Abstract

Using a technique, analogous to coherent population trapping in an atomic system, we propose schemes to create transverse light propagation violating left-right symmetry in a photonic circuit consisting of three coupled waveguides. The frequency windows for the symmetry breaking of the left-right energy flow span over 80 nm. Our proposed system only uses linear passive optical materials and is easy to integrate on a chip.

© 2013 Optical Society of America

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  1. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys.67, 717–754(2004).
    [CrossRef]
  2. J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
    [CrossRef]
  3. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904(2008).
    [CrossRef] [PubMed]
  4. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
    [CrossRef] [PubMed]
  5. Y. Shoji, M. Ito, Y. Shirato, and T. Mizumoto, “MZI optical isolator with si-wire waveguides by surface-activated direct bonding,” Opt. Express20, 18440–18448(2012).
    [CrossRef] [PubMed]
  6. Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
    [CrossRef] [PubMed]
  7. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
    [CrossRef]
  8. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
    [CrossRef]
  9. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94(2009).
    [CrossRef]
  10. M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
    [CrossRef]
  11. Q. Wang, F. Xu, Z. Yu, X. Qian, X. Hu, Y. Lu, and H. Wang, “A bidirectional tunable optical diode based on periodically poled linbo3,” Opt. Express18, 7340–7346(2010).
    [CrossRef] [PubMed]
  12. S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
    [CrossRef] [PubMed]
  13. M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express20, 7672–7684(2012).
    [CrossRef] [PubMed]
  14. Y. Hadad and B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett.105, 233904(2010).
    [CrossRef]
  15. A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
    [CrossRef] [PubMed]
  16. C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
    [CrossRef]
  17. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
    [CrossRef] [PubMed]
  18. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
    [CrossRef]
  19. L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
    [CrossRef] [PubMed]
  20. L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
    [CrossRef]
  21. S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
    [CrossRef]
  22. C. Wang, C. Zhou, and Z. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19, 26948–26955(2011).
    [CrossRef]
  23. C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).
  24. M. O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University, 1997).
    [CrossRef]
  25. S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A78, 013815(2008).
    [CrossRef]
  26. G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
    [CrossRef]
  27. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser & Photon. Rev.3, 243–261(2009).
    [CrossRef]
  28. S. Longhi, “Optical analog of population trapping in the continuum: Classical and quantum interference effects,” Phys. Rev. A79, 023811(2009).
    [CrossRef]
  29. A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
    [CrossRef] [PubMed]
  30. V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
    [CrossRef]
  31. S. Sandhu, M. L. Povinelli, and S. Fan, “Stopping and time reversing a light pulse using dynamics loss tuning of coupled-resonators delay lines,” Opt. Lett.32, 3333–3335(2007).
    [CrossRef] [PubMed]
  32. K. Okamoto, Fundamentals of Optical Waveguides(Academic Press, 2000).
  33. H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE62, 1044–1060(1974).
    [CrossRef]
  34. A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Tech.3, 1135–1146(1985).
    [CrossRef]
  35. H. A. Haus, Waves and Fields in Solid State(Prentice-Hall Inc., 1984).
  36. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
    [CrossRef] [PubMed]
  37. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
    [CrossRef] [PubMed]
  38. R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).
  39. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
    [CrossRef]

2012 (7)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
[CrossRef] [PubMed]

M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express20, 7672–7684(2012).
[CrossRef] [PubMed]

Y. Shoji, M. Ito, Y. Shirato, and T. Mizumoto, “MZI optical isolator with si-wire waveguides by surface-activated direct bonding,” Opt. Express20, 18440–18448(2012).
[CrossRef] [PubMed]

2011 (6)

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
[CrossRef]

Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
[CrossRef] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

C. Wang, C. Zhou, and Z. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19, 26948–26955(2011).
[CrossRef]

2010 (5)

Y. Hadad and B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett.105, 233904(2010).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

Q. Wang, F. Xu, Z. Yu, X. Qian, X. Hu, Y. Lu, and H. Wang, “A bidirectional tunable optical diode based on periodically poled linbo3,” Opt. Express18, 7340–7346(2010).
[CrossRef] [PubMed]

2009 (6)

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
[CrossRef] [PubMed]

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

S. Longhi, “Optical analog of population trapping in the continuum: Classical and quantum interference effects,” Phys. Rev. A79, 023811(2009).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94(2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

2008 (5)

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904(2008).
[CrossRef] [PubMed]

S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A78, 013815(2008).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

2007 (1)

2004 (3)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys.67, 717–754(2004).
[CrossRef]

2000 (1)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

1985 (1)

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Tech.3, 1135–1146(1985).
[CrossRef]

1974 (1)

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE62, 1044–1060(1974).
[CrossRef]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Baets, R.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Bank, S. R.

