Abstract

Measurement uncertainties in the techniques used to characterize loss in photonic waveguides becomes a significant issue as waveguide loss is reduced through improved fabrication technology. Typical loss measurement techniques involve environmentally unknown parameters such as facet reflectivity or varying coupling efficiencies, which directly contribute to the uncertainty of the measurement. We present a loss measurement technique, which takes advantage of the differential loss between multiple paths in an arrayed waveguide structure, in which we are able to gather statistics on propagation loss from several waveguides in a single measurement. This arrayed waveguide structure is characterized using a swept-wavelength interferometer, enabling the analysis of the arrayed waveguide transmission as a function of group delay between waveguides. Loss extraction is only dependent on the differential path length between arrayed waveguides and is therefore extracted independently from on and off-chip coupling efficiencies, which proves to be an accurate and reliable method of loss characterization. This method is applied to characterize the loss of the silicon photonic platform at Sandia Labs with an uncertainty of less than 0.06 dB/cm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (1)

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

2013 (2)

2011 (1)

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

2010 (2)

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

2008 (1)

2002 (1)

2000 (1)

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

1999 (1)

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

1994 (1)

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[Crossref]

1991 (1)

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

1985 (2)

R. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21(13), 581–583 (1985).
[Crossref]

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

1983 (1)

1972 (1)

Adar, R.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Agarwal, A.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Baets, R.

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Blonder, G. E.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Bogaerts, W.

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

Boscolo, S.

Bowers, J.

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

Boynton, N.

N. Boynton, A. Pomerene, A. Lentine, and C. T. DeRose, “Characterization of systematic process variation in a silicon photonic platform,” IEEE Optical Interconnects Conference (OI), 2017 (11–12). IEEE.
[Crossref]

Carpenter, L.-G.

Chen, X.

Cherchi, M.

Coolbaugh, D.

Cunningham, J. E.

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

Davenport, M.

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

DeRose, C.

DeRose, C. T.

N. Boynton, A. Pomerene, A. Lentine, and C. T. DeRose, “Characterization of systematic process variation in a silicon photonic platform,” IEEE Optical Interconnects Conference (OI), 2017 (11–12). IEEE.
[Crossref]

Dumon, P.

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

Dutt, B.

Fan, S.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Foresi, J.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Gawith, C. B. E.

Gehl, M.

Haus, H. A.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Henry, C. H.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Hosseini, E. S.

Hulme, J.

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

Joannopoulos, J. D.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Keck, D. B.

Khan, M. J.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Khokhar, A.-Z.

Khorasaninejad, M.

Kimerling, L. C.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Kippenberg, T. J.

Kistler, R. C.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Komljenovic, T.

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

Krishnamoorthy, A. V.

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

Lacey, J. P. R.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[Crossref]

Lee, K. K.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Lentine, A.

N. Boynton, A. Pomerene, A. Lentine, and C. T. DeRose, “Characterization of systematic process variation in a silicon photonic platform,” IEEE Optical Interconnects Conference (OI), 2017 (11–12). IEEE.
[Crossref]

Lentine, A. L.

Li, G.

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

Li, Z.

Lim, D. R.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Littlejohns, C.

Luan, H. C.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
[Crossref]

Luo, Y.

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

Manalatou, C.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Mashanovich, G.-Z.

Mekis, A.

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

Mickelson, A. R.

Midrio, M.

Mittal, V.

Mohamed, M.

Moresco, M.

Murugan, G. S.

Nedeljkovic, M.

Okamura, Y.

Olsson, N. A.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Payne, F. P.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[Crossref]

Penades, J. S.

Pinguet, T.

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

Pomerene, A.

M. Gehl, D. Trotter, A. Starbuck, A. Pomerene, A. L. Lentine, and C. DeRose, “Active phase correction of high resolution silicon photonic arrayed waveguide gratings,” Opt. Express 25(6), 6320–6334 (2017).
[Crossref] [PubMed]

N. Boynton, A. Pomerene, A. Lentine, and C. T. DeRose, “Characterization of systematic process variation in a silicon photonic platform,” IEEE Optical Interconnects Conference (OI), 2017 (11–12). IEEE.
[Crossref]

Raj, K.

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

Regener, R.

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

Romagnoli, M.

Saini, S. S.

Selvaraj, S. K.

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

Shang, L.

Shani, Y.

R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
[Crossref]

Shubin, I.

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

Sohler, W.

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

Soref, R. A.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Spillane, S. M.

Starbuck, A.

Taebi, S.

Thacker, H.

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

Thourhout, D. V.

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

Tran, M.

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
[Crossref]

Trotter, D.

Trotter, D. C.

Tynes, R.

Vahala, K. J.

Villeneuve, P. R.

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Walker, R.

R. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21(13), 581–583 (1985).
[Crossref]

Watts, M. R.

Wilkinson, J.-S.

Yamamoto, S.

Yao, J.

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

Yoshinaka, S.

Zheng, X.

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

Zortman, W. A.

Appl. Opt. (4)

Appl. Phys. B (1)

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Appl. Phys. Lett. (2)

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000).
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R. Adar, Y. Shani, C. H. Henry, R. C. Kistler, G. E. Blonder, and N. A. Olsson, “Measurement of very low-loss silica on silicon waveguides with a ring resonator,” Appl. Phys. Lett. 58(5), 444–445 (1991).
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Electron. Lett. (1)

R. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21(13), 581–583 (1985).
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IEEE J. Quantum Electron. (2)

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
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IEEE JSTQE (1)

S. K. Selvaraj, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer Linewidth Uniformity in Silicon Nanophotonic Waveguide Devices Using CMOS Fabriacation Technology,” IEEE JSTQE 16, 316–324 (2010).

