Abstract

Many interesting linear optical networks, such as lattice filters and some interferometer meshes, are difficult to fabricate precisely and cannot be configured progressively even using recent algorithms. Our approach allows a broad category of optical networks to be set up progressively and automatically, including correcting for fabrication imprecision. We null interference locally in the network based on inputs calculated by considering the network operated in reverse. Calibration is only required for the network inputs, not for individual components (though this method can also calibrate those). We illustrate specific cases of lattice filters and rectangular meshes of interferometers, and we expect the approach can be applied broadly to networks in which the light only propagates forward in the network.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Perfect optics with imperfect components

David A. B. Miller
Optica 2(8) 747-750 (2015)

Design of optical neural networks with component imprecisions

Michael Y.-S. Fang, Sasikanth Manipatruni, Casimir Wierzynski, Amir Khosrowshahi, and Michael R. DeWeese
Opt. Express 27(10) 14009-14029 (2019)

Tapless and topology agnostic calibration solution for silicon photonic switches

Alexander Gazman, Evgeny Manzhosov, Colm Browning, Meisam Bahadori, Yanir London, Liam Barry, and Keren Bergman
Opt. Express 26(25) 32662-32674 (2018)

References

  • View by:
  • |
  • |
  • |

  1. D. A. B. Miller, “Sorting out light,” Science 347(6229), 1423–1424 (2015).
    [PubMed]
  2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
  3. P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8, 345–348 (2014).
  4. A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. B. Miller, A. Melloni, and F. Morichetti, “Unscrambling light – automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
  5. Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).
  6. 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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
    [PubMed]
  7. J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).
  8. N. M. Estakhri, B. E. Edwards, and N. Engheta, “Solving Integral Equations with Optical Metamaterial-Waveguide Networks,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017).
  9. N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).
  10. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).
  11. J. M. Wyrwas and M. C. Wu, “Dynamic Range of Frequency Modulated Direct-Detection Analog Fiber Optic Links,” J. Lightwave Technol. 27, 5552–5562 (2009).
  12. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
  13. 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).
  14. D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24(11), 12093–12106 (2016).
    [PubMed]
  15. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006).
    [PubMed]
  16. D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21(5), 6360–6370 (2013).
    [PubMed]
  17. D. A. B. Miller, “Self-configuring universal linear optical component,” Photon. Res. 1, 1–15 (2013).
  18. D. A. B. Miller, “Establishing optimal wave communication channels automatically,” J. Lightwave Technol. 31, 3987–3994 (2013).
  19. D. A. B. Miller, “Reconfigurable add-drop multiplexer for spatial modes,” Opt. Express 21(17), 20220–20229 (2013).
    [PubMed]
  20. D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
  21. A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4×4-port universal linear circuit,” Optica 3, 1348–1357 (2016).
  22. C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016).
    [PubMed]
  23. D. A. B. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. U.S.A. 114(17), 4336–4341 (2017).
    [PubMed]
  24. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
    [PubMed]
  25. W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walmsley, “Optimal design for universal multiport interferometers,” Optica 3, 1460–1465 (2016).
  26. S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

2017 (4)

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

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

D. A. B. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. U.S.A. 114(17), 4336–4341 (2017).
[PubMed]

2016 (4)

2015 (6)

S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

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

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).

D. A. B. Miller, “Sorting out light,” Science 347(6229), 1423–1424 (2015).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

2014 (1)

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8, 345–348 (2014).

2013 (6)

2009 (1)

2006 (1)

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Annoni, A.

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

S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

Baehr-Jones, T.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Bogaerts, W.

Boller, K.-J.

Bunandar, D.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Capmany, J.

D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24(11), 12093–12106 (2016).
[PubMed]

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Carminati, M.

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

S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

Carolan, J.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Chen, C.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Ciccarella, P.

Clements, W. R.

Englund, D.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

Fan, S.

D. A. B. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. U.S.A. 114(17), 4336–4341 (2017).
[PubMed]

Ferrari, G.

