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Magnetic field modification of optical magnetic dipoles Gaspar Armelles, Blanca Caballero, Alfonso Cebollada, Antonio García-Martín, and David Meneses-Rodríguez Nano Lett., Just Accepted Manuscript • Publication Date (Web): 03 Feb 2015 Downloaded from http://pubs.acs.org on February 4, 2015
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Magnetic field modification of optical magnetic dipoles G. Armelles*, B. Caballero, A. Cebollada*, A. Garcia-Martin, D. Meneses-Rodríguez IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, E-28760 Tres Cantos, Madrid, Spain
ABSTRACT.
Acting on optical magnetic dipoles opens novel routes to govern light matter interaction. We demonstrate magnetic field modification of the magnetic dipolar moment characteristic of resonant nanoholes in thin magnetoplasmonic films. This is experimentally shown through the demonstration of the Magneto-Optical analogue of Babinet’s principle, where mirror imaged MO spectral dependencies are obtained for two complementary magnetoplasmonic systems: holes in a perforated metallic layer and a layer of disks on a substrate.
KEYWORDS : Active Plasmonics, Optical dipoles, Magnetoplasmonics, Babinet inverted systems. Exploring and acting on the magnetic component of the electromagnetic field (optical magnetic field) in plasmonic nanostructures and metamaterials allows extending the control of
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light matter interaction, not only via the excitation of electric dipoles, but also through magnetic dipoles.1,2,3,4 Many of the systems considered to study these effects make use of Babinet’s principle, which deals with the complementarity of the optical response of structurally complementary systems.5,6,7,8
Figure 1: The effect of a magnetic field on an x-axis oriented electric dipole p (a), excited by a xpolarized wave at normal incidence, in a magnetoplasmonic Au/Co multilayer nanodisk is to induce a component in the y-direction (c). Is the effect of a magnetic field on the Babinet complementary system (a nanohole in a Au/Co multilayer film (b)) also complementary? (d)
An archetype of complementary systems is that which relates metallic disks with holes in a metallic film (Figure 1). This way, and in addition to the well-known case of plasmonic nanodisks exhibiting electric dipole resonances, in recent years it has also been demonstrated that nanoholes in optically thin metallic films exhibit “hole plasmon resonances” that resemble those of equivalent nanodisks.9,10,11,12 The resonant hole can be described as constituted by a magnetic and an electric dipole component,13,14,15 with recent demonstrations of the separation of electric and magnetic components of light using nanoholes in metallic films.16,17,18
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Apart from the obvious interest of investigating inverted systems exhibiting optical magnetism in the visible range, an open question is the feasibility of actually realizing an active control of this optical magnetism and the corresponding light-matter interaction. Amongst the possibilities to endorse active character to plasmonic systems, a recently explored route considers the incorporation of a ferromagnetic component into the structure, allowing the modification of the global optical response by the application of an external magnetic field, via the magneto-optical effect.19,20,21,22,23 For example, in resonant nanodisk structures this MO effect can be viewed as the magnetic field induced rotation of the electric dipole, i.e. an electric dipole active control is produced by an external magnetic field.24,25 This effect is so strong that has even allowed measuring the MO activity in pure noble metal resonant nanoelements.26 Following the previous argumentation, the relevant question is whether the complementary element (a hole) and its corresponding characteristic magnetic dipole will manifest a similar behavior, or in other words, whether the magnetic field modification of an optical magnetic dipole is feasible and measurable. Therefore, the goal of this work is to show that indeed complementary magnetoplasmonic nanohole-nanodisk systems exhibit complementary magnetic field modification of their corresponding electric and magnetic dipoles, giving rise to the MO analogue of the Babinet principle in optics. Nanohole and nanodisk samples were obtained using a partial process of the hole mask colloidal lithography technique.27 To have identical disk/hole distribution and inter-distance in both cases studied, we have used the very same templates for the preparation of the membranes with nanoholes and nanodisks. For this we follow the membrane and disk procedures described in [28] and [29] respectively, which have common steps up to the deposition of the colloidal spheres on a PMMA layer, and then differ (see [28] and [29] for details). The resulting structures
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consisted of a random distribution of 200 nm diameter nanoholes in a 4 x (8 nm Au / 2 nm Co) multilayer grown on a PMMA/glass substrate and a random distribution of 200 nm diameter nanodisks of identical internal structure on a glass substrate. The very similar refractive indices of PMMA and glass substrates make the environment of the fabricated membranes and nanodisks in practical terms optically identical. In both cases, a portion of the substrate was left unprocessed and therefore ended with a continuous film with the same multilayer structure that served as reference. The extinction (1-T) spectra for the obtained magnetoplasmonic disks, membranes, and continuous layers are shown in the insets to Figure 2 (a) and (b), respectively.
Figure 2: Polar MO activities (black lines: rotation, red lines: ellipticity) for nanodisk (a) and nanohole (b) (8 nm Au / 2 nm Co) x 4 multilayer structures. In (b), the same magnitudes are also plotted for a continuous film with identical multilayered composition (dashed lines). The insets correspond to the respective extinction spectra (red curve corresponds to the continuous film). Sketches and representative Atomic Force Microscopy images of nanodisk and nanoholes samples are also shown.
