Abstract

We propose fast and robust mode conversion in multimode waveguides based on Lewis–Riesenfeld invariant theory. The design of mode converters using the multimode driving for dynamical invariant is discussed. Computer-generated planar holograms are used to mimic the shaped pulses driving the states in three-level quantum systems. We show that the invariant-based inverse engineering scheme reduces mode converter length as compared to the common adiabatic scheme.

© 2012 Optical Society of America

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  1. S. Berdagué and P. Facq, Appl. Opt. 21, 1950 (1982).
    [CrossRef]
  2. A. Fratalocchi, R. Asquini, and G. Assanto, Opt. Express 13, 32 (2005).
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  3. A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
    [CrossRef]
  4. K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
    [CrossRef]
  5. G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
    [CrossRef]
  6. G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
    [CrossRef]
  7. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
    [CrossRef]
  8. M. V. Berry, J. Phys. A: Math. Theor. 42, 365303 (2009).
    [CrossRef]
  9. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
    [CrossRef]
  10. S. Longhi, Laser Photon. Rev. 3, 243 (2009).
    [CrossRef]
  11. E. Paspalakis, Opt. Commun. 258, 30 (2006).
    [CrossRef]
  12. A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
    [CrossRef]
  13. S.-Y. Tseng, Y. Kim, C. J. K. Richardson, and J. Goldhar, Appl. Opt. 45, 4864 (2006).
    [CrossRef]
  14. S.-Y. Tseng and M.-C. Wu, IEEE Photon. Technol. Lett. 22, 1211 (2010).
    [CrossRef]
  15. T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, Opt. Express 20, 24085 (2012).
    [CrossRef]
  16. X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
    [CrossRef]
  17. H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
    [CrossRef]
  18. X. Chen and J. G. Muga, Phys. Rev. A 86, 033405 (2012).
    [CrossRef]

2012

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

X. Chen and J. G. Muga, Phys. Rev. A 86, 033405 (2012).
[CrossRef]

T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, Opt. Express 20, 24085 (2012).
[CrossRef]

2011

X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
[CrossRef]

2010

S.-Y. Tseng and M.-C. Wu, IEEE Photon. Technol. Lett. 22, 1211 (2010).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

2009

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

M. V. Berry, J. Phys. A: Math. Theor. 42, 365303 (2009).
[CrossRef]

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
[CrossRef]

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

2006

2005

A. Fratalocchi, R. Asquini, and G. Assanto, Opt. Express 13, 32 (2005).
[CrossRef]

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

1998

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

1982

1969

H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
[CrossRef]

Asquini, R.

Assanto, G.

A. Fratalocchi, R. Asquini, and G. Assanto, Opt. Express 13, 32 (2005).
[CrossRef]

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

Berdagué, S.

Bergmann, K.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Phys. A: Math. Theor. 42, 365303 (2009).
[CrossRef]

Chen, X.

X. Chen and J. G. Muga, Phys. Rev. A 86, 033405 (2012).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

del Campo, A.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

Dridi, G.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Eleuch, E.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Facq, P.

Fratalocchi, A.

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

A. Fratalocchi, R. Asquini, and G. Assanto, Opt. Express 13, 32 (2005).
[CrossRef]

Goldhar, J.

Guérin, S.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Guéry-Odelin, D.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

Hakobyan, V.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Hsiao, F.-C.

Hu, C.

Jauslin, H. R.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Jhang, Y.-W.

Kim, Y.

Kuhn, A.

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
[CrossRef]

Lewis, H. R.

H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
[CrossRef]

Lin, T.-Y.

Lizuain, I.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

Longhi, S.

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

Muga, J. G.

X. Chen and J. G. Muga, Phys. Rev. A 86, 033405 (2012).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

Paspalakis, E.

E. Paspalakis, Opt. Commun. 258, 30 (2006).
[CrossRef]

Rangelov, A. A.

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

Richardson, C. J. K.

Riesenfeld, W. B.

H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
[CrossRef]

Ruschhaupt, A.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

Schmidt, S.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

Shore, B. W.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Torrontegui, E.

X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
[CrossRef]

Tseng, S.-Y.

Vasilev, G. S.

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
[CrossRef]

Vitanov, N. V.

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
[CrossRef]

Wu, M.-C.

S.-Y. Tseng and M.-C. Wu, IEEE Photon. Technol. Lett. 22, 1211 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

S.-Y. Tseng and M.-C. Wu, IEEE Photon. Technol. Lett. 22, 1211 (2010).
[CrossRef]

J. Math. Phys.

H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
[CrossRef]

J. Phys. A: Math. Theor.

M. V. Berry, J. Phys. A: Math. Theor. 42, 365303 (2009).
[CrossRef]

Laser Photon. Rev.

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

Opt. Commun.

E. Paspalakis, Opt. Commun. 258, 30 (2006).
[CrossRef]

Opt. Express

Phys. Rev. A

X. Chen and J. G. Muga, Phys. Rev. A 86, 033405 (2012).
[CrossRef]

X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
[CrossRef]

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, Phys. Rev. A 80, 013417 (2009).
[CrossRef]

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, Phys. Rev. A 80, 043408 (2009).
[CrossRef]

Phys. Rev. Lett.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
[CrossRef]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
[CrossRef]

Rev. Mod. Phys.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Level scheme of a three-level Λ system. (b) Schematic of a CGPH loaded multimode waveguide. (c) Amplitude profiles of the three guided modes.

Fig. 2.
Fig. 2.

Calculated CGPH pattern for mode conversion. Dashed lines indicate the waveguide core.

Fig. 3.
Fig. 3.

BPM simulation of light propagation in a 4 mm mode converter based on the multimode driving scheme. Dashed lines indicate the waveguide core.

Fig. 4.
Fig. 4.

Modal power evolution in a 4 mm mode converter using the multimode driving scheme.

Fig. 5.
Fig. 5.

Normalized modal power at the mode converter output for different device lengths.

Fig. 6.
Fig. 6.

Normalized output power in |Ψ3 against Δn variations (Δn=0.003 at 0%). (a) Invariant-based and (b) STIRAP.

Equations (8)

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

H(z)=2[0κ12(z)0κ21(z)0κ23(z)0κ32(z)0].
I(z)=2[0cosγsinβisinγcosγsinβ0cosγcosβisinγcosγcosβ0]
κ12=2(β˙cotγsinβ+γ˙cosβ),
κ23=2(β˙cotγcosβγ˙sinβ).
|ϕ0=[cosγcosβisinγcosγsinβ],
|ϕ±=12[sinγcosβ±isinβicosγsinγsinβ±icosβ].
κ12=(π/L)cotϵsin(πz/2L),
κ23=(π/L)cotϵcos(πz/2L).

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