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Bradford, M.

Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
[CrossRef] [PubMed]

Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Butsch, A.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
[CrossRef]

Chen, Y.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

Christodoulides, D. N.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Coppa, A.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Crespi, A.

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
[CrossRef] [PubMed]

Della Valle, G.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Doerr, C. R.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Dötsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

Dreisow, F.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Eich, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

EI-Ganainy, R.

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

El-Ganainy, R.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

Eüter, C.

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Fan, S.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94(2009).
[CrossRef]

S. Sandhu, M. L. Povinelli, and S. Fan, “Stopping and time reversing a light pulse using dynamics loss tuning of coupled-resonators delay lines,” Opt. Lett.32, 3333–3335(2007).
[CrossRef] [PubMed]

Feng, L.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Fernandez, T.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Foglietti, V.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Hadad, Y.

Y. Hadad and B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett.105, 233904(2010).
[CrossRef]

Hafezi, M.

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904(2008).
[CrossRef] [PubMed]

Hardy, A.

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Tech.3, 1135–1146(1985).
[CrossRef]

Harris, J. S.

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Solid State(Prentice-Hall Inc., 1984).

Heinrich, M.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Hu, J.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Hu, X.

Huang, J.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Ito, M.

Jalas, D.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Jiang, P.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

Joannopoulos, W. F. J. D.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Kang, M. S.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
[CrossRef]

Keil, R.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

Kim, D. H.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Kimerling, L. C.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Kip, D.

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

Kivshar, Y. S.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

Kottos, T.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

Krause, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Laporta, P.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

Li, Z.

C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).

C. Wang, C. Zhou, and Z. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19, 26948–26955(2011).
[CrossRef]

Lipson, M.

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

Longhi, S.

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
[CrossRef] [PubMed]

S. Longhi, “Optical analog of population trapping in the continuum: Classical and quantum interference effects,” Phys. Rev. A79, 023811(2009).
[CrossRef]

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

S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A78, 013815(2008).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Lordi, V.

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

Lu, M.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Lu, Y.

Makris, K. G.

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

Manipatruni, S.

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
[CrossRef] [PubMed]

Melloni, A.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Mizumoto, T.

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Nolte, S.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides(Academic Press, 2000).

Ornigotti, M.

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

Osellame, R.

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
[CrossRef] [PubMed]

Osgood, R. M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

Pertsch, T.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Petrov, A.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Popovic, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys.67, 717–754(2004).
[CrossRef]

Povinelli, M. L.

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Qian, X.

Rabl, P.

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904(2008).
[CrossRef] [PubMed]

Ramezani, H.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

Renner, H.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Robinson, J. T.

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
[CrossRef] [PubMed]

Ross, C. A.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Russell, P. S. J.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
[CrossRef]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Sandhu, S.

Scherer, A.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University, 1997).
[CrossRef]

Segev, M.

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Shen, J. T.

Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
[CrossRef] [PubMed]

Shen, Y.

Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
[CrossRef] [PubMed]

Shirato, Y.

Shoji, Y.

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Steinberg, B. Z.

Y. Hadad and B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett.105, 233904(2010).
[CrossRef]

Streifer, W.

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Tech.3, 1135–1146(1985).
[CrossRef]

Szameit, A.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Taylor, H. F.

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE62, 1044–1060(1974).
[CrossRef]

Tünnermann, A.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Vanwolleghem, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

Wang, C.

C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).

C. Wang, C. Zhou, and Z. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19, 26948–26955(2011).
[CrossRef]

Wang, H.

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Wang, Q.

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

Xu, F.

Xu, Y.

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

Yariv, A.

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE62, 1044–1060(1974).
[CrossRef]

Yu, Z.

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Q. Wang, F. Xu, Z. Yu, X. Qian, X. Hu, Y. Lu, and H. Wang, “A bidirectional tunable optical diode based on periodically poled linbo3,” Opt. Express18, 7340–7346(2010).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94(2009).
[CrossRef]

Yuen, H. B.

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

Zhong, X.

C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).

Zhou, C.

