Abstract

The power coupling characteristics of a multimode-interference-based 3-dB coupler have been analyzed by using the vector finite-element and least-squares boundary residual methods. The numerical results obtained have been compared with published experimental data to show the accuracy and the versatility of these numerical schemes. The results predict that a full treatment of the two-dimensional cross section is of particular importance for the design and the simulation of effective waveguide devices to enable a study of their important optical properties such as polarization and fabrication tolerances.

© 1998 Optical Society of America

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References

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  1. L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference device based on self-imaging: principle and applications,” J. Lightwave Technol. 13, 615–626 (1995).
    [CrossRef]
  2. R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
    [CrossRef]
  3. T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
    [CrossRef]
  4. J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.
  5. M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
    [CrossRef]
  6. D. C. Chang, E. F. Kuester, “A hybrid method paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
    [CrossRef]
  7. C. M. Weinert, N. Agrawal, “Three-dimensional finite difference simulation of coupling behaviour and loss in multimode interference devices,” IEEE Photon. Technol. Lett. 7, 529–531 (1995).
    [CrossRef]
  8. G. M. Berry, S. V. Burke, “Analysis of optical rib-self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method,” Opt. Quantum Electron. 27, 921–934 (1995).
    [CrossRef]
  9. C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
    [CrossRef]
  10. B. M. A. Rahman, J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2, 682–688 (1984).
    [CrossRef]
  11. B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52–57 (1988).
    [CrossRef]
  12. B. Broberg, S. Lindgren, “Refractive index of In1–xGaxAsyP1–y layers and InP in the transparent wavelength region,” J. Appl. Phys. 55, 3376–3381 (1984).
    [CrossRef]
  13. L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
    [CrossRef]
  14. C. H. Henry, Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron. 27, 523–530 (1991).
    [CrossRef]
  15. L. H. Spiekman, “Compact integrated optical components for telecommunication networks,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990).

1996

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

1995

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference device based on self-imaging: principle and applications,” J. Lightwave Technol. 13, 615–626 (1995).
[CrossRef]

C. M. Weinert, N. Agrawal, “Three-dimensional finite difference simulation of coupling behaviour and loss in multimode interference devices,” IEEE Photon. Technol. Lett. 7, 529–531 (1995).
[CrossRef]

G. M. Berry, S. V. Burke, “Analysis of optical rib-self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method,” Opt. Quantum Electron. 27, 921–934 (1995).
[CrossRef]

C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
[CrossRef]

T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
[CrossRef]

1994

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

1991

C. H. Henry, Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron. 27, 523–530 (1991).
[CrossRef]

1988

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52–57 (1988).
[CrossRef]

1984

B. Broberg, S. Lindgren, “Refractive index of In1–xGaxAsyP1–y layers and InP in the transparent wavelength region,” J. Appl. Phys. 55, 3376–3381 (1984).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2, 682–688 (1984).
[CrossRef]

1981

D. C. Chang, E. F. Kuester, “A hybrid method paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Agrawal, N.

C. M. Weinert, N. Agrawal, “Three-dimensional finite difference simulation of coupling behaviour and loss in multimode interference devices,” IEEE Photon. Technol. Lett. 7, 529–531 (1995).
[CrossRef]

Amersfort, M. R.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Andreadakis, N. C.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Berry, G. M.

G. M. Berry, S. V. Burke, “Analysis of optical rib-self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method,” Opt. Quantum Electron. 27, 921–934 (1995).
[CrossRef]

Bhat, R.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Birbeck, J. C. H.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Broberg, B.

B. Broberg, S. Lindgren, “Refractive index of In1–xGaxAsyP1–y layers and InP in the transparent wavelength region,” J. Appl. Phys. 55, 3376–3381 (1984).
[CrossRef]

Burke, S. V.

G. M. Berry, S. V. Burke, “Analysis of optical rib-self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method,” Opt. Quantum Electron. 27, 921–934 (1995).
[CrossRef]

Caneau, C.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Chang, D. C.

D. C. Chang, E. F. Kuester, “A hybrid method paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Davies, J. B.

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52–57 (1988).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2, 682–688 (1984).
[CrossRef]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
[CrossRef]

Grattan, K. T. V.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

Groen, F. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

Heaton, J. M.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Henry, C. H.

C. H. Henry, Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron. 27, 523–530 (1991).
[CrossRef]

Hernandez-Gil, F.

C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
[CrossRef]

Hilton, K. P.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Jenkins, R. M.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Koza, M. A.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
[CrossRef]

Kuester, E. F.

D. C. Chang, E. F. Kuester, “A hybrid method paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Lebalnc, H. P.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Leybourn, P. J. R.

T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
[CrossRef]

Lindgren, S.

B. Broberg, S. Lindgren, “Refractive index of In1–xGaxAsyP1–y layers and InP in the transparent wavelength region,” J. Appl. Phys. 55, 3376–3381 (1984).
[CrossRef]

Metaal, E. G.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

Moerman, I.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

Mustieles, F. J.

C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
[CrossRef]

Oei, Y. S.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

Parker, J. T.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference device based on self-imaging: principle and applications,” J. Lightwave Technol. 13, 615–626 (1995).
[CrossRef]

Rahman, B. M. A.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52–57 (1988).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2, 682–688 (1984).
[CrossRef]

Rajarajan, M.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

Rajhel, A.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Shani, Y.

