Abstract

Propagation constant errors (PCEs) of guided modes in regions of multimode interference in optical networks were analyzed. Results show that a graded-index waveguide can effectively decrease the PCEs. An example based on an exponential function is presented. Numerical results show that addition of a graded-index waveguide greatly improves device performance in this structure.

© 2002 Optical Society of America

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References

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  1. Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
    [CrossRef]
  2. J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, and K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
    [CrossRef]
  3. 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
    [CrossRef]
  4. R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
    [CrossRef]
  5. R. Ulrich and T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Am. 68, 583–592 (1978).
    [CrossRef]
  6. J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
    [CrossRef]
  7. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).
  8. 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]

1998 (1)

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
[CrossRef]

1997 (2)

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]

Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
[CrossRef]

1992 (2)

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, and K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992).
[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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

1991 (1)

R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

1978 (1)

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Bachman, M.

Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
[CrossRef]

Brown-Goebeler, K.

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

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Chiu, T. H.

J. E. Zucker, K. L. Jones, T. H. Chiu, B. Tell, and 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[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]

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Huang, J. Z.

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
[CrossRef]

Jones, K. L.

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

Kamiya, T.

Kapon, E.

R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

Lai, Q.

Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
[CrossRef]

Melchior, H.

Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
[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]

Osgood, R. M.

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
[CrossRef]

Pennings, E. C. M.

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Scarmozzino, R.

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
[CrossRef]

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

Tell, B.

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

Ulrich, R.

Zucker, J. E.

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

Electron. Lett. (1)

Q. Lai, M. Bachman, and H. Melchior, “Low-loss 1×N multimode interference couplers with homogeneous output power distributions realized in silica on Si material,” Electron. Lett. 33, 1699–1700 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[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]

IEEE 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, and J.-I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992).
[CrossRef]

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10, 1292–1294 (1998).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. (1)

Other (1)

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

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Figures (4)

Fig. 1
Fig. 1

Index distribution of the graded-index MMI region.

Fig. 2
Fig. 2

PCEs for various values of D.

Fig. 3
Fig. 3

PCEs for various values of C and optimized D.

Fig. 4
Fig. 4

Output contrast of a 1×2 MMI coupler.

Equations (10)

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

β0-βmm(m+2)π/3Lπ,
(β0-βm)/(β0-β1)-m(m+2)/30.
Pm=(β0-βm)/(β0-β1)-m(m+2)/3.
knc2-βm2=(m+1)2πWem2,
β0-βmβ0-β1=β0+β1β0+βmm(m+2)3>β0+β1β0+β1m(m+2)3>m(m+2)3.
k2nc2-βm2=(2m+1)v,
β0-βmβ0-β1=mβ0+β1β0+βm<mβ0+β0β0+0<2m.
2m<m(m+2)3.
N(x)=A+B exp(-Cx/D),x[0, D]nc,x[D, D+W]A+B exp[C(x-2D-W)/D],x[D+W, 2D+W],
contrast=-101 logpower2power1,

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