Abstract

Photons are neutral particles which cannot directly interact with an applied magnetic field, but recent studies show that an effective magnetic field can be created for photons by modulating the background permittivity or using magneto-optical (MO) media. In this paper, we demonstrate that when the permittivity tensor of a MO medium is spatially modulated, it can create an effective magnetic field proportional to the gradient of gyrotropic ratio. This field induces a Lorentz force and gives rise to a photonic magneto-Stark (PMS) effect. We prove this effect occurs once the photon’s wave vector and the gradient of gyrotropic ratio are non-parallel, and reaches the maximum when they are perpendicular. The PMS effect provides a new mechanism for wavelength modulation and controlling the direction-dependent propagation of photonic modes.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

2016 (2)

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

2014 (2)

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

Y. Poo, S. Liu, C. Xiao, R. X. Wu, and P. Chen, “Field enhancement of nonreciprocal electromagnetic wave supported by magnetic surface plasmon,” Opt. Express 22(22), 27717–27724 (2014).
[Crossref] [PubMed]

2013 (4)

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

2012 (2)

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref] [PubMed]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6 (11), 782–787 (2012).
[Crossref]

2011 (1)

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

2009 (2)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

A. B. Khanikaev and M. J. Steel, “Low-symmetry magnetic photonic crystals for nonreciprocal and unidirectional devices,” Opt. Express 17(7), 5265–5272 (2009).
[Crossref] [PubMed]

2008 (2)

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

2007 (1)

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[Crossref]

2004 (1)

2002 (1)

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

2001 (1)

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[Crossref] [PubMed]

1999 (1)

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

1998 (2)

S. K. Lyo, “Effect of electron-hole separation on the Landau-level photoluminescence in layered structures in a tilted magnetic field: Magneto-Stark effect,” Phys. Rev. B 58(16), R10187 (1998).
[Crossref]

N. Bahlmann, V. Chandrasekhara, A. Erdmann, R. Gerhardt, P. Hertel, R. Lehmann, D. Salz, F. Teler, and M. Wallenhorst, “Improved design of magnetooptic rib waveguides for optical isolators,” J. Lightwave Technol. 16(5), 818–823 (1998).
[Crossref]

1994 (1)

1991 (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[Crossref] [PubMed]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

1981 (1)

D. A. Harmin, “Hydrogenic Stark effect: Properties of the wave functions,” Phys. Rev. A 24(5), 2491–2512 (1981).
[Crossref]

1961 (1)

D. G. Thomas and J. J. Hopfield, “A magneto-Stark effect and exciton motion in CdS,” Phys. Rev. 124(3), 657–665 (1961).
[Crossref]

Bahlmann, N.

Bankowski, E.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Chandrasekhara, V.

Chang, K.

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

Chen, P.

Chen, Y.

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

Dong, P.

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Dötsch, H.

Durnev, M. V.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Erdmann, A.

Espinola, R. L.

Fan, S.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6 (11), 782–787 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[Crossref]

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Fang, G.

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

Fang, K.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6 (11), 782–787 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref] [PubMed]

Feng, L.

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

Feng, S. L.

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

Figotin, A.

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[Crossref] [PubMed]

Filimonov, Y. A.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Fu, K. C.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Gerhardt, R.

Glazov, M. M.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Gubbiotti, G.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Harmin, D. A.

D. A. Harmin, “Hydrogenic Stark effect: Properties of the wave functions,” Phys. Rev. A 24(5), 2491–2512 (1981).
[Crossref]

Harvey, S.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

He, C.

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

Heng, X.

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

Hertel, P.

Hopfield, J. J.

D. G. Thomas and J. J. Hopfield, “A magneto-Stark effect and exciton motion in CdS,” Phys. Rev. 124(3), 657–665 (1961).
[Crossref]

Ippen, E. P.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Ivchenko, E. L.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Izuhara, T.

Jamali, M.

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Jin, C.

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

Joannopoulos, J. D.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Kalyabin, D. V.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Karin, T.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Khanikaev, A. B.

Krawczyk, M.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Kwon, J. H.

