Abstract

Overlapping-image multimode interference (MMI) couplers, a new class of devices, permit uniform and nonuniform power splitting. A theoretical description directly relates coupler geometry to image intensities, positions, and phases. Among many possibilities of nonuniform power splitting, examples of 1 × 2 couplers with ratios of 15:85 and 28:72 are given. An analysis of uniform power splitters includes the well-known 2 × N and 1 × N MMI couplers. Applications of MMI couplers include mode filters, mode splitters–combiners, and mode converters.

© 1995 Optical Society of America

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  1. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63, 416–419 (1973).
    [CrossRef]
  2. L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 73, 615 (1995).
    [CrossRef]
  3. R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
    [CrossRef]
  4. J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
    [CrossRef]
  5. M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.
  6. M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.
  7. Th. Niemeier, R. Ulrich, “Quadrature outputs from fiber interferometer with 4 × 4 coupler,” Opt. Lett. 11, 677–679 (1986).
    [CrossRef] [PubMed]
  8. E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.
  9. R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
    [CrossRef]
  10. M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
    [CrossRef] [PubMed]
  11. 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]
  12. C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.
  13. E. C. M. Pennings, “Bends in optical ridge waveguides, modeling and applications,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990), ISBN 90-9003413-7.
  14. L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
    [CrossRef]
  15. R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
    [CrossRef] [PubMed]
  16. A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
    [CrossRef]
  17. P. A. Besse, M. Bachmann, H. Melchior, “Phase relations in multi-mode interference couplers and their application to generalized integrated Mach-Zehnder optical switches,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.22–2.23.
  18. G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.
  19. M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.
  20. N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.
  21. Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
    [CrossRef]
  22. P. Latimer, “Talbot plane patterns: grating images or interference effects?,” Appl. Opt. 32, 1078–1083 (1993).
    [CrossRef] [PubMed]
  23. P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

1995 (1)

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 73, 615 (1995).
[CrossRef]

1994 (3)

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
[CrossRef] [PubMed]

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]

1993 (2)

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

P. Latimer, “Talbot plane patterns: grating images or interference effects?,” Appl. Opt. 32, 1078–1083 (1993).
[CrossRef] [PubMed]

1992 (4)

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
[CrossRef] [PubMed]

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

1986 (1)

1973 (1)

1881 (1)

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
[CrossRef]

Aitchison, S.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

Amersfoort, M. R.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

Andreadakis, N. C.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

Bachmann, M.

M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
[CrossRef] [PubMed]

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.

P. A. Besse, M. Bachmann, H. Melchior, “Phase relations in multi-mode interference couplers and their application to generalized integrated Mach-Zehnder optical switches,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.22–2.23.

Baets, R.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Besse, P. A.

M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
[CrossRef] [PubMed]

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

P. A. Besse, M. Bachmann, H. Melchior, “Phase relations in multi-mode interference couplers and their application to generalized integrated Mach-Zehnder optical switches,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.22–2.23.

M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

Bhat, R.

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

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]

Blondeau, R.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Brown-Goebeler, K.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

Bryngdahl, O.

Caneau, C.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Chiu, T. H.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

Curtis, L.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

de Miguel, J. L.

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Deri, R. J.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

Devereux, R. W. J.

Dobbelaere, G.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Dubost, A. H.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

Durhuus, T.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Enard, A.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Ferraras, A.

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Gini, E.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

Glastre, G.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Gómez-Salas, E.

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Gozdz, A. S.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Hawkins, R. J.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Hayes, T. R.

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

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]

R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
[CrossRef] [PubMed]

Hernández-Gil, F.

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[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]

Hoekstra, H. J. W. M.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

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]

R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
[CrossRef] [PubMed]

Joergensen, C.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Jones, K. L.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

Krijnen, G. J. M.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

Lambeck, P. V.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

Latimer, P.

Melchior, H.