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As it can be seen the extinction spectrum of the disks layer shows a strong peak related to the excitation of the plasmon resonance at around 855 nm. On the other hand, in the spectrum of the membrane and overlapped with the monotonic increase of 1-T characteristic of a continuous films (also shown in the inset to Figure 2 (b) as a red dotted line) we observe a dip with a broad minimum at around 920 nm, which is due to the excitation of a hole plasmon resonance. As expected for Babinet complementary structures these two plasmon resonances have a complementary character in their optical response (a peak and a dip in the extinction spectra, respectively). Due to the ferromagnetic component of the system (Co) the optical properties of the structures depend on the magnetization of the ferromagnetic layer, which is controlled by an external magnetic field. If the Co layer is magnetized perpendicular to the sample plane it induces a change in the polarization state of the reflected light (polar Kerr effect). In particular, if the incident light is x polarized the reflected light has also a magnetic field induced y component. The ratio of these two components, E y / E x , is the so-called complex Kerr rotation Φ (CKR), (Φ=θ+iϕ, being θ, the Kerr rotation and ϕ, the Kerr ellipticity, respectively). In Figure 2, we also present the Kerr rotation (black curves) and ellipticity (red curves) spectra of the disks layer (a), and of the membrane and continuous film (dashed lines) (b). The spectral dependence of the polar Kerr rotation and ellipticity of the disks layer are characterized by an sshape and peak features respectively, which are due to the excitation of the plasmon resonance of the disks.30 On the other hand, the membrane spectra have contributions from both the holes and the continuous film. Therefore, the MO spectra of the membrane are characterized by the overall trend exhibited by the continuous film, but with clear deviations in the spectral region
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corresponding to the resonance of the hole. In the case of the Kerr rotation, these deviations have an s-shape structure, while in the Kerr ellipticity, they are basically a peak that is overlapped over the MO spectrum of the continuous film, in a similar qualitative fashion as the contribution of the disk to the MO activity of the disk layers. These experimentally measured magnitudes (polar Kerr rotation and ellipticity) have optical and MO contributions from the continuous film and holes in the membrane case, and from substrate31 and disks in the layer of disks case. To directly compare the MO activity solely due to holes and disks and get rid of continuous film and substrate contributions, we simply have to consider that the electromagnetic fields reflected from the membrane (Em), or the disks layer (Edl), have two components: one accounting for the effect of holes (Eh), or disks (Ed), and the other due to the continuous part of the film (Ec), or substrate (Es), respectively, with Em = Ec +Eh , and
Edl = Ed +Es .
Using this formalism, the CKR of the holes, Φ h = Ehy / Ehx , can be expressed in terms of the CKR of the membrane and continuous layers as:
Φh =
Ecx Ecy Emx Ehy Emy − Ecy Emx Emy Ecx = = − = Φ − Φ Ehx Emx − Ecx Emx − Ecx Emx Emx − Ecx Ecx Emx − Ecx m Emx − Ecx c
(1)
where: Φ m , is the CKR of the membrane ( Φ m = Emy / Emx ) ; Φ c , is the CKR of the continuous layer( Φ c = Ecy / Ecx ). Moreover, Emx =rmEi and Ecx =rcEi , where Ei is the incident light (which is x polarized) and rm, rc are the reflectivity coefficients of the membrane and continuous layers, respectively. Therefore, the previous expression can be written as:
Φ h ==
rm r Φm − c Φc rm − rc rm − rc
(2)
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In a similar way, the CKR of disks, defined as the ratio between the contribution of disks to the y and x components of the reflected field, Φ d = Ed / Ed , can be expressed as: y
Φ d ==
x
rdl Φ dl rdl − rs
(3)
where: Φ dl , is the CKR of the layer of disks ( Φ dl = Edl / Edl ), and rdl, and rs are the reflectivity y
x
coefficients of the layer of disks and the substrate, respectively. With these expressions in hand, in Figure 3 we present the pure disk (black) and hole (red) contribution to the Kerr rotation (a) and ellipticity (b), using the Kerr rotation and ellipticity spectra shown in Figure 2 and the reflectivity coefficients of the membrane, and the continuous and disk layers, respectively. The reflectivity coefficients were calculated using the effective optical constants of the layers obtained from ellipsometry measurements.
