Abstract

We propose a compact and high conversion efficiency asymmetric Y junction mode multiplexer/demultiplexer for applications in on-chip mode-division multiplexing. Traditionally, mode sorting is achieved by adiabatically separating the arms of a Y junction. We shorten the device length using invariant-based inverse engineering and achieve better conversion efficiency than the adiabatic device.

© 2014 Optical Society of America

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  1. H. R. Stuart, Science 289, 281 (2000).
    [CrossRef]
  2. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
    [CrossRef]
  3. S. Berdagué and P. Facq, Appl. Opt. 21, 1950 (1982).
    [CrossRef]
  4. V. Liu, D. A. B. Miller, and S. Fan, Opt. Express 20, 28388 (2012).
    [CrossRef]
  5. W. Chen, P. Wang, and J. Yang, Opt. Express 21, 25113 (2013).
    [CrossRef]
  6. J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, Opt. Lett. 38, 1854 (2013).
    [CrossRef]
  7. W. K. Burns and A. F. Milton, Quantum Electron. 11, 32 (1975).
    [CrossRef]
  8. J. D. Love and N. Riesen, J. Lightwave Technol. 30, 304 (2012).
    [CrossRef]
  9. N. Riesen and J. D. Love, Appl. Opt. 51, 2778 (2012).
    [CrossRef]
  10. J. D. Love, R. W. C. Vance, and A. Joblin, Opt. Quantum Electron. 28, 353 (1996).
    [CrossRef]
  11. X. Sun, H.-C. Liu, and A. Yariv, Opt. Lett. 34, 280 (2009).
    [CrossRef]
  12. R. R. A. Syms, IEEE Photon. Technol. Lett. 4, 1135 (1992).
    [CrossRef]
  13. G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
    [CrossRef]
  14. S. Longhi, Laser Photon. Rev. 3, 243 (2009).
    [CrossRef]
  15. E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, At. Adv. Mol. Opt. Phys. 62, 117 (2013).
  16. S.-Y. Tseng and X. Chen, Opt. Lett. 37, 5118 (2012).
    [CrossRef]
  17. T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, Opt. Express 20, 24085 (2012).
    [CrossRef]
  18. S.-Y. Tseng, Opt. Express 21, 21224 (2013).
    [CrossRef]
  19. S.-Y. Tseng and Y.-W. Jhang, IEEE Photon. Technol. Lett. 25, 2478 (2013).
    [CrossRef]
  20. C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
    [CrossRef]
  21. K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, J. Lightwave Technol. 31, 3387 (2013).
    [CrossRef]
  22. X. Chen, E. Torrontegui, and J. G. Muga, Phys. Rev. A 83, 062116 (2011).
    [CrossRef]
  23. X. Chen and J. G. Muga, Phys. Rev. A 86, 062116 (2011).
  24. S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (2013).
    [CrossRef]
  25. H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).
    [CrossRef]

2014 (1)

C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
[CrossRef]

2013 (7)

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

S.-Y. Tseng and Y.-W. Jhang, IEEE Photon. Technol. Lett. 25, 2478 (2013).
[CrossRef]

J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, Opt. Lett. 38, 1854 (2013).
[CrossRef]

S.-Y. Tseng, Opt. Express 21, 21224 (2013).
[CrossRef]

W. Chen, P. Wang, and J. Yang, Opt. Express 21, 25113 (2013).
[CrossRef]

K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, J. Lightwave Technol. 31, 3387 (2013).
[CrossRef]

2012 (6)

2011 (2)

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

X. Chen and J. G. Muga, Phys. Rev. A 86, 062116 (2011).

2009 (2)

2004 (1)

G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
[CrossRef]

2000 (1)

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

1996 (1)

J. D. Love, R. W. C. Vance, and A. Joblin, Opt. Quantum Electron. 28, 353 (1996).
[CrossRef]

1992 (1)

R. R. A. Syms, IEEE Photon. Technol. Lett. 4, 1135 (1992).
[CrossRef]

1982 (1)

1975 (1)

W. K. Burns and A. F. Milton, Quantum Electron. 11, 32 (1975).
[CrossRef]

1969 (1)

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

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Berdagué, S.

Burns, W. K.

W. K. Burns and A. F. Milton, Quantum Electron. 11, 32 (1975).
[CrossRef]

Cao, H.-X.

C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
[CrossRef]

Chen, W.

Chen, X.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

S.-Y. Tseng and X. Chen, Opt. Lett. 37, 5118 (2012).
[CrossRef]

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

X. Chen and J. G. Muga, Phys. Rev. A 86, 062116 (2011).

Chien, K.-H.

Dadap, J. I.

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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Driscoll, J. B.

Eyal, A.

G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
[CrossRef]

Facq, P.

Fan, S.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Grote, R. R.

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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Guéry-Odelin, D. D.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (2013).
[CrossRef]

Hsiao, F.-C.

Hu, C.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Jhang, Y.-W.

S.-Y. Tseng and Y.-W. Jhang, IEEE Photon. Technol. Lett. 25, 2478 (2013).
[CrossRef]

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

Joblin, A.

J. D. Love, R. W. C. Vance, and A. Joblin, Opt. Quantum Electron. 28, 353 (1996).
[CrossRef]

Lewis, H. R.

