Abstract

A Ring-resonator Mach-Zehnder interferometer (RR-MZI) optical interleaver structure comprising a ring resonator (RR) and a 3 dB directional coupler is proposed. The interleaver is fabricated with 300 nm×300 nm silicon wires on silicon-on-insulator (SOI) wafers. The fabricated interleaver demonstrates a flat-top spectral response, and the measured free spectral range (FSR) is ~20 nm. The insertion loss (IL) of the device is ~-10 dB and the polarization dependent loss (PDL) <5 dB. Both the experimental and simulation results are in good agreement.

© 2008 Optical Society of America

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  1. S. Cao, J. Chen, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," OFC?? 03 Interleaver Workshop, pp. 1-9, http://www.neophotonics.com/down/2.pdf.
  2. H. Arai, H. Nonen, K. Ohira, and T. Chiba, "PLC wavelength splitter for dense WDM transmission system," Hitachi Cable Review 21, 11-16 (2002), http://www.hitachi-cable.co.jp/ICSFiles/afieldfile/2005/11/29/2_review03.pdf.
  3. S. G. Heris, A. Zarifkar, K. Abedi, and M. K. M. Farshi, "Interleavers/deinterleavers based on Michelson- Gires-Tournois interferometers with different structures," in Proceedings of Semiconductor Electronics, Kuala Lumpur, Malaysia (ICSE 2004) 7-9, pp. 573-576 (2004).
  4. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis -A Signal Processing Approach (Wiley, New York, 1999).
  5. B. B. Dingel and M. Izutsu, "Multifunction optical filter with a Michelson-Gires-Tournois interferometer for wavelength-division-multiplexed network system application," Opt. Lett. 23, 1099-1101 (1998).
    [CrossRef]
  6. C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
    [CrossRef]
  7. J. Zhang, L. R. Liu, and Y. Zhou, "Novel and simple approach for designing lattice form interleaver filter," Opt. Express 11, 2217-2224 (2003).
    [CrossRef] [PubMed]
  8. C.-W. Lee, R. B. Wang, P. C. Yeh, and W.-H. Cheng, "Sagnac interferometer based flat-top birefringent interleaver," Opt. Express 14, 4636-4643 (2006.
    [CrossRef] [PubMed]
  9. Y. Zhang, Q. J. Wang, and T. C. Soh, "Optical interleaver," US Patent #2005/0271323A1.
  10. Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
    [CrossRef]
  11. Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
    [CrossRef]
  12. K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, pp. 73-82 (1995).
    [CrossRef]
  13. K. Jinguji, "Synthesis of coherent two-port optical delay-line circuit with ring waveguides," J. Lightwave Technol. 14, 1882-1884 (1996).
    [CrossRef]
  14. M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
    [CrossRef]
  15. S. Bidnyk, A. Balakrishnan, A. Delâge, M. Gao, P. A. Krug, P. Muthukumaran, and M. Pearson, "Novel architecture for design of planar lightwave interleavers," J. Lightwave Technol. 23, 1435-1440 (2005).
    [CrossRef]
  16. C. G. H. Roeloffzen, R. M. de Ridder, G. Sengo, K. Wörhoff, and A. Driessen "Passband flattened interleaver using a Mach-Zehnder interferometer with ring resonator fabricated in SiON waveguide technology," in Proceedings Symposium of IEEE/LEOS (IEEE, 2002) pp.32-35, http://leosbenelux.org/symp02/s02p10.pdf.
  17. K. Wörhoff, C. G. H. Roeloffzen, R. M. de Ridder, G. Sengo, L. T. H. Hilderink, P. V. Lambeck, and A. Driessen, "Tolerance and application of polarization independent waveguide for communication devices," in Proceedings Symposium of IEEE/LEOS (IEEE, 2004) pp. 107-110, http://leosbenelux.org/symp04/s04p107.pdf.
  18. Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
    [CrossRef]
  19. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, "Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction," Opt. Lett. 26, 1888-1890 (2001).
    [CrossRef]
  20. H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
    [CrossRef]
  21. H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).
  22. D. Lauvernier, S. Garidel, M. Zegaoui, J. P. Vilcot, J. Harari, V. Magnin, and D. Decoster, "Optical devices for ultra-compact photonic integrated circuits based on III-V/polymer nanowires," Opt. Express 15, 5333-5341 (2006).
    [CrossRef]

2007

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

2006

2005

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

S. Bidnyk, A. Balakrishnan, A. Delâge, M. Gao, P. A. Krug, P. Muthukumaran, and M. Pearson, "Novel architecture for design of planar lightwave interleavers," J. Lightwave Technol. 23, 1435-1440 (2005).
[CrossRef]

2004

Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
[CrossRef]

2003

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

J. Zhang, L. R. Liu, and Y. Zhou, "Novel and simple approach for designing lattice form interleaver filter," Opt. Express 11, 2217-2224 (2003).
[CrossRef] [PubMed]

2002

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

2001

1998

1996

K. Jinguji, "Synthesis of coherent two-port optical delay-line circuit with ring waveguides," J. Lightwave Technol. 14, 1882-1884 (1996).
[CrossRef]

1995

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, pp. 73-82 (1995).
[CrossRef]

Arakawa, Y.

