Abstract

A unified method was proposed to reduce the beat length of a multimode interference (MMI) coupler. By properly adjusting the phase difference of the N-fold images, the mode evolution is changed to generate self-images at a much shorter distance. The effect of adjusting the phase difference can be regarded as dividing the original MMI coupler into multiple sub-MMI couplers. Such an effect can be applied for both symmetric- and paired-interference cases. We applied the principle to design compact optical splitters operating at dual wavelength bands. The simulation shows that excellent performance with reduced coupler length can be obtained for splitters operating at both 1.3 and 1.55 µm bands.

© 2006 Optical Society of America

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  1. H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
    [CrossRef]
  2. M. Belanger, G. L. Yip, and M. Haruna, "Passive planar multibranch optical power divider: Some design considerations," Appl. Opt. 22, 2283-2289 (1983).
    [CrossRef]
  3. M. Haruna and J. Koyama, "Electro-optic branching waveguide-switch and the application to 1 × 4 optical switching network," J. Lightwave Technol. 1, 233-247 (1983).
  4. R. Baets and P. E. Lagasse, "Calculation of radiation loss in integrated-optic tapers and Y-junctions," Appl. Opt. 21, 1972-1978 (1982).
    [CrossRef] [PubMed]
  5. O. Mikami and S. Zembutsu, "Coupling-length adjustment for an optical direction coupler as a 2 × 2 switch," Appl. Phys. Lett. 35, 38-40 (1979).
    [CrossRef]
  6. H. A. Haus and C. G. Fonstad, "Three waveguide couplers for improved sampling and filtering," IEEE J. Quantum Electron. 17, 2321-2325 (1981).
    [CrossRef]
  7. M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
    [CrossRef]
  8. 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]
  9. K.-C. Lin and W.-Y. Lee, "Guided-wave 1.3/1.55μm wavelength division multiplexer based on multimode interference," Electron. Lett. 32, 1259-1261 (1996).
    [CrossRef]
  10. Y.-J. Lin and S.-L. Lee, "InP-based 1.3/1.55μm wavelength demultiplexer with multimode interference and chirped grating," Opt. and Quantum Electron. 34, 1201-1212 (2002).
    [CrossRef]
  11. Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
    [CrossRef]
  12. Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
    [CrossRef]
  13. O. Bryngdahl, "Image formation using self-imaging techniques," J. Opt. Soc. Amer. 63, 416-419 (1973).
    [CrossRef]
  14. J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in Multimode Interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999).
    [CrossRef]
  15. J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
    [CrossRef]
  16. M. Bachmann, P. A. Besse, and H. Melchior, "General self-imaging properties in N×N multimode interference couplers including phase relations," Appl. Opt. 33, 3905-3911 (1994).
    [CrossRef] [PubMed]
  17. E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
    [CrossRef]
  18. S. Nagai, G. Morishima, H. Inayoshi, and K. Utaka, "Multimode interference photonic switches (MIPS)," J. Lightwave Technol. 20, 675-681 (2002).
    [CrossRef]
  19. M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, and K. T. V. Grattan, "Accurate analysis of MMI devices with two-dimensional confinement," J. Lightwave Technol. 14, 2078-2084 (1996).
    [CrossRef]
  20. J. Z. Huang, R. Scarmozzio, G. Nagy, M. J. Steel, R. M. Osgood, and Jr., "Realization of a compact and single-mode optical passive polarization converter," IEEE Photonics Technol. Lett. 12, 317-319 (2000).
    [CrossRef]

2002 (2)

Y.-J. Lin and S.-L. Lee, "InP-based 1.3/1.55μm wavelength demultiplexer with multimode interference and chirped grating," Opt. and Quantum Electron. 34, 1201-1212 (2002).
[CrossRef]

S. Nagai, G. Morishima, H. Inayoshi, and K. Utaka, "Multimode interference photonic switches (MIPS)," J. Lightwave Technol. 20, 675-681 (2002).
[CrossRef]

2000 (2)

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
[CrossRef]

1999 (2)

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in Multimode Interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999).
[CrossRef]

1997 (1)

E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
[CrossRef]

1996 (2)