Figure 3: Spectral dependence of the Kerr rotation (a) and ellipticity (b) solely due to disks (black lines) and holes (red lines) obtained eliminating continuous film and substrate contributions from the raw data. Apart from an energy shift due to the slightly different positions of the plasmon resonances of Babinet complementary systems, the Kerr rotation and ellipticity
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spectra of the disks are the mirror image of those of the holes. The insets represent the corresponding magnitudes obtained from the calculated electromagnetic fields (see text for details). As it can be observed, the Kerr rotation and ellipticity spectra of the two complementary structures have very similar intensities and shapes: the Kerr rotation has in both cases an s-like shape structure, going from positive to negative values with increasing wavelengths for disks, and basically the mirror behavior, for holes. On the other hand, the Kerr ellipticity spectra of disks and holes are characterized respectively by a positive peak and a dip around the respective disk and hole plasmon resonances. The observed mirror behavior of the Kerr signals from complementary structures is a clear MO analogue of the Babinet principle in optics. To understand its origin it is necessary to look into the underlying physical mechanism responsible for the measured magnitudes. As mentioned before, the MO activity of a resonant magnetoplasmonic nanodisk is due to the magnetic field induced rotation of the electric dipole excited in resonance. The question still open is whether the corresponding rotating dipole in the hole case is of electric or magnetic nature. To determine this, it is necessary to identify the components of the radiated electric and/or magnetic field which univocally correspond to an electric or a magnetic dipole. To do so we have calculated the far field electric and magnetic fields radiated from point electric and magnetic dipoles, identifying the components that unequivocally allow determining the specific electric or magnetic nature of the dipoles originating them.
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Figure 4: (a) Calculated radiated x-component of the electric field for an electric point dipole oscillating along the x-direction (px). (b) Calculated radiated y-component of the magnetic field for the same electric dipole. (c) Calculated radiated x-component of the electric field for a magnetic point dipole oscillating along the y-direction (my). (d) Calculated radiated y-component of the magnetic field for the same magnetic dipole. The electromagnetic field profiles for the rotated dipoles (py and mx) can be obtained by simply interchanging x and y for the field components, and rotating the figure 90 degrees.
In Figure 4 we show these selected components, which correspond to the x and y components of the electric and magnetic field respectively at a height of 600 nm, and are characterized by an ellipsoidal distribution of Ex (a) and a circular distribution of Hy (b). Conversely, the corresponding magnetic dipole (along the y direction) is characterized by a circular distribution of Ex (c) and an ellipsoidal distribution of Hy (d). Going back to the actual considered structures,
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the corresponding calculated Ex and Hy components of the far field radiated (which can be also identified with the field scattered by a disk or a hole) by the two structures are shown in Figure 5 (a) and (c). The scattered field is obtained automatically from the calculation when the total field is divided into “background field” and “scattered field”. The background field consists of the response of the multilayer to the impinging plane wave without the object (either disk or hole), and thus is different in each case: for the disk case the background field corresponds to an air/substrate system, whereas for the hole case it corresponds to an air/multilayer-film/substrate system. As a consequence the scattered field does not contain any contribution from the substrate/film, allowing a direct comparison with the experimental observations.
Figure 5: (a) Calculated radiated x-component of the electric field, excited in a nanodisk in the absence of an external magnetic field. (b) Calculated Magnetic field induced radiated ycomponent (∆Ey=Ey(+Msat)-Ey(-Msat), where Msat is the magnetization at saturation) of the electric field, which can be associated to a rotated electric dipole. (c) Calculated radiated ycomponent of the magnetic field excited in a nanohole in the absence of an external magnetic
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field. (d) Calculated Magnetic field induced radiated x-component of the magnetic field (∆Hx=Hx(+Msat)-Hx(-Msat)), which can be associated to a rotated magnetic dipole.
As it can be seen, both exhibit the ellipsoidal distribution previously calculated considering point dipoles. The effect of applying an external DC magnetic field is to change the electromagnetic field distribution, and in Figure 5 (b) and (d) we show the differences for opposite magnetizations for the characteristic component (i.e. ∆Ey and ∆Hx respectively). As it can be seen, the external magnetic field induces a rotation of the electric dipole of the disk, generating a y component of the radiated electric field, and a rotation of the magnetic dipole, with the subsequent generation of an x component of the corresponding radiated magnetic field. Worth noticing, the finite size of the hole prevents its far field from being described by a magnetic dipole alone, and the contribution of an electric dipole along the x-direction is also excited. We have performed a decomposition of the fields presented in Figure 5 in terms of the normalized dipolar px and my components presented in Figure 4 (and the corresponding py and mx for the rotated fields), following the expressions:
r r r r r r ( E, H )calc = ax ( E, H ) px + by ( E, H )my , r r r r r r (∆E, ∆H )calc = ay ( E, H ) py + bx ( E, H )mx
(4)
where ax, by, ay and bx are the coefficients for the E and H fields generated by their respective normalized dipoles. To give an idea of the relative strength of each dipole, the ratios of the absolute values of by/ax and bx/ay are 5.46 and 1.56, respectively. This implies that, for the finite size holes considered here, the contribution of the magnetic dipole to the far field E and H generated fields is more than 5 times larger than that of the electric dipole. When considering magnetic field induced effects, the ratio of magnetic vs electric dipole contribution decreases,
