Abstract

We propose a novel structure that includes two compact, simply structured, and lossy waveguides for reducing back reflection in MMI combiners. The preferred lossy waveguide consists of a bend section and a tapered section. Theoretical calculations and 2D FDTD analysis were used to confirm the properties of our proposed structure. Significantly and interestingly, for TE modes, the optimized bend radius is about 7.5 µm and the specific back reflectance depends on taper end width. For TM modes, to achieve a back reflection value smaller than −30 dB, the taper length of 30 µm is desired regardless of bend radius. Moreover, the introduction of the lossy waveguide influences neither the MMI design nor its operation.

© 2014 Optical Society of America

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References

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  1. E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
    [Crossref]
  2. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
    [Crossref]
  3. Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
    [Crossref]
  4. D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
    [Crossref]
  5. D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
    [Crossref]
  6. 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(12), 1662–1664 (2000).
    [Crossref]
  7. J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
    [Crossref]
  8. M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002).
    [Crossref]
  9. L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
    [Crossref]
  10. Z. W. K. Utaka, “Horn-shaped multimode interference-based N×1 combiner,” in Proc. 5th Pacific Rim Conference on Lasers and Electro-Optics (2003), THP-8–6.
  11. W. Zhigang and K. Utaka, “Study on tapered multimode interference-based coherent lightwave combiners,” IEICE Trans. Electron. 88, 1005–1012 (2005).
  12. W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).
  13. R. R. A. Syms and J. R. Cozens, Optical Guided Waves and Devices, 1st ed. (McGraw-Hill, 1992), Chap. 5.
  14. T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
    [Crossref]

2012 (1)

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

2006 (1)

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

2005 (1)

W. Zhigang and K. Utaka, “Study on tapered multimode interference-based coherent lightwave combiners,” IEICE Trans. Electron. 88, 1005–1012 (2005).

2004 (1)

L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
[Crossref]

2002 (2)

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002).
[Crossref]

2000 (1)

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(12), 1662–1664 (2000).
[Crossref]

1998 (1)

D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
[Crossref]

1997 (1)

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[Crossref]

1996 (1)

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (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(4), 615–627 (1995).
[Crossref]

1994 (1)

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Baets, R.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

Choi, Y.-W.

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[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(12), 1662–1664 (2000).
[Crossref]

De Merlier, J.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

De Waard, P.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Erasme, D.

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[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(12), 1662–1664 (2000).
[Crossref]

Groen, F.

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[Crossref]

Guiyun, K.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Hammer, M.

Herben, C.

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[Crossref]

Katsuyuki, U.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Kim, D. G.

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

Kim, H.-S.

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

Koumans, R.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Lee, T.-K.

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

Levy, D. S.

D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
[Crossref]

Liu, Y.

L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
[Crossref]

Moerman, I.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

Morthier, G.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

Naganuma, M.

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

Oh, G.-Y.

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

Oku, S.

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

Osgood, R. M.

D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
[Crossref]

Pennings, E.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[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(4), 615–627 (1995).
[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(12), 1662–1664 (2000).
[Crossref]

Scarmozzino, R.

D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
[Crossref]

Shibata, Y.

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

Shuzhong, Y.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Smit, M.

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[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(4), 615–627 (1995).
[Crossref]

Spiekman, L.

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[Crossref]

Utaka, K.

W. Zhigang and K. Utaka, “Study on tapered multimode interference-based coherent lightwave combiners,” IEICE Trans. Electron. 88, 1005–1012 (2005).

Van Caenegem, T.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

Van Daele, P.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

van Groesen, E.

van Roijen, R.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Van Stralen, M.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Verbeck, B.

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

Verstuyft, S.

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

Wang, Q.

L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
[Crossref]

Weigang, Z.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Xiaoyi, D.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Yamamoto, M.

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

Yang, L.

L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
[Crossref]

Yasuo, W.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Yoshimoto, N.

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

Zhi, W.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Zhigang, W.

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

W. Zhigang and K. Utaka, “Study on tapered multimode interference-based coherent lightwave combiners,” IEICE Trans. Electron. 88, 1005–1012 (2005).

