Abstract

Enhancing nonreciprocal light–matter interaction at subwavelength scales has attracted enormous attention due to high demand for compact optical isolators. Here, we propose a significant enhancement of the magneto-optical effect in low-biased gyromagnetic media via photonic doping. Magnetic particles immersed in a gyrotropy-near-zero medium act as dopants that largely modify the macroscopic gyromagnetic effects as well as the gyroelectric ones. Around the resonance frequency, the gyromagnetic activity is largely increased and even exceeds unity, thus providing a photonic band in which the wavenumber of one circularly polarized wave becomes purely imaginary. The sign of gyromagnetic activity flips at two chiral modes, and an equivalent switching of the external bias is revealed. A proof-of-concept low-biased planar isolator is designed with a thickness of only 1/28 wavelength and a degree of isolation achieving as high as 0.94. This methodology is robust against disturbance of the biased magnetic field and can be flexibly extended to other frequencies, thus offering a promising platform to achieve giant optical isolation with infinitesimally intrinsic magneto-optical effects and reduced sizes.

© 2019 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (6)

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D. Floess, M. Hentschel, T. Weiss, H.-U. Habermeier, J. Jiao, S. G. Tikhodeev, and H. Giessen, Phys. Rev. X 7, 021048 (2017).
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2016 (5)

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2015 (2)

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2014 (3)

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, Phys. Rev. Lett. 112, 117402 (2014).
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N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, Nat. Phys. 10, 923 (2014).
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L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, Nat. Photonics 8, 701 (2014).
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2013 (3)

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
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J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
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D. Jalas, A. Y. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. A. Popovic, A. Melloni, and J. D. Joannopoulos, Nat. Photonics 7, 579 (2013).
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2012 (2)

J. C. Banthi, D. Meneses-Rodriguez, F. Garcia, M. U. Gonzalez, A. Garcia-Martin, A. Cebollada, and G. Armelles, Adv. Mater. 24, OP36 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
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2011 (2)

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nat. Photonics 5, 758 (2011).
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2009 (1)

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, J. Magn. Magn. Mater. 321, 843 (2009).
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2008 (1)

C. Tserkezis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, Phys. Rev. B 78, 165114 (2008).
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2007 (1)

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, Phys. Rev. E 76, 026606 (2007).
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2006 (1)

2004 (1)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, Phys. Rev. E 70, 016608 (2004).
[Crossref]

1992 (1)

N. Engheta, D. L. Jaggard, and M. W. Kowarz, IEEE Trans. Anntenas Propag. 40, 367 (1992).
[Crossref]

1969 (1)

P. Schatz and A. McCaffery, Q. Rev. Chem. Soc. 23, 552 (1969).
[Crossref]

Abrishamian, M.

Achouri, K.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, Phys. Rev. Appl. 10, 047001 (2018).
[Crossref]

Akimov, I. A.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
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Alcaraz de la Osa, R.

A. Berger, R. Alcaraz de la Osa, A. K. Suszka, M. Pancaldi, J. M. Saiz, F. Moreno, H. P. Oepen, and P. Vavassori, Phys. Rev. Lett. 115, 187403 (2015).
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Allen, J.

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, Phys. Rev. Lett. 112, 117402 (2014).
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S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, Phys. Rev. Lett. 112, 117402 (2014).
[Crossref]

Alù, A.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, Phys. Rev. Appl. 10, 047001 (2018).
[Crossref]

D. L. Sounas and A. Alù, Phys. Rev. B 97, 115431 (2018).
[Crossref]

C. Coulais, D. Sounas, and A. Alù, Nature 542, 461 (2017).
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M.-A. Miri, F. Ruesink, E. Verhagen, and A. Alù, Phys. Rev. Appl. 7, 064014 (2017).
[Crossref]

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, Nat. Phys. 10, 923 (2014).
[Crossref]

Armelles, G.

G. Armelles, A. Cebollada, F. García, A. García-Martín, and N. de Sousa, ACS Photon. 3, 2427 (2016).
[Crossref]

J. C. Banthi, D. Meneses-Rodriguez, F. Garcia, M. U. Gonzalez, A. Garcia-Martin, A. Cebollada, and G. Armelles, Adv. Mater. 24, OP36 (2012).
[Crossref]

Baets, R.

