Abstract

Indirect interband photonic transition provides a nonmagnetic and linear scheme to achieve optical isolation in integrated photonics. In this paper, we demonstrate that the nonreciprocal transition can be induced through two pathways respectively by different modulation designs. At the end of those pathways, the two final modes have π phaseshift. We call this phenomenon jumping phase control since this approach provides a method to control the mode phase after the conversion. This approach also yields a novel way to generate nonreciprocal phaseshift and may contribute to chip-scale optoelectronic applications.

© 2014 Optical Society of America

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  1. E. Yablonovitch, “One-way road for light,” Nature (London) 461,744 (2009).
    [CrossRef]
  2. Z. Wang, S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl.Phys.B 81, 369–375 (2005).
  3. Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
    [CrossRef] [PubMed]
  4. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
    [CrossRef]
  5. Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
    [CrossRef] [PubMed]
  6. Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
    [CrossRef]
  7. M. Soljačić, C. Luo, John D. Joannopoulos, S. Fan, “Nonlinear Photonic Crystal Microdevices for Optical Integration,” Opt. Lett. 28, 637–639 (2003).
    [CrossRef]
  8. L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
    [CrossRef]
  9. J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
    [CrossRef]
  10. Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
    [CrossRef]
  11. Z. Yu, S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94,171116 (2009).
    [CrossRef]
  12. Z. Yu, S. Fan, “Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions,” IEEE J. Sel. Top. Quantum Electron. 16, 459–466 (2010).
    [CrossRef]
  13. Z. Yu, S. Fan, “Dynamic photonic structure for integrated photonics,” Proc. SPIE 7605, 76050O (2010).
    [CrossRef]
  14. H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
    [CrossRef] [PubMed]
  15. G. Shvets, “Not Every Exit is an Entrance,” Physics 5,78 (2012).
    [CrossRef]
  16. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]

2012

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

G. Shvets, “Not Every Exit is an Entrance,” Physics 5,78 (2012).
[CrossRef]

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

2011

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

2010

Z. Yu, S. Fan, “Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions,” IEEE J. Sel. Top. Quantum Electron. 16, 459–466 (2010).
[CrossRef]

Z. Yu, S. Fan, “Dynamic photonic structure for integrated photonics,” Proc. SPIE 7605, 76050O (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2009

E. Yablonovitch, “One-way road for light,” Nature (London) 461,744 (2009).
[CrossRef]

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu, S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94,171116 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

2008

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

2005

Z. Wang, S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl.Phys.B 81, 369–375 (2005).

2003

1998

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Bi, L.

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

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

Dionne, G. F.

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

Fan, L.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Fan, S.

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

Z. Yu, S. Fan, “Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions,” IEEE J. Sel. Top. Quantum Electron. 16, 459–466 (2010).
[CrossRef]

Z. Yu, S. Fan, “Dynamic photonic structure for integrated photonics,” Proc. SPIE 7605, 76050O (2010).
[CrossRef]

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu, S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94,171116 (2009).
[CrossRef]

Z. Wang, S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl.Phys.B 81, 369–375 (2005).

M. Soljačić, C. Luo, John D. Joannopoulos, S. Fan, “Nonlinear Photonic Crystal Microdevices for Optical Integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Hu, J.

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

Huangfu, J.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Ippen, E. P.

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Jiang, P.

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

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Joannopoulos, John D.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

M. Soljačić, C. Luo, John D. Joannopoulos, S. Fan, “Nonlinear Photonic Crystal Microdevices for Optical Integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Kim, D. H.

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

Kimerling, L. C.

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

Lipson, M.

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

Lira, H.

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

Luo, C.

Niu, B.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Qi, M.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Ran, L.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Ross, C. A.

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

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Shen, H.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Shvets, G.

G. Shvets, “Not Every Exit is an Entrance,” Physics 5,78 (2012).
[CrossRef]

Soljacic, M.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

M. Soljačić, C. Luo, John D. Joannopoulos, S. Fan, “Nonlinear Photonic Crystal Microdevices for Optical Integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Varghese, Leo T.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Wang, B.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Wang, J.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Wang, Z.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

Z. Wang, S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl.Phys.B 81, 369–375 (2005).

Weiner, Andrew M.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Winn, J. N.

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Xuan, Y.

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “One-way road for light,” Nature (London) 461,744 (2009).
[CrossRef]

Yu, Z.

