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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 15635–15642
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Magneto-optical effects in interacting localized and propagating surface plasmon modes

Jorge F. Torrado, Juan B. González-Díaz, María U. González, Antonio García-Martín, and Gaspar Armelles  »View Author Affiliations


Optics Express, Vol. 18, Issue 15, pp. 15635-15642 (2010)
http://dx.doi.org/10.1364/OE.18.015635


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Abstract

We report that the effect of an external magnetic field on the propagation of surface plasmons can be effectively modified through the coupling between localized (LSP) and propagating (SPP) surface plasmons. When these plasmon modes do not interact, the main effect of the magnetic field is a modification of the wavevector of the SPP mode, leaving the LSP virtually unaffected. Once both modes start to interact, there is a strong variation of the magnetic field induced modification of the SPP dispersion curve and, simultaneously, the LSP mode becomes sensitive to the magnetic field.

© 2010 OSA

1. Introduction

Optical systems providing asymmetric propagation between the backward and forward directions are interesting both from the fundamental and the applied point of view [1

1. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

]. This property is well known in magneto-optical materials [2

2. A. Zvezdin, and V. Kotov, Modern Magnetooptics and Magnetooptical Materials, Condensed Matter Physics (Taylor and Francis Group, New York, 1997).

], and for example in conventional optics the design of most optical isolators relies on the Faraday effect. The structuration of the magneto-optical dielectrics in what are called magnetic photonic crystals allows a further control of the effect of the magnetic field on the propagation of light, and with an appropriate design the magnetic field induced modification of the photonic band structure could be as important as to allow the appearance of unidirectional propagating modes [3

3. A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003). [CrossRef]

8

8. 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]

]. These works have opened the door to a new range of magneto-photonic devices immune to back-scattering losses. Considering that surface plasmons (SP) are a promising route toward the development of miniaturized photonic devices [9

9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

,10

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

], and that the magneto-optical actuation in magneto-plasmonic microinterferometers has already been demonstrated [11

11. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. García-Martín, T. Thomay, A. Leitenstorfer, and R. Braschitsch, “Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers,” Nat. Photonics 4, 107 (2010). [CrossRef]

], it seems appropriate to analyze the effect of the nanostructuration of plasmonic system on their behavior under an applied magnetic field.

In a flat and non-structured metal-dielectric interface, a magnetic field applied in the plane of the interface and perpendicular to the SP propagation direction adds a linear modification to the SP wavevector [7

7. 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]

,11

11. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. García-Martín, T. Thomay, A. Leitenstorfer, and R. Braschitsch, “Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers,” Nat. Photonics 4, 107 (2010). [CrossRef]

13

13. R. E. Camley, “Nonreciprocal surface waves,” Surf. Sci. Rep. 7(3-4), 103–187 (1987). [CrossRef]

], leading to an asymmetric propagation of the SP in the forward and backward direction (ω(k) ≠ ω(-k)). If the interface is nanostructurated, the dispersion relation of the surface plasmon is modified [14

14. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996). [CrossRef] [PubMed]

] and this could change the effect that the applied magnetic field has on the surface plasmon propagation. In this letter, we examine the variation under an applied magnetic field of the SP band structure of a metallic plasmonic crystal consisting on a magnetoplasmonic layer, a dielectric spacer and an array of Au nanodisks deposited on the top. Magnetoplasmonic layers are hybrid structures made of noble and ferromagnetic metals, so that its magneto-optical activity is governed by the ferromagnetic component and appreciable changes of the optical properties can be obtained by applying low magnetic fields [11

11. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. García-Martín, T. Thomay, A. Leitenstorfer, and R. Braschitsch, “Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers,” Nat. Photonics 4, 107 (2010). [CrossRef]

,15

15. C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64(23), 235422 (2001). [CrossRef]

17

17. E. Ferreiro-Vila, J. B. González-Díaz, R. Fermento, M. U. González, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, D. Meneses-Rodríguez, and E. Muñoz-Sandoval, “Intertwined magneto-optical and plasmonic effects in Ag/Co/Ag layered structures,” Phys. Rev. B 80(12), 125132 (2009). [CrossRef]

]. Our metallic plasmonic crystal sustains two kinds of SP modes: localized (LSP) on the Au nanodisks and propagating or surface plasmon polaritons (SPP) on the magnetoplasmonic layer, as in purely plasmonic systems [18

