and Near-Field Broad-Band Magneto-Optical Functionalities Using

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Far and near field broad-band magneto-optical functionalities using magnetoplasmonic nanorods Gaspar Armelles, Alfonso Cebollada, Fernando Garcia, Antonio García-Martín, and Nuno de Sousa ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00670 • Publication Date (Web): 10 Nov 2016 Downloaded from http://pubs.acs.org on November 12, 2016

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Far and near field broad-band magneto-optical functionalities using magnetoplasmonic nanorods Gaspar Armelles,∗,† Alfonso Cebollada,† Fernando García,† Antonio García-Martín,∗,† and Nuno de Sousa‡,¶ †IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, Tres Cantos, E-28760 Madrid, Spain ‡Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, 28049, Madrid, Spain. ¶Donostia International Physics Center (DIPC), Paseo Manuel Lardizabal 4, 20018 Donostia-San Sebastian, Spain. E-mail: [email protected]; [email protected]

Abstract We have performed a systematic study of magnetoplasmonic Au/Co/Au nanorods with different long/short axes ratio arranged in a disordered fashion but with the same spatial orientation of their axes. We show that the magneto-optical response can be tuned from the visible to the near infrared range by changing the long/short axes ratio. Moreover, the analysis of the magnetic field induced polarization conversion indicates a different behaviour for far field and for the near field. In particular, the far field polarization conversion of the nanorod does not depend on the incident polarization, whereas the near field does. This anticipates direct consequences for near field inter-

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actions, since the interacting elements at different spatial positions could give rise to different magneto-optical responses.

Keywords Magnetoplasmonics, polarization conversion, active nanoantennas Plasmonic antenna-based optical planar devices are among the most versatile systems in nanophotonics. These devices are formed by the adequate arrangement of individual building blocks with tuned sizes and shapes tailored in the nanoscale. The structures conformed this way provide a large range of functionalities, allowing the design and fabrication of novel elements such as holographic optical devices, 1 metalenses, 2,3 or polarization devices. 4,5 As a general rule, the specific characteristics of such elements are pre-defined by the selection of the working dimensions and spatial configuration. In this aspect, the possibility to endorse them with an active tunable character is of obvious interest. For this purpose, it becomes necessary that some factor that determines the final global optical properties of the system may be switched or tuned in an external way. In this sense, magneto-optically (MO) active elements are excellent candidate components as they precisely modify the optical response of a system under the action of an external magnetic field. 6 Even more, it has recently been put forward that the combined plasmonic and magneto-optical action in novel magnetoplasmonic systems of a large variety of configurations actually allow enhancing the global MO response by the antenna effect of the plasmonic part. 7–11 If one considers ferromagnetic metals as the MO active element, the dimensions of the plasmonic structure remain virtually unaltered, allowing the development of active planar optical devices. Regarding this type of devices, one of the favored plasmonic building blocks within the planar optical structure is a metallic nanorod. The reason lies in that they respond differently for light that is polarized along the two principal axes of the rod, giving rise to resonances whose spectral position can be tailored on demand by simply acting over the shape and dimensions of the nanorod. 12,13

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Adding MO activity to such building blocks may pave the way to a new kind of active metasurfaces, with enhanced optical functionalities, such as, active polarizers or image devices like controlled holographic plates or MO spatial light modulators (MOSLM). 14,15 In similar structures like nanodisks, the MO effect can be viewed as the magnetic field induced rotation of the electric dipole, that is, an electric dipole active control is produced by an external magnetic field. 16,17 In this work we present a simple magneto-plasmonic element that can be used as the essential building block for the development of complex planar optical systems with externally modulated polarization conversion capabilities. This element is a Au/Co/Au nanorod, whose properties will be analyzed by performing a systematic study of the optical and magnetooptical response for different long/short axes ratios. The analysis will be carried out both in the far and near field. The near field case is of paramount importance here since interactions are essential to develop the collective response of the nanorod antenna array. The analyzed nanorods will be around 35nm thick (H ≈ 35nm), 130-150nm wide (W ≈ 130 − 150nm) and the length will go from a disk like shape to 310nm to display an elongated rod shape (L ≈ 130−310nm). See Methods for a detailed description of the fabrication. The thicknesses of the different layers is (from top-to-bottom) 20nm Au / 5nm Co / 8nm Au / 2nm Ti. Let us begin with the more common case of the far field optical and magneto-optical responses. This will serve to characterize the system and to verify the numerical techniques that will be used to perform the near field analysis.

