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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27356–27370
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Mimicking electromagnetically induced transparency in the magneto-optical activity of magnetoplasmonic nanoresonators

G. Armelles, A. Cebollada, A. García-Martín, M. U. González, F. García, D. Meneses-Rodríguez, N. de Sousa, and L. S. Froufe-Pérez  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 27356-27370 (2013)
http://dx.doi.org/10.1364/OE.21.027356


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Abstract

We show that the interaction between a plasmonic and a magnetoplasmonic metallic nanodisk leads to the appearance of magneto-optical activity in the purely plasmonic disk induced by the magnetoplasmonic one. Moreover, at specific wavelengths the interaction cancels the net electromagnetic field at the magnetoplasmonic component, strongly reducing the magneto-optical activity of the whole system. The MO activity has a characteristic Fano spectral shape, and the resulting MO inhibition constitutes the magneto-optical counterpart of the electromagnetic induced transparency.

© 2013 Optical Society of America

1. Introduction

In complex optical structures, the electromagnetic interaction between the constituent elements strongly determines the response of the whole system. Plasmonics offer numerous examples of this, with a variety of complex architectures including core-shell particles [1

1. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

], nanoantennas [2

2. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

4

4. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101(11), 116805 (2008). [CrossRef] [PubMed]

], dimers [5

5. K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

9

9. C. Wadell, T. J. Antosiewicz, and C. Langhammer, “Optical absorption engineering in stacked plasmonic Au-SiO₂-Pd nanoantennas,” Nano Lett. 12(9), 4784–4790 (2012). [CrossRef] [PubMed]

], oligomers [10

10. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010). [CrossRef] [PubMed]

,11

11. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef] [PubMed]

], periodic arrays [12

12. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120(23), 10871–10875 (2004). [CrossRef] [PubMed]

,13

13. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

], etc. The diverse direct consequences of these interactions carry both fundamental and technological implications. The strong enhancement of the electromagnetic field in subwavelength spatial regions [14

14. J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. G. de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005). [CrossRef]

,15

15. A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, “Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles,” Phys. Rev. B 72(16), 165409 (2005). [CrossRef]

], the building up of bright and dark modes [16

16. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005). [CrossRef] [PubMed]

18

18. Z.-J. Yang, Z.-S. Zhang, L.-H. Zhang, Q.-Q. Li, Z.-H. Hao, and Q.-Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett. 36(9), 1542–1544 (2011). [CrossRef] [PubMed]

] or the Fano resonances exhibited in the optical signal [19

19. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

21

21. B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano 5(11), 8999–9008 (2011). [CrossRef] [PubMed]

], to name a few, open research and application areas in the development of nanoantennas, higher sensitivity sensors, novel telecommunication architectures/devices, etc [22

22. A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012). [CrossRef] [PubMed]

25

25. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

]. In order to control and even boost at will such optical responses, one can make use of the geometry and the spatial arrangement of the constituting elements. These morphological and configurational factors determine how the whole entity interacts with an electromagnetic field. In this scenario, the incorporation of magnetic active character into the plasmonic system by adding a ferromagnetic component, to form the so-called magnetoplasmonic structures, introduces an additional degree of freedom. Examples of the potentiality of magnetoplasmonics are the development of active plasmonic configurations whose properties can be externally tuned by the application of a magnetic field or structures with enhanced magneto-optical activity [26

26. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. M. Garcia-Martin, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010). [CrossRef]

30

30. J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat Commun 4, 1599 (2013). [CrossRef] [PubMed]

].