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even though the magnetic dipole contribution dominates, being more than 50% larger than the electric dipole one. This different weights of electric and magnetic dipole contributions to the optical and MO part are due to the different origins of both dipoles: while the electric dipole is originated by charge oscillations and the corresponding magnetic field induced effects are related to the off diagonal elements of the polarizability tensor, the magnetic dipole is originated by currents, and the corresponding magnetic field induced effects depend on the off diagonal elements of the conductivity tensor. From the components of the radiated field of the disks and holes, the Kerr rotation spectra of these two complementary structures can be calculated as:
Φ h,d =
y ∆Eh,d x 2Eh,d
where, Φ h and
(5) y Φ d are the CKR of holes and disks, respectively; ∆Eh,d is the magnetic field
induced y component of the radiated field determined from the difference between the y components for the two orientations of the magnetizations, and Ex is the x component of the radiated field. This expression is the equivalent to the CKR presented in Figure 3, where the contributions from the continuous film and substrate have been removed. The insets in Figure 3 show the spectral dependence of the real (Kerr rotation) and imaginary (Kerr ellipticity) part of this calculated ratio. As it can be observed, the shapes and magnitudes of the calculated Kerr spectra are similar to the experimental ones, reproducing the experimentally observed mirror behavior, and supporting the concept of a Babinet principle MO analogue. The reason for the analogue contribution to the MO activity of complementary structures lies in the common physical origin of this effect for both systems. For nanodisks, it is due to the external magnetic field induced rotation of the electric dipole excited by the electric field component of the electromagnetic wave.24,25 On the other hand, nanoholes mainly respond to the
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magnetic field of light, which generates induction currents in the metal surrounding the hole, responsible in the end of the generated magnetic moment. In this second case, the external magnetic field modifies these induced currents, giving rise to the rotation of the magnetic moment in a similar fashion to the electric one in nanodisks. To conclude, we have shown that complementary magnetoplasmonic systems produce mirror imaged spectral MO responses in the regions where the corresponding plasmon resonances are excited. This is due to the magnetic field modification of their respective characteristic magnetic and electric dipoles. This MO complementarity constitutes the magnetoplasmonic analogue of the Babinet principle recently applied to metamaterials systems. The possibility to consider, not only the currently used magnetoplasmonic nanostructures, but also their complementary ones, for the development of novel systems with improved combined plasmonic and MO characteristics is very promising. For example, this approach may allow developing media with equivalent MO active permeability in a wide spectral range. The introduction of this concept opens a wide variety of routes to control in an active way light-matter interaction, not only via the excitation of electric dipoles, but also via de excitation of magnetic dipoles in Babinet inverted metastructures with magnetoplasmonic character. The present results, even though performed in a pseudo static configuration due to the used experimental setup, can be easily extended to high frequency modification of the magnetic dipole, linked to the intrinsically fast magnetization reversal of ferromagnets.
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AUTHOR INFORMATION Corresponding Author e-mail: [email protected], [email protected] Author Contributions G.A., A.C., A.G.-M., conceived the work and wrote the manuscript, D.M.-R. and A.C. grew the samples, D.M.-R., G.A. and A.C. performed the experimental measurements, and B.C and A.G.M. performed the theoretical calculations. All authors contributed to the analysis and discussion of the results. Funding Sources Funding from Spanish Ministry of Economy and Competitiveness through grants “FUNCOAT” CONSOLIDER CSD2008–00023, MAPS MAT2011–29194-C02–01 is acknowledged. Notes The authors declare no competing financial interests.
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Table of Contents Graphic and Synopsis. Acting on optical magnetic dipoles opens novel routes to govern light matter interaction. We demonstrate magnetic field modification of the magnetic dipolar moment characteristic of resonant nanoholes in thin magnetoplasmonic films. This is experimentally shown through the demonstration of the Magneto-Optical analogue of Babinet’s principle, where mirror imaged MO spectral dependencies are obtained for two complementary magnetoplasmonic systems: holes in a perforated metallic layer and a layer of disks on a substrate.
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22 Belotelov, V.I.; Kreilkamp, L. E.; Akimov, I. A.; Kalish, A. N.; Bykov, D. A.; Kasture, S.; Yallapragada, V. J.; Gopal, A. V.; Grishin, A. M.; Khartsev, S. I.; Nur-E-Alam, M.; Vasiliev, M.; Doskolovich, L. L.; Yakovlev, D. R.; Alameh, K.; Zvezdein, A.
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Commun. 2013, 4, 2128. 23 Armelles, G.; Cebollada, A.; García-Martín, A.; González, M. U. Adv. Opt. Mater. 2013, 1, 10-35. 24 Armelles, G.; Cebollada, A.; García-Martín, A.; González, M. U.; García, F.; MenesesRodríguez, D.; de Sousa, N.; Froufe-Pérez, L. S. Opt. Expr. 2013, 21, 27356-27370. 25 de Sousa, N.; Froufe-Pérez, L.; Armelles, G.; Cebollada, A.; González, M. U.; García, F.; Meneses-Rodríguez, D.; García-Martín, A. Phys. Rev. B 2014, 89, 205419. 26 Sepúlveda, B., González-Díaz, J. B.; García-Martín, A.; Lechuga, L. M.; Armelles, G. Phys. Rev. Lett. 2010, 104, 147401. 27 Fredriksson, H.; Alaverdyan, Y.; Dmitriev, A.; Langhammer, C.; Sutherland, D. S.; Zäch, M.; Kasemo, B. Adv. Mater. 2007, 19, 4297-4302. 28 Kekesi, R.; Meneses-Rodríguez, D.; García-Pérez, F.; González, M. U.; García-Martín, A.; Cebollada, A.; Armelles, G. J. Appl. Phys. 2014, 116, 134306. 29 Meneses-Rodríguez, D.; Ferreiro-Vila, E.; Prieto, P.; Anguita, J.; González, M. U., GarcíaMartín, J. M.; Cebollada, A.; García-Martín, A.; Armelles, G. Small 2011, 7, 3317-3323. 30 González-Díaz, J. B.; García-Martín, A.; García-Martín, J. M.; Cebollada, A.; Armelles, G.; Sepúlveda, B.; Alaverdyan, Y.; Käll, M. Small 2008, 4, 202-205.