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

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

Gasulla, I.

Grillanda, S.

Guglielmi, E.

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

Harris, N. C.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Heideman, R.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Hochberg, M.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Hoekman, M.

Humphreys, P. C.

Itoh, M.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Kolthammer, W. S.

Lahini, Y.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

Laing, A.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Larochelle, H.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Leinse, A.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Lloyd, S.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Lowery, A. J.

Marpaung, D.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Marshall, G. D.

C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Martín-López, E.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Matsuda, N.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Matthews, J. C. F.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Melloni, A.

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

S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

Metcalf, B. J.

Miller, D. A. B.

Morichetti, F.

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

S. Grillanda, F. Morichetti, N. Peserico, P. Ciccarella, A. Annoni, M. Carminati, and A. Melloni, “Non-Invasive Monitoring of Mode-Division Multiplexed Channels on a Silicon Photonic Chip,” J. Lightwave Technol. 33, 1197–1201 (2015).

Mower, J.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

O’Brien, J. L.

C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Oguma, M.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Paesani, S.

Pérez, D.

Peserico, N.

Prabhu, M.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Qiang, X.

Reck, M.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Ribeiro, A.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Roeloffzen, C. G. H.

Ruocco, A.

Russell, N. J.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Sampietro, M.

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

Santagati, R.

Shadbolt, P. J.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Shay, T. M.

Shen, Y.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Silverstone, J. W.

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Skirlo, S.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Soljacic, M.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Soref, R. A.

Sparrow, 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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Steinbrecher, G. R.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

Sun, X.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Thompson, M. G.

C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Vanacker, L.

Walmsley, I. A.

Wang, J.

Wilkes, C. M.

Winzer, P. J.

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8, 345–348 (2014).

Wong, F. N. C.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Wu, M. C.

Wyrwas, J. M.

Zeilinger, A.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Zhao, S.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

Zhou, X.

Zhu, L.

D. A. B. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. U.S.A. 114(17), 4336–4341 (2017).
[PubMed]

Zhuang, L.

J. Lightwave Technol. (3)

Laser Photonics Rev. (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).

Light Sci. Appl. (1)

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

Nat. Photonics (4)

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep Learning with Coherent Nanophotonic Circuits,” Nat. Photonics 11, 441–446 (2017).

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8, 345–348 (2014).

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, D. Bunandar, C. Chen, F. N. C. 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).

Opt. Express (4)

Opt. Lett. (1)

Optica (4)

Photon. Res. (1)

Phys. Rev. A (1)

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92, 032322 (2015).

Phys. Rev. Lett. (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental Realization of Any Discrete Unitary Operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
[PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

D. A. B. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. U.S.A. 114(17), 4336–4341 (2017).
[PubMed]

Science (2)

D. A. B. Miller, “Sorting out light,” Science 347(6229), 1423–1424 (2015).
[PubMed]

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. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349(6249), 711–716 (2015).
[PubMed]

Other (2)