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Lee, K. J.

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Lehmann, R.

Linpeng, X.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Lipson, M.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Lisenkov, I. V.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Liu, S.

Liu, W.

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

Lu, M. H.

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

Ludwig, A.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Lyo, S. K.

S. K. Lyo, “Effect of electron-hole separation on the Landau-level photoluminescence in layered structures in a tilted magnetic field: Magneto-Stark effect,” Phys. Rev. B 58(16), R10187 (1998).
[Crossref]

Manipatruni, S.

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Maradudin, A. A.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[Crossref] [PubMed]

Meitzler, T.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Melkov, G.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Mruczkiewicz, M.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Nikitov, S. A.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Nussenzveig, P.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

Osgood, R. M.

Peeters, F. M.

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

Plihal, M.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[Crossref] [PubMed]

Poo, Y.

Preble, S. F.

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Rai, A. K.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Robinson, J. T.

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

Salz, D.

Seo, S. M.

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Shamonin, M.

Shen, Y.

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

Slavin, A.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Steel, M. J.

Tacchi, S.

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Teler, F.

Thomas, D. G.

D. G. Thomas and J. J. Hopfield, “A magneto-Stark effect and exciton motion in CdS,” Phys. Rev. 124(3), 657–665 (1961).
[Crossref]

Tiberkevich, V.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Tsai, M. C.

Tzuang, L. D.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

Verba, R.

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

Vitebsky, I.

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[Crossref] [PubMed]

Wallenhorst, M.

Wang, Z.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[Crossref]

Wieck, A. D.

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Winn, J. N.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Wu, H. B.

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

Wu, R. X.

Xia, J. B.

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

Xiao, C.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

Yang, H.

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Yu, Z.

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref] [PubMed]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6 (11), 782–787 (2012).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[Crossref]

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, and A. Slavin, “Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars,” Appl. Phys. Lett. 103(8), 082407 (2013).
[Crossref]

K. Chang, J. B. Xia, H. B. Wu, S. L. Feng, and F. M. Peeters, “Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells,” Appl. Phys. Lett. 80(10), 1788–1790 (2002).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. Condens. Matter (1)

W. Liu, Y. Shen, G. Fang, and C. Jin, “Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains,” J. Phys. Condens. Matter 28(19), 196001 (2016).
[Crossref] [PubMed]

Nat. Photonics (3)

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6 (11), 782–787 (2012).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

New J. Phys. (1)

M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. A. Filimonov, D. V. Kalyabin, I. V. Lisenkov, and S. A. Nikitov, “Nonreciprocity of spin waves in metallized magnonic crystal,” New J. Phys. 15(11), 113023 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Plasmas (1)

W. Liu, Y. Shen, W. Liu, and C. Jin, “Magnetically induced Stark-like splitting and asymmetric refractive index effect in plasmonic nanostructures,” Phys. Plasmas 24(5), 052505 (2017).
[Crossref]

Phys. Rev. (1)

D. G. Thomas and J. J. Hopfield, “A magneto-Stark effect and exciton motion in CdS,” Phys. Rev. 124(3), 657–665 (1961).
[Crossref]

Phys. Rev. A (2)

D. A. Harmin, “Hydrogenic Stark effect: Properties of the wave functions,” Phys. Rev. A 24(5), 2491–2512 (1981).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

Phys. Rev. B (4)

C. He, M. H. Lu, X. Heng, L. Feng, and Y. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B 83(7), 075117 (2011).
[Crossref]

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

S. K. Lyo, “Effect of electron-hole separation on the Landau-level photoluminescence in layered structures in a tilted magnetic field: Magneto-Stark effect,” Phys. Rev. B 58(16), R10187 (1998).
[Crossref]

T. Karin, X. Linpeng, M. M. Glazov, M. V. Durnev, E. L. Ivchenko, S. Harvey, A. K. Rai, A. Ludwig, A. D. Wieck, and K. C. Fu, “Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault,” Phys. Rev. B 94(4), 041201 (2016).
[Crossref]

Phys. Rev. B Condens. Matter (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

P. Dong, S. F. Preble, J. T. Robinson, S. Manipatruni, and M. Lipson, “Inducing photonic transitions between discrete modes in a silicon optical microcavity,” Phys. Rev. Lett. 100(3), 033904 (2008).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

Sci. Rep. (1)

M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, “Spin wave nonreciprocity for logic device applications,” Sci. Rep. 3(1), 3160 (2013).
[Crossref] [PubMed]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, (Princeton University, Princeton, NJ, 1995).