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University, 1997).
[CrossRef]

Appl. Phys. Lett. (3)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on machzehnder interferometer,” Appl. Phys. Lett.76, 2158–2160(2000).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106(2008).
[CrossRef]

V. Lordi, H. B. Yuen, S. R. Bank, and J. S. Harris, “Quantum-confined stark effect of gainnas(sb) quantum wells at 1300–1600 nm,” Appl. Phys. Lett.85, 902–904(2004).
[CrossRef]

J. Lightwave Tech. (1)

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Tech.3, 1135–1146(1985).
[CrossRef]

Laser & Photon. Rev. (1)

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

Nat. Photon. (1)

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photon.5, 758–762(2011).
[CrossRef]

Nat. Photonics (2)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94(2009).
[CrossRef]

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553(2011).
[CrossRef]

Nat. Phys. (1)

C. Eüter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of paritytime symmetry in optics,” Nat. Phys.6, 192–195(2010).
[CrossRef]

Nature (2)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461, 772–775(2009).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084(2004).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126(2008).
[CrossRef]

Phys. Rev. A (3)

S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A78, 013815(2008).
[CrossRef]

S. Longhi, “Optical analog of population trapping in the continuum: Classical and quantum interference effects,” Phys. Rev. A79, 023811(2009).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A82, 043803(2010).
[CrossRef]

Phys. Rev. Lett. (8)

Y. Hadad and B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett.105, 233904(2010).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett.105, 126804(2010).
[CrossRef] [PubMed]

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett.102, 213903(2009).
[CrossRef] [PubMed]

Y. Shen, M. Bradford, and J. T. Shen, “Single-photon diode by exploiting the photon polarization in a waveguide,” Phys. Rev. Lett.107, 173902(2011).
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904(2008).
[CrossRef] [PubMed]

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum rabi model,” Phys. Rev. Lett.108, 163601(2012).
[CrossRef] [PubMed]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103, 093902(2009).
[CrossRef] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100, 103904(2008).
[CrossRef] [PubMed]

Proc. IEEE (1)

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE62, 1044–1060(1974).
[CrossRef]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys.67, 717–754(2004).
[CrossRef]

Sci. Rep. (1)

C. Wang, X. Zhong, and Z. Li, “Linear and passive silicon optical isolator,” Sci. Rep.2, 1–6(2012).

Science (4)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science335, 447–450(2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science333, 729–733(2011).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y. Xu, M. Lu, Y. Chen, Y. Fainman, and A. Scherer, “Response to comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–c(2012).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, W. F. J. D. Joannopoulos, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “nonreciprocal light propagation in a silicon photonic circuit,” Science335, 38–b(2012).
[CrossRef]

Scientific Rep. (1)

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Scientific Rep.1, 94(2011).

Other (3)

M. O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University, 1997).
[CrossRef]

K. Okamoto, Fundamentals of Optical Waveguides(Academic Press, 2000).

H. A. Haus, Waves and Fields in Solid State(Prentice-Hall Inc., 1984).

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Figures (9)

Fig. 1
Fig. 1

Light trapping in a photonic circuit consisting of three waveguides embedded in a Wwide, Llong substrate. The coupling κ13κ23. d13,23is the distance between two waveguides. The dielectric constants of substrate is εs, while εi(i∈ {1, 2, 3}) is the constant profile of corresponding individual waveguides Diwithout others. The widths of waveguides are ti, respectively.

Fig. 2
Fig. 2

(a) The waveguide structure for left-right nonrecipricity. The straight waveguide D3is 4 μm wide around its center w3(0) = 26.7 μm. The waveguides D1and D2with width t1= t2= 2 μm are curves along their varying central positions w1(z) and w2(z) defined as w1[z][μm] = 31 for z< 1.1 mm; w1[z][μm] = 34 for z> 1.6 mm and w1[z][μm] = 31 + 3(1 + sin(2π(z− 1350)/1000))/2 for 1.1 mm ≤ z≤ 1.6 mm. w2[z] is constant 22 μm for z< 0.1 mm and 23.4 μm for z> 1.1 mm. During the transition region, w2[z][μm] = 22 + 1.4(1 + sin(2π(z− 600)/2000))/2 for 0.1 mm ≤ z≤ 1.1mm. (b) The coupling as a function of propagating distance z. Blue lines (i) for κ13, red lines (ii) for κ23. Solid lines for coupling rates are evaluated by Eq. (5), while dashed lines indicates coupling rates for fitting the numerical results. Detailedly, the coupling rates for fitting are κ13(z)[mm−1]=4 for z< 1.1 mm; κ13(z)[mm−1]=0.03 for z> 1.44 mm and κ13(z)[mm−1]=0.03+3.97(1−sin(2π(z−1270)/680))/2.0 for 1.1 mm ≤z≤ 1.44 mm. While κ23(z) is 0.6 mm−1for z< 0.24 mm and 8.5 mm−1for z> 1.1 mm, and 0.6 + 7.9(1 + sin(2π(z− 670)/1720))/2.0 for 0.24 mm ≤z≤ 1.1 mm. Here λ0= 1.55 μm.

