Abstract

We present a study of the effect of imperfections on the transmission and crosstalk in programmable photonic meshes with feedback loops consisting of tunable couplers and phase shifters. The many elements in such a mesh can generate a multitude of parasitic paths when the couplers and phase shifters deviate even slightly from their nominal value. Performing Monte Carlo simulations, we show that small stochastic imperfections in the phase and coupling (<1.0%) can introduce unwanted interferences and resonances and significantly deteriorate the frequency response of the circuit. We also demonstrate that, in the presence of imperfections, the programming strategy of the unused couplers can reduce effects of such parasitics.

© 2020 Chinese Laser Press

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References

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  1. L. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
    [Crossref]
  2. L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2, 854–859 (2015).
    [Crossref]
  3. A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port self-configuring universal linear optical component,” in Progress in Electromagnetics Research Symposium (PIERS) (2016), Vol. 3, pp. 3372–3375.
  4. D. A. Miller, “Silicon photonics: meshing optics with applications,” Nat. Photonics 11, 403–404 (2017).
    [Crossref]
  5. A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
    [Crossref]
  6. D. Pérez, I. Gasulla, and J. Capmany, “Toward programmable microwave photonics processors,” J. Lightwave Technol. 36, 519–532 (2018).
    [Crossref]
  7. A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
    [Crossref]
  8. B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
    [Crossref]
  9. D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
    [Crossref]
  10. D. A. B. Miller, “Self-configuring universal linear optical component (Invited),” Photon. Res. 1, 1–15 (2013).
    [Crossref]
  11. J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
    [Crossref]
  12. D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
    [Crossref]
  13. N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
    [Crossref]
  14. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
    [Crossref]
  15. N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
  18. S. Pai, B. Bartlett, O. Solgaard, and D. A. Miller, “Matrix optimization on universal unitary photonic devices,” Phys. Rev. Appl. 11, 064044 (2019).
    [Crossref]
  19. D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24, 12093–12106 (2016).
    [Crossref]
  20. D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
    [Crossref]
  21. D. Pérez, I. Gasulla, and J. Capmany, “Programmable multifunctional integrated nanophotonics,” Nanophotonics 7, 1351–1371 (2018).
    [Crossref]
  22. D. Pérez and J. Capmany, “Scalable analysis for arbitrary photonic integrated waveguide meshes,” Optica 6, 19–27 (2019).
    [Crossref]
  23. A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
    [Crossref]
  24. W. Bogaerts, M. Fiers, M. Sivilotti, and P. Dumon, “The IPKISS photonic design framework,” in Optical Fiber Communications Conference and Exhibition (OFC) (2016), pp. 1–3.
  25. F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
    [Crossref]
  26. D. Oliveira, M. D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, G. Ferrari, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of silicon photonics microring filter array for hitless reconfigurable add–drop,” J. Lightwave Technol. 37, 3939–3947 (2019).
    [Crossref]

2019 (3)

2018 (3)

2017 (5)

D. A. Miller, “Silicon photonics: meshing optics with applications,” Nat. Photonics 11, 403–404 (2017).
[Crossref]

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref]

2016 (3)

2015 (3)

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref]

D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
[Crossref]

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2, 854–859 (2015).
[Crossref]

2014 (1)

F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
[Crossref]

2013 (3)

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
[Crossref]

D. A. B. Miller, “Self-configuring universal linear optical component (Invited),” Photon. Res. 1, 1–15 (2013).
[Crossref]

2011 (2)

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[Crossref]

L. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Aguiar, M. D.

Alsing, P. M.

Annoni, A.

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

Baehr-Jones, T.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

Barbieri, M.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Bartlett, B.

S. Pai, B. Bartlett, O. Solgaard, and D. A. Miller, “Matrix optimization on universal unitary photonic devices,” Phys. Rev. Appl. 11, 064044 (2019).
[Crossref]

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Bienstman, P.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

Bogaerts, W.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

W. Bogaerts, M. Fiers, M. Sivilotti, and P. Dumon, “The IPKISS photonic design framework,” in Optical Fiber Communications Conference and Exhibition (OFC) (2016), pp. 1–3.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port self-configuring universal linear optical component,” in Progress in Electromagnetics Research Symposium (PIERS) (2016), Vol. 3, pp. 3372–3375.

Boller, K.-J.

Bowers, J.

L. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Broome, M. A.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Bunandar, D.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

Cao, W.

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref]

Capmany, J.