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

Balakrishnan, A.

Bidnyk, S.

Cerrina, F.

Chang, S. J.

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Chen, Y. J.

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Cheng, W. H.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Cheng, W.-H.

Chu, T.

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

Decoster, D.

Delâge, A.

Dingel, B. B.

Gao, M.

Garidel, S.

Harari, J.

Hibino, Y.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Himeno, A.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Hsieh, C. H.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Ishida, S.

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

Izutsu, M.

James Wen, Z. Q.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Jinguji, K.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

K. Jinguji, "Synthesis of coherent two-port optical delay-line circuit with ring waveguides," J. Lightwave Technol. 14, 1882-1884 (1996).
[CrossRef]

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, pp. 73-82 (1995).
[CrossRef]

Kawachi, M.

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, pp. 73-82 (1995).
[CrossRef]

Kimerling, L. C.

Kitoh, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Krug, P. A.

Lauvernier, D.

Lee, C. -W.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Lee, C.-W.

Lee, K. K.

Lim, D. R.

Liu, L. R.

Magnin, V.

McMichael, I.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Muthukumaran, P.

Ni, C. Y.

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Oguma, M.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Pearson, M.

Shibata, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Shin, J.

Soh, Y. C.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
[CrossRef]

Vilcot, J. P.

Wang, Q. J.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
[CrossRef]

Wang, R. B.

C.-W. Lee, R. B. Wang, P. C. Yeh, and W.-H. Cheng, "Sagnac interferometer based flat-top birefringent interleaver," Opt. Express 14, 4636-4643 (2006.
[CrossRef] [PubMed]

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Wang, Z. P.

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Yamda, H.

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

Yeh, P. C.

C.-W. Lee, R. B. Wang, P. C. Yeh, and W.-H. Cheng, "Sagnac interferometer based flat-top birefringent interleaver," Opt. Express 14, 4636-4643 (2006.
[CrossRef] [PubMed]

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Zegaoui, M.

Zhang, J.

Zhang, Y.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
[CrossRef]

Zhou, Y.

IEEE Photon. Technol. Lett.

C. H. Hsieh, R. B. Wang, Z. Q. James Wen, I. McMichael, P. C. Yeh, C. -W. Lee, and W. H. Cheng, "Flat-top interleavers using two Gires-Tournois etalons as phase-dispersive mirrors in a Michelson interferometer," IEEE Photon. Technol. Lett. 15, 242-244 (2003).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings," IEEE Photon. Technol. Lett. 14, 328-330 (2002).
[CrossRef]

Z. P. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photon. Technol. Lett. 17, 585-587 (2005).
[CrossRef]

IEEE Photon.Technol. Lett.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "All-fiber 3 x 3 interleaver design with flat-top passband," IEEE Photon.Technol. Lett. 16, 168-170 (2004).
[CrossRef]

J. Lightwave Technol.

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, pp. 73-82 (1995).
[CrossRef]

K. Jinguji, "Synthesis of coherent two-port optical delay-line circuit with ring waveguides," J. Lightwave Technol. 14, 1882-1884 (1996).
[CrossRef]

S. Bidnyk, A. Balakrishnan, A. Delâge, M. Gao, P. A. Krug, P. Muthukumaran, and M. Pearson, "Novel architecture for design of planar lightwave interleavers," J. Lightwave Technol. 23, 1435-1440 (2005).
[CrossRef]

H. Yamda, T. Chu, S. Ishida, and Y. Arakawa, "Si Photonic wire waveguide devices," J. Lightwave Technol. 12, 1371-1379 (2006).

Opt. Express

Opt. Lett.

Other

Y. Zhang, Q. J. Wang, and T. C. Soh, "Optical interleaver," US Patent #2005/0271323A1.

S. Cao, J. Chen, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," OFC?? 03 Interleaver Workshop, pp. 1-9, http://www.neophotonics.com/down/2.pdf.

H. Arai, H. Nonen, K. Ohira, and T. Chiba, "PLC wavelength splitter for dense WDM transmission system," Hitachi Cable Review 21, 11-16 (2002), http://www.hitachi-cable.co.jp/ICSFiles/afieldfile/2005/11/29/2_review03.pdf.

S. G. Heris, A. Zarifkar, K. Abedi, and M. K. M. Farshi, "Interleavers/deinterleavers based on Michelson- Gires-Tournois interferometers with different structures," in Proceedings of Semiconductor Electronics, Kuala Lumpur, Malaysia (ICSE 2004) 7-9, pp. 573-576 (2004).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis -A Signal Processing Approach (Wiley, New York, 1999).