M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
[CrossRef] [PubMed]

P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

P. A. Besse, M. Bachmann, H. Melchior, “Phase relations in multi-mode interference couplers and their application to generalized integrated Mach-Zehnder optical switches,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.22–2.23.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.

Mikkelsen, B.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Nadler, Ch.

M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.

Niemeier, Th.

Pagnod, P.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

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.

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

Pennings, E. C. M.

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 73, 615 (1995).
[CrossRef]

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

E. C. M. Pennings, “Bends in optical ridge waveguides, modeling and applications,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990), ISBN 90-9003413-7.

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

Ratovelomanana, F.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
[CrossRef]

Rodríguez, F.

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Rondi, D.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Scherer, A.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Shah, V.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Smit, M. K.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

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 devices based on self-imaging: principles and applications,” J. Lightwave Technol. 73, 615 (1995).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

Song, J. I.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Soole, J. B. D.

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Stegeman, G. I.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

Stubkjaer, K. E.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

Tell, B.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

ten Kate, G. M.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

Ulrich, R.

van Dam, C.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

van der Heijden, J.

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

van der Keijden, J. M. M.

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

van Dongen, T.

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

van Ham, F. P. G. M.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

van Roijen, R.

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

van Stralen, M. J. N.

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

Veerman, F. B.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

Verbeek, B.

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

Verbeek, B. H.

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

Villeneuve, A.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

Vodjdani, N.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

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]

Zucker, J. E.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (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]

R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Keijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994).
[CrossRef]

J. Lightwave Technol. (3)

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[CrossRef]

L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 73, 615 (1995).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1849 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Philos. Mag. (1)

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
[CrossRef]

Photon. Technol. Lett. (2)

R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact, monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

A. Ferraras, F. Rodríguez, E. Gómez-Salas, J. L. de Miguel, F. Hernández-Gil, “Useful formulas for multimode interference power splitter/combiner design,” Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Other (10)

P. A. Besse, M. Bachmann, H. Melchior, “Phase relations in multi-mode interference couplers and their application to generalized integrated Mach-Zehnder optical switches,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.22–2.23.

G. J. M. Krijnen, A. Villeneuve, G. I. Stegeman, S. Aitchison, P. V. Lambeck, H. J. W. M. Hoekstra, “Modelling of a versatile all-optical Mach-Zehnder switch,” in International Symposium on Guided-Wave Optoelectronics (Weber Research Institute, Brooklyn, N.Y., 1994), paper VII.6.

M. J. N. van Stralen, R. van Roijen, E. Pennings, J. van der Heijden, T. van Dongen, B. Verbeek, “Design and fabrication of integrated InGaAsP ring lasers with MMI-couplers,” in Proceedings of the European Conference on Integrated Optics (Ville de Neuchatel, Neuchatel, Switzerland, 1993), pp. 2.24–2.25.

N. Vodjdani, F. Ratovelomanana, A. Enard, G. Glastre, D. Rondi, R. Blondeau, T. Durhuus, C. Joergensen, B. Mikkelsen, K. E. Stubkjaer, P. Pagnod, R. Baets, G. Dobbelaere, “All optical wavelength conversion at 5 Gbit/s with monolithic integration of semiconductor optical amplifiers in a passive asymmetric Mach-Zehnder interferometer,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 95–98.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, P. A. Besse, M. Bachmann, H. Melchior, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the European Conference on Integrated Optics (Delft U. Press, Delft, The Netherlands, 1995), pp. 275–278.

E. C. M. Pennings, “Bends in optical ridge waveguides, modeling and applications,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1990), ISBN 90-9003413-7.

E. C. M. Pennings, R. J. Deri, R. Bhat, T. R. Hayes, N. C. Andreadakis, “Ultracompact integrated all-passive optical 90° hybrid using self-imaging,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1992), pp. 461–464.

