Abstract

We propose a fast quasiadiabatic approach to the design of optical waveguide devices. This approach distributes the system adiabaticity homogeneously over the device length, thus providing a shortcut to adiabaticity at a shorter device length. A mode sorting asymmetric Y junction is designed by redistributing the adiabaticity of a conventional linearly separating Y junction. Simple procedures for the design of fast quasiadiabatic devices are outlined, and the designed Y junction features large bandwidth at a shorter length than the conventional linearly separating Y junction. The proposed device is verified with beam propagation simulations. A mode conversion efficiency of larger than 99% is observed for the designed Y junction over a 220 nm range.

© 2017 Optical Society of America

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References

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  1. M. Born and V. Fock, “Beweis des adiabatensatzes,” Z. Phys. 51, 165–169 (1928).
    [Crossref]
  2. W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11, 32–39 (1975).
    [Crossref]
  3. A. F. Milton and W. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13, 828–835 (1977).
    [Crossref]
  4. W. J. Stewart and J. D. Love, “Design limitation on tapers and couplers in single mode fibers,” Proc. 5th IOOC/11th ECOC, 559–562 (1985).
  5. R. R. A. Syms and P. G. Peall, “The digital optical switch: analogous directional coupler devices,” Opt. Commun. 69, 235–238 (1989).
    [Crossref]
  6. R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett. 4, 1135–1138 (1992).
    [Crossref]
  7. A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
    [Crossref]
  8. T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
    [Crossref]
  9. M. R. Watts, H. A. Haus, and E. P. Ippen, “Integrated mode-evolution-based polarization splitter,” Opt. Lett. 30, 967–969 (2005).
    [Crossref] [PubMed]
  10. M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express 13, 9381–9387 (2005).
    [Crossref] [PubMed]
  11. 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]
  12. J. D. Love and N. Riesen, “Single, few-, and multimode Y-junctions,” J. Lightw. Technol. 30, 304–309 (2012).
    [Crossref]
  13. N. Riesen and J. D. Love, “Design of mode-sorting asymmetric Y-junctions,” Appl. Opt. 51, 2778–2783 (2012).
    [Crossref] [PubMed]
  14. S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, and J. Bland-Hawthorn, “Mode-selective photonic lanterns for space-division multiplexing,” Opt. Express 22, 1036–1044 (2014).
    [Crossref] [PubMed]
  15. S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
    [Crossref]
  16. 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]
  17. 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]
  18. S.-Y. Tseng and X. Chen, “Engineering of fast mode conversion in multimode waveguides,” Opt. Lett. 37, 5118–5120 (2012).
    [Crossref] [PubMed]
  19. 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]
  20. S.-Y. Tseng, “Counterdiabatic mode-evolution based coupled-waveguide devices,” Opt. Express 21, 21224–21235 (2013).
    [Crossref] [PubMed]
  21. 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]
  22. S.-Y. Tseng, “Robust coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 39, 6600–6603 (2014).
    [Crossref] [PubMed]
  23. X. Chen, R.-D. Wen, and S.-Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Optics Express 24, 18322–18331 (2016).
    [Crossref] [PubMed]
  24. 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]
  25. 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]
  26. S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
    [Crossref]

2016 (1)

X. Chen, R.-D. Wen, and S.-Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Optics Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

2015 (2)

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, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

2014 (6)

2013 (2)

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]

2012 (4)

2009 (1)

2005 (2)

1998 (2)

A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
[Crossref]

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
[Crossref]

1992 (1)

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

1989 (1)

R. R. A. Syms and P. G. Peall, “The digital optical switch: analogous directional coupler devices,” Opt. Commun. 69, 235–238 (1989).
[Crossref]

1977 (1)

A. F. Milton and W. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13, 828–835 (1977).
[Crossref]

1975 (1)

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

1928 (1)

M. Born and V. Fock, “Beweis des adiabatensatzes,” Z. Phys. 51, 165–169 (1928).
[Crossref]

Al-Bader, S.

A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
[Crossref]

Ban, Y.

Bland-Hawthorn, J.

Born, M.

M. Born and V. Fock, “Beweis des adiabatensatzes,” Z. Phys. 51, 165–169 (1928).
[Crossref]

Burns, W.

A. F. Milton and W. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13, 828–835 (1977).
[Crossref]

Burns, W. K.

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

Busch, Th.

S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

Chen, X.

Chiu, Y.-F.

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]

Ercan, B.

Fock, V.

M. Born and V. Fock, “Beweis des adiabatensatzes,” Z. Phys. 51, 165–169 (1928).
[Crossref]

Fontaine, N. K.

Gillet, J.

S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

Greenberg, M.

Gross, S.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
[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]

Haus, H. A.

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]

Ippen, E. P.

Jhang, Y.-W.

Leon-Saval, S. G.

Lin, T.-Y.

Liu, H.-C.

Love, J. D.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
[Crossref]

J. D. Love and N. Riesen, “Single, few-, and multimode Y-junctions,” J. Lightw. Technol. 30, 304–309 (2012).
[Crossref]

N. Riesen and J. D. Love, “Design of mode-sorting asymmetric Y-junctions,” Appl. Opt. 51, 2778–2783 (2012).
[Crossref] [PubMed]

W. J. Stewart and J. D. Love, “Design limitation on tapers and couplers in single mode fibers,” Proc. 5th IOOC/11th ECOC, 559–562 (1985).

Martínez-Garaot, S.

S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

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]

Milton, A. F.

