Abstract

Ferrimagnetic material with remanence holds the potential to realize unidirectional propagation of the electromagnetic field by taking advantage of magnetoplasmon in the subwavelength regime. Here, we theoretically investigate magnetoplasmons in a layered structure consisting of a dielectric sandwiched by two magnetic materials with anti-parallel remanent magnetization directions, which shows a complete unidirectional propagating region for both even and odd symmetry modes when the thickness of the dielectric is smaller than a certain value. Additionally, the even symmetry mode supported by such a one-way waveguide can be effectively, with low insertion loss, excited by the fundamental transverse-electric mode of a traditional metal slab waveguide. Relying on low insertion loss and a one-way propagation feature, we propose a broadband and subwavelength isolator working at the microwave region. Our results demonstrate that remanence based magnetoplasmons provide a promising way to realize devices below the diffraction limit with new functionalities.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
    [Crossref]
  2. S. A. Maier, Plasmonics (Springer-Verlag GmbH, 2007).
  3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
    [Crossref]
  4. 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]
  5. V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
    [Crossref]
  6. L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950 (2015).
    [Crossref]
  7. H. Zhu and C. Jiang, “Broadband unidirectional electromagnetic mode at interface of anti-parallel magnetized media,” Opt. Express 18(7), 6914 (2010).
    [Crossref]
  8. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. 37(11), 1895 (2012).
    [Crossref]
  9. X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
    [Crossref]
  10. K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
    [Crossref]
  11. J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
    [Crossref]
  12. K. Liu, A. Torki, and S. He, “One-way surface magnetoplasmon cavity and its application for nonreciprocal devices,” Opt. Lett. 41(4), 800 (2016).
    [Crossref]
  13. P. A. D. Gonçalves and N. M. R. Peres, An Introduction to Graphene Plasmonics (WORLD SCIENTIFIC, 2015).
  14. D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
    [Crossref]
  15. Y. You, P. A. D. Gonçalves, L. Shen, M. Wubs, X. Deng, and S. Xiao, “Magnetoplasmons in monolayer black phosphorus structures,” Opt. Lett. 44(3), 554 (2019).
    [Crossref]
  16. D. M. Pozar, Microwave Engineering (John Wiley and Sons Ltd, 2011).
  17. C. K. Seewald and J. R. Bray, “Ferrite-filled antisymmetrically biased rectangular waveguide isolator using magnetostatic surface wave modes,” IEEE Trans. Microwave Theory Tech. 58(6), 1493–1501 (2010).
    [Crossref]
  18. M. F. Farooqui, A. Nafe, and A. Shamim, “Inkjet printed ferrite-filled rectangular waveguide x-band isolator,” in 2014 IEEE MTT-S International Microwave Symposium (IMS2014), (IEEE, 2014).
  19. W. Marynowski, “Integrated broadband edge-guided mode isolator with antiparallel biasing of the ferrite slabs,” IEEE Microw. Wirel. Components Lett. 28(5), 392–394 (2018).
    [Crossref]
  20. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
    [Crossref]
  21. A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
    [Crossref]

2019 (1)

2018 (1)

W. Marynowski, “Integrated broadband edge-guided mode isolator with antiparallel biasing of the ferrite slabs,” IEEE Microw. Wirel. Components Lett. 28(5), 392–394 (2018).
[Crossref]

2017 (3)

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

2016 (1)

2015 (1)

2012 (3)

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. 37(11), 1895 (2012).
[Crossref]

X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
[Crossref]

V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
[Crossref]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

H. Zhu and C. Jiang, “Broadband unidirectional electromagnetic mode at interface of anti-parallel magnetized media,” Opt. Express 18(7), 6914 (2010).
[Crossref]

C. K. Seewald and J. R. Bray, “Ferrite-filled antisymmetrically biased rectangular waveguide isolator using magnetostatic surface wave modes,” IEEE Trans. Microwave Theory Tech. 58(6), 1493–1501 (2010).
[Crossref]

2008 (1)

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]

2006 (1)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref]

1973 (1)

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

1972 (1)

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Altug, H.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Boyd, R. W.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Bray, J. R.

C. K. Seewald and J. R. Bray, “Ferrite-filled antisymmetrically biased rectangular waveguide isolator using magnetostatic surface wave modes,” IEEE Trans. Microwave Theory Tech. 58(6), 1493–1501 (2010).
[Crossref]

Brewer, R.

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

Brion, J. J.

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Burstein, E.

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

de Abajo, F. J. G.

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

Deng, X.