IEEE Photonics J. (1)

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics J. 3(3), 567–579 (2011).
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IEEE Photonics Technol. Lett. (1)

M. Tran, T. Komljenovic, J. Hulme, M. Davenport, and J. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28(14), 1517–1520 (2016).
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Opt. Express (4)

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C. Chauveau, P. Labeye, J. M. Fedeli, S. Blaize and G. Lerondel, “Study of the uniformity of 300mm wafer through ring-resonator analysis,” Photonics in Switching (PS) (2012).

S. K. Selvaraja, P. D. Heyn, G. Winroth, P. Ong, G. Lepage, C. Cailler, A. Rigny, K. K. Bourdelle, W. Bogaerts, D. V. Thourhout, J. V. Campenhout, and P. Absil, “Highly uniform and low-loss passive silicon photonics devices using a 300mm CMOS platform” Optical Fiber Communication Conference (OFC), paper Th2A.33 (2014).

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Ford, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” Optical Fiber Communication Conference (OFC), paper Th2A.37 (2014).
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Z. Su, E. S. Hosseini, E. Timurdogan, J. Sun, G. Leake, D. D. Coolbaugh, and M. R. Watts, “Reduced Wafer-Scale Frequency Variation in Adiabatic Microring Resonators,” Optical Fiber Communication Conference (OFC), paper Th2A.55, (2014).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) A microscope image of one of the arrayed waveguide structures used in this study. It consists of 15 (depicted) or 35 arrayed waveguides of a fixed width and etch type (fully etched embedded strip or partially etched rib waveguide). Each of the arrayed waveguides has 32 180° bends to accommodate a small footprint design, which is 4x4 mm2 (depicted) and 8x8 mm2 in this study. (b) A microscope image of the star couplers used in these loss measurements. The center waveguide on the bottom is used as the input/output channel to the M arrayed waveguides at the top. The other two waveguides on the bottom act as buffers to ensure coupling is the same for all waveguides and are tapered off to avoid any type of reflection. The practicality of this design choice is evident for an AWG with more than a single input/out, and is implemented in this study for simplicity. The yellow region in the middle is the FPR, and is where the entering light is modeled as a Gaussian beam. (c) Microscope image of 16 180° bends in the shortest arrayed waveguide, which tapers from a 3 µm wide partially etched rib waveguide in the straight section to a 400 nm fully etched embedded strip waveguide in the bent region to avoid excitation of higher order modes.
Fig. 2
Fig. 2 Schematic representation of the SWI used in this study which consists of a clock MZI which is used to ensure linear sampling of optical frequency ν and a measurement MZI which is used to measure the device under test (DUT).
Fig. 3
Fig. 3 (a) Group delay domain spectra 400 nm wide fully etched embedded strip arrayed waveguides with peak transmission circled in red and (b) the quadratic function fit to the integrated transmission from each of the M arrayed waveguides (b).
Fig. 4
Fig. 4 Extracted waveguide loss as a function of waveguide width using the arrayed waveguide structure and the loss model due to scattering and free carrier absorption for (a) fully etched embedded strip waveguide and (b) partially etched rib waveguide. The uncertainty in loss measurement is attributed to variation in waveguide loss due to uncertainty in process variations.
Fig. 5
Fig. 5 Experimentally extracted effective group index and group index simulation results as a function of waveguide width for fully etched embedded strip waveguides (a) and partially etched rib waveguide (b).

Equations (14)

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t m SC1 = T 0 exp{ [ ( m M+1 2 )δr ] 2 ω 2 (z) },m=1,2,3,M
ω(z)= ω 0 (z) 1+ ( λz n FPR π ω 0 2 ) 2
t m wg exp[ ( j 2πν n eff (ν) c α(ν) )( L 0 +mΔL) ]
t m e ξ m (ν)+j ϕ m (ν)
ξ m (ν)= [ ( m M+1 2 )δr ω(z) ] 2 α(ν)×( L 0 +mΔL),m=1,2,M
ϕ m (ν)= 2πν n eff (ν) c ( L 0 +mΔL),m=1,2,M
E(ν)= E ref exp( j 2πν n eff ref (ν) L ref c )+ E 0 m M e ξ m (ν)+j ϕ m (ν)
I(ν)= I ref + I 0 m,k M e ξ m (ν)+ ξ k (ν) cos[ 2πν n eff (ν) c (mk)ΔL ] +2 I ref I 0 m M e ξ m (ν) cos{ 2πν c [ n eff ref (ν) L ref n eff (ν)( L 0 +mΔL) ] }
( ϕ ref ϕ m ) ν = 2π c [ ( n eff ref (ν)+ν n eff ref (ν) ν ) L ref ( n eff (ν)+ν n eff (ν) ν )( L 0 +mΔL) ] = 2π c [ n g ref (ν) L ref n g (ν)( L 0 +mΔL) ]
I int (ν)= I ref I 0 m M e δ m (ν) cos{ 2πν c [ n g ref (ν) L ref n g (ν)( L 0 +mΔL)] }
F[ I int (ν)]= I int (t)= I ref I 0 m M e ξ m (ν) Δν δ(t± τ m )
τ m = 1 c [ n g ref (ν) Δν L ref n g (ν) Δν ( L 0 +mΔL)]
α tot = σ 2 2 k 0 d 4 n 1 g(V) f e (x,γ)+Δ α h × Γ Si
g( V )= U 2 V 2 1+W f e ( x, γ )= x { [ ( 1+ x 2 ) 2 +2 x 2 γ 2 ] 1 2 +1 x 2 } 1/2 [ ( 1+ x 2 ) 2 +2 x 2 γ 2 ] 1 2 Δ α h =6.0× 10 18 ×Δ N h

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