Abstract

Add-drop filters (ADFs) are an essential component in optical interconnection using dense wavelength-division multiplexing. Silicon photonic ADFs based on contra-directional coupling have been well developed, but those based on grating-assisted co-directional coupling (GACC) have never been studied. This paper reports an ADF based on GACC in a vertical hybrid structure (VHS). which consists of two width-modulated silicon strip waveguides with a large lateral gap and a wide silicon nitride strip waveguide above them. The VHS makes it possible for the ADF to have a narrow 3-dB bandwidth as well as a short grating length. An efficient analysis method for design is explained, and the ADF is designed. Theoretical investigation of the ADF demonstrates that the ADF has a 3-dB bandwidth of 1.16 nm and a grating length of 1.13 mm, which are similar to those of ADFs based on contra-directional coupling. As an application, the ADF is used for a nonvolatile switchable ADF by adding an optical phase change material strip above the silicon nitride waveguide. The nonvolatile switchable ADF is shown to have an extinction ratio larger than 30 dB. The investigated ADF requires neither waveguides in close proximity nor grating teeth with dimensions close to the resolution of deep UV lithography. In this regard, it has the advantage of ease of fabrication as compared to ADFs based on contra-directional coupling. Therefore, the ADF is expected to play a key role in optical interconnection using dense wavelength-division multiplexing, prevailing over ADFs based on contra-directional coupling.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (8)

A. F. J. Levi, “Silicon photonics’ last-meter problem: Economics and physics still pose challenges to “fiber to the processor” tech,” IEEE Spectr. 55(9), 38–43 (2018).
[Crossref]

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

H. Qiu, J. Jiang, P. Yu, D. Mu, J. Yang, X. Jiang, H. Yu, R. Cheng, and L. Chrostowski, “Narrow-band add-drop filter based on phase-modulated grating-assisted contra-directional couplers,” J. Lightwave Technol. 36(17), 3760–3764 (2018).
[Crossref]

Z. Wang, M. Ma, and L. R. Chen, “Integrated optical add-drop multiplexer in SOI based on mode selection and Bragg reflection,” IEEE Photonics Technol. Lett. 30(24), 2107–2110 (2018).
[Crossref]

S. Paul, M. Kuittinen, M. Roussey, and S. Honkanen, “Multi-wavelength add-drop filter with phase-modulated shifted Bragg grating,” Opt. Lett. 43(13), 3144–3147 (2018).
[Crossref] [PubMed]

J. C. C. Mak, Q. Wilmart, S. Olivier, S. Menezo, and J. K. S. Poon, “Silicon nitride-on-silicon bi-layer grating couplers designed by a global optimization method,” Opt. Express 26(10), 13656–13665 (2018).
[Crossref] [PubMed]

K. J. Miller, R. F. Haglund, and S. M. Weiss, “Optical phase change materials in integrated silicon photonic devices: review,” Opt. Mater. Express 8(8), 2415–2429 (2018).
[Crossref]

Q. Zhang, Y. Zhang, J. Li, R. Soref, T. Gu, and J. Hu, “Broadband nonvolatile photonic switching based on optical phase change materials: beyond the classical figure-of-merit,” Opt. Lett. 43(1), 94–97 (2018).
[Crossref] [PubMed]

2017 (4)

Y. Kim and M.-S. Kwon, “Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon,” Nanoscale 9(44), 17429–17438 (2017).
[Crossref] [PubMed]

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

J. Jiang, H. Qiu, G. Wang, Y. Li, T. Dai, D. Mu, H. Yu, J. Yang, and X. Jiang, “Silicon lateral-apodized add-drop filter for on-chip optical interconnection,” Appl. Opt. 56(30), 8425–8429 (2017).
[Crossref] [PubMed]

2015 (3)

2014 (2)

2013 (4)

2011 (1)

2010 (1)

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

2009 (1)

2005 (3)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Coupling to nanophotonic waveguides using a dual grating-assisted directional coupler,” IEE Proc., Optoelectron. 152(1), 41–48 (2005).
[Crossref]

G. Masanovic, G. Reed, W. Headley, B. Timotijevic, V. Passaro, R. Atta, G. Ensell, and A. Evans, “A high efficiency input/output coupler for small silicon photonic devices,” Opt. Express 13(19), 7374–7379 (2005).
[Crossref] [PubMed]

2004 (1)

1992 (1)

W. Huang and J. Hong, “A transfer matrix approach based on local normal modes for coupled waveguides with periodic perturbations,” J. Lightwave Technol. 10(10), 1367–1375 (1992).
[Crossref]

Abadía, N.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Adibi, A.