Focusing our attention on complex interacting plasmonic systems with magneto-optical activity, it is convenient to consider a simple picture by factorizing the component elements in simple units, those excited by the electromagnetic field, i.e. point-like dipoles. A point dipole in the presence of an external, steady, magnetic field, experiences a modification of its dipole moment that depends on the relative dipole-magnetic field orientation. In particular, if they are perpendicularly oriented, the dipole rotates due to the Lorentz force [31

31. B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104(14), 147401 (2010). [CrossRef] [PubMed]

], and this rotation can be seen as a new degree of freedom for the interactions in plasmonic structures. Moreover, the Lorentz force depends on the material, being stronger for ferromagnetic components. This makes it possible to design structures where this force is spatially different by selecting different materials in its interior, therefore enriching the interaction pattern. In this work we will explore this phenomenology using nanodisks dimers consisting of a magnetoplasmonic and a plasmonic unit. We will show that, due to the electromagnetic interaction, a pronounced dip in the spectral dependence of the magneto-optical activity is observed, exhibiting a characteristic Fano shape. This reduction of the magneto-optical activity is similar to the electromagnetically induced transparency effects observed in numerous physical systems [32

32. S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990). [CrossRef] [PubMed]

36

36. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef] [PubMed]

].

2. Coupled oscillators: mechanical and dipolar models

Let us start by using a simplified model system that considers the plasmonic components, from a classical point of view, as masses coupled by springs (coupled spring resonators) [9

9. C. Wadell, T. J. Antosiewicz, and C. Langhammer, “Optical absorption engineering in stacked plasmonic Au-SiO₂-Pd nanoantennas,” Nano Lett. 12(9), 4784–4790 (2012). [CrossRef] [PubMed]

]. In this case, the simple plasmonic structure without external magnetic field would be two point masses coupled in one dimension [Fig. 1(a)
Fig. 1 (a) Spring model representing a two coupled masses system excited by an harmonic force, F(t), along x axis. Left side: uncharged masses. Right side-(Media 1): one of the masses (blue) is charged (q) and a static magnetic field (B) is applied along the z direction, inducing a Lorentz force, Fl(t), along the y direction. The y-movement is transferred to the other mass through the coupling. (b) Two interacting electric dipoles, representing two metallic disks, excited by an incident beam polarized along the x axis. Left side: No disk has magneto-optical activity and the reflected (Er) and transmitted (Et) light have the same polarization direction than the incident (Ei) light. Right side: one of the disks (blue) has magneto-optical activity and a static magnetic field (B) applied along the z direction induces a rotation of its electric dipole, which is transferred to the other dipole through the interaction. The rotation modifies the polarization direction of the reflected (Er) and transmitted (Et) light.
, left side]. This system is characterized by two resonant eigenmodes, symmetric and anti-symmetric in character. Now, still classically, if one of the masses is charged and a magnetic field is present (applied along the z-direction), that mass would experience a Lorentz force along the y-direction [Fig. 1(a), right side] (Media 1) and therefore it will also move along the y-axis. Due to the interaction, this movement is transferred to the uncharged particle (see Appendix A for the full development of equations governing this system).

Going now to the real plasmonic case, simple structures that resemble this two coupled spring resonators system are metallic disks dimers spatially separated by a dielectric. The interaction between the electric dipoles gives rise to bright and dark modes (or more precisely, superradiant and subradiant modes), whose spectral position and character can be tuned by the thickness of the separating dielectric [7

7. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

,37

37. T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25(4), 659–667 (2008). [CrossRef]

,38

38. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-13287. [CrossRef] [PubMed]

]. In the simple model presented in Fig. 1(b), left side, the bright mode corresponds to the configuration in which the electric dipoles are oriented parallel to each other (symmetric mode), while in the dark case the dipoles are oriented antiparallel (anti-symmetric mode). In both cases the electric dipoles are along x-axis (parallel to the electric field of the incoming light). If one of the disks has ferromagnetic character, the application of a magnetic field along z direction will induce a rotation of its associated dipole about this axis [Fig. 1(b), right side]. Extrapolating what it is obtained in the spring-mass case, the transverse oscillation induced in the uncharged mass will manifest here as an induced rotation of the dipole of the non-ferromagnetic metallic disk. The combined rotation of both dipoles will cause polarization conversion effects. In this sense, magneto-optics (MO) is the appropriate tool to explore this new degree of freedom, since it provides a direct measurement of the magnetic field induced polarization conversion.