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

Z. Yu, S. Fan, “Dynamic photonic structure for integrated photonics,” Proc. SPIE 7605, 76050O (2010).
[CrossRef]

Z. Yu, S. Fan, “Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions,” IEEE J. Sel. Top. Quantum Electron. 16, 459–466 (2010).
[CrossRef]

Z. Yu, S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94,171116 (2009).
[CrossRef]

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Appl. Phys. Lett.

Z. Yu, S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94,171116 (2009).
[CrossRef]

Appl.Phys.B

Z. Wang, S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl.Phys.B 81, 369–375 (2005).

Comp. Phys. Commun.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

Z. Yu, S. Fan, “Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions,” IEEE J. Sel. Top. Quantum Electron. 16, 459–466 (2010).
[CrossRef]

Nat. Photonics

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

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Nature (London)

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature (London) 461, 772–776 (2009).
[CrossRef]

E. Yablonovitch, “One-way road for light,” Nature (London) 461,744 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. B

J. N. Winn, S. Fan, J. D. Joannopoulos, E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1998).
[CrossRef]

Phys. Rev. Lett.

H. Lira, Z. Yu, S. Fan, M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109,033901 (2012).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100,013905 (2008).
[CrossRef] [PubMed]

Physics

G. Shvets, “Not Every Exit is an Entrance,” Physics 5,78 (2012).
[CrossRef]

Proc. Natl. Acad. Sci.

Z. Wang, Z. Wang, J. Wang, B. Wang, J. Huangfu, John D. Joannopoulos, M. Soljacic, L. Ran, “Gyrotropic response in the absence of a bias field,” Proc. Natl. Acad. Sci. 109, 13194–13197 (2012).
[CrossRef] [PubMed]

Proc. SPIE

Z. Yu, S. Fan, “Dynamic photonic structure for integrated photonics,” Proc. SPIE 7605, 76050O (2010).
[CrossRef]

Science

L. Fan, J. Wang, Leo T. Varghese, H. Shen, B. Niu, Y. Xuan, Andrew M. Weiner, M. Qi, “An All-Silicon Passive Optical Diode,” Science 335, 447–450 (2012).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Band structure of a silicon slab waveguide. The arrows indicate indirect photonic transition from mode I to mode II. (b) The optimal modulation profile at a certain time in piecewise form. Modulation is applied to the whole cross section of waveguide.

Fig. 2
Fig. 2

Spatial evolution of the electric field amplitudes of two modes under perfect phase-matching modulation. The red dashed line and the blue dotted line represent A2 with initial phase ϕ2 = π/2 and ϕ2 = −π/2, respectively.

Fig. 3
Fig. 3

The normalized electric field profiles of even mode and odd mode. The two arrows represent the symmetric mode can be converted to antisymmetric modes with π phase shift through different paths, separately.

Fig. 4
Fig. 4

Nonreciprocal frequency transition in silicon slab waveguide (a,c) The incident photon number flux and transmitted flux are indicated with red solid and blue dot lines when light is incident from left (a) or right (c), respectively. (b,d) The distribution of electric fields from FDTD simulation, showing the conversion only occurs in one propagation direction. The arrows represent the direction of incidence.

Fig. 5
Fig. 5

Schematic of an optical isolator based on Mach-Zehdner interferometer. (a) The modulation profiles applied on the upper and lower arms excite transitions through different paths. (b) The conversion through upper arm has π phaseshift with the transition through lower arm. (c) Light propagating from the opposite direction is unaffected. Arrows indicate propagation directions.

Equations (6)

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

Δ ε = δ ( x ) cos ( Ω t + Λ z )
E ( x , z , t ) = A 1 ( z ) E 1 ( x ) e i ( ω 1 t k 1 z ) + A 2 ( z ) E 2 ( x ) e i ( ω 2 t k 2 z )
d A 1 d z = i C 1 A 2 d A 2 d z = i C 2 A 1
A 1 = a 1 × cos ( K z + ϕ 1 ) A 2 = a 2 × cos ( K z + ϕ 2 )
Δ ε = { δ cos ( Ω t + Λ z + π ) , 0 < x < d 2 δ cos ( Ω t + Λ z ) , d 2 < x < 0
Δ ε = { δ cos ( Ω t + Λ z ) , 0 < x < d 2 δ cos ( Ω t + Λ z + π ) , d 2 < x < 0

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