D. Jalas, A. Y. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. A. Popovic, A. Melloni, and J. D. Joannopoulos, Nat. Photonics 7, 579 (2013).
[Crossref]

Banthi, J. C.

J. C. Banthi, D. Meneses-Rodriguez, F. Garcia, M. U. Gonzalez, A. Garcia-Martin, A. Cebollada, and G. Armelles, Adv. Mater. 24, OP36 (2012).
[Crossref]

Baryshev, A. V.

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, J. Magn. Magn. Mater. 321, 843 (2009).
[Crossref]

Bayer, M.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
[Crossref]

Belotelov, V. I.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
[Crossref]

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[Crossref]

Berger, A.

A. Berger, R. Alcaraz de la Osa, A. K. Suszka, M. Pancaldi, J. M. Saiz, F. Moreno, H. P. Oepen, and P. Vavassori, Phys. Rev. Lett. 115, 187403 (2015).
[Crossref]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nat. Photonics 5, 758 (2011).
[Crossref]

Caballero, B.

B. Caballero, A. García-Martín, and J. C. Cuevas, ACS Photon. 3, 203 (2016).
[Crossref]

Caloz, C.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, Phys. Rev. Appl. 10, 047001 (2018).
[Crossref]

Cebollada, A.

G. Armelles, A. Cebollada, F. García, A. García-Martín, and N. de Sousa, ACS Photon. 3, 2427 (2016).
[Crossref]

J. C. Banthi, D. Meneses-Rodriguez, F. Garcia, M. U. Gonzalez, A. Garcia-Martin, A. Cebollada, and G. Armelles, Adv. Mater. 24, OP36 (2012).
[Crossref]

Chen, H.

Z. Wang, L. Jing, K. Yao, Y. Yang, B. Zheng, C. M. Soukoulis, H. Chen, and Y. Liu, Adv. Mater. 29, 1700412 (2017).
[Crossref]

Z. Wang, K. Yao, M. Chen, H. Chen, and Y. Liu, Phys. Rev. Lett. 117, 157401 (2016).
[Crossref]

Chen, M.

Z. Wang, K. Yao, M. Chen, H. Chen, and Y. Liu, Phys. Rev. Lett. 117, 157401 (2016).
[Crossref]

Chen, X.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, Phys. Rev. E 70, 016608 (2004).
[Crossref]

Chen, Y.

Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, Nat. Photonics 10, 657 (2016).
[Crossref]

Cheng, F.

Z. Wang, F. Cheng, T. Winsor, and Y. Liu, Nanotechnology 27, 412001 (2016).
[Crossref]

Chin, J. Y.

D. Floess, J. Y. Chin, A. Kawatani, D. Dregely, H.-U. Habermeier, T. Weiss, and H. Giessen, Light Sci. Appl. 4, e284 (2015).
[Crossref]

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
[Crossref]

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[Crossref]

Clerk, A. A.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, Nat. Phys. 13, 465 (2017).
[Crossref]

Coulais, C.

C. Coulais, D. Sounas, and A. Alù, Nature 542, 461 (2017).
[Crossref]

Cuevas, J. C.

B. Caballero, A. García-Martín, and J. C. Cuevas, ACS Photon. 3, 203 (2016).
[Crossref]

Cui, T. J.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, Phys. Rev. E 76, 026606 (2007).
[Crossref]

de Sousa, N.

G. Armelles, A. Cebollada, F. García, A. García-Martín, and N. de Sousa, ACS Photon. 3, 2427 (2016).
[Crossref]

Deck-Léger, Z.-L.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, Phys. Rev. Appl. 10, 047001 (2018).
[Crossref]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nat. Photonics 5, 758 (2011).
[Crossref]

Dmitriev, A.

Dong, C.-H.

Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, Nat. Photonics 10, 657 (2016).
[Crossref]

Dregely, D.

D. Floess, J. Y. Chin, A. Kawatani, D. Dregely, H.-U. Habermeier, T. Weiss, and H. Giessen, Light Sci. Appl. 4, e284 (2015).
[Crossref]

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, Phys. Rev. X 3, 041019 (2013).
[Crossref]

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[Crossref]

Edwards, B.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, Science 355, 1058 (2017).
[Crossref]

Eich, M.