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31 Maccaferri, N.; Kataja, M.; Bonanni, V.; Bonetti, S.; Pirzadeh, Z.; Dmitriev, A.; van Dijken, S.; Åkerman, J.; Vavassori, P. Phys. Stat. Solidi A 2014, 211, 1067-1075.
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Communication
Magnetic field modification of optical magnetic dipoles Gaspar Armelles, Blanca Caballero, Alfonso Cebollada, Antonio García-Martín, and David Meneses-Rodríguez Nano Lett., Just Accepted Manuscript • Publication Date (Web): 03 Feb 2015 Downloaded from http://pubs.acs.org on February 4, 2015
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Magnetic field modification of optical magnetic dipoles G. Armelles*, B. Caballero, A. Cebollada*, A. Garcia-Martin, D. Meneses-Rodríguez IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, E-28760 Tres Cantos, Madrid, Spain
ABSTRACT.
Acting on optical magnetic dipoles opens novel routes to govern light matter interaction. We demonstrate magnetic field modification of the magnetic dipolar moment characteristic of resonant nanoholes in thin magnetoplasmonic films. This is experimentally shown through the demonstration of the Magneto-Optical analogue of Babinet’s principle, where mirror imaged MO spectral dependencies are obtained for two complementary magnetoplasmonic systems: holes in a perforated metallic layer and a layer of disks on a substrate.
KEYWORDS : Active Plasmonics, Optical dipoles, Magnetoplasmonics, Babinet inverted systems. Exploring and acting on the magnetic component of the electromagnetic field (optical magnetic field) in plasmonic nanostructures and metamaterials allows extending the control of
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light matter interaction, not only via the excitation of electric dipoles, but also through magnetic dipoles.1,2,3,4 Many of the systems considered to study these effects make use of Babinet’s principle, which deals with the complementarity of the optical response of structurally complementary systems.5,6,7,8
Figure 1: The effect of a magnetic field on an x-axis oriented electric dipole p (a), excited by a xpolarized wave at normal incidence, in a magnetoplasmonic Au/Co multilayer nanodisk is to induce a component in the y-direction (c). Is the effect of a magnetic field on the Babinet complementary system (a nanohole in a Au/Co multilayer film (b)) also complementary? (d)
An archetype of complementary systems is that which relates metallic disks with holes in a metallic film (Figure 1). This way, and in addition to the well-known case of plasmonic nanodisks exhibiting electric dipole resonances, in recent years it has also been demonstrated that nanoholes in optically thin metallic films exhibit “hole plasmon resonances” that resemble those of equivalent nanodisks.9,10,11,12 The resonant hole can be described as constituted by a magnetic and an electric dipole component,13,14,15 with recent demonstrations of the separation of electric and magnetic components of light using nanoholes in metallic films.16,17,18
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Apart from the obvious interest of investigating inverted systems exhibiting optical magnetism in the visible range, an open question is the feasibility of actually realizing an active control of this optical magnetism and the corresponding light-matter interaction. Amongst the possibilities to endorse active character to plasmonic systems, a recently explored route considers the incorporation of a ferromagnetic component into the structure, allowing the modification of the global optical response by the application of an external magnetic field, via the magneto-optical effect.19,20,21,22,23 For example, in resonant nanodisk structures this MO effect can be viewed as the magnetic field induced rotation of the electric dipole, i.e. an electric dipole active control is produced by an external magnetic field.24,25 This effect is so strong that has even allowed measuring the MO activity in pure noble metal resonant nanoelements.26 Following the previous argumentation, the relevant question is whether the complementary element (a hole) and its corresponding characteristic magnetic dipole will manifest a similar behavior, or in other words, whether the magnetic field modification of an optical magnetic dipole is feasible and measurable. Therefore, the goal of this work is to show that indeed complementary magnetoplasmonic nanohole-nanodisk systems exhibit complementary magnetic field modification of their corresponding electric and magnetic dipoles, giving rise to the MO analogue of the Babinet principle in optics. Nanohole and nanodisk samples were obtained using a partial process of the hole mask colloidal lithography technique.27 To have identical disk/hole distribution and inter-distance in both cases studied, we have used the very same templates for the preparation of the membranes with nanoholes and nanodisks. For this we follow the membrane and disk procedures described in [28] and [29] respectively, which have common steps up to the deposition of the colloidal spheres on a PMMA layer, and then differ (see [28] and [29] for details). The resulting structures
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consisted of a random distribution of 200 nm diameter nanoholes in a 4 x (8 nm Au / 2 nm Co) multilayer grown on a PMMA/glass substrate and a random distribution of 200 nm diameter nanodisks of identical internal structure on a glass substrate. The very similar refractive indices of PMMA and glass substrates make the environment of the fabricated membranes and nanodisks in practical terms optically identical. In both cases, a portion of the substrate was left unprocessed and therefore ended with a continuous film with the same multilayer structure that served as reference. The extinction (1-T) spectra for the obtained magnetoplasmonic disks, membranes, and continuous layers are shown in the insets to Figure 2 (a) and (b), respectively.