M. Bachmann, M. K. Smit, P. A. Besse, E. Gini, H. Melchior, L. B. Soldano, “Polarization-insensitive low-voltage optical waveguide switch using InGaAsP/InP four-port Mach-Zehnder interferometer,” in Optical Fiber Conference and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 32–33.

M. Bachmann, Ch. Nadler, P. A. Besse, H. Melchior, “Compact polarization-insensitive multi-leg 1 × 4 Mach-Zehnder switch in InGaAsP/InP,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 519–522.

P. A. Besse, E. Gini, M. Bachmann, H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” in Proceedings of the European Conference on Optical Communication (Istituto Internationale delle Comunicazioni, Genova, Italy, 1994), pp. 669–672.

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Figures (12)

Fig. 1
Fig. 1

Schematic view of a N × N MMI coupler (N = 4). Light from the input waveguide is launched into the MMI section, propagated, and imaged into the output waveguides.

Fig. 2
Fig. 2

General N × N MMI coupler with access waveguides for arbitrary N. Note the existence of upright and mirrored images. Parameter a can be chosen freely between 0 ≤ aW/N. At its limits of a = 0 or a = W/N, images merge in pairs. An overlapping-image MMI coupler is formed.

Fig. 3
Fig. 3

MMI section with input light distribution f (x) and eigenmodes E i (x) of the structure. Functions E i (x) and f(x) are antisymmetrically extended to a virtual MMI section and periodically repeated on the whole x axes.

Fig. 4
Fig. 4

Self-images formed at the output of a MMI coupler of length L N M in the extended MMI coupler. Half of the images are upright and half of them are mirrored. For input shifting along the arrow, outputs are shifted according to the arrows also. For input positions in which upright and mirrored images interfere, overlapping-image MMI couplers are obtained.

Fig. 5
Fig. 5

Illustration of possible values of spacing s, permitting equally intense output images in overlapping-image MMI couplers. Arrows mark the channels with zero intensity, and vertical lines represent channels with constant light intensity.

Fig. 6
Fig. 6

Image formation for light input at the center of the MMI coupler. The upper section shows imaging of symmetrical input and the lower section shows that of antisymmetrical input, respectively. The whole length of the MMI coupler is one imaging length, 3L c . Note that for both input configurations K images are obtained at L = (3M/4K)L c for any integer K and M without common divisor. Image positions, however, differ for symmetrical and antisymmetrical inputs. This allows for mode filtering or mode splitting.

Fig. 7
Fig. 7

Image formation for light input at one third of the MMI coupler. Only symmetrical light distributions (upper section) form a reduced number of equally intense self-images: K images at L = (M/K)L c . Antisymmetrical light distributions (lower section) do not form equally intense self-images at a reduced length. The total device length is 3L c .

Fig. 8
Fig. 8

Overlapping-image MMI couplers with a reduced number of self-images. For input channel i, output channels j with odd i + j always have zero light intensities. The number of images is reduced. Intensities and phases of the remaining self-images are given in the text. Uniform as well as nonuniform power splitting is possible.

Fig. 9
Fig. 9

Geometrical arrangement of 1 × K splitter with symmetrical input at the center. K equally intense images are obtained at a device length of L = 3L c /4K. Phases of the images are given in the text.

Fig. 10
Fig. 10

Geometrical arrangement of 2 × K splitter with symmetrical input at two thirds of the width. K equally intense images are obtained at a device length of L = L c /K. Phases of the images are given in the text.

Fig. 11
Fig. 11

Overlapping-image MMI couplers allow for new functionalities, such as a mode filter, a mode splitter–combiner, and a mode converter. A, schematic of a mode filter for symmetrical light distributions. B and C, the same device with different input distributions, showing filtering of the symmetrical and antisymmetrical part of the input light distribution, respectively. Symmetrical and antisymmetrical inputs appear at different outputs. The device is a mode splitter–combiner. The lowest antisymmetrical mode is converted into a symmetrical mode. The device is a mode converter.