D. Jalas, A. Y. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. A. Popovic, A. Melloni, and J. D. Joannopoulos, Nat. Photonics 7, 579 (2013).
[Crossref]

Engheta, N.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, Science 355, 1058 (2017).
[Crossref]

N. Engheta, D. L. Jaggard, and M. W. Kowarz, IEEE Trans. Anntenas Propag. 40, 367 (1992).
[Crossref]

Estep, N. A.

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, Nat. Phys. 10, 923 (2014).
[Crossref]

Fan, S.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, Nat. Photonics 8, 701 (2014).
[Crossref]

D. Jalas, A. Y. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. A. Popovic, A. Melloni, and J. D. Joannopoulos, Nat. Photonics 7, 579 (2013).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

Fang, K.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, Nat. Phys. 13, 465 (2017).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, Nat. Photonics 8, 701 (2014).
[Crossref]

Fedotov, V. A.

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[Crossref]

Floess, D.

D. Floess and H. Giessen, Rep. Prog. Phys. 81, 116401 (2018).
[Crossref]

D. Floess, M. Hentschel, T. Weiss, H.-U. Habermeier, J. Jiao, S. G. Tikhodeev, and H. Giessen, Phys. Rev. X 7, 021048 (2017).
[Crossref]

D. Floess, J. Y. Chin, A. Kawatani, D. Dregely, H.-U. Habermeier, T. Weiss, and H. Giessen, Light Sci. Appl. 4, e284 (2015).
[Crossref]

Freude, W.

D. Jalas, A. Y. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. A. Popovic, A. Melloni, and J. D. Joannopoulos, Nat. Photonics 7, 579 (2013).
[Crossref]

Fujikawa, R.

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, J. Magn. Magn. Mater. 321, 843 (2009).
[Crossref]

Gantzounis, G.

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Figures (4)

Fig. 1.
Fig. 1. Schematic illustration of enhanced gyrotropic responses via photonic doping. A gyromagnetic slab (gray region) is biased with a low magnetic field (B0) and thus has a weak gyromagnetic response (μg0, εg=0). While doping the medium with photonic dopants (colored regions with irregular shapes), nontrivial gyromagnetic and gyroelectric responses can be created, with enlarged effective parameters μgeffμg and εgeffεg. The impedances in two directions become largely different and lead to the nontrivial performance of nonreciprocal isolation.
Fig. 2.
Fig. 2. Nonreciprocal performance of the doped gyromagnetic slab. (a) Schematic illustration of doped structure. (b), (c) Transmittance of the gyromagnetic slab (b) without and (c) with the photonic doping. The black dashed line denotes the unbiased condition. The red and blue solid lines represent the condition with an external magnetic field. (d) Electric field distribution at 21.5 GHz. The doped gyromagnetic slab is transparent for the forward RCP waves yet opaque for the backward ones. (e) Chiral surface current distributions of the magnetic dopants. Handedness is calculated by the Stokes parameters. Positive (τ>0) and negative (τ<0) ellipticity angles correspond to opposite handedness.
Fig. 3.
Fig. 3. Retrieved effective parameters for the doped gyromagnetic slab. (a) Effective impedance of the photonic doping of magnetic dopants. The magnetic resonant mode splits into two chiral resonances with the external biased field. At f2=21.5GHz, the effective impedance for RCP waves is close to the characteristic impedance of vacuum. The impedance for LCP waves has a zero real part and therefore results in total reflection. (b)–(d) Effective parameters of (b) refractive indices, (c) permeability, and (d) permittivity for circular polarization. Large discrepancy of permeability/permittivity between two circularly polarized waves reveals the significant enhancement of gyromagnetic/gyroelectric responses.
Fig. 4.
Fig. 4. Robustness of the isolation performance to the variation in external magnetic field. (a) Dependence of the isolation on magnetic field. (b) Dependence of maximum isolation frequency (normalized to f0=21.5GHz) on the magnetic field. The neighboring isolation spectra are offset by two along the vertical axis. (c) Refractive index of the host gyromagnetic slab under different biased fields at 21.5 GHz. The refractive index varies extremely slowly as the external field increases.

Equations (1)

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Z±=(1+S11±)2S21±2(1S11±)2S21±2,ein±k0d=X±±i1X±2,

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