Abstract

We present a unique comparison of ridge-type directional couplers (DC) and multi-mode interferometers (MMI) in terms of their transformational relationship. The two devices are intimately related as the MMI is derived from the DC. We show for the first time the continuous evolution from the two-mode coupling characteristic of DC to the multi-mode mixing and interference characteristic of MMI, as the DC is structurally transformed into the MMI. We also show that DC can be designed to have the MMI features of compactness and polarization-insensitivity, two traits that reflect their shared lineage. However, the design of DC requires careful control of a large set of design parameters, while the MMI design is more robust and involves fewer design variables.

©2004 Optical Society of America

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References

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  1. R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron QE-22, 911 (1986).
    [Crossref]
  2. Lucas B. Soldano and Erik C. M. Pennings, “Optical Multi-mode Interference Devices based on Self-Imaging: Principles and Applications,” J. Lightwave Technology 13, 615 (1995).
    [Crossref]
  3. 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 Technology 17, 243 (1999).
    [Crossref]
  4. Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
    [Crossref]
  5. M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
    [Crossref]
  6. W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
    [Crossref]
  7. N. Yoshimoto, Y. Shibata, S. Oku, S. Kondo, and Y. Noguchi, “Design and demonstration of polarization-insensitive Mach-Zehnder switch using a lattice-matched InGaAlAs/InAlAs MQW and deep-etched high-mesa waveguide structure,” J. Lightwave Technol. 17, 1662 (1999).
    [Crossref]
  8. Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
    [Crossref]
  9. M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

2003 (1)

Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
[Crossref]

2000 (1)

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

1999 (3)

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

N. Yoshimoto, Y. Shibata, S. Oku, S. Kondo, and Y. Noguchi, “Design and demonstration of polarization-insensitive Mach-Zehnder switch using a lattice-matched InGaAlAs/InAlAs MQW and deep-etched high-mesa waveguide structure,” J. Lightwave Technol. 17, 1662 (1999).
[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 Technology 17, 243 (1999).
[Crossref]

1995 (1)

Lucas B. Soldano and Erik C. M. Pennings, “Optical Multi-mode Interference Devices based on Self-Imaging: Principles and Applications,” J. Lightwave Technology 13, 615 (1995).
[Crossref]

1992 (1)

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

1986 (1)

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron QE-22, 911 (1986).
[Crossref]

Bian, Zhixi

Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
[Crossref]

Chaudhuri, S. K.

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

Chi, S.

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

Chin, M. K.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

Darmawan, S.

M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

Forber, R. A.

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron QE-22, 911 (1986).
[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 Technology 17, 243 (1999).
[Crossref]

Ho, S. T.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Huang, W. P.

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

Kondo, S.

Lee, C. W.

M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

Lee, S. Y.

M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

Liu, B.

Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
[Crossref]

Ma, Yong

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

Marom, E.

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron QE-22, 911 (1986).
[Crossref]

Noguchi, Y.

Oku, S.

Park, Seoijin

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

Pennings, Erik C. M.

Lucas B. Soldano and Erik C. M. Pennings, “Optical Multi-mode Interference Devices based on Self-Imaging: Principles and Applications,” J. Lightwave Technology 13, 615 (1995).
[Crossref]

Pierson, T.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[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 Technology 17, 243 (1999).
[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 Technology 17, 243 (1999).
[Crossref]

Ren, Z.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Shakouri, A.

Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
[Crossref]

Shibata, Y.

Soldano, Lucas B.

Lucas B. Soldano and Erik C. M. Pennings, “Optical Multi-mode Interference Devices based on Self-Imaging: Principles and Applications,” J. Lightwave Technology 13, 615 (1995).
[Crossref]

Tiong Ho, Seng

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

Wang, L.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Wang, Liwei

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

Wu, S. L.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Xu, C.

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

Yoshimoto, N.

Youtsey, C.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Zhao, W.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

Zhou, Y. G.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

IEEE J. Quantum Electron (1)

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron QE-22, 911 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

Zhixi Bian, B. Liu, and A. Shakouri, “InP-based passive ring-resonator-coupled lasers,” IEEE J. Quantum Electron. 39, 859 (2003).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Yong Ma, Seoijin Park, Liwei Wang, and Seng Tiong Ho, “Ultracompact Multimode Interference 3-dB Coupler with Strong Lateral Confinement by Deep Dry Etching,” IEEE Photon. Technol. Lett. 12, 492 (2000).
[Crossref]

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhou, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620 (1999).
[Crossref]

J. Lightwave Technol. (1)

J. Lightwave Technology (3)

W. P. Huang, C. Xu, S. Chi, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technology 10, 295 (1992).
[Crossref]

Lucas B. Soldano and Erik C. M. Pennings, “Optical Multi-mode Interference Devices based on Self-Imaging: Principles and Applications,” J. Lightwave Technology 13, 615 (1995).
[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 Technology 17, 243 (1999).
[Crossref]

Other (1)

M. K. Chin, C. W. Lee, S. Y. Lee, and S. Darmawan, “High-index contrast waveguides and devices,” Opt. Commun. (to be published).

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Figures (4)

Fig. 1.
Fig. 1. (a) Cross section of a directional coupler with shallower gap region and deeper outer walls. (b) Coupling length of DC as a function of etch depth (dc=0.3 µm, ncore=3.42), and (c) waveguide width (dc=0.5 µm, ncore=3.337).
Fig. 2.
Fig. 2. The transition from DC to MMI as the gap depth is reduced. (d) and (e) show the Type I and the Type II MMI, respectively.
Fig. 3.
Fig. 3. The power distribution (for TE mode) vs. propagation distance corresponding to the various gap depths showing the transition from DC characteristic to MMI characteristic. Other parameters are dc=0.5 µm, ncore=3.337, nclad=3.17, w=1.5 µm, g=0.5 µm. (f) corresponds to the structure of Fig. 2(c) and does not include the transition to the port waveguides
Fig. 4.
Fig. 4. The change of modal (TE) effective indices with changing gap depth, showing he transition from DC to MMI (left), and with changing MMI width, showing the transition from Type I to Type II MMI (right) (parameters same as in Fig. 3).

Tables (1)

Tables Icon

Table 1. MMI lengths for cross couplers and 3-dB couplers as the MMI is changed from Type I to Type II. All lengths are calculated for the wavelength λo=1.55 µm. Numbers with * are the Lπ values that arise near the restricted interference condition W mmi=3D.

Equations (2)

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L c = π β e β o = λ o 2 ( n e n o )
L π π ( β o β 1 ) = λ 2 ( n 0 n 1 ) = 4 3 n r W eq 2 λ 0

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