Aguiar, D.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Arakawa, Y.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

Atta, R.

Baehr-Jones, T.

Baets, R.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
[Crossref]

Barwicz, T.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Bhaskaran, H.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Bodenmüller, D.

Bogaerts, W.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
[Crossref]

Böhm, M.

Boroojerdi, M. T.

M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Bandwidth Tunable SOI Add-Drop Filter,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.111.
[Crossref]

Chavez Boggio, J. M.

Chen, L. R.

Z. Wang, M. Ma, and L. R. Chen, “Integrated optical add-drop multiplexer in SOI based on mode selection and Bragg reflection,” IEEE Photonics Technol. Lett. 30(24), 2107–2110 (2018).
[Crossref]

J. Wang and L. R. Chen, “Low crosstalk Bragg grating/Mach-Zehnder interferometer optical add-drop multiplexer in silicon photonics,” Opt. Express 23(20), 26450–26459 (2015).
[Crossref] [PubMed]

Chen, R.

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

Cheng, R.

Chrostowski, L.

Chu, T.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

Dahlem, M. S.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Dai, T.

Domash, L.

Dumon, P.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
[Crossref]

Eftekhar, A. A.

Eisermann, R.

El-Fiky, E.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Ensell, G.

Evans, A.

Fard, S. T.

Flueckiger, J.

Fremberg, T.

Gan, F.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Greenberg, M.

Gu, T.

Guglielmi, E.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Haglund, R. F.

Haynes, R.

Headley, W.

Hochberg, M.

Holzwarth, C. W.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Hong, J.

W. Huang and J. Hong, “A transfer matrix approach based on local normal modes for coupled waveguides with periodic perturbations,” J. Lightwave Technol. 10(10), 1367–1375 (1992).
[Crossref]

Honkanen, S.

Hosseini, P.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Hu, J.

Hu, T.

Huang, W.

W. Huang and J. Hong, “A transfer matrix approach based on local normal modes for coupled waveguides with periodic perturbations,” J. Lightwave Technol. 10(10), 1367–1375 (1992).
[Crossref]

Huang, Y.

Ippen, E. P.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Ishida, S.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

Jacques, M.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Jaeger, N. A.

Jaeger, N. A. F.

Jaenen, P.

Jiang, G.

Jiang, J.

Jiang, X.

Kärtner, F. X.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Kim, Y.

Y. Kim and M.-S. Kwon, “Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon,” Nanoscale 9(44), 17429–17438 (2017).
[Crossref] [PubMed]

Kirk, A. G.

M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Bandwidth Tunable SOI Add-Drop Filter,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.111.
[Crossref]

Kuittinen, M.

Kwon, M.-S.

Y. Kim and M.-S. Kwon, “Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon,” Nanoscale 9(44), 17429–17438 (2017).
[Crossref] [PubMed]

Levi, A. F. J.

A. F. J. Levi, “Silicon photonics’ last-meter problem: Economics and physics still pose challenges to “fiber to the processor” tech,” IEEE Spectr. 55(9), 38–43 (2018).
[Crossref]

Li, J.

Li, T.

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

Li, X.

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

Li, Y.

Lin, C.

Lisker, M.

Liu, Y.

Lo, G.-Q.

Ma, E.

Ma, M.

Z. Wang, M. Ma, and L. R. Chen, “Integrated optical add-drop multiplexer in SOI based on mode selection and Bragg reflection,” IEEE Photonics Technol. Lett. 30(24), 2107–2110 (2018).
[Crossref]

Mak, J. C. C.

Masanovic, G.

Masanovic, G. Z.

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Coupling to nanophotonic waveguides using a dual grating-assisted directional coupler,” IEE Proc., Optoelectron. 152(1), 41–48 (2005).
[Crossref]

Melloni, A.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Ménard, M.

