Abstract

A 4 × 4 reconfigurable Mach–Zehnder interferometer (MZI)-based linear optical processor is investigated through its theoretical analyses and characterized experimentally. The linear transformation matrix of the structure is theoretically determined using its building block, which is a 2 × 2 reconfigurable MZI. To program the device, the linear transformation matrix of a given application is decomposed into that of the constituent MZIs of the structure. Thus, the required phase shifts for implementing the transformation matrix of the application by means of the optical processor are determined theoretically. Due to random phase offsets in the MZIs resulting from fabrication process variations, they are initially configured through an experimental protocol. The presented calibration scheme allows to straightforwardly characterize the MZIs to mitigate the possible input phase errors and determine the bar and cross states of each MZI for tuning it at the required sate before programming the device. After the configuration process, the device can be programmed to construct the linear transformation matrix of the application. In this regard, using the required bias voltages, the phase shifts obtained from the decomposition process are applied to the phase shifters of the MZIs in the device.

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  1. D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.
  2. D. A. Miller, “Self-aligning universal beam coupler,” Opt. Express, vol. 21, no. 5, pp. 6360–6370, 2013.
  3. Y. Shen, “Deep learning with coherent nanophotonic circuits,” Nature Photon., vol. 11, no. 7, pp. 441–446, 2017.
  4. , “A single layer neural network implemented by a $4\times 4$ MZI-based optical processor,” IEEE Photonics J., vol. 11, no. 6, pp. 1–12, Dec. 2019.
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  6. D. A. Miller, “Self-configuring universal linear optical component,” Photon. Res., vol. 1, no. 1, pp. 1–15, 2013.
  7. D. A. Miller, “Establishing optimal wave communication channels automatically,” J. Lightw. Technol., vol. 31, no. 24, pp. 3987–3994, 2013.
  8. R. Burgwal, “Using an imperfect photonic network to implement random unitaries,” Opt. Express, vol. 25, no. 23, pp. 28 236–28 245, 2017.
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  12. L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems. Cambridge, UK: Cambridge Univ. Press, 2015.
  13. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis. New York, NY, USA: Wiley, 1999.
  14. G. P. Agrawal, Lightwave Technology: Components and Devices. NJ, USA: Wiley, 2004.

2019 (1)

, “A single layer neural network implemented by a $4\times 4$ MZI-based optical processor,” IEEE Photonics J., vol. 11, no. 6, pp. 1–12, Dec. 2019.

2018 (1)

D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.

2017 (3)

R. Burgwal, “Using an imperfect photonic network to implement random unitaries,” Opt. Express, vol. 25, no. 23, pp. 28 236–28 245, 2017.

N. C. Harris, “Quantum transport simulations in a programmable nanophotonic processor,” Nature Photon., vol. 11, no. 7, pp. 447–452, 2017.

Y. Shen, “Deep learning with coherent nanophotonic circuits,” Nature Photon., vol. 11, no. 7, pp. 441–446, 2017.

2013 (3)

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Agrawal, G. P.

G. P. Agrawal, Lightwave Technology: Components and Devices. NJ, USA: Wiley, 2004.

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Burgwal, R.

R. Burgwal, “Using an imperfect photonic network to implement random unitaries,” Opt. Express, vol. 25, no. 23, pp. 28 236–28 245, 2017.

Capmany, J.

D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.

Chrostowski, L.

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems. Cambridge, UK: Cambridge Univ. Press, 2015.

Gomariz, E. S.

D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.

Harris, N. C.

N. C. Harris, “Quantum transport simulations in a programmable nanophotonic processor,” Nature Photon., vol. 11, no. 7, pp. 447–452, 2017.

Hochberg, M.

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems. Cambridge, UK: Cambridge Univ. Press, 2015.

Le Gall, F.

F. Le Gall, “Powers of tensors and fast matrix multiplication,” in Proc. 39th Int. Symp. Symbolic Algebr. Comput., Waikoloa, HI, USA: ACM, 2014, pp. 296–303.

Liboiron-Ladouceur, O.

R. B. Priti, Y. Xiong, and O. Liboiron-Ladouceur, “Efficiency improvement of an O-band SOI-MZI thermo-optic matrix switch,” in Proc. IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 823–824.

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis. New York, NY, USA: Wiley, 1999.

Miller, D. A.

Perez, D.

D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.

Priti, R. B.

R. B. Priti, Y. Xiong, and O. Liboiron-Ladouceur, “Efficiency improvement of an O-band SOI-MZI thermo-optic matrix switch,” in Proc. IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 823–824.

Reck, M.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Shen, Y.

Y. Shen, “Deep learning with coherent nanophotonic circuits,” Nature Photon., vol. 11, no. 7, pp. 441–446, 2017.

Xiong, Y.

R. B. Priti, Y. Xiong, and O. Liboiron-Ladouceur, “Efficiency improvement of an O-band SOI-MZI thermo-optic matrix switch,” in Proc. IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 823–824.

Zeilinger, A.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis. New York, NY, USA: Wiley, 1999.

IEEE Photonics J. (1)

, “A single layer neural network implemented by a $4\times 4$ MZI-based optical processor,” IEEE Photonics J., vol. 11, no. 6, pp. 1–12, Dec. 2019.

J. Lightw. Technol. (2)

D. Perez, E. S. Gomariz, and J. Capmany, “Programmable true-time delay lines using integrated waveguide meshes,” J. Lightw. Technol., vol. 36, no. 19, pp. 4591–4601, 2018.

D. A. Miller, “Establishing optimal wave communication channels automatically,” J. Lightw. Technol., vol. 31, no. 24, pp. 3987–3994, 2013.

Nature Photon. (2)

Y. Shen, “Deep learning with coherent nanophotonic circuits,” Nature Photon., vol. 11, no. 7, pp. 441–446, 2017.

N. C. Harris, “Quantum transport simulations in a programmable nanophotonic processor,” Nature Photon., vol. 11, no. 7, pp. 447–452, 2017.

Opt. Express (2)

R. Burgwal, “Using an imperfect photonic network to implement random unitaries,” Opt. Express, vol. 25, no. 23, pp. 28 236–28 245, 2017.

D. A. Miller, “Self-aligning universal beam coupler,” Opt. Express, vol. 21, no. 5, pp. 6360–6370, 2013.

Photon. Res. (1)

Phys. Rev. Lett. (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett., Kobe, Japan, vol. 73, 1994, pp. 58–61. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.73.58

Other (5)

F. Le Gall, “Powers of tensors and fast matrix multiplication,” in Proc. 39th Int. Symp. Symbolic Algebr. Comput., Waikoloa, HI, USA: ACM, 2014, pp. 296–303.

R. B. Priti, Y. Xiong, and O. Liboiron-Ladouceur, “Efficiency improvement of an O-band SOI-MZI thermo-optic matrix switch,” in Proc. IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 823–824.

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems. Cambridge, UK: Cambridge Univ. Press, 2015.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis. New York, NY, USA: Wiley, 1999.

G. P. Agrawal, Lightwave Technology: Components and Devices. NJ, USA: Wiley, 2004.

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