Fig. 12
Fig. 12

Generalized phase diversity relation in N × N MMI couplers. At outputs j the signals from two inputs are mixed with phase differences varying in constant steps. The figure represents the term 2πA j /N of Eq. (60) as a function of output number j.

Tables (1)

Tables Icon

Table 1 Overlapping-Image MMI Couplers Permit Nonuniform Splitting Ratiosa

Equations (60)

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L N M = M N 3 L c ,
L c 4 n W 2 3 λ .
r exp ( j Φ ) = 1 N exp ( j φ 1 ) + 1 N exp ( j φ 2 ) .
r exp ( j Φ ) = 2 N cos ( Δ φ 2 ) exp ( j φ ¯ ) .
r 2 = 4 N cos 2 ( Δ φ 2 ) , Φ = { φ ¯ for cos ( Δ φ 2 ) > 0 φ ¯ + π for cos ( Δ φ 2 ) < 0.
f out ( x ) = 1 C q = 0 N - 1 f in ( x - x q ) exp ( j φ q ) ,
x q = ( 2 q - N ) M N W ,
φ q = q ( N - q ) M N π .
C = exp ( j 2 π n λ L N M ) q = 0 N - 1 exp [ j π M N q ( N - q ) ] .
C = N exp ( - j φ 0 ) , φ 0 = - 2 π n λ L N M = 1 - π 4 ( N - 1 ) .
x i in = i M N W ,             with integer i .
x j out = x q + x i in = M W - j M N W ,             with even i + j .
φ 1 = φ q , φ 2 = φ q + i + b π ,
b = 1 symmetrical input , b = 0 , antisymmetrical input .
Δ φ i j = φ 1 - φ 2 - ( N - j ) i M N π - b π , φ i j ¯ = φ 1 + φ 2 2 = - ( i 2 + j 2 ) M N π 4 + j M π 2 + b π 2 .
r i j 2 = 4 N cos 2 [ ( N - j ) i M N π 2 - b π 2 ] , Φ i j = { - ( i 2 + j 2 ) M N π 4 + j M π 2 + b π 2 for cos [ ( N - j ) i M N π 2 - b π 2 ] > 0 - ( i 2 + j 2 ) M N π 4 + j M π 2 + b π 2 + π for cos [ ( N - j ) i M N π 2 - b π 2 ] < 0.
s = i M N π = x i in π W .
x i in = Z W 2             or x i in = Z W 3 .
i = Z M N 2 = Z N 2 = N 2 .
x in = M W 2 ,
x j out = M W - j M N W             for     j + N 2 even .
r j 2 = { 4 / N for M ( N - j ) - 2 b = 4 k 2 / N for M ( N - j ) - 2 b = 4 k ± 1 0 for M ( N - j ) - 2 b = 4 k + 2 , Φ j = { - N M π 16 - j 2 M N π 4 + j M π 2 + b π 2 for M ( N - j ) - 2 b = 8 k , 8 k ± 1 - N M π 16 - j 2 M N π 4 + j M π 2 + b π 2 + π for M ( N - j ) - 2 b = otherwise .
r j 2 = 2 N = 1 K .
Φ j = { - j 2 M K π 8 + j M π 2 - M K π 8 + b π 2 for             M ( 2 K - j ) - 2 b = 8 k ± 1 , k integer - j 2 M K π 8 + j M π 2 - M K π 8 + b π 2 + π for             M ( 2 K - j ) - 2 b = otherwise .
r j 2 = { 4 / N = 1 / K for M ( 2 K - j 2 ) - b even 0 for M ( 2 K - j 2 ) - b odd .
