Abstract

In this paper, we propose the use of the invariant based shortcuts to adiabaticity for the analysis of directional couplers. By describing the dynamical evolution of the system using the eigenstates of the invariant through new parameterizations, the system stability against errors in coupling coefficient and propagation constants mismatch is connected with the new parameters, which can be linked back to system parameters through inverse engineering. The merits and limitations of the conventional tapered directional coupler designs with various window functions are obtained through the analysis. We then propose an optimal design of compact directional couplers that is stable against errors in input wavelength and coupling coefficient simultaneously. The designed directional coupler has better tolerance, as compared to the conventional resonant couplers with smooth shape functions of Hamming and Blackman. These results are verified by beam propagation simulations.

© 2016 Optical Society of America

Full Article  |  PDF Article
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    [Crossref]
  3. R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photonics Technol. Lett. 4, 1135–1138 (1992).
    [Crossref]
  4. G. T. Paloczi, A. Eyal, and A. Yariv, “Wavelength-insensitive nonadiabatic mode evolution couplers,” IEEE Photonics Technol. Lett. 16, 515–517 (2004).
    [Crossref]
  5. 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]
  6. A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
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    [Crossref]
  8. R. C. Alferness and P. S. Cross, “Filter characteristics of codirectional coupled waveguides with weighted coupling,” IEEE. J. Quantum Electron. 14, 843–847 (1978).
    [Crossref]
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    [Crossref]
  10. 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]
  11. 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]
  12. S.-Y. Tseng and X. Chen, “Engineering of fast mode conversion in multimode waveguides,” Opt. Lett. 37, 5118–5120 (2012).
    [Crossref] [PubMed]
  13. S.-Y. Tseng, “Counterdiabatic mode-evolution based coupled-waveguide devices,” Opt. Express 21, 21224–21235 (2013).
    [Crossref] [PubMed]
  14. 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]
  15. S.-Y. Tseng, R.-D. Wen, Y.-F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22, 18849–18859 (2014).
    [Crossref] [PubMed]
  16. S.-Y. Tseng, “Robust coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 39, 6600–6603 (2014).
    [Crossref] [PubMed]
  17. 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, 2306–2309 (2014).
    [Crossref] [PubMed]
  18. X. Chen, H.-W. Wang, Y. Ban, and S.-Y. Tseng, “Short-length and robust polarization rotators in periodically poled lithium niobate via shortcuts to adiabaticity,” Opt. Express 22, 24169–24178 (2014).
    [Crossref] [PubMed]
  19. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
    [Crossref] [PubMed]
  20. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
    [Crossref] [PubMed]
  21. X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
    [Crossref]
  22. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
    [Crossref]
  23. 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]
  24. 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]
  25. 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]
  26. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).
  27. 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]
  28. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (John Wiley and Sons, 2001).
    [Crossref]
  29. T.-H. Pan and S.-Y. Tseng, “Short and robust silicon mode (de)multiplexers using shortcuts to adiabaticity,” Opt. Express 23, 10405–10412 (2015).
    [Crossref] [PubMed]

2015 (1)

2014 (4)

2013 (5)

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

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]

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]

2012 (3)

2011 (1)

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

2010 (2)

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

2009 (2)

2004 (1)

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

1998 (2)

1997 (1)

B. E. Little, “Filter synthesis for coupled waveguides,” J. Lightwave Technol. 15, 1149–1155 (1997).
[Crossref]

1992 (1)

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

1979 (1)

R. C. Alferness, “Optical directional couplers with weighted coupling,” Appl. Phys. Lett. 35, 260–262 (1979).
[Crossref]

1978 (1)

R. C. Alferness and P. S. Cross, “Filter characteristics of codirectional coupled waveguides with weighted coupling,” IEEE. J. Quantum Electron. 14, 843–847 (1978).
[Crossref]

1973 (1)

A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[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.

Alferness, R. C.

R. C. Alferness, “Optical directional couplers with weighted coupling,” Appl. Phys. Lett. 35, 260–262 (1979).
[Crossref]

R. C. Alferness and P. S. Cross, “Filter characteristics of codirectional coupled waveguides with weighted coupling,” IEEE. J. Quantum Electron. 14, 843–847 (1978).
[Crossref]

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]

Ban, Y.

Chen, X.