M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Bandwidth Tunable SOI Add-Drop Filter,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.111.
[Crossref]

Menezo, S.

Milanizadeh, M.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Miller, K. J.

Morichetti, F.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Morsy-Osman, M.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Mu, D.

Nemchuk, N.

Olivier, S.

Passaro, V.

Passaro, V. M. N.

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Coupling to nanophotonic waveguides using a dual grating-assisted directional coupler,” IEE Proc., Optoelectron. 152(1), 41–48 (2005).
[Crossref]

Patel, D.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Paul, S.

Pernice, W. H. P.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Plant, D. V.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Poon, J. K. S.

Popovic, M. A.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Pourabolghasem, R.

Qiu, H.

Rakich, P. T.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Reed, G.

Reed, G. T.

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Coupling to nanophotonic waveguides using a dual grating-assisted directional coupler,” IEE Proc., Optoelectron. 152(1), 41–48 (2005).
[Crossref]

Ríos, C.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Roth, M. M.

Roussey, M.

Saber, M. G.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

Sacher, W. D.

Sampietro, M.

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Scherer, T.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Selvaraja, S. K.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
[Crossref]

Shao, H.

Shi, W.

Smith, H. I.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

Sodagar, M.

Soref, R.

Stegmaier, M.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Taubner, T.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Timotijevic, B.

Van Thourhout, D.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
[Crossref]

Wang, D.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
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Wang, J.

Wang, X.

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M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
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Z. Wang, M. Ma, and L. R. Chen, “Integrated optical add-drop multiplexer in SOI based on mode selection and Bragg reflection,” IEEE Photonics Technol. Lett. 30(24), 2107–2110 (2018).
[Crossref]

Watts, M. R.

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
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Weiss, S. M.

Wilmart, Q.

Wright, C. D.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Wu, M.

Wuttig, M.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Xing, Z.

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
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H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

Yang, J.

Yu, H.

Yu, P.

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D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

Zhang, Q.

Zhang, W.

Zhang, Y.

Zhou, Z.

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

Zimmermann, L.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical add-drop multiplexers based on Si-wire waveguides,” Appl. Phys. Lett. 86(19), 191107 (2005).
[Crossref]

IEE Proc., Optoelectron. (1)

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Coupling to nanophotonic waveguides using a dual grating-assisted directional coupler,” IEE Proc., Optoelectron. 152(1), 41–48 (2005).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[Crossref]

IEEE Photonics J. (1)

M. G. Saber, Z. Xing, D. Patel, E. El-Fiky, N. Abadía, Y. Wang, M. Jacques, M. Morsy-Osman, and D. V. Plant, “A CMOS compatible ultracompact silicon photonic optical add-drop multiplexer with misaligned sidewall Bragg gratings,” IEEE Photonics J. 9(3), 6601010 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Z. Wang, M. Ma, and L. R. Chen, “Integrated optical add-drop multiplexer in SOI based on mode selection and Bragg reflection,” IEEE Photonics Technol. Lett. 30(24), 2107–2110 (2018).
[Crossref]

IEEE Spectr. (1)

A. F. J. Levi, “Silicon photonics’ last-meter problem: Economics and physics still pose challenges to “fiber to the processor” tech,” IEEE Spectr. 55(9), 38–43 (2018).
[Crossref]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. B (1)

Nanoscale (1)

Y. Kim and M.-S. Kwon, “Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon,” Nanoscale 9(44), 17429–17438 (2017).
[Crossref] [PubMed]

Nat. Photonics (2)

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Opt. Express (6)

Opt. Fiber Technol. (1)

Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon photonics for data centers,” Opt. Fiber Technol. 44, 13–23 (2018).
[Crossref]

Opt. Lett. (5)

Opt. Mater. Express (1)

Other (3)

M. A. Popovic, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
[Crossref]

D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of hitless add-drop filter array based on microrings,” in Advanced Photonics 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper IW4I.8.

