Abstract

We show that it is possible to obtain 2×2 waveguide couplers with new power splitting ratios for cross coupling of 7%, 64%, 80% and 93% by cascading two short MMI sections. These couplers have simple geometry and low loss. They offer valuable new possibilities for designing waveguide power taps, high-Q ring resonators, ladder-structure optical filters, and loop-mirror partial reflectors.

© 2007 Optical Society of America

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References

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  1. L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
    [CrossRef]
  2. D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
    [CrossRef]
  3. G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
    [CrossRef]
  4. S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
    [CrossRef]
  5. S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
    [CrossRef]
  6. V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
    [CrossRef]
  7. M. G. Kane, I. Glesk, J. P. Sokoloff, and P. R. Prucnal, "Asymmetric optical loop mirror: analysis of an all-optical switch," Appl. Opt. 33, 6833-6842 (1994).
    [CrossRef] [PubMed]
  8. D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
    [CrossRef]
  9. M. Bachmann, P. A. Besse, and H. Melchior:, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
    [CrossRef] [PubMed]
  10. J. Leuthold C. H. Joyner, "Multimode interference couplers with tunable power splitting ratios," J. Lightwave Technol. 19, 700-707 (2001).
    [CrossRef]
  11. Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
    [CrossRef]
  12. D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
    [CrossRef]
  13. BeamPROP, version 5.1, RSoft Inc., NY (2005).
  14. FimmProp, version 4.3, Photon Design, Oxford, UK (2004).

2003 (2)

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

2002 (1)

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

2001 (1)

1999 (1)

1997 (1)

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

1996 (1)

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

1995 (3)

S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
[CrossRef]

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior:, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
[CrossRef] [PubMed]

1994 (1)

1988 (1)

D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
[CrossRef]

Bachmann, M.

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior:, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
[CrossRef] [PubMed]

Besse, P. A.

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior:, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
[CrossRef] [PubMed]

Forrest, S. R.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

Glesk, I.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

M. G. Kane, I. Glesk, J. P. Sokoloff, and P. R. Prucnal, "Asymmetric optical loop mirror: analysis of an all-optical switch," Appl. Opt. 33, 6833-6842 (1994).
[CrossRef] [PubMed]

Hamacher, M.

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

Heidrich, H.

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

Hibino, Y.

S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
[CrossRef]

Hunziker, W.

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

Kane, M. G.

Lai, Q.

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

Lenz, G.

Levy, D. S.

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

Li, C.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

Li, Y. M.

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

Madsen, C. K.

Matsuo, S.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

Melchior, H.

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior:, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
[CrossRef] [PubMed]

Menon, V. M.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

Mortimore, D. B.

D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
[CrossRef]

Oda, K.

S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
[CrossRef]

Ohiso, Y.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

Okamoto, H.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

Osgood, R. M.

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Prucnal, P. R.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

M. G. Kane, I. Glesk, J. P. Sokoloff, and P. R. Prucnal, "Asymmetric optical loop mirror: analysis of an all-optical switch," Appl. Opt. 33, 6833-6842 (1994).
[CrossRef] [PubMed]

Rabus, D. G.

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

Scarmozzino, R.

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

Segawa, T.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

Sokoloff, J. P.

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Suzuki, S.

S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
[CrossRef]

Tong, W.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

Troppenz, U.

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

Xia, F.

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

Yoshikuni, Y.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, "Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers," Electron. Lett.,  32, 1576-1577 (1996).
[CrossRef]

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

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, "A widely tunable optical filter using ladder-type structure," IEEE Photonics Technol. Lett. 15, 1114-1116 (2003).
[CrossRef]

V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest, "All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer," IEEE Photonics Technol. Lett. 15, 254-256 (2003).
[CrossRef]

D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. OsgoodJr. "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photonics Technol. Lett. 9, 1373-1375 (1997)
[CrossRef]

J. Lightwave Technol. (5)

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
[CrossRef]

J. Leuthold C. H. Joyner, "Multimode interference couplers with tunable power splitting ratios," J. Lightwave Technol. 19, 700-707 (2001).
[CrossRef]

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
[CrossRef]

S. Suzuki, K. Oda, and Y. Hibino, "Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz," J. Lightwave Technol. 13, 1766-1770 (1995)
[CrossRef]

Other (2)

BeamPROP, version 5.1, RSoft Inc., NY (2005).

FimmProp, version 4.3, Photon Design, Oxford, UK (2004).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagrams of a generic 2×2 MMI coupler: (a) in plan view showing the notations used in this paper, and (b) in cross-section showing the basic layer structure in the waveguide ridge.

Fig. 2.
Fig. 2.

The simulated 2-D field maps for four different cascaded MMI couplers with K=0.07 (a), 0.93 (b), 0.64 (c), and 0.80 (d). The values for total transmittance and K are obtained by 2-D BPM simulations.

Fig. 3.
Fig. 3.

(a) The dependence of the total transmittances on the deviation of the input wavelength from the design wavelength. (b) The corresponding variation of the K values.

Tables (1)

Tables Icon

Table I Transfer functions of MMI-A, MMI-B, MMI-C, and MMI-D

Equations (5)

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

L π = 4 n s W e 2 3 λ 0 = 4 n s r 2 s 2 3 λ 0 A r 2 s 2 ,
[ HUV B HUV X ± HUV X HUV B ± ] = [ HV B HV X ± HV X HV B ] [ HU B HU X ± HU X HU B ] ,
KUV = HUV X ± 2 HUV X ± 2 + HUV B ± 2 ,
F = π 1 K K .
R = 2 H B H X ± 2 .

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