X. Chen, H.-W. Wang, Y. Ban, and S.-Y. Tseng, “Short-length and robust polarization rotators in periodically poled lithium niobate via shortcuts to adiabaticity,” Opt. Express 22, 24169–24178 (2014).
[Crossref] [PubMed]

S.-Y. Tseng, R.-D. Wen, Y.-F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22, 18849–18859 (2014).
[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]

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]

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]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

Chiu, Y.-F.

Cross, P. S.

R. C. Alferness and P. S. Cross, “Filter characteristics of codirectional coupled waveguides with weighted coupling,” IEEE. J. Quantum Electron. 14, 843–847 (1978).
[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]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

Eyal, A.

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

Guérin, S.

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]

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]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

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 (John Wiley and Sons, 2001).
[Crossref]

Kitoh, T.

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

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.

Little, B. E.

B. E. Little, “Filter synthesis for coupled waveguides,” J. Lightwave Technol. 15, 1149–1155 (1997).
[Crossref]

Liu, H.-C.

Lizuain, I.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics 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, 2306–2309 (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, 2306–2309 (2014).
[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]

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]

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]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 16, 515–517 (2004).
[Crossref]

Pan, T.-H.

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]

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]

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]

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, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

Scarmozzino, R.

Schmidt, S.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

Schneider, V. M.

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 Photonics 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.

T.-H. Pan and S.-Y. Tseng, “Short and robust silicon mode (de)multiplexers using shortcuts to adiabaticity,” Opt. Express 23, 10405–10412 (2015).
[Crossref] [PubMed]

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, 2306–2309 (2014).
[Crossref] [PubMed]

S.-Y. Tseng, “Robust coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 39, 6600–6603 (2014).
[Crossref] [PubMed]

X. Chen, H.-W. Wang, Y. Ban, and S.-Y. Tseng, “Short-length and robust polarization rotators in periodically poled lithium niobate via shortcuts to adiabaticity,” Opt. Express 22, 24169–24178 (2014).
[Crossref] [PubMed]

S.-Y. Tseng, R.-D. Wen, Y.-F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22, 18849–18859 (2014).
[Crossref] [PubMed]

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

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]

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]

Wang, H.-W.

Wen, R.-D.

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 Photonics Technol. Lett. 16, 515–517 (2004).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Schematic of the directional coupler under consideration.
Fig. 2
Fig. 2 Parameters for directional coupler design, including waveguide width WL,R and separation D, for (a) resonant protocols and (b) optimal protocol.
Fig. 3
Fig. 3 BPM simulations for three resonant couplers (with (a) linear, (b) Hamming, and (c) Blackman functions) and (d) optimal coupler. White lines denote the waveguide cores.
Fig. 4
Fig. 4 Coupling efficiency versus (a) input wavelength, (b) spacing, and (c) waveguide width errors.

Tables (1)

Tables Icon

Table 1 The parameters c1 and c2 for optimization.

Equations (18)

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i d d z [ A + A ] = 2 [ Δ Ω Ω Δ ] [ A + A ] ,
| ψ 0 ( z ) = e i γ / 2 ( cos θ 2 e i β / 2 sin θ 2 e i β / 2 ) ,
| ψ ( z ) = e i γ / 2 ( sin θ 2 e i β / 2 cos θ 2 e i β / 2 ) .
θ ˙ = Ω sin β ,
β ˙ = Ω cot θ cos β Δ ,
γ ˙ = θ ˙ cot β / sin θ .
θ ( 0 ) = π , θ ( L ) = 0 .
P 1 1 4 | 0 L d z e i γ ( i η Δ sin θ + 2 η Ω θ ˙ sin 2 θ ) | 2 .
q Ω = 1 2 2 P 1 η Ω 2 = 1 4 | 0 L d z e i γ 2 θ ˙ sin 2 θ | 2 ,
q Δ = 1 2 2 P 1 η Δ 2 = 1 4 | 0 L d z e i γ sin θ | 2 .
θ l ( z ) = π ( s 1 ) ,
θ h ( z ) = 0.426 sin ( 2 π s ) π ( s 1 ) ,
θ b ( z ) = 0.5952 sin ( 2 π s ) 0.0476 sin ( 4 π s ) π ( s 1 ) .
P = 1 2 1 2 cos [ ( 1 + η Ω ) 0 L | Ω | d z ] .
0 L | Ω | d z = 0 L | θ ˙ | d z = π ,
q Δ = 1 4 | 0 L d z sin θ | 2 ,
γ ( z ) = θ + c 1 sin ( 2 θ ) + c 2 sin ( 4 θ ) ,
0 L | Ω | d z = 0 L | θ ˙ / sin β | d z = 2.31 π ,

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