Figure 2: Polar MO activities (black lines: rotation, red lines: ellipticity) for nanodisk (a) and nanohole (b) (8 nm Au / 2 nm Co) x 4 multilayer structures. In (b), the same magnitudes are also plotted for a continuous film with identical multilayered composition (dashed lines). The insets correspond to the respective extinction spectra (red curve corresponds to the continuous film). Sketches and representative Atomic Force Microscopy images of nanodisk and nanoholes samples are also shown.
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As it can be seen the extinction spectrum of the disks layer shows a strong peak related to the excitation of the plasmon resonance at around 855 nm. On the other hand, in the spectrum of the membrane and overlapped with the monotonic increase of 1-T characteristic of a continuous films (also shown in the inset to Figure 2 (b) as a red dotted line) we observe a dip with a broad minimum at around 920 nm, which is due to the excitation of a hole plasmon resonance. As expected for Babinet complementary structures these two plasmon resonances have a complementary character in their optical response (a peak and a dip in the extinction spectra, respectively). Due to the ferromagnetic component of the system (Co) the optical properties of the structures depend on the magnetization of the ferromagnetic layer, which is controlled by an external magnetic field. If the Co layer is magnetized perpendicular to the sample plane it induces a change in the polarization state of the reflected light (polar Kerr effect). In particular, if the incident light is x polarized the reflected light has also a magnetic field induced y component. The ratio of these two components, E y / E x , is the so-called complex Kerr rotation Φ (CKR), (Φ=θ+iϕ, being θ, the Kerr rotation and ϕ, the Kerr ellipticity, respectively). In Figure 2, we also present the Kerr rotation (black curves) and ellipticity (red curves) spectra of the disks layer (a), and of the membrane and continuous film (dashed lines) (b). The spectral dependence of the polar Kerr rotation and ellipticity of the disks layer are characterized by an sshape and peak features respectively, which are due to the excitation of the plasmon resonance of the disks.30 On the other hand, the membrane spectra have contributions from both the holes and the continuous film. Therefore, the MO spectra of the membrane are characterized by the overall trend exhibited by the continuous film, but with clear deviations in the spectral region
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corresponding to the resonance of the hole. In the case of the Kerr rotation, these deviations have an s-shape structure, while in the Kerr ellipticity, they are basically a peak that is overlapped over the MO spectrum of the continuous film, in a similar qualitative fashion as the contribution of the disk to the MO activity of the disk layers. These experimentally measured magnitudes (polar Kerr rotation and ellipticity) have optical and MO contributions from the continuous film and holes in the membrane case, and from substrate31 and disks in the layer of disks case. To directly compare the MO activity solely due to holes and disks and get rid of continuous film and substrate contributions, we simply have to consider that the electromagnetic fields reflected from the membrane (Em), or the disks layer (Edl), have two components: one accounting for the effect of holes (Eh), or disks (Ed), and the other due to the continuous part of the film (Ec), or substrate (Es), respectively, with Em = Ec +Eh , and
Edl = Ed +Es .
Using this formalism, the CKR of the holes, Φ h = Ehy / Ehx , can be expressed in terms of the CKR of the membrane and continuous layers as:
Φh =
Ecx Ecy Emx Ehy Emy − Ecy Emx Emy Ecx = = − = Φ − Φ Ehx Emx − Ecx Emx − Ecx Emx Emx − Ecx Ecx Emx − Ecx m Emx − Ecx c
(1)
where: Φ m , is the CKR of the membrane ( Φ m = Emy / Emx ) ; Φ c , is the CKR of the continuous layer( Φ c = Ecy / Ecx ). Moreover, Emx =rmEi and Ecx =rcEi , where Ei is the incident light (which is x polarized) and rm, rc are the reflectivity coefficients of the membrane and continuous layers, respectively. Therefore, the previous expression can be written as:
Φ h ==
rm r Φm − c Φc rm − rc rm − rc
(2)
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In a similar way, the CKR of disks, defined as the ratio between the contribution of disks to the y and x components of the reflected field, Φ d = Ed / Ed , can be expressed as: y
Φ d ==
x
rdl Φ dl rdl − rs
(3)
where: Φ dl , is the CKR of the layer of disks ( Φ dl = Edl / Edl ), and rdl, and rs are the reflectivity y
x
coefficients of the layer of disks and the substrate, respectively. With these expressions in hand, in Figure 3 we present the pure disk (black) and hole (red) contribution to the Kerr rotation (a) and ellipticity (b), using the Kerr rotation and ellipticity spectra shown in Figure 2 and the reflectivity coefficients of the membrane, and the continuous and disk layers, respectively. The reflectivity coefficients were calculated using the effective optical constants of the layers obtained from ellipsometry measurements.