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

K.-C. Lin and W.-Y. Lee, "Guided-wave 1.3/1.55μm wavelength division multiplexer based on multimode interference," Electron. Lett. 32, 1259-1261 (1996).
[CrossRef]

1995 (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]

1994 (1)

1992 (1)

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

1983 (1)

M. Belanger, G. L. Yip, and M. Haruna, "Passive planar multibranch optical power divider: Some design considerations," Appl. Opt. 22, 2283-2289 (1983).
[CrossRef]

1982 (1)

1981 (2)

H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
[CrossRef]

H. A. Haus and C. G. Fonstad, "Three waveguide couplers for improved sampling and filtering," IEEE J. Quantum Electron. 17, 2321-2325 (1981).
[CrossRef]

1979 (1)

O. Mikami and S. Zembutsu, "Coupling-length adjustment for an optical direction coupler as a 2 × 2 switch," Appl. Phys. Lett. 35, 38-40 (1979).
[CrossRef]

1973 (1)

O. Bryngdahl, "Image formation using self-imaging techniques," J. Opt. Soc. Amer. 63, 416-419 (1973).
[CrossRef]

Bachmann, M.

Baets, R.

Belanger, M.

M. Belanger, G. L. Yip, and M. Haruna, "Passive planar multibranch optical power divider: Some design considerations," Appl. Opt. 22, 2283-2289 (1983).
[CrossRef]

Besse, P. A.

Birbeck, J. C. H.

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Bryngdahl, O.

O. Bryngdahl, "Image formation using self-imaging techniques," J. Opt. Soc. Amer. 63, 416-419 (1973).
[CrossRef]

Dagens, B.

Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
[CrossRef]

Donnelly, J. P.

E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
[CrossRef]

Fonstad, C. G.

H. A. Haus and C. G. Fonstad, "Three waveguide couplers for improved sampling and filtering," IEEE J. Quantum Electron. 17, 2321-2325 (1981).
[CrossRef]

Gottesman, Y.

Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
[CrossRef]

Grattan, K. T. V.

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

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

Haruna, M.

M. Belanger, G. L. Yip, and M. Haruna, "Passive planar multibranch optical power divider: Some design considerations," Appl. Opt. 22, 2283-2289 (1983).
[CrossRef]

Haus, H. A.

H. A. Haus and C. G. Fonstad, "Three waveguide couplers for improved sampling and filtering," IEEE J. Quantum Electron. 17, 2321-2325 (1981).
[CrossRef]

Heaton, J. M.

J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in Multimode Interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999).
[CrossRef]

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Hilton, K. P.

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Ho, S. T.

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Inayoshi, H.

Jenkins, R. M.

J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in Multimode Interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999).
[CrossRef]

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Lagasse, P. E.

Lee, S.-L.

Y.-J. Lin and S.-L. Lee, "InP-based 1.3/1.55μm wavelength demultiplexer with multimode interference and chirped grating," Opt. and Quantum Electron. 34, 1201-1212 (2002).
[CrossRef]

Lee, W.-Y.

K.-C. Lin and W.-Y. Lee, "Guided-wave 1.3/1.55μm wavelength division multiplexer based on multimode interference," Electron. Lett. 32, 1259-1261 (1996).
[CrossRef]

Lin, K.-C.

K.-C. Lin and W.-Y. Lee, "Guided-wave 1.3/1.55μm wavelength division multiplexer based on multimode interference," Electron. Lett. 32, 1259-1261 (1996).
[CrossRef]

Lin, Y.-J.

Y.-J. Lin and S.-L. Lee, "InP-based 1.3/1.55μm wavelength demultiplexer with multimode interference and chirped grating," Opt. and Quantum Electron. 34, 1201-1212 (2002).
[CrossRef]

Ma, Y.

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Melchior, H.

Mikami, O.

O. Mikami and S. Zembutsu, "Coupling-length adjustment for an optical direction coupler as a 2 × 2 switch," Appl. Phys. Lett. 35, 38-40 (1979).
[CrossRef]

Mikoshiba, N.

H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
[CrossRef]

Molter, L. A.

E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
[CrossRef]

Morishima, G.

Nagai, S.

Park, S.

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Parker, J. T.

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[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]

Rahman, B. M. A.