N. M. Estakhri, B. E. Edwards, and N. Engheta, “Solving Integral Equations with Optical Metamaterial-Waveguide Networks,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 A waveguide Mach-Zehnder interferometer block (inside dashed line), showing phase shifters ϕ in the “Top” input arm and θ in the upper interferometer branch, beamsplitters BSL and BSR, and “mostly-transparent” detectors DR and DB. The labelling of the ports as “Top”, “Left”, “Right” and “Bottom” corresponds with ports on a simple cube beamsplitter. The “backward” vectors, indicated with dashed arrows, are only calculated beams from a hypothetical specific backwards input.
Fig. 2
Fig. 2 Lattice filter of K two-beam interferometers, shown as blocks, each with split ratio and relative phase parameters θj and ϕj, respectively, and with time delays τ between the blocks.
Fig. 3
Fig. 3 An example two-dimensional mesh that can implement an arbitrary unitary transform between inputs and outputs according to the scheme of Ref [25], shown here for five inputs and outputs. Individual blocks correspond to the MZI block of Fig. 1, and they are indexed here according to their block “row” i and block “column” j, as in the parameters θij and ϕij, and the resulting matrix D ij .
Fig. 4
Fig. 4 An OSM for configuring an MZI mesh, using a chain of MZIs (MZ1 to MZ5), for the example of a mesh with 5 inputs. Each MZI has phase shifters on both the upper (θUj) and lower (θLj) arms. A set of 5 mostly-transparent detectors is placed either on the “lower” output arms (shown as D1 to D5), or, alternatively, on the “upper” output arms (shown as D1 ' to D5 ' ). Phase shifters ϕM1 to ϕM5 are provided for each of the input guides. The first phase shifters inside the mesh that is to be configured, here ϕ11 to ϕ22, are also shown. The output waveguides, MO1 to MO5, form the input waveguides for the mesh to be configured. During the first parts of the process to calibrate the mesh with an external light source, power P C is shone into the bottom waveguide MC, but no power is shone into the guides MI1 to MI5. During actual use of the mesh to perform its desired operation, all the MZIs are set to their “cross” state, and the input light of interest is shone into input waveguides MI1 to MI5. The set of phase shifters ϕM1 to ϕM5 are provided for phase equalization or compensation of the inputs, and these are set in a final part of the calibration procedure.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

| ψ F w d I n [ E T E L ] , | ψ F w d O u t [ E R E B ]
D M Z I = i exp ( i θ 2 ) [ exp ( i ϕ ) sin ( θ / 2 ) cos ( θ / 2 ) exp ( i ϕ ) cos ( θ / 2 ) sin ( θ / 2 ) ]
| ψ F w d O u t [ E R E B ] = D M Z I [ E T E L ] D M Z I | ψ F w d I n
| ψ B w d O u t = B | ψ B w d I n
| ψ B w d O u t = ( D ) | ψ B w d I n
| ψ F w d O u t P C = D | ψ F w d I n P C = D | ψ B w d O u t = D [ ( D ) | ψ B w d I n ] = D D | ψ B w d I n = | ψ B w d I n
[ X i n B w d 1 Y i n B w d 1 ] = ( D 1 ) [ 1 0 ]
[ X i n 1 Y i n 1 ] = [ X i n B w d 1 Y i n B w d 1 ]
[ X i n 1 Y i n 1 ] = D 1 [ 1 0 ]
[ X i n B w d 2 Y i n B w d 2 ] = ( D 1 ) ( D 2 ) [ 1 0 ]
[ X i n 2 Y i n 2 ] = [ X i n B w d 2 Y i n B w d 2 ] = D 1 D 2 [ 1 0 ]
[ X i n p Y i n p ] = D 1 D 2 D p [ 1 0 ]
| ψ F w d I n = | ψ B w d O u t * [ E 1 T E 1 B E 2 T E 2 B E 3 T ] T
| ψ B w d O u t = C 1 [ 1 0 0 0 0 ]
| ψ B w d O u t = C 1 [ 0 0 1 0 0 ]
| ψ B w d O u t = C 1 C 2 [ 0 1 0 0 0 ]
| ψ B w d O u t = C 1 C 2 [ 0 0 0 1 0 ]
| ψ B w d O u t = C 1 C 2 C 3 [ 1 0 0 0 0 ] and | ψ B w d O u t = C 1 C 2 C 3 [ 0 0 1 0 0 ]
| ψ B w d O u t = C 1 C 2 C 3 C 4 [ 0 1 0 0 0 ] and | ψ B w d O u t = C 1 C 2 C 3 C 4 [ 0 0 0 1 0 ]
| ψ B w d O u t = C 1 C 2 C 3 C 4 C 5 [ 1 0 0 0 0 ] and | ψ B w d O u t = C 1 C 2 C 3 C 4 C 5 [ 0 0 1 0 0 ]

Metrics