M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Bandwidth Tunable SOI Add-Drop Filter,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.111.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Structure of the ADF. The Si strips and the SiN strip are embedded in SiO2. The GACC is achieved in the VHS by periodically modulating the widths of the Si strips. The VHS can be considered as the periodic stack of sub-VHSs 1 and 2. The average VHS means the VHS without the width modulation. In other words, the average VHS has the Si strips of width WSi.
Fig. 2
Fig. 2 Analysis results for the design of the ADF. (a) Electric field profiles of TEev, TEod, TEN0, and TEN1. (b) Comparison of the results obtained from methods 1, 2, and 3, which are colored black, red, and blue, respectively. The solid (Λ) and dashed (Np) curves were obtained from methods 1 and 2. The squares for Λ and the circles for Np were obtained from method 3. (c) Dependence of Λ on WSiN. (d) Dependence of Lg on WSiN. (e) Dependence of the 3-dB bandwidth Δλ1/2 on WSiN. In (c)–(e), the curves for HSiN = 400, 500, and 600 nm are colored black, red, and blue, respectively. The solid, dashed, and dotted curves show the dependences for Vgap = 150, 185, and 220 nm, respectively. The boxes show the interval of WSiN for which synchronous coupling between TMod and TEN0 of the sub-VHSs happens.
Fig. 3
Fig. 3 Characteristics of the ADF. (a) Dependences of Lg and Δλ1/2 on ΔW. The inset shows the dependence of Λ on ΔW. The solid and dashed curves were obtained from method 2; the symbols were obtained from method 3. The black curves were calculated by using Eq. (5); the red curves were calculated by using the approximate equation N p =π/| t 2 |. (b) Transmission spectra. The spectra of T21 and T31 are colored black and red, respectively. The symbols were obtained from method 3. The solid curves were calculated by using Eqs. (1) and (2). The insets show the spectra in dB in a narrow wavelength interval. Δλ is wavelength detuning from λc = 1.55 μm. The minimum of T31 in the right inset is clamped to −16 dB for clear demonstration.
Fig. 4
Fig. 4 Changes in λc and T21 at λc depending on (a) WSi, (b) WSiN, (c) HSiN, and (d) Vgap. Δλc means the change in λc. The squares for Δλc and the circles for T21 at λc were obtained from method 3. The straight lines with the slope calculated with Eq. (6) are fitted to the squares.
Fig. 5
Fig. 5 Transmission spectra of the asymmetric ADF. Δλ is wavelength detuning from λc = 1.55 μm. (a) and (b) were calculated in the case that the right Si strip is 0.6 nm wider than the left Si strip. (c) and (d) were calculated in the case that the SiN strip is displaced by 12 nm from the central position. The symbols were obtained from method 3. The solid curves in (a) and (b) were calculated by using the coupled-mode theory for three waveguides (see Appendices). The solid curves in (c) and (d) show the spectra of the symmetric ADF for comparison.
Fig. 6
Fig. 6 Nonvolatile switchable ADF. (a) Schematic diagram of its structure. (b) Electric field profile of TEN0 in the case of a-GSST. (c) Electric field profile of TEN0 in the case of c-GSST.
Fig. 7
Fig. 7 Influences of Wgsst and Ggap on the nonvolatile switchable ADF. The panels show how (a) Λ, (b) Np, (c) T21 at λc in the case of a-GSST, and (d) T31 at λc in the case of c-GSST depend on Wgsst for Ggap = 50 (black squares), 100 (red circles), and 150 (blue triangles) nm.
Fig. 8
Fig. 8 Spectra of T21 and T31 in the case of a-GSST (closed symbols) and in the case of c-GSST (open symbols). Δλ is wavelength detuning from λc = 1.55 μm. The solid lines are guides for the eye.
Fig. 9
Fig. 9 T21 and T31 spectra of the ADF with WSiN = 1.4 μm. (a) Coupling between TEod and TMN0. (b) Coupling between TEod and TEN1. (c) Coupling between TEod and TEN1 when Np is reduced to 100.
Fig. 10
Fig. 10 T21 and T31 spectra of the ADF. (a) Coupling between TEod and TMN0 for WSiN = 1.7 μm. (b) Coupling between TEod and TEN1 for WSiN = 1.7 μm. (c) Coupling between TEod and TMN0 and that between TEod and TEN1 for WSiN = 2.0 μm. (d) Coupling between TEev and TMod and that between TEod and TMev for WSiN = 2.0 μm.
Fig. 11
Fig. 11 T21 and T31 spectra of the asymmetric ADF. (a) Case of the ADF the right Si strip of which has a larger width and a smaller refractive index than the left Si strip. The symbols show its spectra calculated by using method 3. For comparison, the solid curves show the spectra of the symmetric ADF in Fig. 3(b). (b) Case of the truly asymmetric ADF which has the left Si strip of width 500 nm and the right Si strip of width 480 nm. The width change of the left Si strip is 20 nm, and that of the right Si strip is 22.7 nm. The spectra were calculated by using Eqs. (16)–(18). Δλ is wavelength detuning from λc = 1.55 μm.