3. Optical and magneto-optical response of nanoresonators

The analyzed structures consist of a pure Au nanodisk separated by a SiO2 spacer from a 2nmCo/4nmAu multilayer nanodisk. The presence of Au in the bottom magnetoplasmonic disk reduces its optical losses as compared to a pure ferromagnetic metal disk [29

29. G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013). [CrossRef]

].The disks were fabricated using hole-mask colloidal lithography and evaporation (electron beam evaporation for Co and SiO2 layers and thermal evaporation for Au layers) [28

28. J. C. Banthí, D. Meneses-Rodríguez, F. García, M. U. González, A. García-Martín, A. Cebollada, and G. Armelles, “High magneto-optical activity and low optical losses in metal-dielectric Au/Co/Au-SiO2 magnetoplasmonic nanodisks,” Adv. Mater. 24(10), OP36–OP41 (2012). [CrossRef] [PubMed]

,39

39. H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole–mask colloidal lithography,” Adv. Mater. 19(23), 4297–4302 (2007). [CrossRef]

]. In Fig. 2(a)
Fig. 2 (a) Schematic drawing of the nanoresonators composed of a purely plasmonic Au disk and a magnetoplasmonic Au/Co superlattice disk separated by a dielectric spacer. (b) Polar Kerr loop of a characteristic sample. The presence of multiple Co/Au interfaces reduces the value of the magnetic field needed to saturate the nanodisks in the direction perpendicular to the sample plane. (c), (d) Cross section and planar view SEM pictures, respectively, of a representative sample. The images show the homogeneous and random distribution of nanoresonators and their truncated conical shape and internal structure.
we show a sketch of the internal structure of each disk with the characteristic individual layer thickness. The Au/Co multilayer disk exhibits perpendicular magnetic anisotropy, reducing the magnetic field required to achieve saturation in polar configuration [Fig. 2(b)]. Figure 2(c) presents a cross section Scanning Electron Microscopy image of the same structure showing the truncated nanocone shape of the obtained nanoresonators, whose typical lower and upper disk diameters are 110-120nm and 70-90nm respectively. In this cross section image, both the metallic and dielectric components of the nanodisks are clearly distinguishable. Additionally, in Fig. 2(d) a top view image of a representative structure, showing the homogeneous distribution of the disks over large areas, is presented.

In the left column of Fig. 3
Fig. 3 (a) Extinction and (b) MO activity spectra of the nanoresonators as a function of SiO2 thickness. The different dashed horizontal lines indicate the zero value for each spectrum above the line. The 3D graphs on top of each panel show the results obtained from theoretical calculations of the same structures. The blue, green and red diamonds appearing in the experimental MO response for 20 nm SiO2 correspond to the spectral positions where the Ez field distributions are calculated [see Fig. 4].
we show the measured extinction spectra as a function of the SiO2 spacer thickness. As it can be seen, the spectral dependence of the extinction strongly varies as a function of the dielectric thickness, i.e. with the interdisk interaction. For the extreme case of thick SiO2 (50 nm), both metallic disks interact weakly, and as a consequence two peaks corresponding to the individual disk resonances are observed. Thus, the high-energy peak can be identified with the resonance of the top metallic disk (smaller diameter) and the low energy one with that of the bottom one (larger diameter). As the SiO2 spacer gets thinner, the position and relative intensity of both resonances changes. In this situation, both modes become hybridized [1

1. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

,7

7. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

] and we can no longer talk of individual modes but of complex modes of symmetric and anti-symmetric character. The symmetric mode, occurring at higher energies, strongly couples to the incident light and as a consequence has a larger extinction (bright or superradiant mode). On the other hand, the anti-symmetric mode, occurring at lower energies, couples weakly to the light, resulting in a lower extinction peak (dark or subradiant mode). Qualitatively, the symmetric mode is clearly observed for all the structures, while the anti-symmetric one gradually decreases in intensity, shifting to lower energies as the spacer becomes thinner, becoming practically unobservable for SiO2 thickness below 15 nm.

