Abstract

We design silicon ridge/rib waveguide directional couplers which are simultaneously tolerant to width, height, coupling gap, and etch depth variations. Using wafer-scale measurements of structures fabricated in the IMEC Standard Passives process, we demonstrate the normalized standard deviation in the per-length coupling coefficient (a metric for the splitting ratio variation) of the variation-tolerant directional couplers is up to 4 times smaller than that of strip waveguide designs. The variation-tolerant couplers are also the most broadband and the deviation in the coupling coefficient shows the lowest spectral dependence.

© 2014 Optical Society of America

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  1. P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
    [CrossRef]
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    [CrossRef]
  4. W. A. Zortman, D. C. Trotter, M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18, 23598–23607 (2010).
    [CrossRef] [PubMed]
  5. A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
    [CrossRef]
  6. S. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010).
    [CrossRef]
  7. S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
    [CrossRef]
  8. J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
    [CrossRef] [PubMed]
  9. P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
    [CrossRef] [PubMed]
  10. P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, J. Van Campenhout, D. Van Thourhout, “Fabrication-tolerant four-channel wavelength-division-multiplexing filter based on collectively tuned Si microrings,” J. Lightwave Technol. 31, 2785–2792 (2013).
    [CrossRef]
  11. C. K. Madesen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley, 1999).
    [CrossRef]
  12. B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [CrossRef]
  13. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photonics Technol. Lett. 14, 483–485 (2002).
    [CrossRef]
  14. W. D. Sacher, W. M. J. Green, S. Assefa, T. Barwicz, P. Pan, S. M. Shank, Y. A. Vlasov, J. K. S. Poon, “Coupling modulation of microrings at rates beyond the linewidth limit,” Opt. Express 21, 9722–9733 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. D. Thomson, Y. Hu, G. Reed, J. M. Fedeli, “Low loss MMI couplers for high performance mzi modulators,” IEEE Photonics Technol. Lett. 22, 1485–1487 (2010).
    [CrossRef]
  17. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
    [CrossRef]

2013

2012

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

2011

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

2010

2009

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

2002

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photonics Technol. Lett. 14, 483–485 (2002).
[CrossRef]

1997

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Absil, P.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, J. Van Campenhout, D. Van Thourhout, “Fabrication-tolerant four-channel wavelength-division-multiplexing filter based on collectively tuned Si microrings,” J. Lightwave Technol. 31, 2785–2792 (2013).
[CrossRef]

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Asghari, M.

Assefa, S.

Baehr-Jones, T.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

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

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

Barwicz, T.

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

Bogaerts, W.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, J. Van Campenhout, D. Van Thourhout, “Fabrication-tolerant four-channel wavelength-division-multiplexing filter based on collectively tuned Si microrings,” J. Lightwave Technol. 31, 2785–2792 (2013).
[CrossRef]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

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

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Chu, S.

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

Cunningham, J.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

Cunningham, J. E.

Danziger, S.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

De Coster, J.

De Heyn, P.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, J. Van Campenhout, D. Van Thourhout, “Fabrication-tolerant four-channel wavelength-division-multiplexing filter based on collectively tuned Si microrings,” J. Lightwave Technol. 31, 2785–2792 (2013).
[CrossRef]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

Dong, P.

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

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

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

Fedeli, J. M.

D. Thomson, Y. Hu, G. Reed, J. M. Fedeli, “Low loss MMI couplers for high performance mzi modulators,” IEEE Photonics Technol. Lett. 22, 1485–1487 (2010).
[CrossRef]

Fedeli, J.-M.

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

Feng, D.

Feng, N.-N.

Fernandez, L.

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Foresi, J.

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Fulbert, L.

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
[CrossRef]

Green, W. M. J.

Haus, H.

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Hautala, J.

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Hochberg, M.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

Hu, Y.

D. Thomson, Y. Hu, G. Reed, J. M. Fedeli, “Low loss MMI couplers for high performance mzi modulators,” IEEE Photonics Technol. Lett. 22, 1485–1487 (2010).
[CrossRef]

Krishnamoorthy, A.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

Krishnamoorthy, A. V.

Kumar, R.

J. R. Ong, R. Kumar, S. Mookherjea, “Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon microring filters,” IEEE Photonics Technol. Lett. 25, 1543–1546 (2013).
[CrossRef]

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

Laine, J. P.

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Lepage, G.

Li, G.

Liang, H.

Liao, S.

Little, B.

B. Little, S. Chu, H. Haus, J. Foresi, J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Lo, G.-Q.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

Luo, Y.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Madesen, C. K.