18. J. Cesario, R. Quidant, G. Badenes, and S. Enoch, “Electromagnetic coupling between a metal nanoparticle grating and a metallic surface,” Opt. Lett. 30(24), 3404–3406 (2005). [CrossRef]

,19

19. A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: Experiment and numerical calculations,” Phys. Rev. B 74(15), 155435 (2006). [CrossRef]

]. Upon the right excitation conditions these two plasmon modes may interact [19

19. A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: Experiment and numerical calculations,” Phys. Rev. B 74(15), 155435 (2006). [CrossRef]

22

22. A. Ghoshal, I. Divliansky, and P. G. Kik, “Experimental observation of mode-selective anticrossing in surface-plasmon-coupled metal nanoparticle arrays,” Appl. Phys. Lett. 94(17), 171108 (2009). [CrossRef]

], modifying the dispersion curves and leading to hybrid LSP/SPP modes due to the strong coupling between them. Here we show that, through the analysis of the magneto-optical response, we are able to follow this interaction/hybridization process. Moreover, we demonstrate that these interactions substantially alter the effect of the magnetic field on both SP modes. This result points out the feasibility of designing more complex magnetoplasmonic structures with tailored asymmetric propagation.

2. Magneto-optical measurements configuration

Samples were fabricated using several deposition and lithography steps. A trilayer of 16 nm Au / 10 nm Co/ 6 nm Au was deposited on glass by sputtering and covered by a thermally evaporated 20 nm thick SiO2 layer. Squared arrays of gold nanodisks were fabricated on top by means of electron beam lithography followed by thermal evaporation and lift-off. The disk diameter and height are 110 nm and 20 nm respectively. The array period has been varied from 300 nm to 400 nm.

The sketch of the experimental configuration is displayed as an inset in Fig. 1
Fig. 1 (a) Spectral dependence of the TMOKE signal for an angle of incidence of 50° in the regions without and with (300 nm array periodicity) gold disks. The insets show the sketch of the experimental configuration and the evolution of the reflectivity with the applied magnetic field. (b) “Renormalized” TMOKE signal, corresponding to the TMOKE signal of the region with disks minus that of the region without disks.
. The magnetic field is applied in the plane of the sample (xy) and perpendicular to the plane of incidence (xz). The incident and reflected light are p-polarized. The lower inset on the figures shows the dependence of the reflected light (measured at wavelength 532 nm) on the applied magnetic field. This provides information on the magnetic field dependence of the y component of the Co layer magnetization My. The shape of this loop is the same in sample regions with and without disks. As can be seen, the magnetic field needed to saturate the Co layer is 10 mT. The transverse Magneto-Optical Kerr Effect (TMOKE) signal is then defined as the normalized difference of the reflectivity upon reversal at saturation:

TMOKER(+M)R(M)R(+M)+R(M).
(1)

Figure 1(a) shows the TMOKE signal for an angle of incidence θinc of 50 degrees and a period of the array of 300 nm, together with that of one sample region without disks (consisting only of the metallic trilayer covered by the SiO2 layer). As can be observed, the TMOKE signal of the region without disks shows no particular features and its intensity decreases as we increase the wavelength, as expected for MO response of a continuous Co film [23

23. C. Dehesa-Martinez, L. Blanco-Gutierrez, M. Vélez, J. Diaz, L. M. Alvarez-Prado, and J. M. Alameda, “Magneto-optical transverse Kerr effect in multilayers,” Phys. Rev. B 64(2), 024417 (2001). [CrossRef]

]. On the other, the spectrum of the disks region presents additional features that can be associated with the LSP and SPP modes as we will see below. At this point, we would like to point out that the TMOKE allows to distinguish the SPP from the LSP. For the SPP the magnetic field modulates the SPP wavevector, which induces a shift of the reflectivity curve [16

16. J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukascew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007). [CrossRef]

,17

17. E. Ferreiro-Vila, J. B. González-Díaz, R. Fermento, M. U. González, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, D. Meneses-Rodríguez, and E. Muñoz-Sandoval, “Intertwined magneto-optical and plasmonic effects in Ag/Co/Ag layered structures,” Phys. Rev. B 80(12), 125132 (2009). [CrossRef]

], manifesting thus in a “S-type” shape signal, whereas for the LSP the effect is a variation of the intensity [24

24. G. Armelles, J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, M. Ujué González, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 16(20), 16104–16112 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-20-16104. [CrossRef] [PubMed]

,25

25. J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4(2), 202–205 (2008). [CrossRef] [PubMed]

], giving rise to a “peak-type” signal.