To understand this phenomenology we have performed rigorous simulations for both the extinction and MO response, based on scattering matrix techniques [41

41. 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]

,42

42. B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012). [CrossRef]

] and FDTD [43

43. FDTD Solutions” software from Lumerical Inc. (www.lumerical.com).

] as well as FEM [44

44. COMSOL Multiphysics®.

] codes. The three methods provide equivalent results. The evolution of the spectra as a function of the SiO2 thickness is depicted as 3D graphs on top of the corresponding columns in Fig. 3, exhibiting a very good agreement with the experimental results, both regarding the intensity, spectral shape, and peak position evolution. In addition to the mentioned extinction and MO activity, the performed simulations allow also obtaining the EM field distribution in regions around the nanodisks. As an example we present in Fig. 4
Fig. 4 (a) Calculated near field intensity of the Ez component for a nanoresonator with 20 nm SiO2 spacer in two planes above the top disk and below the bottom one, with the incident field polarized along the x direction and in the absence of an external magnetic field. This distribution reflects the excitation of two dipoles along the x direction. The insets indicate the corresponding charges and dipole orientations (indicated by the black arrows) according to the Ez distribution for the different cases. The red (blue) arrows in the insets represent the positive (negative) values of the Ez field component. (b) Difference of the Ez components for magnetic saturation along opposite directions in the same planes and for the same structure. This difference accounts for the effect of the applied magnetic field: The appearance of a dipole along the y direction for both the magnetoplasmonic (intrinsic dipole) and the plasmonic (induced dipole) disks. In both cases, the components for three different wavelengths labelled as diamonds in Fig. 3 are shown.
the near field distribution of the z-component of the electric field, for the sample with 20 nm SiO2 spacer, in two planes at ten nanometres above the top and below the bottom disks respectively, both in the absence of an external magnetic field and as the difference for magnetic saturations along opposite directions. These distributions have been calculated for the three wavelengths corresponding to the two maxima and the minimum of the MO activity (labelled with red, green and blue diamonds in Fig. 3).

The Ez component without external magnetic field (extinction measurements situation) is presented in the left panel of Fig. 4. There, for the low energy position (red framed) the EM distribution for each metallic disk resembles that of a point dipole oscillating along the x-direction, with similar Ez intensity for both upper and lower disk, and with the individual dipoles (represented by the black arrows in Fig. 4) oriented antiparallel. (Note that the Ez field of a dipole changes sign when it is seen from above or from below). This situation therefore corresponds to the aforementioned anti-symmetric configuration. On the other hand, for the high energy position (blue framed) the EM distribution for each metallic disk corresponds also to a dipole-like distribution along the x-direction but now the individual dipoles corresponding to the disks are oriented parallel to each other (symmetric mode). As it can be seen, the intensity of the Ez component for both disks is, again, similar, but larger than that for the low energy case. This is consistent with the higher extinction value obtained for the symmetric mode respect to the anti-symmetric one. Finally, at the intermediate energy (green framed), the distribution is still dipolar-like and would correspond to a symmetric-like mode, but the intensity distribution is not equally distributed, with a larger value of the Ez component in the upper disk than for the lower one.

Next, in the right panel of Fig. 4 we show the difference between Ez components at magnetic saturation along opposite directions, Ez(H)-Ez(-H) (MO measurements situation) which reflects the magnetic field effect on the field distributions of the system eliminating the purely optical contribution. For the three energies, a dipolar-like distribution is still observed, but the resulting balance between magnetic saturation along opposite directions is an Ez component corresponding to a point dipole oscillating along the y-direction. In other words, the effect of the magnetic field is to induce a “dipole” along the y-direction that is two orders of magnitude smaller in intensity than the dipole generated along the x-direction.

On the other hand, regarding the symmetry character of the resulting modes, it is maintained for high and low energies with respect to the case of no magnetic field applied: anti-symmetric and symmetric for low and high energy respectively. Regarding the intensities of the Ez fields, it is similar for top and bottom disks and for both energies. The induction by the magnetic field of a dipole along y-direction is pretty intuitive for the bottom disk, since it is simply due to the presence of ferromagnetic material in it. What is in principle not as intuitive is the presence of the same component in the upper disk, since it has no ferromagnetic nature. This y-component in the upper disk is induced by the “dipole” of the bottom disk, reaching a sizeable magnitude. More interestingly, the situation for the intermediate energy, corresponding to the minimum of the MO activity, is quite different. In this case both lower and upper disks, regardless the presence of a ferromagnetic component in its interior, exhibit almost zero MO-induced “dipoles”.