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

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

Rajarajan, M.

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

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

Rao, E. V. K.

Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
[CrossRef]

Sasaki, H.

H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
[CrossRef]

Shki, E.

H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
[CrossRef]

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]

Thoen, E. R.

E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
[CrossRef]

Utaka, K.

Wang, L.

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Wight, D. R.

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Wongcharoen, T.

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

Yip, G. L.

M. Belanger, G. L. Yip, and M. Haruna, "Passive planar multibranch optical power divider: Some design considerations," Appl. Opt. 22, 2283-2289 (1983).
[CrossRef]

Zembutsu, S.

O. Mikami and S. Zembutsu, "Coupling-length adjustment for an optical direction coupler as a 2 × 2 switch," Appl. Phys. Lett. 35, 38-40 (1979).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

O. Mikami and S. Zembutsu, "Coupling-length adjustment for an optical direction coupler as a 2 × 2 switch," Appl. Phys. Lett. 35, 38-40 (1979).
[CrossRef]

J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, "Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides," Appl. Phys. Lett. 61, 1754-1756 (1992).
[CrossRef]

Electron. Lett. (1)

K.-C. Lin and W.-Y. Lee, "Guided-wave 1.3/1.55μm wavelength division multiplexer based on multimode interference," Electron. Lett. 32, 1259-1261 (1996).
[CrossRef]

IEEE J. Quantum Electron. (3)

H. A. Haus and C. G. Fonstad, "Three waveguide couplers for improved sampling and filtering," IEEE J. Quantum Electron. 17, 2321-2325 (1981).
[CrossRef]

E. R. Thoen, L. A. Molter, and J. P. Donnelly, "Exact modal analysis and optimization of N×N×1 cascaded waveguide structures with multimode guiding sections," IEEE J. Quantum Electron. 33, 1299-1307 (1997).
[CrossRef]

H. Sasaki, E. Shki, and N. Mikoshiba, "Propagation characteristics of optical guided wave in asymmetric branching waveguides," IEEE J. Quantum Electron. 17, 1051-1058 (1981).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in Multimode Interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999).
[CrossRef]

Y. Ma, S. Park, L. Wang, and S. T. Ho, "Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching," IEEE Photon. Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Y. Gottesman, E. V. K. Rao, and B. Dagens, "A novel design proposal to minimize reflections in deep-ridge multimode interference couplers," IEEE Photon. Technol. Lett. 12, 1662-1664 (2000).
[CrossRef]

J. Lightwave Technol. (4)

S. Nagai, G. Morishima, H. Inayoshi, and K. Utaka, "Multimode interference photonic switches (MIPS)," J. Lightwave Technol. 20, 675-681 (2002).
[CrossRef]

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

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, "A rigorous comparison of the performance of directional couplers with multimode interference devices," J. Lightwave Technol. 17, 243-248 (1999).
[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]

J. Opt. Soc. Amer. (1)

O. Bryngdahl, "Image formation using self-imaging techniques," J. Opt. Soc. Amer. 63, 416-419 (1973).
[CrossRef]

Opt. and Quantum Electron. (1)

Y.-J. Lin and S.-L. Lee, "InP-based 1.3/1.55μm wavelength demultiplexer with multimode interference and chirped grating," Opt. and Quantum Electron. 34, 1201-1212 (2002).
[CrossRef]

Other (2)

M. Haruna and J. Koyama, "Electro-optic branching waveguide-switch and the application to 1 × 4 optical switching network," J. Lightwave Technol. 1, 233-247 (1983).

J. Z. Huang, R. Scarmozzio, G. Nagy, M. J. Steel, R. M. Osgood, and Jr., "Realization of a compact and single-mode optical passive polarization converter," IEEE Photonics Technol. Lett. 12, 317-319 (2000).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

The modal field distribution of a MMI coupler [8]. Symbol m represents the number of mode. The squares and circles mark the zero-crossings of the non-excited modes for the paired- and symmetric-type excitation, respectively.

Fig. 2.
Fig. 2.

Simulated light evolution along the MMI coupler for the symmetric-interference type. The dotted squares mark the phase shift regions. From left to right, the plots are for the conventional MMI and the ones with phase shifts on the two- to five-fold images.