To unmask the TMOKE signal from the featureless spectral shape associated with the MO response of the continuous Co layer, we will analyze the difference between the TMOKE signal of the regions with and without disks. This “renormalized” TMOKE is seen in Fig. 1(b) where the two structures, S-like and peak-type, labeled P1 (Δ) and L (○) respectively, are depicted and their energy locations are to be taken at the zero-crossing of the S-feature for P1 and at the top most of the peak for L.

3. Results and discussion

Moreover, the theoretical spectra shown in Fig. 3 also confirm that the main effect of the magnetic field on the SPP is to modify its wavevector, since in the spectral region of the SPP mode the theoretical TMOKE spectra and the energy derivative spectra have a similar shape. The calculated magnetic field-induced modification of the SPP wavevector, ΔE, is also shown in Fig. 4(b) (continuous red line). As can be observed the theoretical curve reproduces the experimental trends: as we increase the k value the modification of the SPP wavevector decreases. On the other hand, the calculated spectra also allows to extract the ΔE modifications for the LSP (dot-dashed black line), which experimentally are beyond the resolution capabilities of our system. For the LSP, ΔE increases as we increase the k value, and this increase is due to the interaction with the SPP mode. In the interaction region there is a transfer of character between the localized and the propagating modes, and in particular we see here how the magnetic field-induced effect decreases in the SPP mode to pass to the LSP one. We understand this exchange of sensitivity to the magnetic field between the two plasmon modes as a direct demonstration of the strong coupling between them. Finally, the dotted line included in Fig. 4(b) corresponds to the calculated SPP wavevector modulation for a Au/Co/Au trilayer covered by 20 nm SiO2 with no disks on the top, showing as a reference the values of the modulation when no LSP-SPP interaction is involved (note that the k values here have been translated by one reciprocal wavevector to plot this modulation together with the values corresponding to the metallic plasmonic crystal structure). As can be seen, there is a small dependence of ΔE with the wavevector, due to the spectral behavior of the magneto-optical constants; however, this dependence is much less abrupt than in the case comprising LSP-SPP interaction.

4. Conclusions

Summarizing, far from the LSP-SPP interaction region, the magnetic field induces the expected wavevector modification for the SPP mode whereas the frequency of the LSP mode hardly depends on the Co magnetization. However, once both modes start to interact and due to their coupling, there is a strong reduction of the dependence of the SPP dispersion curve with the Co magnetization, this dependence being transferred to the LSP mode. Moreover, in this work we have analyzed the situation with a fixed thickness of the SiO2 spacer layer. Being the surface plasmons surface waves with exponential decays, the interaction between both modes will be highly dependent on the thickness of the spacer and the overlap between the two modes. The analysis of the behavior of the system as a function of the thickness of the SiO2 layer would be of high interest, in order to identify the configuration of maximum coupling between the two modes.

From a more general point of view, these results show that the nanostructuration of the magnetoplasmonic system does indeed modify the effect of the magnetic field on the SP modes, being this study a first step towards the development of more complex systems where the asymmetric propagation of surface plasmons can be further engineered.

Acknowledgments

This work was supported by the EU (NMP3-SL- 2008-214107-Nanomagma), the Spanish MICINN (“MAGPLAS” MAT2008-06765-C02-01/NAN and “FUNCOAT” CONSOLIDER INGENIO 2010 CSD2008-00023), the Comunidad de Madrid (“NANOBIOMAGNET” S2009/MAT-1726 and “MICROSERES-CM” S2009/TIC-1476), and CSIC (“CRIMAFOT” PIF08-016-4). We thank A. Cebollada and J. M. García-Martín for growing and characterizing the Au/Co/Au trilayers and reading this manuscript, and R. Quidant and G. Badenes for fruitful discussions.

References and links

1.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

2.

A. Zvezdin, and V. Kotov, Modern Magnetooptics and Magnetooptical Materials, Condensed Matter Physics (Taylor and Francis Group, New York, 1997).

3.

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003). [CrossRef]

4.

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]

5.

F. D. M. 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]

6.

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]

7.

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]

8.

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]

9.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

10.

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

11.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. García-Martín, T. Thomay, A. Leitenstorfer, and R. Braschitsch, “Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers,” Nat. Photonics 4, 107 (2010). [CrossRef]

12.

R. F. Wallis, in Electromagnetic surface modes (John Wiley & Sons, 1982), chap. 15 – Surface magnetoplasmons on semiconductors, pp. 575–631.

13.