4. Discussion

From the observation of the resulting Ez components, one can conclude that the application of a magnetic field has three main effects: First, it generates a “dipolar” component along the y-direction not present without magnetic field; second, mediated by the interaction between the disks, the bottom disk, which has a ferromagnetic component, induces a “dipole” along the y-direction in the upper disk, in other words it generates a MO activity in a disk which has no ferromagnetic nature; third, there is a spectral region were both “dipoles” vanish almost completely, and therefore, the MO activity is strongly reduced.

To understand the physical origin of this phenomenology, let us consider the field distributions obtained for the intermediate energy region shown in the left panel of Fig. 4. In that region, the intensity of the field at the bottom disk clearly decreases with respect to the other two energies considered. This suggests that the electric field induced by the upper disk destructively interferes with the incoming electric field. This can be understood from the simple model based on two interacting point dipoles. In this model the different components of the dipoles can be expressed as:
{p1x=E0,1xDα1[1+Gα2xx(eiδGα1)G3α1(α2xx2+α2xy2)eiδ]p1y=E0,1xDGα1α2xy[eiδ+Gα1]p2x=E0,1xD[α2xxG2α1(α2xx2+α2xy2)][eiδ+Gα1]p2y=E0,1xDα2xy[eiδ+Gα1],
(1)
where D=12G2α1α2xx+G4α12(α2xx2+α2xy2), E0,1x is the amplitude of the incident electric field at point dipole p1, δ is the phase difference of the incident field at the two dipole positions, αi,jk are the corresponding components of the polarizability tensor of each dipole, and G is the field propagator (the complete derivation of these expressions is given in Appendix B).

This phenomenon can be viewed as the MO counterpart of the electromagnetic induced transparency. For a specific spectral region, the EM interaction between the two disks gives rise to a situation where the total EM field at the MO active element is minimized, therefore strongly reducing the MO activity of the whole system (see Eq. (1). This is observed in Fig. 5(a)
Fig. 5 Fano resonance in the magneto-optical activity. (a) Experimental spectra of the MO activity for the structures with 20 nm and 50 nm SiO2 spacer, corresponding to interacting and non-interacting situations, respectively. For the interacting situation a clear Fano resonance shape is observed. The inset shows the difference between the two spectra, resulting in a narrow peak. (b) Theoretical MO activity spectra obtained for a structure with 20nm SiO2 spacer and for the same structure but without the upper metallic disk. The inset shows the MO spectra obtained using the simple point dipole model.
, where we present the experimental MO activities for two different situations corresponding to very weak interaction (the 50 nm SiO2 structure) and a situation where the two disks clearly interact (the 20 nm SiO2 structure). For the very weak interacting system only a broad peak is observed, corresponding to the MO activity of the magnetoplasmonic disk. However, for the system where the two metallic disks interact, a narrow dip with a clear Fano-like shape is obtained. The difference between both spectra is also shown (inset), presenting a narrow peak.

5. Summary

In conclusion, MO activity in non-MO elements can be induced via electromagnetic interaction with MO active elements. This effect has been shown in magnetoplasmonic resonators consisting of a Au plasmonic disk separated by a SiO2 layer from a MO active magnetoplasmonic (Au/Co) disk. When a magnetic field is applied perpendicular to the disks, it produces an electric dipole along the perpendicular direction of the electric field of the incoming light in the MO active disk. This electric dipole induces a MO activity in the non-magnetic Au disk. Additionally, we have shown the existence of an electromagnetically induced magneto-optical transparency in these systems. This is due to the interference at the MO disk between the incidence electromagnetic field and that generated by the non-MO one, leading to a Fano-like spectral dependence of the MO activity and to a strong reduction of the MO activity. This may find applications in sensing architectures based on MO-Fano resonances. Optical Fano resonances have already demonstrated their potential applicability [45