Results and discussion In Figure 1 we present the transmission spectra at normal incidence for polarized light along the short axis (black curve) and long axis (red curve) of the nanorods, for three structures, a nanodisk, and two nanorods 290 and 305nm long. As it can be observed, each spectrum presents one well-defined minimum. In the spectra for light polarized along the

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short axis the minima are located at basically the same wavelength, whereas for those where the light is polarized along the long axis the minimum appears red-shifted as the length of the nanorod increases. These features relate themselves immediately to localized surface plasmon resonances (LSPR), since the spectral position of LSPR depends on the size of the particle along the polarization direction, red-shifting as the size increases. In our case the size of the short axis is the same for all cases, and hence the minimum stays at virtually the same position; however, when exploring the polarization along the long axis, the resonance position red shifts as the length increases. This basically means that we are able to generate nanorod antenna arrays with optical anisotropies whose magnitude can be finely tuned by varying the rods L/W aspect ratio.

Figure 1: Optical transmission spectra at normal incidence for polarized light along the short axis (black curve) and long axis (red curve) for three structures: (a) a nanodisk, and two nanorods (b) 290 and (c) 305nm long, accompanied by the corresponding AFM images. By virtue of the ferromagnetic component of the nanorod, the layers also show MO activity, which allows the modification of the optical properties (dielectric tensor) of the layer in the presence of an external magnetic field. In particular, if the magnetic field is applied perpendicular to the sample plane (Polar configuration), the resulting effect on the optical response appears as a change in the polarization state of the reflected light (Polar 4


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Kerr effect). This change in the polarization state reflected light can be related to the  of the   rpp rsp  Fresnel coefficients of the reflectivity matrix   as follows: rps rss θp + iǫp =

rsp rps , θs + iǫs = , rpp rss

(1)

where θp,s and ǫp,s are the Kerr rotation and ellipticity when the incident light is p− or s−polarized, respectively. In Figure 2(a), (d), and (g) we show the spectral dependence of the modulus of the complex Kerr rotation for p− and s−polarized light impinging at normal incidence with respect to the sample plane (also called magneto-optical activity MOA) for a magnetic field of 1.2 Teslas (high enough to reach a saturation state) for the three structures shown in Figure 1.

It would be possible to reduce the field needed to magnetically saturate the

structure using a more complex fabrication scheme that involves substituting the actual individual Au and Co layers by Au/Co multilayers with equivalent Co vs. Au ratio but with thinner (1,1 nm thick) Co layers. This strategy has previously been employed to obtain layers with perpendicular magnetic anisotropy, therefore allowing magnetic saturation along the surface normal with relatively small magnetic fields. 18,19 In optically isotropic systems the two polarizations are degenerated at normal incidence, and thus the MOA should be independent on polarization (as is for the disk like shape). Since our system presents optical anisotropy, this will no longer be the case. 20–22 For the sake of simplicity, we establish that the wave is p−polarized when the polarization is along the long axis of the nanorods (red) and s−polarized when the polarization is along the short axis (black). As the rods length increases two different effects can be observed. The first is that the MOA evolves from a narrow peak for the disks case ( Figure 2 (a)), with no difference between p− and s− as mentioned before, to a broad structured band for the longest rods ( Figure 2(g). The second is that the difference between p− and s− MOAs is increased as the rod length increases (in the same direction as the optical anisotropy does, as seen

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1 using the data from the spectra of the first and second columns of Figure 2. Within experimental error, and for all rod lengths, both curves, rps and rsp , are identical, pointing to a pure optical origin of the anisotropy of the MO activity. Remarkably, here comes the first important result regarding the polarization conversion coefficients themselves, rps and rsp , which is that the polarization conversion efficiency, p−to−s (rps ) or s−to−p (rsp ) does not depend on the polarization state of the impinging light. Additionally, as the length of the rods increases, the spectral dependence of these magnitudes evolves from a single, well defined peak for disks (s− and p− resonances appear at the very same spectral position) to a broad peak due to the big but not total overlap of the two resonances, to finally reflect a double-peak structure for the longest rods where the two resonances are clearly separated. These two peaks reveal that the polarization conversion coefficient will show enhancements, or resonant behavior, whenever any of the resonant states, either the initial s− (p−) or the final state p− (s−), involved in the polarization conversion process rsp (rps ) is excited, widening therefore the band width at which plasmon enhanced MO activity is achieved. To verify these statements, we have performed theoretical calculations of the electromagnetic response of isolated nanorods (see inset in Figure 3) upon illumination from a linearly polarized plane wave by using the Discrete Dipole Approximation. 23 The nanorods are basically a half-cylinder of ellipsoidal cross-section (whose length will be varied to mimic the fabricated rods) capped with two quarters of an ellipsoid (one at each end). The radius of the cylinder, as well as the capping quarter-ellipsoid, is 65nm (leading to a short axis of the nanorod of 130nm), whereas the height is 35nm. The length of the cylinder will vary from 0 (disk like of 130nm in diameter, no anisotropy) to 180nm (giving rise to a long axis of 310nm, similar to the experimental case). In Figure 3(a)-(c) we can see the normalized far field intensity (R|Eff |, where R is the far field point location) in the backward direction for the component along the polarization direction (R|Ess | - black lines,