Equations (26)

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T 21 = 1 4 [ cos( sy )cos( δy ) ] 2 + 1 4 [ δ s sin( sy )sin( δy ) ] 2 ,
T 31 = 1 4 [ cos( sy )+cos( δy ) ] 2 + 1 4 [ δ s sin( sy )+sin( δy ) ] 2 ,
Δ λ 1/2 =1.093 λ c 2 /( L g Δ n g ),
t (n,j)(m,i) = (m,i)|(n,j) (m,i)|(m,i) (n,j)|(n,j) .
N p =[ sgn(ϕ)πα ]/ϕ,
λ c X = λ c Δ n g ( n ev,1 n N0,1 ) X .
E ev = 1 2 E left + 1 2 E right ,
E od = 1 2 E left + 1 2 E right .
E Si = 1 2 exp(i β ev L g )exp(iδ L g )×[ cos( s L g )+ iδ s sin( s L g ) ] E ev 1 2 exp(i β od L g ) E od ,
κ=| κ out κ in |/π,
κ out in = π 2 η 0 λ ( n Si 2 n SiO 2 )×( out in E ev * E N0 dxdz + n SiO 2 n Si 2 out in E ev,y * E N0,y dxdz ),
T 21 = 1 4 | exp(iδ L g )[ cos( s L g )+ iδ s sin( s L g ) ]1 | 2 = 1 4 [ cos( s L g )cos( δ L g ) ] 2 + 1 4 [ δ s sin( s L g )sin( δ L g ) ] 2 ,
T 31 = 1 4 | exp(iδ L g )[ cos( s L g )+ iδ s sin( s L g ) ]+1 | 2 = 1 4 [ cos( s L g )+cos( δ L g ) ] 2 + 1 4 [ δ s sin( s L g )+sin( δ L g ) ] 2 .
2= 1 4 [ cos( π 1+ α 2 )cos( πα ) ] 2 + 1 4 [ α 1+ α 2 sin( π 1+ α 2 )sin( πα ) ] 2 .
Δδ=ακ=πΔ( n ev,a n N0,a λ ) π 2 Δ λ 1/2 Δ n g λ c 2 .
d a 1 /dy=i κ 13 a 3 exp(i2 δ 13 y),
d a 2 /dy=i κ 23 a 3 exp(i2 δ 23 y),
d a 3 /dy=i κ 13 * a 1 exp(i2 δ 13 y)+i κ 23 * a 2 exp(i2 δ 23 y),
d dy [ A 1 A 2 A 3 ]=i[ δ d 0 κ 13 0 δ d κ 23 κ 13 * κ 23 * δ s ][ A 1 A 2 A 3 ],
ζ 3 + δ s ζ 2 ( κ 13 2 + κ 23 2 + δ d 2 )ζ+( κ 23 2 κ 13 2 ) δ d δ d 2 δ s =0.
v j =[ κ 13 ( δ d + ζ j ) κ 23 ( δ d ζ j ) δ d 2 ζ j 2 ].
[ a 1 (y) a 2 (y) a 3 (y) ]= D δ V D ζ V 1 [ a 1 (0) a 2 (0) a 3 (0) ],
a 1 (y)= 1 2 [ 1+exp(iδy)cos(sy)+ i δ s exp(iδy)sin(sy) ],
a 2 (y)= 1 2 [ 1+exp(iδy)cos(sy)+ i δ s exp(iδy)sin(sy) ].
a 1 (y)= 1 2 κ a 2 [ κ 23 2 + κ 13 2 cos( 2 κ a y ) ],
a 2 (y)= κ 13 * κ 23 κ a 2 sin 2 ( κ a 2 y ),

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