Φ j = { - K M π 4 - j 2 M K π 16 + j M π 2 + b π 2 for M ( K - j 4 ) - b 2 even - K M π 4 - j 2 M K π 16 + j M π 2 + b π 2 + π for M ( K - j 4 ) - b 2 odd ,
Φ j = 3 M K π 4 - j 2 M K π 16 + j M π 4 .
L K M = M K 3 4 L c ,
i = Z M N 3 = Z N 3 = 2 N 3 = 2 K .
x in = M 2 W 3 ,
x j out = M W - j 3 M K W ,             with j even .
r j 2 = { 0 for j = 6 k 1 / K for j = 6 k ± 2 ,
Φ j = { - K M π 3 - j 2 M K π 12 + j M π 2 + π 2 for M ( 3 K - j ) = 6 k + 1 , 6 k + 2 - K M π 3 - j 2 M K π 12 + j M π 2 + π 2 + π for M ( 3 K - j ) = 6 k - 1 , 6 k - 2.
L K M = M K L c
x i in = i W N ,             i = ( 0 ) , 1 , 2 , 3 , , N - 1 , ( N ) ,
x j out = W - j W N ,             j = ( 0 ) , 1 , 2 , 3 , , N - 1 , ( N ) , and i + j even .
r i j 2 = 4 N cos 2 [ ( N - j ) i π 2 N - b π 2 ] , Φ i j = { - ( i 2 + j 2 ) π 4 N + j π 2 + b π 2 for cos [ ( N - j ) i π 2 N - b π 2 ] > 0 - ( i 2 + j 2 ) π 4 N + j π 2 + b π 2 + π for cos [ ( N - j ) i π 2 N - b π 2 ] < 0.
100 : 0 , 85 : 15 , 72 : 28 , 50 : 50.
x in = W 2
L = 3 L c 4 K
r 2 = 1 K .
p = 1 2 + j 4 .
x p out = W - W K ( p - 1 2 ) ,             with p = 1 , 2 , , K .
Φ p = φ 0 * + π K ( p - 1 ) ( K - p ) .
φ 0 * = φ 0 + π 4 K ( 3 K 2 + 2 K - 1 ) = - 2 π n λ L - π 4 K ( K 2 - 3 K + 1 ) ,
x in = 2 W 3
L = L c K
r 2 = 1 K .
j = 6 k + 2 j = 3 p - 1 p odd , j = 6 k - 2 j = 3 p - 2 p even .
x p out = W - W K ( p - 1 3 ) ,             p odd , x p out = W - W K ( p - 2 3 ) ,             p even .
Φ p = φ 0 + π 12 K ( 8 K 2 - 1 ) + π 4 K p ( 2 K + 2 - 3 p ) ,             p odd , Φ p = φ 0 + π 12 K ( 8 K 2 - 6 K - 4 ) + π 4 K p ( 2 K + 4 - 3 p ) ,             p even ,
Φ p = φ 0 * + π 4 K p ( 2 K + 2 - 3 p ) ,             p odd , Φ p = φ 0 * + π 4 K p ( 2 K + 4 - 3 p ) - π 4 K ( 2 K + 1 ) ,             p even ,
φ 0 3 = φ 0 + π 12 K ( 8 K 2 - 1 ) = - 2 π n λ L - π 12 K ( K 2 - 3 K + 1 ) .
x in = W 3 ,
Φ p = φ 0 * + π 4 K ( 2 p - 3 p 2 ) - π 4 ( K - 2 ) ,             p odd , Φ p = φ 0 * + π 4 K ( 4 p - 3 p 2 - 1 ) - π 4 ( K - 2 ) + π ,             p even .
r p 2 = 4 N cos 2 ( π 2 - p 2 π N ) ,             with p = 1 , 2 , 3 , , < N / 2.
x i in = i W N = i W 12 .
x j out = W - j W N = W - j W 12 ,             with i + j even .
φ i j - φ 2 j = φ i 2 - φ 22 + 2 π N A i A j , A ξ = ( ξ - 2 ) / 2 for ξ even , A ξ = N - ( ξ + 1 ) / 2 for ξ odd ,
φ i j - φ i j = ( φ i 2 - φ i 2 ) + 2 π N ( A i - A i ) A j .

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