45. A. A. Yanik, A. E. Cetin, M. Huang, A. Artar, S. H. Mousavi, A. Khanikaev, J. H. Connor, G. Shvets, and H. Altug, “Seeing protein monolayers with naked eye through plasmonic Fano resonances,” Proc. Natl. Acad. Sci. U.S.A. 108(29), 11784–11789 (2011). [CrossRef] [PubMed]

47

47. P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gómez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5(6), 5151–5157 (2011). [CrossRef] [PubMed]

]. Additionally, plasmon excitation enhancement of the MO activity has also shown improvement of the performance of standard plasmonic sensors [48

48. B. Sepúlveda, A. Calle, L. M. Lechuga, and G. Armelles, “Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor,” Opt. Lett. 31(8), 1085–1087 (2006). [CrossRef] [PubMed]

,49

49. V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011). [CrossRef] [PubMed]

]. Combining both effects may allow the generation of novel sensing platforms based on MO-Fano resonances. Since the observed phenomenon is driven by the resonance of the upper disk, modifications of the dielectric environment may strongly affect it and, as a consequence, the overall observed Fano resonance characteristics.

Appendix A - Spring-mass model

A physically simple and intuitive model for studying interacting, resonant systems is the damped driven coupled oscillators. This model has been already employed to give a simple picture for systems with two interacting plasmonic modes [9

9. C. Wadell, T. J. Antosiewicz, and C. Langhammer, “Optical absorption engineering in stacked plasmonic Au-SiO₂-Pd nanoantennas,” Nano Lett. 12(9), 4784–4790 (2012). [CrossRef] [PubMed]

,11

11. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef] [PubMed]

,50

50. Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74(2), 259–266 (2006). [CrossRef]

,51

51. T. J. Antosiewicz, S. P. Apell, C. Wadell, and C. Langhammer, “Absorption enhancement in lossy transition metal elements of plasmonic nanosandwiches,” J. Phys. Chem. C 116(38), 20522–20529 (2012). [CrossRef]

]. Going one step further, we can introduce in this mechanical model effects like those of a MO activity in the materials by considering charged masses in a static magnetic field. The presence of the magnetic field and a charged element give rise to the appearance of a Lorentz force Fl=qr˙×B. In the case considered here, the static magnetic field is applied perpendicularly to the driving, external force, therefore the Lorentz force will be perpendicular to both an thus define a plane of movement. Let’s say that the external force is in the x-direction and the magnetic field in the z-direction, then the Lorentz force will be in the y-direction and the plane of movement of the masses will be the x-y plane.

The equations of motion of this model read:
m1r¨1=F1k1r1k12(r1r2)B1r˙1m2r¨2=F2k2r2k12(r2r1)B2r˙2,
(2)
where the particle positions ri are restricted to the x-y plane and referred to its equilibrium state, ki are spring constants, k12is the interaction between the particles, mi are their masses and, more importantly, the damping terms Bi are tensors:
Bi=bi+Fli=[bi00bi]+[0qBiqBi0]
(3)
arising from the Lorentz force:
Fli=qBi[0110](r˙xr˙y).
(4)
It is easy to see that in the absence of a magnetic field, and considering only the friction force in a homogeneous medium, B can be regarded as a scalar term (diagonal with equal eigenvalues) b.

Now, without losing generality, we further assume that m1=m2m, and assume that the external driving force has an harmonic temporal dependence eiωt. Thus, using the following definitions:
ωi2ki/mω122k12/mΓiBi/m(γiωc,iωc,iγi)
(5)
the equations of motion in frequency space become:
1=(ω2ω12+iωΓ1ω122)r1+(ω122)r22=(ω2ω22+iωΓ2ω122)r2+(ω122)r1
(6)
where i is the corresponding Fourier component of the external force, Fi/mi.

