Abstract

We demonstrated that non-reciprocal wave propagation could be manipulated by a magnetic rod chain under bias DC magnetic fields. Made of ferrite material YIG and designed working in the microwave X-band, the rod chain exhibited almost a total reflection when the incident wave obliquely impinged on the rod chain, but exhibited nearly a total transmission when the wave reversed its propagation direction. The non-reciprocal wave propagation was due to the non-reciprocal diffraction of the rod chain for the orders 0 and ± 1. Further, the non-reciprocal wave propagation was directly observed by using the field mapping technique. The unique non-reciprocal wave property of the magnetic rod chain provides a new way to control the flow of EM waves.

© 2017 Optical Society of America

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References

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  1. H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
    [Crossref]
  2. Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005).
    [Crossref] [PubMed]
  3. Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
    [Crossref] [PubMed]
  4. 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]
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2016 (1)

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (1)

2011 (2)

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

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

2009 (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

2008 (4)

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[Crossref]

2005 (1)

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]

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]

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]

Cao, X. W.

Chen, J.

Chen, Y. F.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Chen, Y.-F.

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

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

Cui, H. X.

Dong, H. Y.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

Fan, S.

Fang, N. X.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

Feng, L.

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

Fung, K. H.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

Guo, Q. H.

Guo, T. J.

Haldane, F. D.

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[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]

He, C.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

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

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

John, S.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[Crossref]

Li, Q. B.

Li, T. F.

Li, Z.

Lu, M. H.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Lu, M.-H.

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

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]

Poo, Y.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Z. Li, R. X. Wu, Q. B. Li, and Y. Poo, “Realization of self-guided unidirectional waveguides by a chain of gyromagnetic rods,” Appl. Opt. 54(6), 1267–1272 (2015).
[Crossref] [PubMed]

Raghu, S.

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

Takeda, H.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (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]

Wang, J.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005).
[Crossref] [PubMed]

Wu, R. X.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Z. Li, R. X. Wu, Q. B. Li, and Y. Poo, “Realization of self-guided unidirectional waveguides by a chain of gyromagnetic rods,” Appl. Opt. 54(6), 1267–1272 (2015).
[Crossref] [PubMed]

Xiao, C.

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Yang, M.

Appl. Opt. (1)

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]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[Crossref]

Phys. Rev. B (2)

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

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

Phys. Rev. Lett. (2)

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

Sci. Rep. (1)

Y. Poo, C. He, C. Xiao, M. H. Lu, R. X. Wu, and Y. F. Chen, “Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking,” Sci. Rep. 6(1), 29380 (2016).
[Crossref] [PubMed]

Other (2)

D. M. Pozar, Microwave Engineering, 3 (John Wiley, 2005).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th expanded ed. (Cambridge University Press, 1999).

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Figures (5)
Fig. 1
Fig. 1 (a) Schematic diagram of diffraction of the rod chain. The red arrow ki is the wave vector of incident wave. The green arrows, k t n± and k t n− , are the wave vector of transmitted diffraction waves of ± n-th order, and the yellow arrows, k t n+ and k r n− , are the wave vector of reflected waves of ± n-th order (b) The reflectance and transmittance of the different diffraction orders when an incident wave impinges on the rod chain in the angle + 45° with respect to x-axis. (c) The reflectance and transmittance at incident angle −45°. In panels (c) and (d), the black dot-line is the total of the reflectance and transmittance of the diffraction orders 0 and ± 1. The sum equals to one indicating no other diffraction orders to be considered. (d) Schematic diagram of the non-reciprocal wave reflection of the rod chain. The red arrows show the rod chain totally reflects the incident wave. When the direction of wave propagation is reversed, the wave goes along green arrows, showing a total transmission. Because of rotation symmetry of the rod chain, the transmitted wave is non-reciprocal too.

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Fig. 2
Fig. 2 Reflectance and transmittance of the ring rod chain for the diffraction orders zero and ± 1 under bias magnetic field (a) H0 = + 800 Oe and (b) H0 = −800 Oe. The sum of all reflectance and transmittance equals one indicating no other orders of diffraction present. (c) and (d) are the electric field distribution when a Gaussian beam projects on the rod chain at angle 45°. The arrow shows the direction of the incident wave. The panel (c) is with H0 = + 800 Oe, and the panel (d) is with H0 = −800 Oe. (e) and (f) are the close view of the electric field distribution around the ring rod. The direction of bias magnetic field H0 corresponds to that of panels (c) and (d), respectively.

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Fig. 3
Fig. 3 Reflectance and transmittance of zero-order and negative first-order diffraction as a function of incident angle and frequency. The left column is for the zero-order reflectance R0 and right column for the negative first-order transmittance T-1 at positive and negative incident angles.

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Fig. 4
Fig. 4 (a) The schematic diagram of experimental setup. The green arrow shows the direction of reflected waves and purple arrow shows the direction of refracted waves. (b) The image of the sample in the practical experimental setup. (c) and (d) are experimental results of the power distribution around the rod chain sample under bias magnetic field H0 = 800 Oe at 9.43 GHz. The direction of the bias magnetic field is, respectively, (c) outward and (d) inward the paper plane.

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Fig. 5
Fig. 5 Field mapping results at frequency 8.91GHz for bias magnetic field (a) H0 = + 800 Oe. The incident wave is reflected. (b) H0 = −800 Oe. The incident wave is negative refracted. The triangular regions out of the incident wave channels are filled with absorber.

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Equations (4)

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

μ ¯ ¯ =( μ iκ 0 −iκ μ 0 0 0 1 ),
μ=1+ ω m ( ω 0 +jαω) ( ω 0 +jαω) 2 − ω 2 ,
κ= ω m ω ( ω 0 +jαω) 2 − ω 2 ,
{ k iy = k ty n± ±nG k iy = k ry n± ±nG ,

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