Abstract

We propose short and robust directional couplers designed by shortcuts to adiabaticity, based on Lewis-Riesenfeld invariant theory. The design of directional couplers is discussed by combining invariant-based inverse engineering and perturbation theory. The error sensitivity of the coupler is minimized by optimizing the evolution of dynamical invariant with respect to coupling coefficient/input wavelength variations. The proposed robust coupler devices are verified with beam propagation simulations.

© 2014 Optical Society of America

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  1. A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightwave Technol. 16, 1907–1914 (1998).
    [CrossRef]
  2. T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightwave Technol. 16, 277–283 (1998).
    [CrossRef]
  3. X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34, 280–282 (2009).
    [CrossRef] [PubMed]
  4. R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett. 4, 1135–1138 (1992).
    [CrossRef]
  5. G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
    [CrossRef]
  6. S.-Y. Tseng, “Counterdiabatic mode-evolution based coupled-waveguide devices,” Opt. Express 21, 21224–21235 (2013).
    [CrossRef] [PubMed]
  7. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev. 3, 243–261 (2009).
    [CrossRef]
  8. E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
    [CrossRef]
  9. T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, “Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides,” Opt. Express 20, 24085–24092 (2012).
    [CrossRef] [PubMed]
  10. S.-Y. Tseng and X. Chen, “Engineering of fast mode conversion in multimode waveguides,” Opt. Lett. 37, 5118–5120 (2012).
    [CrossRef] [PubMed]
  11. S. Martínez-Garaot, S.-Y. Tseng, and J. G. Muga, “Compact and high conversion efficiency mode-sorting asymmetric Y junction using shortcuts to adiabaticity,” Opt. Lett. 39, 2306 (2014).
    [CrossRef] [PubMed]
  12. X. Chen and J. G. Muga, “Engineering of fast population transfer in three-level systems,” Phys. Rev. A 86, 033405 (2012).
    [CrossRef]
  13. S.-Y. Tseng and Y.-W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photon. Technol. Lett. 25, 2478–2481 (2013).
    [CrossRef]
  14. A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
    [CrossRef]
  15. D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
    [CrossRef] [PubMed]
  16. X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
    [CrossRef]
  17. X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
    [CrossRef]
  18. H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458–1473 (1969).
    [CrossRef]
  19. C.-L. Chen, Foundations for Guided-Wave Optics (Wiley, 2007).
  20. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).
  21. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).
  22. D. R. Rowland, Y. Chen, and A. W. Snyder, “Tapered mismatched couplers,” J. Lightwave Technol. 9, 567–570 (1991).
    [CrossRef]

2014 (1)

2013 (5)

S.-Y. Tseng, “Counterdiabatic mode-evolution based coupled-waveguide devices,” Opt. Express 21, 21224–21235 (2013).
[CrossRef] [PubMed]

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

S.-Y. Tseng and Y.-W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photon. Technol. Lett. 25, 2478–2481 (2013).
[CrossRef]

2012 (4)

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, “Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides,” Opt. Express 20, 24085–24092 (2012).
[CrossRef] [PubMed]

S.-Y. Tseng and X. Chen, “Engineering of fast mode conversion in multimode waveguides,” Opt. Lett. 37, 5118–5120 (2012).
[CrossRef] [PubMed]

X. Chen and J. G. Muga, “Engineering of fast population transfer in three-level systems,” Phys. Rev. A 86, 033405 (2012).
[CrossRef]

2011 (1)

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[CrossRef]

2009 (2)

2004 (1)

G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
[CrossRef]

1998 (2)

1992 (1)

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett. 4, 1135–1138 (1992).
[CrossRef]

1991 (1)

D. R. Rowland, Y. Chen, and A. W. Snyder, “Tapered mismatched couplers,” J. Lightwave Technol. 9, 567–570 (1991).
[CrossRef]

1969 (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458–1473 (1969).
[CrossRef]

Al-Bader, S.

Alonso, D.

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

Chen, C.-L.