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

Lin, T.-Y.

Liu, H.-C.

Liu, V.

Longhi, S.

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

Love, J. D.

Lu, M.

Martínez-Garaot, S.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Miller, D. A. B.

Milton, A. F.

W. K. Burns and A. F. Milton, Quantum Electron. 11, 32 (1975).
[CrossRef]

Modugno, M.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Muga, J. G.

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (2013).
[CrossRef]

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

X. Chen and J. G. Muga, Phys. Rev. A 86, 062116 (2011).

Osgood, R. M.

Paloczi, G. T.

G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
[CrossRef]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Riesen, N.

Riesenfeld, W. B.

H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

Souhan, B.

Stuart, H. R.

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

Sun, X.

Syms, R. R. A.

R. R. A. Syms, IEEE Photon. Technol. Lett. 4, 1135 (1992).
[CrossRef]

Torrontegui, E.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

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

Tseng, S.-Y.

C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
[CrossRef]

S.-Y. Tseng, Opt. Express 21, 21224 (2013).
[CrossRef]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (2013).
[CrossRef]

S.-Y. Tseng and Y.-W. Jhang, IEEE Photon. Technol. Lett. 25, 2478 (2013).
[CrossRef]

K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, J. Lightwave Technol. 31, 3387 (2013).
[CrossRef]

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

S.-Y. Tseng and X. Chen, Opt. Lett. 37, 5118 (2012).
[CrossRef]

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Vance, R. W. C.

J. D. Love, R. W. C. Vance, and A. Joblin, Opt. Quantum Electron. 28, 353 (1996).
[CrossRef]

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Wang, P.

Wilner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J.

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yariv, A.

X. Sun, H.-C. Liu, and A. Yariv, Opt. Lett. 34, 280 (2009).
[CrossRef]

G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
[CrossRef]

Yeih, C.-S.

C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
[CrossRef]

K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, J. Lightwave Technol. 31, 3387 (2013).
[CrossRef]

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Appl. Opt. (2)

At. Adv. 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, At. Adv. Mol. Opt. Phys. 62, 117 (2013).

IEEE Photon. Technol. Lett. (4)

S.-Y. Tseng and Y.-W. Jhang, IEEE Photon. Technol. Lett. 25, 2478 (2013).
[CrossRef]

C.-S. Yeih, H.-X. Cao, and S.-Y. Tseng, IEEE Photon. Technol. Lett. 26, 123 (2014).
[CrossRef]

R. R. A. Syms, IEEE Photon. Technol. Lett. 4, 1135 (1992).
[CrossRef]

G. T. Paloczi, A. Eyal, and A. Yariv, IEEE Photon. Technol. Lett. 16, 515 (2004).
[CrossRef]

J. Lightwave Technol. (2)

J. Math. Phys. (1)

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

Laser Photon. Rev. (1)

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

Nat. Photonics (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Wilner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

J. D. Love, R. W. C. Vance, and A. Joblin, Opt. Quantum Electron. 28, 353 (1996).
[CrossRef]

Phys. Rev. A (2)

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

X. Chen and J. G. Muga, Phys. Rev. A 86, 062116 (2011).

Phys. Rev. Lett. (1)

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Phys. Rev. Lett. 111, 213001 (2013).
[CrossRef]

Quantum Electron. (1)

W. K. Burns and A. F. Milton, Quantum Electron. 11, 32 (1975).
[CrossRef]

Science (1)

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

Cited By

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Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Schematic of the asymmetric Y junction.

Fig. 2.
Fig. 2.

Conversion efficiencies of a linearly separating Y junction using the second mode as the input for different device lengths.

Fig. 3.
Fig. 3.

Parameters for the invariant-based Y junction.

Fig. 4.
Fig. 4.

Mode-sorting operation of the invariant based Y junction. Input (a) fundamental mode (b) second mode.

Fig. 5.
Fig. 5.

Mode-sorting operation of the linearly separating Y junction. Input (a) fundamental mode (b) second mode.

Fig. 6.
Fig. 6.

Output field profile of the Y junctions. Solid: invariant based. Dashed: linearly separating. Dash-dotted: waveguide walls. Input (a) fundamental mode (b) second mode.

Fig. 7.
Fig. 7.

Conversion efficiencies as a function of width variation using the second mode as the input.

Equations (9)

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

MCF=|βAβB|θγAB,
ddz[AB]=i[λ(z)δ(z)δ(z)λ(z)][AB]=iH[AB],
δ(0)=ω0,λ(0)=0,δ(L)=0,λ(L)=λL,
I(z)=12(cosθsinθeiφsinθeiφcosθ),
|ϕ+(z)=(cosθ2eiφsinθ2),|ϕ(z)=(sinθ2cosθ2eiφ).
δ(z)=θ˙(z)/sinφ(z),
λ(z)=δ(z)cotθ(z)cosφ(z)φ˙(z).
θ(0)=π/2,φ(0)=π,θ(L)=0,θ˙(L)=0.
θ˙(0)=θ¨(0)=φ˙(0)=0,θ(0)=ω0λ˙(0),φ¨(0)=λ˙(0),φ(L)=π/2,φ˙(L)=λL/3

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