L. D. Landau and E. M. Lifshitz, “Quantum Mechanics - Non-Relativistic Theory, 3rd ed. (Pergamon, 1977).

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Figures (4)

Fig. 1
Fig. 1 PMS splitting under the presence of spatially modulated MO ratio, where k 0 is the wave vector in vacuum. The pure-color background means a constant α, while the gradient one means α is gradiently modulated. When α=0(even if α0), the eigenvalue of wave vector is 360-degree degenerate. When α is a non-zero constant, the degeneracy is eliminated almost everywhere except for α//k (time-reversal symmetry). The PMS splitting is proportional | k | and isometric between states |k and | k. It reaches the maximum when θ=π/2 and θ=3π/2 ( αk).
Fig. 2
Fig. 2 Distribution function of gyrotropic ratio α (Eq. (10). C=1.5× 10 2 .
Fig. 3
Fig. 3 Effective magnetic field acts on waves propagating along different directions. α is determined from Eq. (10) (Fig. 2), where C=1.5× 10 2 . For the left columns, the medium is non-magnetic, and for the right columns, we use MO medium with gradient gyrotropic ratio along x axis. (a) θ=0, (b) θ= π 4 , (c) θ= π 2 , (d) θ= 3π 4 , (e) θ=π, (f) θ= 5π 4 , (g) θ= 3π 2 , (h) θ= 7π 4 . For θ=0 and θ=π, the gradient of gyrotropic ratio is parallel to the wave vector, and the PMS effect does not occur. For 0<θ<π, the effective magnetic field “squeezes” the wave, while for π<θ<2π, it “stretches” the wave. It seems that a “Lorentz force”, produced by the effective magnetic field, is simultaneously “pulling” or “pushing” the wave at the crest and trough.
Fig. 4
Fig. 4 Characteristic profiles for cylindrical wave propagating in MO media with different gyrotropic ratio functions. For gradiently modulated The permittivity functions for (b) ~(f) are chosen as Eq. (10). (a) α=const, (b) C=0.5× 10 2 , (c) C=2× 10 2 . (d) C=0.5× 10 2 , (e) C=2× 10 2 , (f) C=0.5× 10 2 for y>0 and C=0.5× 10 2 for y<0, (g) C=2× 10 2 for y>0 and C=2× 10 2 for y<0. When α is constant, the MO activity has no influence on the wave shape. With the increase of α, the wavelength is strongly direction-dependent.

Equations (12)

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

H S = M p (B×k) z
×( ε 1 ×H)= k 2 H
ε=( ε // iη 0 iη ε // 0 0 0 ε ), ε 1 =( ε // ε // 2 η 2 iη ε // 2 η 2 0 iη ε // 2 η 2 ε // ε // 2 η 2 0 0 0 1 ε )( 1 ε // iη ε // 2 0 iη ε // 2 1 ε // 0 0 0 1 ε )
x ( iη ε // 2 H z y 1 ε // H z x ) y ( iη ε // 2 H z x + 1 ε // H z y )= k 2 H z
( L ^ + L ^ S ) H z = k 2 H z s
L ^ = x ( 1 ε // x ) y ( 1 ε // y )
L ^ S =i( α x y α y x )
L ^ S = (α× k ^ ) z
B eff (p)= 2p α
α(x,y)={ C x λ ,| x λ |<20 0,| x λ |20 , ModulatingAera NonmagneticAera
L S,k k =k| L ^ S | k = ψ k (r) ( α(r)× k ^ ψ k (r) ) z d 2 r
ψ k (1) (r)= k k L S,k k k 2 k 2 ψ k (r)

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