C. G. H. Roeloffzen, R. M. de Ridder, G. Sengo, K. Wörhoff, and A. Driessen "Passband flattened interleaver using a Mach-Zehnder interferometer with ring resonator fabricated in SiON waveguide technology," in Proceedings Symposium of IEEE/LEOS (IEEE, 2002) pp.32-35, http://leosbenelux.org/symp02/s02p10.pdf.

K. Wörhoff, C. G. H. Roeloffzen, R. M. de Ridder, G. Sengo, L. T. H. Hilderink, P. V. Lambeck, and A. Driessen, "Tolerance and application of polarization independent waveguide for communication devices," in Proceedings Symposium of IEEE/LEOS (IEEE, 2004) pp. 107-110, http://leosbenelux.org/symp04/s04p107.pdf.

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Figures (11)

Fig. 1.
Fig. 1.

(a) Schematic of the RR-MZI comprised of a RR that replaces the directional coupler of a conventional MZI and a 3 dB directional coupler in the RR-MZI output terminal. (b) RR structure.

Fig. 2.
Fig. 2.

(a) Phase shifts of the through and drop lights after RR. The phase difference between the through (blue curve) and drop (red curve) lights as a function of Δθ (frequency) is +π/2, -π/2, alternately. Fig. 2(b) shows the phase shifts of the through and drop in the lead A and B, respectively. Phase difference between them is 0, π alternately.

Fig. 3.
Fig. 3.

Relative light intensities of leads A and B versus frequency.

Fig. 4.
Fig. 4.

(a) Transmission of Lead A; if t is in the region of 0.23~0.63, the relative light intensity loss is less than -0.5 dB; if in the region of 0.33~0.51, the loss is less than -0.1 dB. (b) |H|2 is varied with the self-coefficient under the condition of lossless, i.e., Δθ=π. t=√2-1 is denoted by red dashed line.

Fig. 5.
Fig. 5.

(a) Characteristics of the passband. (b) Characteristics of the rejection band. (c) Characteristics of the phase and the relative group delay of the proposed interleaver.

Fig. 6.
Fig. 6.

(a) SEM picture of the RR-MZI. (b) 3 dB directional coupler; the coupling length is 2.79 µm and the coupling gap between two waveguides is 300 nm. (c) Coupler with the incident waveguide and the ring resonator; the coupling length is 4.7µm and the contact arc radius is 4.19 µm. (d) SEM picture of a cross section of the DC; the gap between the two waveguides is ~300 nm. (e) SEM picture of SSC; the width of the tip is 150 nm and the length of taper is 200 µm.

Fig. 7.
Fig. 7.

(a) IL and PDL of lead A. (b) IL and PDL of lead B.

Fig. 8.
Fig. 8.

(a) Measured losses of silicon wire. (b) Measured losses of SSC.

Fig. 9.
Fig. 9.

(a) Measured losses of the 3 dB DC. (b) Measured losses of the DC of the RR; the blue and red curves denote straight and cross waveguides, and the black curve represents the reference waveguide. Both DCs have the same full length. The purple curve represents the total insertion loss of DC.

Fig. 10.
Fig. 10.

Crosstalk versus loss in the RR DC. p 2 is reduced from 1.0 to 0.2 by steps of 0.2, and the corresponding curves are arranged from right to left.

Fig. 11.
Fig. 11.

Measurement and fitting results.

Equations (6)

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{ H ( through ) = E ( through ) E ( input ) = t [ γ exp ( i θ ) 1 ] t 2 γ exp ( i θ ) 1 H ( drop ) = E ( drop ) E ( input ) = γ exp ( i θ 2 ) κ 2 t 2 γ exp ( i θ ) 1 ,
{ H ( A ) 2 = 1 2 H ( through ) + i H ( drop ) 2 = X ( θ ) 2 X ( θ ) 2 + Y ( θ ) 2 H ( B ) 2 = 1 2 i H ( through ) + H ( drop ) 2 = Y ( θ ) 2 X ( θ ) 2 + Y ( θ ) 2 ,
{ H ( A ) 2 = 1 1 + tan 4 ( π 4 θ 4 ) 1 1 + ( π 4 θ 4 ) 4 when θ ( 4 N + 1 ) π H ( B ) 2 = 1 1 + tan 4 ( π 4 + θ 4 ) 1 1 + ( π 4 + θ 4 ) 4 when θ ( 4 N 1 ) π .
τ = ϕ ω = T c ϕ θ ,
ϕ θ = 2 3 cos ( θ ) .
{ H ( A ) 2 = [ X ( θ ~ ) Δ p 2 t sin ( θ ~ ) ] 2 + [ Δ p 2 t cos ( θ ~ ) ] 2 [ Δ p 2 + X ( θ ~ ) ] 2 + [ Δ p 2 + Y ( θ ~ ) ] 2 H ( B ) 2 = [ Y ( θ ~ ) + Δ p 2 t sin ( θ ~ ) ] 2 + [ Δ p 2 t cos ( θ ~ ) ] 2 [ Δ p 2 + X ( θ ~ ) ] 2 + [ Δ p 2 + Y ( θ ~ ) ] 2 ,

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