Figure 3: Spectral dependence of the Kerr rotation (a) and ellipticity (b) solely due to disks (black lines) and holes (red lines) obtained eliminating continuous film and substrate contributions from the raw data. Apart from an energy shift due to the slightly different positions of the plasmon resonances of Babinet complementary systems, the Kerr rotation and ellipticity
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spectra of the disks are the mirror image of those of the holes. The insets represent the corresponding magnitudes obtained from the calculated electromagnetic fields (see text for details). As it can be observed, the Kerr rotation and ellipticity spectra of the two complementary structures have very similar intensities and shapes: the Kerr rotation has in both cases an s-like shape structure, going from positive to negative values with increasing wavelengths for disks, and basically the mirror behavior, for holes. On the other hand, the Kerr ellipticity spectra of disks and holes are characterized respectively by a positive peak and a dip around the respective disk and hole plasmon resonances. The observed mirror behavior of the Kerr signals from complementary structures is a clear MO analogue of the Babinet principle in optics. To understand its origin it is necessary to look into the underlying physical mechanism responsible for the measured magnitudes. As mentioned before, the MO activity of a resonant magnetoplasmonic nanodisk is due to the magnetic field induced rotation of the electric dipole excited in resonance. The question still open is whether the corresponding rotating dipole in the hole case is of electric or magnetic nature. To determine this, it is necessary to identify the components of the radiated electric and/or magnetic field which univocally correspond to an electric or a magnetic dipole. To do so we have calculated the far field electric and magnetic fields radiated from point electric and magnetic dipoles, identifying the components that unequivocally allow determining the specific electric or magnetic nature of the dipoles originating them.
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Figure 4: (a) Calculated radiated x-component of the electric field for an electric point dipole oscillating along the x-direction (px). (b) Calculated radiated y-component of the magnetic field for the same electric dipole. (c) Calculated radiated x-component of the electric field for a magnetic point dipole oscillating along the y-direction (my). (d) Calculated radiated y-component of the magnetic field for the same magnetic dipole. The electromagnetic field profiles for the rotated dipoles (py and mx) can be obtained by simply interchanging x and y for the field components, and rotating the figure 90 degrees.
In Figure 4 we show these selected components, which correspond to the x and y components of the electric and magnetic field respectively at a height of 600 nm, and are characterized by an ellipsoidal distribution of Ex (a) and a circular distribution of Hy (b). Conversely, the corresponding magnetic dipole (along the y direction) is characterized by a circular distribution of Ex (c) and an ellipsoidal distribution of Hy (d). Going back to the actual considered structures,
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the corresponding calculated Ex and Hy components of the far field radiated (which can be also identified with the field scattered by a disk or a hole) by the two structures are shown in Figure 5 (a) and (c). The scattered field is obtained automatically from the calculation when the total field is divided into “background field” and “scattered field”. The background field consists of the response of the multilayer to the impinging plane wave without the object (either disk or hole), and thus is different in each case: for the disk case the background field corresponds to an air/substrate system, whereas for the hole case it corresponds to an air/multilayer-film/substrate system. As a consequence the scattered field does not contain any contribution from the substrate/film, allowing a direct comparison with the experimental observations.
Figure 5: (a) Calculated radiated x-component of the electric field, excited in a nanodisk in the absence of an external magnetic field. (b) Calculated Magnetic field induced radiated ycomponent (∆Ey=Ey(+Msat)-Ey(-Msat), where Msat is the magnetization at saturation) of the electric field, which can be associated to a rotated electric dipole. (c) Calculated radiated ycomponent of the magnetic field excited in a nanohole in the absence of an external magnetic
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field. (d) Calculated Magnetic field induced radiated x-component of the magnetic field (∆Hx=Hx(+Msat)-Hx(-Msat)), which can be associated to a rotated magnetic dipole.