C. H. Henry, Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron. 27, 523–530 (1991).
[CrossRef]

Smit, M. K.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

Smith, G. W.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Soldano, L. B.

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference device based on self-imaging: principle and applications,” J. Lightwave Technol. 13, 615–626 (1995).
[CrossRef]

Soole, J. B. D.

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

Spiekman, L. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

L. H. Spiekman, “Compact integrated optical components for telecommunication networks,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990).

Vazquez, C.

C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
[CrossRef]

Weinert, C. M.

C. M. Weinert, N. Agrawal, “Three-dimensional finite difference simulation of coupling behaviour and loss in multimode interference devices,” IEEE Photon. Technol. Lett. 7, 529–531 (1995).
[CrossRef]

Wight, D. R.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

Wongcharoen, T.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

Appl. Phys. Lett.

R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994).
[CrossRef]

IEEE J. Quantum Electron.

C. H. Henry, Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron. 27, 523–530 (1991).
[CrossRef]

IEEE Photon. Technol. Lett.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, I. Moerman, M. K. Smit, “Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,” IEEE Photon. Technol. Lett. 6, 1008–1010 (1994).
[CrossRef]

C. M. Weinert, N. Agrawal, “Three-dimensional finite difference simulation of coupling behaviour and loss in multimode interference devices,” IEEE Photon. Technol. Lett. 7, 529–531 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

D. C. Chang, E. F. Kuester, “A hybrid method paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

J. Appl. Phys.

B. Broberg, S. Lindgren, “Refractive index of In1–xGaxAsyP1–y layers and InP in the transparent wavelength region,” J. Appl. Phys. 55, 3376–3381 (1984).
[CrossRef]

J. Lightwave Technol.

C. Vazquez, F. J. Mustieles, F. Hernandez-Gil, “Three-dimensional method for simulation of multimode interference couplers,” J. Lightwave Technol. 13, 2296–2299 (1995).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2, 682–688 (1984).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52–57 (1988).
[CrossRef]

T. F. Krauss, R. M. De La Rue, P. J. R. Leybourn, “Impact of output coupler configuration on operating characteristics of semiconductor ring laser,” J. Lightwave Technol. 13, 1500–1507 (1995).
[CrossRef]

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference device based on self-imaging: principle and applications,” J. Lightwave Technol. 13, 615–626 (1995).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

Opt. Quantum Electron.

G. M. Berry, S. V. Burke, “Analysis of optical rib-self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method,” Opt. Quantum Electron. 27, 921–934 (1995).
[CrossRef]

Other

J. B. D. Soole, M. R. Amersfort, H. P. Lebalnc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, “Use of multimode interference couplers to broaden the passband of dispersive integrated WDM filters,” in Integrated Photonics Research, Vol. 7 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 44–47.

L. H. Spiekman, “Compact integrated optical components for telecommunication networks,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990).

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of a 2-D MMI-based 3-dB coupler and cross section of access waveguides.

Fig. 2
Fig. 2

Resultant field profiles inside the MMI section at z = 0+ μm.

Fig. 3
Fig. 3

Resultant field at z = 120 μm.

Fig. 4
Fig. 4

Resultant field at z = 240 μm.

Fig. 5
Fig. 5

Power coupling efficiency of the 3-dB coupler for the 1-D approximation.

Fig. 6
Fig. 6

Resultant coupled field in the MMI section at z = 0+ μm for a 2-D structure.

Fig. 7
Fig. 7

Resultant field at z = 115 μm for a 3-dB coupler.

Fig. 8
Fig. 8

Resultant field at z = 230 μm for a cross coupler.

Fig. 9
Fig. 9

Power transfer curve for a 3-dB coupler of 2-D confinement.

Fig. 10
Fig. 10

Variation of the excess loss with the axial distance for the 3-dB coupler.

Fig. 11
Fig. 11

Variation of the excess loss with the axial distance for the cross coupler.

Fig. 12
Fig. 12

Variation of the power imbalance with the axial distance for the 3-dB coupler.

Fig. 13
Fig. 13

Power transfer characteristics of the 3-dB coupler for different MMI widths.

Fig. 14
Fig. 14

Comparison of the power transfer curves for the TE (solid) and TM (dashed) polarizations.

Tables (2)

Tables Icon

Table 1 Propagation Constants (β n ), Coupling Lengths (Lcn), and Transmission Coefficients (τ) for the Planar MMI Structure for a Series of TE Modes

Tables Icon

Table 2 Propagation Constants, Coupling Lengths, and Transmission (τ) and Reflection (ρ) Coefficients for the 2-D MMI Structure for a Series of Hy Modes

Equations (5)

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

L cn = π β 0 - β n ,
J = Ω   | E t I - E t II | 2 + α Z 0 2 | H t I - H t II | 2 d Ω ,
H x ,   y ,   z = i = 0 M - 1   b i H i x ,   y exp - j β 0 - β i z ,
excess   loss     - 10   log 10 P cross + P bar P in ,
Imbalance   dB     - 10   log 10 P bar P cross ,

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