the output of the bend is a fundamental property when two or more components are cascaded. Ghost images in the spectral response, cross talk, and asymmetries of the transfer function are successfully reduced. Some examples that use buried, rib, ridge, and diffused waveguides are presented and discussed.

© 2003 Optical Society of America

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  1. A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
    [CrossRef]
  2. A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.
  3. T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
    [CrossRef]
  4. T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
    [CrossRef]
  5. E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” Proc. IEE 129, 278–280 (1982).
  6. S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
    [CrossRef]
  7. R. Baets, P. E. Lagasse, “Loss calculation and design of arbitrarily curved integrated-optic waveguides,” J. Opt. Soc. Am. 73, 177–182 (1983).
    [CrossRef]
  8. M. Munowitz, D. J. Vezzetti, “Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers,” J. Lightwave Technol. 10, 1570–1573 (1992).
    [CrossRef]
  9. J. Saijonmaa, D. Yevick, “Beam-propagation analysis of loss in bent optical waveguides and fibers,” J. Opt. Soc. Am. 73, 1785–1791 (1983).
    [CrossRef]
  10. C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
    [CrossRef]
  11. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).
  12. S. J. Hewlett, F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375–383 (1995).
    [CrossRef]
  13. X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
    [CrossRef]

2001 (2)

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

1998 (1)

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

1996 (1)

X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[CrossRef]

1995 (2)

S. J. Hewlett, F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

1993 (1)

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

1992 (1)

M. Munowitz, D. J. Vezzetti, “Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers,” J. Lightwave Technol. 10, 1570–1573 (1992).
[CrossRef]

1983 (2)

1982 (1)

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” Proc. IEE 129, 278–280 (1982).

Baets, R.

Carniel, F.

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Costa, R.

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.

El-Mikati, H. A.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

Grattan, K. T. V.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

Hewlett, S. J.

S. J. Hewlett, F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

Hirono, T.

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

Huang, W. P.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Kawachi, M.

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

Kitoh, T.

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

Kohtoku, M.

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

Ladouceur, F.

S. J. Hewlett, F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

Lagasse, P. E.

Leijtens, X. J. M.

X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[CrossRef]

Lourec, P. Le

X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[CrossRef]

Lui, W. W.

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

Martinelli, M.

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.

Melloni, A.

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.

Munowitz, M.

M. Munowitz, D. J. Vezzetti, “Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers,” J. Lightwave Technol. 10, 1570–1573 (1992).
[CrossRef]

Neumann, E.-G.

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” Proc. IEE 129, 278–280 (1982).

Obayya, S. S. A.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

Rahman, B. M. A.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

Saijonmaa, J.

Smit, M. K.

X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[CrossRef]

Takato, N.

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

Vezzetti, D. J.

M. Munowitz, D. J. Vezzetti, “Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers,” J. Lightwave Technol. 10, 1570–1573 (1992).
[CrossRef]

Xu, C. L.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Yasu, M.

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

Yevick, D.

Yokoyama, K.

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

Yoshikuni, Y.

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

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

X. J. M. Leijtens, P. Le Lourec, M. K. Smit, “S-matrix oriented CAD-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Hirono, M. Kohtoku, Y. Yoshikuni, W. W. Lui, K. Yokoyama, “Optimized offset to eliminate first-order mode excitation at the junction of straight and curved waveguides,” IEEE Photon. Technol. Lett. 10, 982–984 (1998).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, H. A. El-Mikati, “Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides,” IEEE Photonics Technol. Lett. 13, 681–683 (2001).
[CrossRef]

J. Lightwave Technol. (5)

M. Munowitz, D. J. Vezzetti, “Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers,” J. Lightwave Technol. 10, 1570–1573 (1992).
[CrossRef]

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

T. Kitoh, N. Takato, M. Yasu, M. Kawachi, “Bending loss reduction in silica-based waveguides by using lateral offsets,” J. Lightwave Technol. 13, 555–562 (1995).
[CrossRef]

S. J. Hewlett, F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. IEE (1)

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” Proc. IEE 129, 278–280 (1982).

Other (2)

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 641–642.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

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Figures (10)

Fig. 1
Fig. 1

Straight–bend–straight geometry.

Fig. 2
Fig. 2

Beating of the first two straight modes in a monomode bent waveguide and definition of the beat length LB and of the beat depth d. The bending radius is R=1.5 mm. In the inset the considered waveguide is shown.

Fig. 3
Fig. 3

Matched bend condition in the Rθ plane for the considered ridge waveguide.

Fig. 4
Fig. 4

Intensity patterns of the fields propagating in (a) the matched bend and (b) the unmatched bend. See text for the dimensions.

Fig. 5
Fig. 5

S-bend geometry.

Fig. 6
Fig. 6

Intensity of the fundamental and first leaky mode along the S bend of Fig. 5.

Fig. 7
Fig. 7

Beat depth. Solid curves, TE; dashed curves, TM.

Fig. 8
Fig. 8

Beat length. Solid curves, TE; dashed curves, TM.

Fig. 9
Fig. 9

Total losses versus the lateral offset of the straight–bend–straight structure. The length of the bend is LB. Bending radius: buried, 5 mm; rib, 3.5 mm; ridge, 2 mm. Solid curves, TE; dashed curves, TM.

Fig. 10
Fig. 10

Effect of (a) a matched S bend and (b) an unmatched S bend on an Y branch.

Tables (1)

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Table 1 Imbalance and Losses of a MMI Coupler

Equations (12)

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

LB=2πβb1-βb2,
βb1-βb2=[(β1-β2)2+4β1β2c122/R2]1/2,
βb1-βb2=[(β1-β2)2+4κ2]1/2,
β2=β1-2πLB2-4κ21/2,
κ=c12β1β2R.
d=4κ2(β1-β2)2+4κ2,
κ=πLB d,
β2=β1-2πLB 1-d.
R=[(2πm/θ)2-4β1β2c122]1/2β1-β2,
-θ/2θ/2[R2(β1-β2)2+4β1β2c122]1/2dα=2mπ,
J=1-a22±a2±a21-a22,
Ts=J2TPb2J2PLJ1TPb1J1.

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