As it can be seen, both exhibit the ellipsoidal distribution previously calculated considering point dipoles. The effect of applying an external DC magnetic field is to change the electromagnetic field distribution, and in Figure 5 (b) and (d) we show the differences for opposite magnetizations for the characteristic component (i.e. ∆Ey and ∆Hx respectively). As it can be seen, the external magnetic field induces a rotation of the electric dipole of the disk, generating a y component of the radiated electric field, and a rotation of the magnetic dipole, with the subsequent generation of an x component of the corresponding radiated magnetic field. Worth noticing, the finite size of the hole prevents its far field from being described by a magnetic dipole alone, and the contribution of an electric dipole along the x-direction is also excited. We have performed a decomposition of the fields presented in Figure 5 in terms of the normalized dipolar px and my components presented in Figure 4 (and the corresponding py and mx for the rotated fields), following the expressions:
r r r r r r ( E, H )calc = ax ( E, H ) px + by ( E, H )my , r r r r r r (∆E, ∆H )calc = ay ( E, H ) py + bx ( E, H )mx
(4)
where ax, by, ay and bx are the coefficients for the E and H fields generated by their respective normalized dipoles. To give an idea of the relative strength of each dipole, the ratios of the absolute values of by/ax and bx/ay are 5.46 and 1.56, respectively. This implies that, for the finite size holes considered here, the contribution of the magnetic dipole to the far field E and H generated fields is more than 5 times larger than that of the electric dipole. When considering magnetic field induced effects, the ratio of magnetic vs electric dipole contribution decreases,
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even though the magnetic dipole contribution dominates, being more than 50% larger than the electric dipole one. This different weights of electric and magnetic dipole contributions to the optical and MO part are due to the different origins of both dipoles: while the electric dipole is originated by charge oscillations and the corresponding magnetic field induced effects are related to the off diagonal elements of the polarizability tensor, the magnetic dipole is originated by currents, and the corresponding magnetic field induced effects depend on the off diagonal elements of the conductivity tensor. From the components of the radiated field of the disks and holes, the Kerr rotation spectra of these two complementary structures can be calculated as:
Φ h,d =
y ∆Eh,d x 2Eh,d
where, Φ h and
(5) y Φ d are the CKR of holes and disks, respectively; ∆Eh,d is the magnetic field
induced y component of the radiated field determined from the difference between the y components for the two orientations of the magnetizations, and Ex is the x component of the radiated field. This expression is the equivalent to the CKR presented in Figure 3, where the contributions from the continuous film and substrate have been removed. The insets in Figure 3 show the spectral dependence of the real (Kerr rotation) and imaginary (Kerr ellipticity) part of this calculated ratio. As it can be observed, the shapes and magnitudes of the calculated Kerr spectra are similar to the experimental ones, reproducing the experimentally observed mirror behavior, and supporting the concept of a Babinet principle MO analogue. The reason for the analogue contribution to the MO activity of complementary structures lies in the common physical origin of this effect for both systems. For nanodisks, it is due to the external magnetic field induced rotation of the electric dipole excited by the electric field component of the electromagnetic wave.24,25 On the other hand, nanoholes mainly respond to the
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magnetic field of light, which generates induction currents in the metal surrounding the hole, responsible in the end of the generated magnetic moment. In this second case, the external magnetic field modifies these induced currents, giving rise to the rotation of the magnetic moment in a similar fashion to the electric one in nanodisks. To conclude, we have shown that complementary magnetoplasmonic systems produce mirror imaged spectral MO responses in the regions where the corresponding plasmon resonances are excited. This is due to the magnetic field modification of their respective characteristic magnetic and electric dipoles. This MO complementarity constitutes the magnetoplasmonic analogue of the Babinet principle recently applied to metamaterials systems. The possibility to consider, not only the currently used magnetoplasmonic nanostructures, but also their complementary ones, for the development of novel systems with improved combined plasmonic and MO characteristics is very promising. For example, this approach may allow developing media with equivalent MO active permeability in a wide spectral range. The introduction of this concept opens a wide variety of routes to control in an active way light-matter interaction, not only via the excitation of electric dipoles, but also via de excitation of magnetic dipoles in Babinet inverted metastructures with magnetoplasmonic character. The present results, even though performed in a pseudo static configuration due to the used experimental setup, can be easily extended to high frequency modification of the magnetic dipole, linked to the intrinsically fast magnetization reversal of ferromagnets.
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AUTHOR INFORMATION Corresponding Author e-mail: [email protected], [email protected] Author Contributions G.A., A.C., A.G.-M., conceived the work and wrote the manuscript, D.M.-R. and A.C. grew the samples, D.M.-R., G.A. and A.C. performed the experimental measurements, and B.C and A.G.M. performed the theoretical calculations. All authors contributed to the analysis and discussion of the results. Funding Sources Funding from Spanish Ministry of Economy and Competitiveness through grants “FUNCOAT” CONSOLIDER CSD2008–00023, MAPS MAT2011–29194-C02–01 is acknowledged. Notes The authors declare no competing financial interests.
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Table of Contents Graphic and Synopsis. Acting on optical magnetic dipoles opens novel routes to govern light matter interaction. We demonstrate magnetic field modification of the magnetic dipolar moment characteristic of resonant nanoholes in thin magnetoplasmonic films. This is experimentally shown through the demonstration of the Magneto-Optical analogue of Babinet’s principle, where mirror imaged MO spectral dependencies are obtained for two complementary magnetoplasmonic systems: holes in a perforated metallic layer and a layer of disks on a substrate.
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31 Maccaferri, N.; Kataja, M.; Bonanni, V.; Bonetti, S.; Pirzadeh, Z.; Dmitriev, A.; van Dijken, S.; Åkerman, J.; Vavassori, P. Phys. Stat. Solidi A 2014, 211, 1067-1075.
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