In matrix form, this reads as:
M(r1r2)[((Ω12ω122)I+ωωc,1σ2)ω122Iω122I((Ω22ω122)I+ωωc,2σ2)](r1r2)=(12),
(7)
where I is the 2x2 unit matrix, σ2 is the 2x2 Pauli matrix (σ2(0ii0)) and Ωi2ω2ωi2+iωγi.

In the case we are interested in, only one of the particles has MO activity, which is the same as to say that either ωc,1or ωc,2is zero (we have chosen ωc,1to be zero). In order to mimic the photonic case, the external driving force is also special, and is applied to both particles along the x-direction only. The solution is then:
{x1=xD[[Ω12Ω22ω122(Ω12+Ω22)](Ω222ω122)ω2ωc2(Ω12ω122)]y1=xD[iωωcω122(Ω122ω122)]x2=xD[[Ω12Ω22ω122(Ω12+Ω22)](Ω122ω122)]y2=xD[iωωc(Ω12ω122)(Ω122ω122)],
(8)
where D=ω1282(Ω12ω122)ω124(Ω22ω122)+[(Ω22ω122)2ω2ωc2](Ω12ω122)2.

In Fig. 6
Fig. 6 Oscillation amplitude as a function of the frequency of masses 1 (uncharged) and 2 (charged) along x- (left panel) and y- (right panel) direction by using a simple spring-mass model. Inset: Frame of a video showing schematically the evolution with the frequency of the masses’ oscillation for frequency values around the minimum in x-amplitude for the charged mass 2 (in the video, the y-amplitude has been multiplied by a factor 10, and the frequency has been scaled as ωvid = (1 + (ω-0.93) × 50)ω2 for clarity in the visualization) (Media 2).
(Media 2) we show the results obtained from Eq. (9), using x=1 m/s2, ω1 = 0.9ω2, γ1 = 0.02ω2, γ2=0.05ω2, ω12=0.25ω2, ωc=0.01ω2.

Notice that the above exposed problem to solve can be generally written as:

[a0c00a0cc0db0cbd][x1y1x2y2]=A[1010].
(9)

Therefore the solution reads as:
[x1y1x2y2]=AD[ad2dc2+b2abc2c3dcabcabc2ad2dc2+b2abcac3dcac3dcabcada2c2aa2bbcac3dcaba2da2c2a][1010],
(10)
where D=c42ac2d+a2(d2+b2). This in the end gives rise to:

{x1=AD[(c2ad)(cd)+b2a]y1=AD[bc(ca)]x2=AD[(c2ad)(ca)]y2=AD[ba(ca)].
(11)

Appendix B - Point dipole model

It is convenient to work with dimensionless quantities α=k3α˜4π and p=k3p˜4πε0, being p˜the usual electric dipole. It is important to notice that with this definition the optical theorem for a scalar absorptionless particle reads as (2/3)|α|2=Im{α}.

The interaction between the two dipoles is given by the Green tensor, which in its dimensionless form is:
G(r,r)=eikR4πR{(kR)2+ikR1(kR)2I+(kR)23ikR+3(kR)2RRR2}.
(13)
where R is the vector connecting r and r’.

With those definitions the electric field incident on a particle of an ensemble of N particles is given by

Ei=E0,i+ijNG(ri,rj)pj.
(14)

Since the incident wave (E0(r)=E0eikzux) is polarized along the x-axis and its wavevector is parallel to the z-axis (short axis of the particles), the polarization of the particles lies in the x-y plane,
αi=[αi,xxαi,xy0αi,xyαi,xx000αi,zz],
(15)
and the Green tensor that describes the interaction of the two particles (placed along z axis) is diagonal given by:
G(r1,r2)=G(r2,r1)=GI=eikd4πd(kd)2+ikd1(kd)2I,
(16)
being d the distance between the particles. One has to take into account that with the geometry described above the z-direction plays no role and can be excluded. The equations to deal with are:
{α11p1=E0,1+Gp2=E0,1x+Gp2α21p2=E0,2+Gp1=E0,1xeiδ+Gp1
(16)
where αi is the 2x2 x-y part of the tensor described in Eq. (17), and δ = -kd is the phase difference on the incoming wave due to the separation distance d (normally δ1).