Y. You, P. A. D. Gonçalves, L. Shen, M. Wubs, X. Deng, and S. Xiao, “Magnetoplasmons in monolayer black phosphorus structures,” Opt. Lett. 44(3), 554 (2019).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950 (2015).
[Crossref]

Eyderman, S.

V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
[Crossref]

Fan, S.

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]

Farooqui, M. F.

M. F. Farooqui, A. Nafe, and A. Shamim, “Inkjet printed ferrite-filled rectangular waveguide x-band isolator,” in 2014 IEEE MTT-S International Microwave Symposium (IMS2014), (IEEE, 2014).

Gonçalves, P. A. D.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Hartstein, A.

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

He, S.

Hu, B.

Jiang, C.

Jiang, X.

X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
[Crossref]

Kuzmiak, V.

V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
[Crossref]

Li, W.

X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
[Crossref]

Liu, K.

Maier, S. A.

S. A. Maier, Plasmonics (Springer-Verlag GmbH, 2007).

Maradudin, A. A.

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

Marynowski, W.

W. Marynowski, “Integrated broadband edge-guided mode isolator with antiparallel biasing of the ferrite slabs,” IEEE Microw. Wirel. Components Lett. 28(5), 392–394 (2018).
[Crossref]

Nafe, A.

M. F. Farooqui, A. Nafe, and A. Shamim, “Inkjet printed ferrite-filled rectangular waveguide x-band isolator,” in 2014 IEEE MTT-S International Microwave Symposium (IMS2014), (IEEE, 2014).

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref]

Pan, D.

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

Peres, N. M. R.

P. A. D. Gonçalves and N. M. R. Peres, An Introduction to Graphene Plasmonics (WORLD SCIENTIFIC, 2015).

Pozar, D. M.

D. M. Pozar, Microwave Engineering (John Wiley and Sons Ltd, 2011).

Schulz, S. A.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Seewald, C. K.

C. K. Seewald and J. R. Bray, “Ferrite-filled antisymmetrically biased rectangular waveguide isolator using magnetostatic surface wave modes,” IEEE Trans. Microwave Theory Tech. 58(6), 1493–1501 (2010).
[Crossref]

Shamim, A.

M. F. Farooqui, A. Nafe, and A. Shamim, “Inkjet printed ferrite-filled rectangular waveguide x-band isolator,” in 2014 IEEE MTT-S International Microwave Symposium (IMS2014), (IEEE, 2014).

Shen, L.

Y. You, P. A. D. Gonçalves, L. Shen, M. Wubs, X. Deng, and S. Xiao, “Magnetoplasmons in monolayer black phosphorus structures,” Opt. Lett. 44(3), 554 (2019).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950 (2015).
[Crossref]

Torki, A.

Tsakmakidis, K. L.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Upham, J.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Vakakis, A. F.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Vanwolleghem, M.

V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
[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]

Wallis, R. F.

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Wang, Q. J.

Wang, Z.

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950 (2015).
[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]

Wu, J.-J.

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

Wubs, M.

Xiao, S.

Xu, H.

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

Yang, T.-J.

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

You, Y.

Yu, R.

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

Yu, 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]

Zhang, X.

X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
[Crossref]

Zhang, Y.

Zheng, X.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Zhu, H.

Zou, J.

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

Appl. Phys. Lett. (1)

X. Zhang, W. Li, and X. Jiang, “Confined one-way mode at magnetic domain wall for broadband high-efficiency one-way waveguide, splitter and bender,” Appl. Phys. Lett. 100(4), 041108 (2012).
[Crossref]

IEEE Microw. Wirel. Components Lett. (1)

W. Marynowski, “Integrated broadband edge-guided mode isolator with antiparallel biasing of the ferrite slabs,” IEEE Microw. Wirel. Components Lett. 28(5), 392–394 (2018).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

C. K. Seewald and J. R. Bray, “Ferrite-filled antisymmetrically biased rectangular waveguide isolator using magnetostatic surface wave modes,” IEEE Trans. Microwave Theory Tech. 58(6), 1493–1501 (2010).
[Crossref]

J. Phys. C: Solid State Phys. (1)

A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, “Surface polaritons on semi-infinite gyromagnetic media,” J. Phys. C: Solid State Phys. 6(7), 1266–1276 (1973).
[Crossref]

Nat. Commun. (1)

D. Pan, R. Yu, H. Xu, and F. J. G. de Abajo, “Topologically protected dirac plasmons in a graphene superlattice,” Nat. Commun. 8(1), 1243 (2017).
[Crossref]

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Opt. Commun. (1)

J. Zou, Y. You, X. Deng, L. Shen, J.-J. Wu, and T.-J. Yang, “High-efficiency tunable y-branch power splitters at terahertz frequencies,” Opt. Commun. 387, 153–156 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