Fig. 3
Fig. 3

Left-right nonreciprocity corresponding to Fig. 2(a). The field propagates from left to right in photonic circuits. (a) Light incident into the waveguide D2; (c) light enters the waveguide D1; (b) and (d) Intensities of field at the middle of waveguides D1[blue lines (i)], D2[red lines (ii)] and D3[green lines (iii)]. Dashed thin lines are the corresponding plots by solving Eq. (4).

Fig. 4
Fig. 4

Numerical simulation of propagation of light in Fig. 2(a). The field incident into port PR1propagates from right to left. (a) Distribution of field (intensity), (b) Intensities of field at the middle of waveguides D1[blue lines (i)], D2[red lines (ii)],D3[green lines (iii)]. Dashed lines are the fitting plots evaluated by Eq. (4)using the same parameters as in Fig. 3.

Fig. 5
Fig. 5

Nonreciprocal transmission as a function of frequency of input light using structure as in Fig. 2(a). Thin blue lines (i) and (iii) show the light trapped in waveguide D1, thick red lines (ii) and (iv) show the light energy in D2. Solid lines for light launching to D2, dashed lines for light input into D1.

Fig. 6
Fig. 6

Nonreciprocal transmission in the structure as in Fig. 2(a)changes in the length (a), width (b) of, gap (c) between waveguide. (a) scale the device by ηzin the z-direction; (b) scale the width of waveguides D1and D2; (c) shift the center of waveguides by gas w1[z] + gand w2[z] − g. Thin blue lines (i) and (iii) show the light trapped in waveguide D1, thick red lines (ii) and (iv) show the light energy in D2. Solid lines for light launching to D2, dashed lines for light input into D1.

Fig. 7
Fig. 7

Nonreciprocal transmission as the structure as in Fig. 2(a)changes of the global refractive index ℜ[εcore] (a), refractive index ℜ[ε3] (b) and loss ℑ[εcore] of waveguide D3. Thin blue lines (i) and (iii) show the light trapped in waveguide D1, thick red lines (ii) and (iv) show the light energy in D2. Solid lines for light launching to D2, dashed lines for light input into D1.

Fig. 8
Fig. 8

(a) The waveguide structure for left-right nonreciprocity at λ= 800 nm. Similar to Fig. 1(a), the straight waveguide D3is 1 μm wide around its center w3(0) = 26.7 μm. The waveguides D1and D2with width t1= t2= 0.6 μm are curves along their varying central positions w1(z) and w2(z) defined as w1[z][μm] = 28.4 for z< 1.2 mm; w1[z][μm] = 30.4 for z> 3.1 mm and w1[z][μm] = 28.4 + 2(1 + sin(2π(z− 2150)/3800))/2 for 1.2 mm ≤ z≤ 3.1 mm. w2[z] is constant 24 μm for z< 0.2 mm and 23.4 μm for z> 1.95 mm. During the transition region, w2[z][μm] = 24 + 1.4(1 + sin(2π(z− 1075)/3500))/2 for 0.2 mm ≤ z≤ 1.95mm. (b) Nonreciprocal transmission as a function of frequency of input light in (a). Thin blue lines (i) and (iii) show the light trapped in waveguide D1, thick red lines (ii) and (iv) show the light energy in D2. Solid lines for light launching to D2, dashed lines for light input into D1. The Gaussian profile of input light is adjusted to be wp= 0.375 nmwide.

Fig. 9
Fig. 9

Left-right nonreciprocity corresponding to Fig. 8(a). The field propagates from left to right in photonic circuits. (a) Light incident into the waveguide D2; (c) light enters the waveguide D1; (b) and (d) Intensities of field at the middle of waveguides D1[blue lines (i)], D2[red lines (ii)] and D3[green lines (iii)].

Equations (9)

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2 E z 2 + 2 E x 2 + k 0 2 ε ( x , z ) E = 0 ,
2 j β ψ z 2 ψ x 2 + k 0 2 [ ε ( x , z ) n eff 2 ] ψ .
E = i = 1 , 2 , 3 A i E i = i = 1 , 2 , 3 A i ψ i e ± j β i z ,
A 1 z = j Δ 13 A 1 + j κ 13 ( z ) A 3
A 2 z = j Δ 23 A 1 + j κ 23 ( z ) A 3
A 3 z = j κ 13 ( z ) A 1 + j κ 23 ( z ) A 2 γ A 3 ,
κ m n = k 0 2 s δ ε n E m * E n d S β m s E m * E m d S ,
γ = 11.6 mm 1 ,
Δ 13 = Δ 23 = 23 mm 1 .

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