C. K. Madesen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley, 1999).
[CrossRef]

Mekis, A.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Mookherjea, S.

J. R. Ong, R. Kumar, S. Mookherjea, “Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon microring filters,” IEEE Photonics Technol. Lett. 25, 1543–1546 (2013).
[CrossRef]

Ong, J. R.

J. R. Ong, R. Kumar, S. Mookherjea, “Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon microring filters,” IEEE Photonics Technol. Lett. 25, 1543–1546 (2013).
[CrossRef]

Pan, P.

Pantouvaki, M.

Pinguet, T.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Poon, J. K. S.

Prather, D.

T. Baehr-Jones, T. Pinguet, G.-Q. Lo, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[CrossRef]

Raj, K.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Reed, G.

D. Thomson, Y. Hu, G. Reed, J. M. Fedeli, “Low loss MMI couplers for high performance mzi modulators,” IEEE Photonics Technol. Lett. 22, 1485–1487 (2010).
[CrossRef]

Rosseel, E.

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Sacher, W. D.

Selvaraja, S.

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

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Shafiiha, R.

Shank, S. M.

Shubin, I.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Tabat, M.

S. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in IEEE International Conference on Group IV Photonics (GFP)(2011), pp. 71–73.
[CrossRef]

Thacker, H.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Thomson, D.

D. Thomson, Y. Hu, G. Reed, J. M. Fedeli, “Low loss MMI couplers for high performance mzi modulators,” IEEE Photonics Technol. Lett. 22, 1485–1487 (2010).
[CrossRef]

Trotter, D. C.

Van Campenhout, J.

Van Thourhout, D.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, J. Van Campenhout, D. Van Thourhout, “Fabrication-tolerant four-channel wavelength-division-multiplexing filter based on collectively tuned Si microrings,” J. Lightwave Technol. 31, 2785–2792 (2013).
[CrossRef]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

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

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
[CrossRef]

Verheyen, P.

Vlasov, Y. A.

Watts, M. R.

Yao, J.

A. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3, 567–579 (2011).
[CrossRef]

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photonics Technol. Lett. 14, 483–485 (2002).
[CrossRef]

Zhao, J. H.

C. K. Madesen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley, 1999).
[CrossRef]

Zheng, X.

Zortman, W. A.

Electron. Lett.

P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, L. Fulbert, “Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab,” Electron. Lett. 45, 581–582 (2009).
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Figures (6)

Fig. 1
Fig. 1

Cross-section schematic of a ridge waveguide directional coupler with the geometric parameters indicated.

Fig. 2
Fig. 2

Fractional change in Δn with respect to (a) correlated changes in w and g, (b) waveguide height, h, (c) partially etched slab thickness, t. The nominal values of h and t are 220 nm and 150 nm, respectively, and the wavelength is 1550 nm. The variation-tolerant design point of w = g = 400 nm is highlighted.

Fig. 3
Fig. 3

(a) Optical microscope image of the MZI test structure. (b) Output spectrum of a typical test structure with w = g = 400 nm and L = 4 μm. The extinction ratio can be clearly and reliably measured as a function of wavelength.

Fig. 4
Fig. 4

K vs. coupling length for (a) strip and (b) ridge waveguide couplers from a representative die. A 50:50 MMI splitting ratio is assumed in this case. The fits of the data to K = sin2(κLL + κ0) have R2 > 0.995.

Fig. 5
Fig. 5

Wafer maps of κL in μm−1 for three coupler geometries. The designed values of w and g in nm are noted. The black dots denote the positions of the measured dies.

Fig. 6
Fig. 6

(a) K vs. wavelength for different coupler designs of a representative die. The dashed lines denote the linear least squares fits to the measured data (solid lines) (b) The per-length coupling variation σ κ L κ L as a function of wavelength.

Tables (1)

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Table 1 Wafer-scale measurements of strip and ridge directional couplers at λ = 1550 nm

Equations (6)

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K = sin 2 ( π Δ n λ L ) ,
K α = 2 sin 1 ( K ) K ( 1 K ) 1 Δ n Δ n α .
Δ n w Δ n g 0 .
K ( λ ) = 1 2 ± 1 2 1 [ E R ( λ ) 1 E R ( λ ) + 1 ] 2 .
E R ( λ ) = S [ 1 K ( λ ) ] + K ( λ ) + 2 S K ( λ ) [ 1 K ( λ ) ] S [ 1 K ( λ ) ] + K ( λ ) 2 S K ( λ ) [ 1 K ( λ ) ] .
K λ = 2 sin 1 ( K ) K ( 1 K ) 1 κ L κ L λ .

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