Electron. Lett. (1)

Y. Shibata, S. Oku, M. Yamamoto, N. Yoshimoto, and M. Naganuma, “Quantitative analysis of optical reflection in a multimode interference 3 dB coupler using a low-coherence interferometric reflectometer,” Electron. Lett. 32(24), 2266–2268 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (5)

D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimental assessment of the reflection of passive multimode interference couplers,” IEEE Photon. Technol. Lett. 9(12), 1604–1606 (1997).
[Crossref]

D. S. Levy, R. Scarmozzino, and R. M. Osgood, “Length reduction of tapered N x N MMI devices,” IEEE Photon. Technol. Lett. 10(6), 830–832 (1998).
[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(12), 1662–1664 (2000).
[Crossref]

J. De Merlier, G. Morthier, S. Verstuyft, T. Van Caenegem, I. Moerman, P. Van Daele, and R. Baets, “Experimental demonstration of all-optical regeneration using an MMI-SOA,” IEEE Photon. Technol. Lett. 14(5), 660–662 (2002).
[Crossref]

E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans, and B. Verbeck, “Reflection properties of multimode interference devices,” IEEE Photon. Technol. Lett. 6(6), 715–718 (1994).
[Crossref]

IEICE Trans. Electron. (1)

W. Zhigang and K. Utaka, “Study on tapered multimode interference-based coherent lightwave combiners,” IEICE Trans. Electron. 88, 1005–1012 (2005).

J. Lightwave Technol. (2)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002).
[Crossref]

J. Semicond. (1)

W. Zhigang, Z. Weigang, W. Zhi, K. Guiyun, Y. Shuzhong, D. Xiaoyi, U. Katsuyuki, and W. Yasuo, “Tapered multimode interference combiners for coherent receivers,” J. Semicond. 27, 328–335 (2006).

Opt. Commun. (1)

T.-K. Lee, G.-Y. Oh, H.-S. Kim, D. G. Kim, and Y.-W. Choi, “A high-Q biochemical sensor using a total internal reflection mirror-based triangular resonator with an asymmetric Mach–Zehnder interferometer,” Opt. Commun. 285(7), 1807–1813 (2012).
[Crossref]

Opt. Eng. (1)

L. Yang, Y. Liu, and Q. Wang, “Study on the internal reflection of the multimode-interference-type device,” Opt. Eng. 43(10), 2322–2326 (2004).
[Crossref]

Other (2)

Z. W. K. Utaka, “Horn-shaped multimode interference-based N×1 combiner,” in Proc. 5th Pacific Rim Conference on Lasers and Electro-Optics (2003), THP-8–6.

R. R. A. Syms and J. R. Cozens, Optical Guided Waves and Devices, 1st ed. (McGraw-Hill, 1992), Chap. 5.

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Figures (17)

Fig. 1
Fig. 1 Proposed structure with two Lossy Waveguides added to conventional MMI.
Fig. 2
Fig. 2 Variation in back reflection with respect to input phase difference in the absence of a lossy waveguide.
Fig. 3
Fig. 3 Refractive index profile of tapered waveguide without a bend section.
Fig. 4
Fig. 4 Index profile of tapered waveguide with bend section.
Fig. 5
Fig. 5 E field distribution with taper length 20 µm for TE mode and TM mode.
Fig. 6
Fig. 6 E field distribution at tip region with taper length 20 µm for TE mode and TM mode.
Fig. 7
Fig. 7 Back reflection by FDTD vs. length of tapered waveguide without bend section.
Fig. 8
Fig. 8 E-field distribution under condition of bend radius 8 µm (left) and 1.5µm (right) with the same taper length of 30 µm for TE modes.
Fig. 9
Fig. 9 Variation in back reflection with respect to taper length for TE modes with different bend radii, when the end width = 0 nm.
Fig. 10
Fig. 10 Variation in back reflection with respect to taper length for TE modes with different bend radii, when the end width = 100 nm.
Fig. 11
Fig. 11 Variation in back reflection with respect to the bend radius for TE modes with different end width.
Fig. 12
Fig. 12 Straight-bend-straight connection with bend radius 1.5 µm and 5 µm for TE mode.
Fig. 13
Fig. 13 E field distribution at enlarged tip region for taper length = 40 µm with bend radii = 1.5 µm, 5 µm, 7.5 µm and 9 µm for TE mode, the tip region located in the dashed circle.
Fig. 14
Fig. 14 Variation in back reflection changes with respect to taper length for TM mode with different bend radii, when the end width = 0 nm.
Fig. 15
Fig. 15 Variation in back reflection changes with respect to taper length for TM mode with different bend radii when the end width = 100 nm.
Fig. 16
Fig. 16 E field distribution at enlarged tip region for taper length = 40 µm with bend radii = 1.5 µm, 4 µm, 6 µm and 8 µm for TM mode, the tip region located in the dashed circle.
Fig. 17
Fig. 17 Variation in back reflection with respect to input phase difference for the MMI with lossy waveguide, as obtained by FDTD simulation.

Equations (3)

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

T = [ ( E 1 2 ) 2 + ( E 2 2 ) 2 + E 1 E 2 cos ( Δ φ ) ] / ( E 1 2 + E 2 2 ) .
T = cos 2 ( Δ φ / 2 ) .
R b a c k = ( 1 T ) * R 0 / 2 = 0.16564 sin 2 ( Δ φ / 2 ) .

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