Abstract

Variable power splitting ratio 2×2 MMI couplers using multi-mode waveguide holograms are analyzed. Theoretical analysis shows that variable splitting ratios can be obtained with surface relief holograms on MMI couplers with fixed dimensions. Devices with paired-imaging lengths are designed on a silicon-on-insulator (SOI) platform. Beam propagation simulations are used to verify a matrix theory analysis and to investigate proposed device performance. Fabrication tolerance of the proposed device is also analyzed.

© 2007 Optical Society of America

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  1. L. B. Soldano and E. C.M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
    [CrossRef]
  2. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
    [CrossRef]
  3. M. Bachmann, P. A. Besse, and H. Melchior, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Appl. Opt. 34, 6898-6910 (1995).
    [CrossRef] [PubMed]
  4. P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
    [CrossRef]
  5. D. S. Levy, Y.M. Li, R. Scarmozzino, R.M. OsgoodJr., "A multimode interference-based variable power splitter in GaAs-AlGaAs," IEEE Photon. Technol. Lett. 9, 1373-1375 (1997).
    [CrossRef]
  6. D. J. Y. Feng, T. S. Lay, and T. Y. Chang, "Waveguide couplers with new power splitting ratios made possible by cascading of short multimode interference sections," Opt. Express 15, 1588-1593 (2007),://www.opticsinfobase.org/abstract.cfm?URI=oe-15-4-1588>
    [CrossRef] [PubMed]
  7. S.-Y. Tseng, Y. Kim, C. J. K. Richardson, and J. Goldhar, "Implementation of discrete unitary transformations by multimode waveguide holograms," Appl. Opt. 45, 4864-4872 (2006).
    [CrossRef] [PubMed]
  8. H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
    [CrossRef]
  9. 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]
  10. K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
    [CrossRef]
  11. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
    [CrossRef]
  12. G. R. Hadley, "Wide-angle beam propagation using Pade approximant operators," Opt. Lett 17, 1426-1428 (1992).
    [CrossRef] [PubMed]
  13. K. Kawano and T. Kiton, Introduction to Optical Waveguide Analysis (Wiley, New York, 2001).
    [CrossRef]
  14. Optical Modesolver, Photonics Research Laboratory, University of Maryland, MD (2006), http://www.photonics.umd.edu/software/modesolver.zip

2007

2006

S.-Y. Tseng, Y. Kim, C. J. K. Richardson, and J. Goldhar, "Implementation of discrete unitary transformations by multimode waveguide holograms," Appl. Opt. 45, 4864-4872 (2006).
[CrossRef] [PubMed]

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[CrossRef]

2005

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

2001

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

1999

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

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

1996

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

1995

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

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

1994

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

1992

G. R. Hadley, "Wide-angle beam propagation using Pade approximant operators," Opt. Lett 17, 1426-1428 (1992).
[CrossRef] [PubMed]

Aalto, T.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[CrossRef]

Bachmann, M.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

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

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

Besse, P. A.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

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

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

Chang, T. Y.

Fang, C.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Feng, D. J. Y.

Fukuda, H.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Gini, E.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

Goldhar, J.

Hadley, G. R.

G. R. Hadley, "Wide-angle beam propagation using Pade approximant operators," Opt. Lett 17, 1426-1428 (1992).
[CrossRef] [PubMed]

Harjanne, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[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]

Itabashi, S.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

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]

Kapulainen, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[CrossRef]

Kim, Y.

Lay, T. S.

Levy, D. S.

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

Li, Y.M.

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

Liu, Z.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Melchior, H.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

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

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

Morita, H.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Osgood, R.M.

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

Pennings, E. C.M.

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

Richardson, C. J. K.

Scarmozzino, R.

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

Shi, W.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Shoji, T.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Smit, M. K.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[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]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

Solehmainen, K.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[CrossRef]

Takahashi, J.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Takahashi, M.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Tamechika, E.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Tseng, S.-Y.

Tsuchizawa, T.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Watanabe, T.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Wei, H.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Yamada, K.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

Yu, J.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Zhang, X.

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[CrossRef]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

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

H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, "Fabrication of 4×4 tapered MMI coupler with large cross section," IEEE Photon. Technol. Lett. 13, 466-468 (2001).
[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]

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photon. Technol. Lett. 18, 2287-2289 (2006).
[CrossRef]

J. Lightwave Technol.

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]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1001-1009 (1994).
[CrossRef]

P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, "New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios," J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

Opt. Express

Opt. Lett

G. R. Hadley, "Wide-angle beam propagation using Pade approximant operators," Opt. Lett 17, 1426-1428 (1992).
[CrossRef] [PubMed]

Other

K. Kawano and T. Kiton, Introduction to Optical Waveguide Analysis (Wiley, New York, 2001).
[CrossRef]

Optical Modesolver, Photonics Research Laboratory, University of Maryland, MD (2006), http://www.photonics.umd.edu/software/modesolver.zip

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of 2×2 MMI power splitter based on silicon-on-insulator (SOI) rib structure.

Fig. 2.
Fig. 2.

Calculated hologram for variable splitting ratio 2×2 MMI coupler using wide-angle beam propagation method (WA-BPM).

Fig. 3.
Fig. 3.

Simulated bar port and cross port outputs with different index modulation on MMI. Curves are theoretical fits calculated from Eq.(8) and Eq.(9).

Fig. 4.
Fig. 4.

Simulated variation in power output ratio between bar and cross ports with respect to input wavelength. The variations are normalized with the ratio at the designed wavelength of 1550nm.

Fig. 5.
Fig. 5.

Simulated total transmittance with respect to input wavelength.

Equations (10)

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

L π = 4 n c W e 2 3 λ ,
V o = exp ( i K L H ) V i ,
T = 1 2 [ 1 i i 1 ] .
V e = T V E .
V E ( L ) = exp ( i K L H ) V e ( 0 ) = H V e ( 0 )
K = [ 0 κ κ 0 ] ,
V e ( L ) = TH V e ( 0 ) = 1 2 [ cos κ L H + sin κ L H i ( cos κ L H sin κ L H ) i ( cos κ L H sin κ L H ) cos κ L H + sin κ L H ] V e ( 0 ) .
bar : 1 2 ( 1 + sin 2 κ L H )
cross : 1 2 ( 1 sin 2 κ L H ) .
k jk = πλ 4 n c W e 2 ( j 2 k 2 ) .

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