With that it is easy to see that we end with the following set of equations:
M(p1p2)[α11GIGIα21](p1p2)=(E0,1E0,1eiδ),
(17)
which has the same structure as Eq. (10) for only one MO dipole (dipole 2).

The solution is now straightforward:
{p1x=E0,1xDα1[1+Gα2xx(eiδGα1)G3α1(α2xx2+α2xy2)eiδ]p1y=E0,1xDGα1α2xy[eiδ+Gα1]p2x=E0,1xD[α2xxG2α1(α2xx2+α2xy2)][eiδ+Gα1]p2y=E0,1xDα2xy[eiδ+Gα1],
(18)
where D=12G2α1α2xx+G4α12(α2xx2+α2xy2).

As it can be seen in Fig. 5, the agreement of the point dipole model with the experimental results and with more elaborated models is very good. Fig. 7
Fig. 7 Wavelength dependence of the normalized dipole magnitudes along the x- (left panel) and y- (right panel) directions obtained using a point dipole model.
shows the results obtained from Eq. (19) for intermediate interaction. It is worth noticing that for the interaction considered the dipole in the y-direction is two orders of magnitude smaller than that in the x-direction, following the results obtained for the fields using the rigorous calculation [Fig. 4]. Also the relative intensities of the dipoles follow that of the fields.

Acknowledgments

We acknowledge J.C. Banthí for his assistance in the growth and characterization of some of the studied samples, B. Caballero for her help with numerical codes, and LINAN-IPICYT (México) for the facilities for SEM characterization. Funding from Spanish Ministry of Economy and Competitiveness through grants “FUNCOAT” CONSOLIDER CSD2008–00023, “NANOLIGHT” CONSOLIDER CSD2007-00046 and MAPS MAT2011–29194-C02–01, and from Comunidad de Madrid through grants “NANOBIOMAGNET” S2009/MAT-1726 and “MICROSERES-CM” S2009/TIC-1476 is acknowledged. L.S. F.-P. acknowledges support from the European Social Fund and CSIC through a JAE-Doc grant.

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OCIS Codes
(160.3820) Materials : Magneto-optical materials
(230.3810) Optical devices : Magneto-optic systems
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: July 30, 2013
Revised Manuscript: September 23, 2013
Manuscript Accepted: September 24, 2013
Published: November 4, 2013

Virtual Issues
Surface Plasmon Photonics (2013) Optics Express

Citation
G. Armelles, A. Cebollada, A. García-Martín, M. U. González, F. García, D. Meneses-Rodríguez, N. de Sousa, and L. S. Froufe-Pérez, "Mimicking electromagnetically induced transparency in the magneto-optical activity of magnetoplasmonic nanoresonators," Opt. Express 21, 27356-27370 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-27356


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References

  1. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003). [CrossRef] [PubMed]
  2. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005). [CrossRef] [PubMed]
  3. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single «bowtie» nanoantennas resonant in the visible,” Nano Lett.4(5), 957–961 (2004). [CrossRef]
  4. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett.101(11), 116805 (2008). [CrossRef] [PubMed]
  5. K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett.3(8), 1087–1090 (2003). [CrossRef]
  6. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun.220(1-3), 137–141 (2003). [CrossRef]
  7. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small3(2), 294–299 (2007). [CrossRef] [PubMed]
  8. L. V. Brown, H. Sobhani, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Heterodimers: plasmonic properties of mismatched nanoparticle pairs,” ACS Nano4(2), 819–832 (2010). [CrossRef] [PubMed]
  9. C. Wadell, T. J. Antosiewicz, and C. Langhammer, “Optical absorption engineering in stacked plasmonic Au-SiO₂-Pd nanoantennas,” Nano Lett.12(9), 4784–4790 (2012). [CrossRef] [PubMed]
  10. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett.10(7), 2721–2726 (2010). [CrossRef] [PubMed]
  11. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010). [CrossRef] [PubMed]
  12. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys.120(23), 10871–10875 (2004). [CrossRef] [PubMed]
  13. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008). [CrossRef] [PubMed]
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