Fig. 3.
Fig. 3.

Wave evolution along a MMI for paired-interference type excitation without phase shift (a), with out-of–phase phase shifts on 2-fold (b), 3-fold (c), and 4-fold images (d), with in-phase phase shifts on the 2-fold images (e), and with a pair of 0 and π phase shifts on the 4-fold images (f). The squares indicate the phase adjustment spots.

Fig. 4.
Fig. 4.

Schematic diagram of the 1×N dual-band optical power splitter.

Fig. 5.
Fig. 5.

Light intensity along the MMI coupler at 1.3-µm (a) and 1.55-µm (b). The phase shift region is indicated with a rectangulat mark. The phase shift region locates at (x, z)=(11.25, 9965.5) µm with an area of 22.5×145 µm2.

Fig. 6.
Fig. 6.

Imbalance and excess loss versus the deviation in device length (a) and deviation in wavelength (b).

Fig. 7.
Fig. 7.

Light intensity along a 1×3 MMI coupler of symmetric-interference type at 1.3- (a) and 1.55-µm (b). The phase shift regions are indicated with rectangulat marks. The phase shift regions locate at (x, z)=(17.3, 6492.6) µm and (x, z)=(-17.3, 6492.6) µm, respectively, with an area of 17.3×198 µm2

Fig. 8.
Fig. 8.

Imbalance and excess loss versus the deviation in device length (a) and deviation in wavelength (b).for the 1×3 MMI coupler. The solid and dashed lines show the performance for the TE and TM polarization, respectively.

Tables (4)

Tables Icon

Table 1. Phase differences before and after applying phase shifts for symmetric interference cases

Tables Icon

Table 2. Phase differences before and after applying phase shifts for paired-interference type excitation

Tables Icon

Table 3. Optimal solutions for 1×2 dual-band splitters

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Table 4. Optimal design parameters for 1×3 dual-band splitter

Equations (18)

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Φ ( x , z ) = m c m φ m ( x ) exp ( j β m z ) ,
β m = 2 π n r λ 0 ( m + 1 ) 2 π λ 0 4 n r W e 2 ,
L π = π β 0 β 1 4 n r W e 2 3 λ 0 .
φ m ( x ) = { sin [ ( m + 1 ) π x W e ] for m = odd cos [ ( m + 1 ) π x W e ] for m = even ,
Ψ ( x ) = Φ ( x , 0 ) + Φ ( x , 0 ) e j π = m : odd c m φ m ( x ) = m : odd c m sin ( ( m + 1 ) π W e x ) ,
Ψ ( x ) = m : even d m cos ( ( m + 1 ) π W e 2 x ) + m : odd d m sin ( ( m + 1 ) π W e 2 x ) ,
d m = { c m cos [ ( m + 1 ) π 2 ] for m = odd c m sin [ ( m + 1 ) π 2 ] for m = even ,
β m = 2 π n r λ 0 ( m + 1 ) 2 π λ 0 4 n r ( W e 2 ) 2 ,
Ψ ( x ) = Φ ( x , 0 ) + Φ ( ( x W e 3 ) , 0 ) e j π + Φ ( ( x + W e 3 ) , 0 ) e j π
Ψ ( x ) = m = 0 , 2 , 4 , 3 c m cos ( ( m + 1 ) π W e 3 x ) + m = 1 , 3 , 5 , 3 c m sin ( ( m + 1 ) π W e 3 x ) ,
β m = 2 π n r λ 0 ( m + 1 ) 2 π λ 0 4 n r ( W e 3 ) 2 .
Δ θ = 2 π λ 0 · Δ n r · L m .
L MMI = q 1 · ( L c , λ 1 N ) q 2 · ( L c , λ 2 N )
L d 1 = s 1 · ( L c , λ 1 N ) s 2 · L c , λ 2 ,
L d 2 = s 1 · ( L c , λ 1 N 2 ) s 2 · ( L c , λ 2 N ) ,
L d 1 = s 3 · ( L c , λ 2 N ) s 4 · ( L c , λ 1 )
L d 2 = s 3 · ( L c , λ 2 N 2 ) = s 4 · ( L c , λ 1 N ) .
P im = 10 · log ( P O max P O min )

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