R. E. Camley, “Nonreciprocal surface waves,” Surf. Sci. Rep. 7(3-4), 103–187 (1987). [CrossRef]

14.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996). [CrossRef] [PubMed]

15.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64(23), 235422 (2001). [CrossRef]

16.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukascew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007). [CrossRef]

17.

E. Ferreiro-Vila, J. B. González-Díaz, R. Fermento, M. U. González, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, D. Meneses-Rodríguez, and E. Muñoz-Sandoval, “Intertwined magneto-optical and plasmonic effects in Ag/Co/Ag layered structures,” Phys. Rev. B 80(12), 125132 (2009). [CrossRef]

18.

J. Cesario, R. Quidant, G. Badenes, and S. Enoch, “Electromagnetic coupling between a metal nanoparticle grating and a metallic surface,” Opt. Lett. 30(24), 3404–3406 (2005). [CrossRef]

19.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: Experiment and numerical calculations,” Phys. Rev. B 74(15), 155435 (2006). [CrossRef]

20.

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95(11), 116802 (2005). [CrossRef] [PubMed]

21.

Y. Chu and K. B. Crozier, “Experimental study of the interaction between localized and propagating surface plasmons,” Opt. Lett. 34(3), 244–246 (2009). [CrossRef] [PubMed]

22.

A. Ghoshal, I. Divliansky, and P. G. Kik, “Experimental observation of mode-selective anticrossing in surface-plasmon-coupled metal nanoparticle arrays,” Appl. Phys. Lett. 94(17), 171108 (2009). [CrossRef]

23.

C. Dehesa-Martinez, L. Blanco-Gutierrez, M. Vélez, J. Diaz, L. M. Alvarez-Prado, and J. M. Alameda, “Magneto-optical transverse Kerr effect in multilayers,” Phys. Rev. B 64(2), 024417 (2001). [CrossRef]

24.

G. Armelles, J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, M. Ujué González, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 16(20), 16104–16112 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-20-16104. [CrossRef] [PubMed]

25.

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4(2), 202–205 (2008). [CrossRef] [PubMed]

26.

A. García-Martín, G. Armelles, and S. Pereira, “Light transport in photonic crystals composed of magneto-optically active materials,” Phys. Rev. B 71(20), 205116 (2005). [CrossRef]

OCIS Codes
(210.3810) Optical data storage : Magneto-optic systems
(210.3820) Optical data storage : Magneto-optical materials
(240.6680) Optics at surfaces : Surface plasmons
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 21, 2010
Revised Manuscript: June 16, 2010
Manuscript Accepted: June 17, 2010
Published: July 8, 2010

Citation
Jorge F. Torrado, Juan B. González-Díaz, María U. González, Antonio García-Martín, and Gaspar Armelles, "Magneto-optical effects in interacting localized and propagating surface plasmon modes," Opt. Express 18, 15635-15642 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15635


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References

  1. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]
  2. A. Zvezdin and V. Kotov, Modern Magnetooptics and Magnetooptical Materials, Condensed Matter Physics (Taylor and Francis Group, New York, 1997).
  3. A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003). [CrossRef]
  4. 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]
  5. F. D. M. 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]
  6. 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]
  7. 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]
  8. 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]
  9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  10. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
  11. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. García-Martín, T. Thomay, A. Leitenstorfer, and R. Braschitsch, “Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers,” Nat. Photonics 4, 107 (2010). [CrossRef]
  12. R. F. Wallis, "Surface magnetoplasmons on semiconductors," in Electromagnetic surface modes (John Wiley & Sons, 1982), Chap. 15 – , pp. 575–631.
  13. R. E. Camley, “Nonreciprocal surface waves,” Surf. Sci. Rep. 7(3-4), 103–187 (1987). [CrossRef]
  14. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996). [CrossRef] [PubMed]
  15. C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64(23), 235422 (2001). [CrossRef]
  16. J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukascew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007). [CrossRef]
  17. E. Ferreiro-Vila, J. B. González-Díaz, R. Fermento, M. U. González, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, D. Meneses-Rodríguez, and E. Muñoz-Sandoval, “Intertwined magneto-optical and plasmonic effects in Ag/Co/Ag layered structures,” Phys. Rev. B 80(12), 125132 (2009). [CrossRef]
  18. J. Cesario, R. Quidant, G. Badenes, and S. Enoch, “Electromagnetic coupling between a metal nanoparticle grating and a metallic surface,” Opt. Lett. 30(24), 3404–3406 (2005). [CrossRef]
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