D. Pérez and J. Capmany, “Scalable analysis for arbitrary photonic integrated waveguide meshes,” Optica 6, 19–27 (2019).
[Crossref]

D. Pérez, I. Gasulla, and J. Capmany, “Toward programmable microwave photonics processors,” J. Lightwave Technol. 36, 519–532 (2018).
[Crossref]

D. Pérez, I. Gasulla, and J. Capmany, “Programmable multifunctional integrated nanophotonics,” Nanophotonics 7, 1351–1371 (2018).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref]

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24, 12093–12106 (2016).
[Crossref]

Carminati, M.

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
[Crossref]

Carolan, J.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
[Crossref]

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref]

Chen, C.

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

Chen, L.

L. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Clements, W. R.

Crudgington, L.

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref]

De Heyn, P.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

Dumon, P.

W. Bogaerts, M. Fiers, M. Sivilotti, and P. Dumon, “The IPKISS photonic design framework,” in Optical Fiber Communications Conference and Exhibition (OFC) (2016), pp. 1–3.

Englund, D.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

Fanto, M. L.

Ferrari, G.

D. Oliveira, M. D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, G. Ferrari, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of silicon photonics microring filter array for hitless reconfigurable add–drop,” J. Lightwave Technol. 37, 3939–3947 (2019).
[Crossref]

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
[Crossref]

Fiers, M.

W. Bogaerts, M. Fiers, M. Sivilotti, and P. Dumon, “The IPKISS photonic design framework,” in Optical Fiber Communications Conference and Exhibition (OFC) (2016), pp. 1–3.

Fraile, F. J.

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

Gasulla, I.

D. Pérez, I. Gasulla, and J. Capmany, “Programmable multifunctional integrated nanophotonics,” Nanophotonics 7, 1351–1371 (2018).
[Crossref]

D. Pérez, I. Gasulla, and J. Capmany, “Toward programmable microwave photonics processors,” J. Lightwave Technol. 36, 519–532 (2018).
[Crossref]

D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref]

D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24, 12093–12106 (2016).
[Crossref]

Gates, J. C.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Grillanda, S.

F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
[Crossref]

Guglielmi, E.

D. Oliveira, M. D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, G. Ferrari, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of silicon photonics microring filter array for hitless reconfigurable add–drop,” J. Lightwave Technol. 37, 3939–3947 (2019).
[Crossref]

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

Hall, E.

L. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Harris, N. C.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

Harrold, C.

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref]

Hashimoto, T.

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5, 1623–1631 (2018).
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N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
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Humphreys, P. C.

W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walsmley, “Optimal design for universal multiport interferometers,” Optica 3, 1460–1465 (2016).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
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D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
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Kolthammer, W. S.

Kundys, D.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
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D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
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D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
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N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
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Marshall, G. D.

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
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D. Perez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
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W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walsmley, “Optimal design for universal multiport interferometers,” Optica 3, 1460–1465 (2016).
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Miller, D. A.

S. Pai, B. Bartlett, O. Solgaard, and D. A. Miller, “Matrix optimization on universal unitary photonic devices,” Phys. Rev. Appl. 11, 064044 (2019).
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D. A. Miller, “Silicon photonics: meshing optics with applications,” Nat. Photonics 11, 403–404 (2017).
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A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
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Miller, D. A. B.

Morichetti, F.

D. Oliveira, M. D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, G. Ferrari, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of silicon photonics microring filter array for hitless reconfigurable add–drop,” J. Lightwave Technol. 37, 3939–3947 (2019).
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A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
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F. Morichetti, S. Grillanda, M. Carminati, G. Ferrari, M. Sampietro, M. J. Strain, M. Sorel, and A. Melloni, “Non-invasive on-chip light observation by contactless waveguide conductivity monitoring,” IEEE J. Sel. Top. Quantum Electron. 20, 292–301 (2014).
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N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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S. Pai, B. Bartlett, O. Solgaard, and D. A. Miller, “Matrix optimization on universal unitary photonic devices,” Phys. Rev. Appl. 11, 064044 (2019).
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N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
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M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port self-configuring universal linear optical component,” in Progress in Electromagnetics Research Symposium (PIERS) (2016), Vol. 3, pp. 3372–3375.

Roeloffzen, C. G. H.

