Abstract

Many advanced optical functions, including spatial mode converters, linear optics quantum computing gates, and arbitrary linear optical processors for communications and other applications could be implemented using meshes of Mach–Zehnder interferometers in technologies such as silicon photonics, but performance is limited by beam splitters that deviate from the ideal 5050 split. We propose a new architecture and a novel self-adjustment approach that automatically compensate for imperfect fabricated split ratios anywhere from 8515 to 1585. The entire mesh can be both optimized and programmed after initial fabrication, with progressive algorithms, without calculations or calibration, and even using only sources and detectors external to the mesh. Hence, one universal field-programmable linear array optical element could be mass fabricated, with broad process tolerances, and then configured automatically for a wide range of complex and precise linear optical functions.

© 2015 Optical Society of America

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References

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  1. D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
    [Crossref]
  2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, J. Lightwave Technol. 30, 521 (2012).
    [Crossref]
  3. S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, and J. Bland-Hawthorn, Opt. Express 22, 1036 (2014).
    [Crossref]
  4. H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, Opt. Lett. 39, 197 (2014).
    [Crossref]
  5. D. A. B. Miller, Opt. Express 21, 20220 (2013).
    [Crossref]
  6. A. Laing and J. L. O’Brien, “Super-stable tomography of any linear optical device,” arXiv:1208.2868 (2012).
  7. S. Rahimi-Keshari, M. A. Broome, R. Fickler, A. Fedrizzi, T. C. Ralph, and A. G. White, Opt. Express 21, 13450 (2013).
    [Crossref]
  8. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
    [Crossref]
  9. J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
    [Crossref]
  10. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
    [Crossref]
  11. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
    [Crossref]
  12. J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).
  13. J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.
  14. H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
    [Crossref]
  15. D. A. B. Miller, J. Opt. Soc. Am. A 30, 238 (2013).
    [Crossref]
  16. D. A. B. Miller, Opt. Express 20, 23985 (2012).
    [Crossref]
  17. D. A. B. Miller, Photon. Res. 1, 1 (2013).
    [Crossref]
  18. D. A. B. Miller, Opt. Express 21, 6360 (2013).
    [Crossref]
  19. D. A. B. Miller, J. Lightwave Technol. 31, 3987 (2013).
    [Crossref]

2014 (2)

2013 (8)

2012 (3)

2009 (1)

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[Crossref]

2007 (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Ahmed, N.

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Birnbaum, K. M.

Bitauld, D.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Bland-Hawthorn, J.

Bolle, C.

Broome, M. A.

Burrows, E. C.

Chen, Z.-B.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

Dolinar, S. J.

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Englund, D.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

Ercan, B.

Erkmen, B. I.

Esmaeelpour, M.

Essiambre, R.-J.

Fedrizzi, A.

Fickler, R.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[Crossref]

Fontaine, N. K.

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[Crossref]

Gnauck, A. H.

Harris, N. C.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

Huang, H.

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Lahini, Y.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

Laing, A.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

A. Laing and J. L. O’Brien, “Super-stable tomography of any linear optical device,” arXiv:1208.2868 (2012).

Lavery, M. P. J.

Leon-Saval, S. G.

Li, H. W.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Lingle, R.

Lu, C.-Y.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

McCurdy, A. H.

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Miller, D. A. B.

Mower, J.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

Mumtaz, S.

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[Crossref]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Niskanen, A. O.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

O’Brien, J. L.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[Crossref]

A. Laing and J. L. O’Brien, “Super-stable tomography of any linear optical device,” arXiv:1208.2868 (2012).

Padgett, M. J.

Pan, J.-W.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

Peckham, D. W.

Politi, A.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Rahimi-Keshari, S.

Ralph, T. C.

S. Rahimi-Keshari, M. A. Broome, R. Fickler, A. Fedrizzi, T. C. Ralph, and A. G. White, Opt. Express 21, 13450 (2013).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Randel, S.

Reck, M.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Ren, Y.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[Crossref]

Rogawski, D.

Ryf, R.

Salazar-Gil, J. R.

Shadbolt, P.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Sierra, A.

Steinbrecher, G. R.

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

Tur, M.

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[Crossref]

Wabnig, J.

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Weinfurter, H.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

White, A. G.

Willner, A. E.

Willner, M. J.

Winzer, P. J.

Xie, G.

Yan, Y.

Yue, Y.

Zeilinger, A.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Zukowski, M.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

Nat. Photonics (2)

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[Crossref]

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[Crossref]

New J. Phys. (1)

H. W. Li, J. Wabnig, D. Bitauld, P. Shadbolt, A. Politi, A. Laing, J. L. O’Brien, and A. O. Niskanen, New J. Phys. 15, 063017 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Photon. Res. (1)

Phys. Rev. Lett. (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[Crossref]

Rev. Mod. Phys. (2)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

Other (3)

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “Towards high-fidelity quantum computation and simulation on a programmable photonic integrated circuit,” arXiv:1406.3255v2 (2014).

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, in Conference on Lasers and Electro-Optics (Optical Society of America, 2014), paper FM2A.3.

A. Laing and J. L. O’Brien, “Super-stable tomography of any linear optical device,” arXiv:1208.2868 (2012).

Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. Arbitrary 3×3 unitary transformer based on MZI blocks Bij as described in Fig. 2, with input (WIi) and output or “channel” (WCj) waveguides. The dashed boxes represent optional “dummy” blocks set to the “bar” (straight-through) state that could be added for greater equality of loss or phase delay. The detectors D1–D3 are optional, depending on whether detectors are included within the blocks.
Fig. 2.
Fig. 2. MZI block configurations. (a) “Top,” “Bottom,” “Left,” and “Right” label waveguides in correspondence with the faces of a conventional cube beam splitter. BSL and BSR are the nominally 5050 beam splitters. The fabricated split ratios of all beam splitters may differ from this ideal split ratio. DR and DB are optional detectors, which will be mostly transparent, sampling a small amount of the power in their respective waveguides to give the signal for the feedback loops used to set up the block’s function. (b) shows those beam splitters themselves implemented with additional MZIs that may also include beam splitters with fabricated split ratios unintentionally different from 5050.
Fig. 3.
Fig. 3. (a) 1PRmax(RL,RR) [or, equivalently, PBmin(RL,RR)]. (b) Convergence of 5050 alignment algorithm. The diagonal lines represent the expressions δRL=δRR and δRL=δRR that correspond to the minimums of 1PRmax(RL,RR) and PRmin(RL,RR), respectively.

Equations (7)

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PR=12+2{δRLδRR[(14δRL2)(14δRR2)]1/2cosθ}.
PRmin=12+2{δRLδRR[(14δRL2)(14δRR2)]1/2}.
PRmax=12+2{δRLδRR+[(14δRL2)(14δRR2)]1/2}.
δRLδRR={[(1/4)δRL2][(1/4)δRR2]}1/2cosθ.
δRL2δRR2[(1/4)δRL2][(1/4)δRR2],
δRL2+δRR21/4.
|δR|1/80.35.

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