C.-L. Chen, Foundations for Guided-Wave Optics (Wiley, 2007).

Chen, X.

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

S.-Y. Tseng and X. Chen, “Engineering of fast mode conversion in multimode waveguides,” Opt. Lett. 37, 5118–5120 (2012).
[CrossRef] [PubMed]

X. Chen and J. G. Muga, “Engineering of fast population transfer in three-level systems,” Phys. Rev. A 86, 033405 (2012).
[CrossRef]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[CrossRef]

Chen, Y.

D. R. Rowland, Y. Chen, and A. W. Snyder, “Tapered mismatched couplers,” J. Lightwave Technol. 9, 567–570 (1991).
[CrossRef]

Daems, D.

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

del Campo, A.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

Eyal, A.

G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
[CrossRef]

Guérin, S.

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

Guéry-Odelin, D.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

Hsiao, F.-C.

Hu, C.

Ibáñez, S.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

Jhang, Y.-W.

Kawano, K.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).

Kitoh, T.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).

Lewis, H. R.

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458–1473 (1969).
[CrossRef]

Lin, T.-Y.

Liu, H.-C.

Longhi, S.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Lu, X.-J.

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

Martínez-Garaot, S.

S. Martínez-Garaot, S.-Y. Tseng, and J. G. Muga, “Compact and high conversion efficiency mode-sorting asymmetric Y junction using shortcuts to adiabaticity,” Opt. Lett. 39, 2306 (2014).
[CrossRef] [PubMed]

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

Modugno, M.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

Muga, J. G.

S. Martínez-Garaot, S.-Y. Tseng, and J. G. Muga, “Compact and high conversion efficiency mode-sorting asymmetric Y junction using shortcuts to adiabaticity,” Opt. Lett. 39, 2306 (2014).
[CrossRef] [PubMed]

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

X. Chen and J. G. Muga, “Engineering of fast population transfer in three-level systems,” Phys. Rev. A 86, 033405 (2012).
[CrossRef]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).

Osgood, R. M.

Paloczi, G. T.

G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
[CrossRef]

Ramadan, T. A.

Riesenfeld, W. B.

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458–1473 (1969).
[CrossRef]

Rowland, D. R.

D. R. Rowland, Y. Chen, and A. W. Snyder, “Tapered mismatched couplers,” J. Lightwave Technol. 9, 567–570 (1991).
[CrossRef]

Ruschhaupt, A.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

Scarmozzino, R.

Schneider, V. M.

Snyder, A. W.

D. R. Rowland, Y. Chen, and A. W. Snyder, “Tapered mismatched couplers,” J. Lightwave Technol. 9, 567–570 (1991).
[CrossRef]

Sugny, D.

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

Sun, X.

Syahriar, A.

Syms, R. R. A.

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett. 4, 1135–1138 (1992).
[CrossRef]

Torrontegui, E.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[CrossRef]

Tseng, S.-Y.

Yariv, A.

X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34, 280–282 (2009).
[CrossRef] [PubMed]

G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
[CrossRef]

Adv. At. Mol. Opt. Phys. (1)

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. At. Mol. Opt. Phys. 62, 117–169 (2013).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett. 4, 1135–1138 (1992).
[CrossRef]

G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photon. Technol. Lett. 16, 515–517 (2004).
[CrossRef]

S.-Y. Tseng and Y.-W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photon. Technol. Lett. 25, 2478–2481 (2013).
[CrossRef]

J. Lightwave Technol. (3)

J. Math. Phys. (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458–1473 (1969).
[CrossRef]

Laser and Photon. Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev. 3, 243–261 (2009).
[CrossRef]

New J. Phys. (1)

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (3)

X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. G. Muga, “Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors,” Phys. Rev. A 88, 033406 (2013).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[CrossRef]

X. Chen and J. G. Muga, “Engineering of fast population transfer in three-level systems,” Phys. Rev. A 86, 033405 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[CrossRef] [PubMed]

Other (3)

C.-L. Chen, Foundations for Guided-Wave Optics (Wiley, 2007).

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).

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