V. Kuzmiak, S. Eyderman, and M. Vanwolleghem, “Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field,” Phys. Rev. B 86(4), 045403 (2012).
[Crossref]

Phys. Rev. Lett. (2)

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[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]

Science (2)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref]

Other (4)

P. A. D. Gonçalves and N. M. R. Peres, An Introduction to Graphene Plasmonics (WORLD SCIENTIFIC, 2015).

S. A. Maier, Plasmonics (Springer-Verlag GmbH, 2007).

D. M. Pozar, Microwave Engineering (John Wiley and Sons Ltd, 2011).

M. F. Farooqui, A. Nafe, and A. Shamim, “Inkjet printed ferrite-filled rectangular waveguide x-band isolator,” in 2014 IEEE MTT-S International Microwave Symposium (IMS2014), (IEEE, 2014).

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Figures (6)

Fig. 1.
Fig. 1. Schematic of a one-way waveguide based on ferrimagnetic material with remanence. The red arrow indicates the propagating direction and $d_0$ denotes the thickness of the dielectric layer. The remanent magnetization directions of the gyromagnetic materials are along $\pm \mathbf {\hat {z}}$.
Fig. 2.
Fig. 2. Dispersion relations of MPs in the proposed structure when the thicknesses of the dielectric layer $d_0$ are of the values (a) $0.035 \lambda _r$, (b) $0.145 \lambda _r$, (c) $0.75 \lambda _r$ and (d) $1.20 \lambda _r$. The red(green) lines represent the dispersion curves of the even(odd) symmetry modes. The dashed lines indicate the light-lines, and the dot-dash lines are the dispersion curves of MPs propagating at a single dielectric-ferrite interface. The purple areas are the zones of bulk modes in the ferrimagnetic materials, and the yellow areas indicate the CUP regions. The light-blue lines in (b) are the first-three order modes of the traditional metal slab waveguide (discussed in Section 4).
Fig. 3.
Fig. 3. Propagation lengths for MPs as a function of the dielectric thickness $d_0$ when $\omega = 0.75 \omega _r$. The dielectrics are assumed to be air with $\epsilon _r = 1$ in (a) and glass with $\epsilon _r = 4.28$ in (b). The red lines indicate the modes with even symmetry and the green lines are odd symmetry modes. The maximal propagation length for the mode with even symmetry is marked with a red circle in each panel.
Fig. 4.
Fig. 4. Reflection (a), transmission (b) and absorption (c) as a function of the dielectric thickness $d_0$ and the distance of the two metal slabs $d_p$ when the fundamental TE mode of a metal slab waveguide is coupled into the proposed one-way waveguide. The operating frequency is $0.75 \omega _r$ and the relaxation angular frequency of YIG is $\nu = 5 \times 10^{-3} \omega$. The dielectric filled in the metal slab waveguide is silicon with $\epsilon _d = 11.9$.
Fig. 5.
Fig. 5. (a) Reflection, transmission and absorption as a function of frequency for both forward and backward propagating directions of the isolator. Solid lines with circles denote the forward propagation while dashed lines with dots for the backward propagation. The dielectric thickness of the one-way waveguide is $d_0 = 0.145 \lambda _r$, the distance between the two metal slabs is $d_p = 0.43 \lambda _r$, and the length of the one-way waveguide is $L_0 = 0.5 \lambda _r$. (b)-(c) Electric field distributions for the forward and backward directions when the operating frequency $\omega = 0.75 \omega _r$, respectively. Red arrows denote the propagating directions of the electromagnetic wave. (d) The isolation ratio as a function of frequency when $L_0 = 0.5 \lambda _r$ and $\omega = 0.75 \omega _r$. (e) The isolation ratio as a function of the length of the one-way waveguide when $\omega = 0.75 \omega _r$.
Fig. 6.
Fig. 6. Three dimensional simulation results of the isolator extended from our 2D case. The width in the $z$-axis is $20 \mathrm {mm}$ and other parameters are the same as in Figs. 5(b) and 5(c).

Equations (13)

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μm(ω)=[μiκ0iκμ0001]
μ=1,
κ=ωrω,
Ez(x,y)=Aeαyeikx,y>d02
Ez(x,y)=(B1eαdy+B2eαdy)eikx,y<|d02|
Ez(x,y)=Ceαyeikx.y<d02
α+κkαdμv+tanhαdd02=0
α+κkαdμv+cothαdd02=0
α+κkkyμvtankyd02=0
α+κkkyμv+cotkyd02=0
dc=λr2ϵr.
μ=1+iνωrω2+ν2,
κ=ωωrω2+ν2,

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