A. F. Milton and W. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13, 828–835 (1977).
[Crossref]

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[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, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

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]

Orenstein, M.

Osgood, R. M.

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
[Crossref]

Pan, T.-H.

Peall, P. G.

R. R. A. Syms and P. G. Peall, “The digital optical switch: analogous directional coupler devices,” Opt. Commun. 69, 235–238 (1989).
[Crossref]

Ramadan, T. A.

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
[Crossref]

Riesen, N.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
[Crossref]

J. D. Love and N. Riesen, “Single, few-, and multimode Y-junctions,” J. Lightw. Technol. 30, 304–309 (2012).
[Crossref]

N. Riesen and J. D. Love, “Design of mode-sorting asymmetric Y-junctions,” Appl. Opt. 51, 2778–2783 (2012).
[Crossref] [PubMed]

Ruschhaupt, A.

S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[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]

Ryf, R.

Salazar-Gil, J. R.

Scarmozzino, R.

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
[Crossref]

Schneider, V. M.

A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
[Crossref]

Stewart, W. J.

W. J. Stewart and J. D. Love, “Design limitation on tapers and couplers in single mode fibers,” Proc. 5th IOOC/11th ECOC, 559–562 (1985).

Sun, X.

Syahriar, A.

A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
[Crossref]

Syms, R. R. A.

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

R. R. A. Syms and P. G. Peall, “The digital optical switch: analogous directional coupler devices,” Opt. Commun. 69, 235–238 (1989).
[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]

Tseng, S.-Y.

X. Chen, R.-D. Wen, and S.-Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Optics Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

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]

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, “Robust coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 39, 6600–6603 (2014).
[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, “Counterdiabatic mode-evolution based coupled-waveguide devices,” Opt. Express 21, 21224–21235 (2013).
[Crossref] [PubMed]

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.

Watts, M. R.

Wen, R.-D.

X. Chen, R.-D. Wen, and S.-Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Optics Express 24, 18322–18331 (2016).
[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]

Withford, M. J.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
[Crossref]

Yariv, A.

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]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

A. F. Milton and W. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13, 828–835 (1977).
[Crossref]

IEEE Photon. Technol. Lett. (1)

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

J. Lightw. Technol. (3)

A. Syahriar, V. M. Schneider, and S. Al-Bader, “The design of mode evolution couplers,” J. Lightw. Technol. 16, 1907–1914 (1998).
[Crossref]

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: design rules and optimization,” J. Lightw. Technol.,  16, 277–283 (1998).
[Crossref]

J. D. Love and N. Riesen, “Single, few-, and multimode Y-junctions,” J. Lightw. Technol. 30, 304–309 (2012).
[Crossref]

Laser Photon. Rev. (1)

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photon. Rev. 8, L81–L85 (2014).
[Crossref]

Opt. Commun. (1)

R. R. A. Syms and P. G. Peall, “The digital optical switch: analogous directional coupler devices,” Opt. Commun. 69, 235–238 (1989).
[Crossref]

Opt. Express (7)

Opt. Lett. (5)

Optics Express (1)

X. Chen, R.-D. Wen, and S.-Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Optics Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

Phys. Rev. A (1)

S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, Th. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92, 043406 (2015).
[Crossref]

Z. Phys. (1)

M. Born and V. Fock, “Beweis des adiabatensatzes,” Z. Phys. 51, 165–169 (1928).
[Crossref]

Other (1)

W. J. Stewart and J. D. Love, “Design limitation on tapers and couplers in single mode fibers,” Proc. 5th IOOC/11th ECOC, 559–562 (1985).

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Figures (8)

Fig. 1
Fig. 1 Schematic of the mode sorting asymmetic Y junction.
Fig. 2
Fig. 2 Device adiabaticities [Eq. (1)] for the linearly separating Y junction (dotted) and the FAQUAD Y junction (solid). This figure also shows the adiabaticity measure in terms of the control parameter [A(z) in Eq. (5)].
Fig. 3
Fig. 3 Waveguide separations D(z) for the linearly separating Y junction (dotted) and the FAQUAD Y junction (solid).
Fig. 4
Fig. 4 BPM simulated fractional power (conversion efficiency) in waveguides A and B of the FAQUAD and linearly separating Y junctions using the fundamental mode of the stem waveguide as the input for different device lengths.
Fig. 5
Fig. 5 Geometries of the designed mode sorting asymmetic Y junctions. (a) FAQUAD design (b) linear design.
Fig. 6
Fig. 6 BPM simulated mode sorting operation of the FAQUAD Y junction. Input (a) fundamental mode (b) second mode.
Fig. 7
Fig. 7 BPM simulated mode sorting operation of the linearly separating Y junction. Input (a) fundamental mode (b) second mode.
Fig. 8
Fig. 8 Simulated wavelength dependence of the conversion efficiencies of the FAQUAD and the linearly separating Y junctions.

Equations (9)

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

| m | n ˙ β m β n | 1 ,
| m / n ˙ β m β n | = c
| γ ˙ m | γ | n β m β n | = c ,
M C F = | β A β B | θ γ A B ,
c l i n ( z ) = D f L | a | D | b β a β b | = D f L A ( z ) ,
| d D d z a | D | b β a β b | = c .
d D d z = c A ( z ) = D f L c c l i n ( z ) ,
D ( 0 ) = 0 , D ( L ) = D f .
D F A Q U A D ( z ) = D f 0 z ( 1 / c l i n ( z ) ) d z 0 L ( 1 / c l i n ( z ) ) d z .

Metrics