Rudolph, T.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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D. Oliveira, M. D. Aguiar, M. Milanizadeh, E. Guglielmi, F. Zanetto, G. Ferrari, M. Sampietro, F. Morichetti, and A. Melloni, “Automatic tuning of silicon photonics microring filter array for hitless reconfigurable add–drop,” J. Lightwave Technol. 37, 3939–3947 (2019).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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S. Pai, B. Bartlett, O. Solgaard, and D. A. Miller, “Matrix optimization on universal unitary photonic devices,” Phys. Rev. Appl. 11, 064044 (2019).
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Sorel, M.

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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
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D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X. M. Jin, M. Barbieri, W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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Zhuang, L.

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Figures (9)

Fig. 1.
Fig. 1. (a) Summary of the simulation flow to study effects of parasitics. (b) Schematic representation of the seven-cell hexagonal mesh, where 2×2 couplers are connected to the phase shifters (PSs) through silicon waveguides. (c) For each mesh configuration, couplers are categorized to routing couplers (involved in defining light paths) and unused couplers (their state, in principle, does not affect the light paths). Orange and gray colors show cross and bar states of the routing couplers; unused couplers are shown only by the blue. Note that, in normal bar bias (NB bias), unused couplers are programmed in the bar state, while, in normal cross bias (NC bias), they are programmed in the cross state.
Fig. 2.
Fig. 2. (a) Schematic of a routed path (with Lpath=10Lu) within a seven-cell mesh. (b) Transmission spectra of the mesh for two types of biasing: normal bar (NB), where unused couplers are biased in the bar state (red curves), and normal cross (NC), where unused couplers are biased in the cross state (green curves). The results are plotted for σk=0.05%, 0.4%, and 1.0% from left to right. (c) Intensity spread analysis of the transmission in the output for random variations of σk=0.05%, 0.4%, and 1.0%. Red and green error bars correspond to the NB and NC biases.
Fig. 3.
Fig. 3. Intensity spread analysis of different configurations of the seven-cell mesh to study both simple and complex paths. Blue couplers are in the bar (cross) state for the NB (NC) bias. Random variations of σk=0.05%, 0.4%, and 1.0% are chosen for the Monte Carlo simulations. Red and green error bars correspond to the NB and NC bias, respectively.
Fig. 4.
Fig. 4. Intensity spread analysis of the (a) transmission and (b) crosstalk of double- and multipaths. Similar to the Fig. 2(c), error bars are plotted for σk=0.05%, 0.4%, and 1.0%.
Fig. 5.
Fig. 5. (a) Schematic of the three different configured MZIs in the seven-cell hexagonal mesh (A: ΔL=6Lu, B: ΔL=4Lu, C: ΔL=10Lu). (b) Transmission response of the MZIs for NB (red) and NC (green) biases, where only 10 cycles of the Monte Carlo simulations have been plotted for better visibility. (c) Correlation-based analysis of the configured MZIs for (σk, σϕ) pairs of (0.05%, 17°), (1.0%, 17°), and (1.0%, 2°).
Fig. 6.
Fig. 6. (a) Schematic of three different configured ring resonators in the seven-cell hexagonal mesh. (b) Transmission response of the selected configurations for NB (red) and NC (green) biases, where 10 cycles of the Monte Carlo simulations have been used. (c) Correlation-based analysis of the configured ring resonators for (σk, σϕ) pairs of (0.05%, 17°), (1.0%, 17°), and (1.0%, 2°).
Fig. 7.
Fig. 7. Intensity spread analysis of a 1×4 splitter in the seven-cell hexagonal mesh. Red and green bars show NB and NC biases, respectively. Similar to Fig. 2(c), error bars are plotted for σk=0.05%, 0.4%, and 1.0%. For NC bias, blue couplers are in the cross state (k=1), while they are in the bar state (k=0) for NB bias.
Fig. 8.
Fig. 8. Intensity spread analysis of a 1×16 splitter in a seven-cell hexagonal mesh. Red and green bars also show NB and NC biases, respectively. Similar to Fig. 2(c), error bars are plotted for σk=0.05%, 0.4%, and 1.0%. For NC bias, blue couplers are in the cross state (k=1), while they are in the bar state (k=0) for the NB bias.
Fig. 9.
Fig. 9. Transmission spread analysis of a single path (with ΔL=8Lu) for different biasing schemes with σk=0.05%, 0.4%, and 1.0%.

Equations (4)

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min=min{min[T(λ)]5,,min[T(λ)]95},
mean=mean{mean[T(λ)]5,,mean[T(λ)]95},
max=max{max[T(λ)]5,,max[T(λ)]95}.
Corr˜(S,R)2=Corr(S,R)2Corr(S,S)2|MAX·Corr(R,R)2|MAX.