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Figure 3: Far field electromagnetic intensity in the backscattered direction, normalized by the distance of the observation point. The left hand panel, Figures (a) to (c), displays the normalized fields for the same polarization as the incident one, p-polarized in red lines while s-polarized in black open dots, for bars with 130nm width, and different lengths of the long axis, namely 130nm (a), 220nm (b) and 310nm (c). The red shift experienced by the resonance for p-polarization as the length of the long axis increases is clearly captured. Figures (d) to (f), contain the polarization conversion for p-polarized incidence in red lines while for s-polarized in black open dots. As it can be seen the spectral shape is the same irrespective of the incidence polarization. The red shift experienced by the resonance along the long axis can be seen first as a broadening of the peak (e) and then as a second, low frequency peak. The overlap between the two resonances gives rise to a broadband almost uniform polarization conversion region. and R|Epp |- red lines) for the different length of the long axes (a) 130nm, disk like geometry, (b) 220nm and (c) 310nm. This quantity is equivalent to the experimental Fresnel coefficients |rss | and |rpp |. As we can see the behavior is very similar to the experimental one depicted in Figure 2. For the polarization along the short axis we obtain a fixed position for the resonance location, whereas for the long axis the spectral position is a function of the length of the axis. In Figure 3(d)-(f) we present the polarization conversion, i.e. the normalized far 8


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field intensity in the backward direction for the component along the converted direction, (s−to−p R|Esp | - black lines, and p−to−s R|Eps |- red lines) for the same length of the long axes. Again the agreement with the Fresnel coefficients rsp and rps is remarkable. The curves for the two incident polarizations appear overlaid on one another since, as mentioned before, the polarization conversion in the far field does not depend on the initial polarization state. The modification of the spectral position for the long axis resonance is the responsible for the broadening and final splitting of the initial single peak for the isotropic structure. This fact can be seen as consistent with a description based on the behavior of a sole dipole in the far field.

This has already been successfully employed by Maccaferri and

coworkers 22 where they considered the MO response of a collection of ellipsoidal ferromagnetic nanoparticles, each described as a single dipole. They showed that the MO response presented a marked dependence with the polarization of the incident beam, with features similar to those presented in Figure 2(g). However, the properties of the polarization conversion itself were not explicitly discussed. Indeed, from the static polarizability α0 (the actual polarizability α0 including radiative corrections is given by α = (α0 −1 − Iik 3 /(6π))−1 ) of a prolate ellipsoid, 12,23 it is possible to already infer that the polarization conversion does not depend on the incident polarization. For that case, the static polarization of one of these particles is described by:



 V  α0 =  3  



(ǫ−1)[1+Ly (ǫ−1)]+Ly ǫ2M O [1+Lx (ǫ−1)][1+Ly (ǫ−1)]+(Lx ǫM O )(Ly ǫM O )

ǫM O [1+Lx (ǫ−1)][1+Ly (ǫ−1)]+(Lx ǫ0 )(Ly ǫM O )

0

−ǫM O [1+Lx (ǫ−1)][1+Ly (ǫ−1)]+(Lx ǫM O )(Ly ǫM O )

(ǫ−1)[1+Lx (ǫ−1)]+Lx ǫ2M O [1+Lx (ǫ−1)][1+Ly (ǫ−1)]+(Lx ǫM O )(Ly ǫM O )

0

0

0

(ǫ−1) [1+Lz (ǫ−1)]

(2)

where Lx , Ly and Lz are the geometrical factors of the particle in each direction, V is the volume of the nanoparticle, ǫ is the diagonal element of the dielectric tensor, and ǫM O is the off-diagonal (magneto-optically induced) element. Notice that we have chosen the s−polarization to be aligned with the x−direction and the p-polarization to be aligned with 9


    

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the y−polarization, so we can now refer to the orientation axes of the nanorod. It can be readily seen that the absolute value of the polarization conversion is independent of the incidence since αyx = −αxy , as evidenced by the experimental and theoretical findings. Let us now verify that the far field can be seen indeed as an effective single dipole. Within our approach, the far field intensities are obtained from the contributions of all the dipoles 2 P involved in the discretization, using Eexact = kǫ0 p Gff (rff , rp ) Pp where the Green function ff ikRp at the far field is given by Gff (rff , rp ) = e4πRp I − uRp ⊗ uRp , Rp = rff −rp , Rp = |Rp | where ff indicates the observation point (at the far field) and p the location of the given dipole. In order to get insight of the origin of the far field features it would be useful to visualize the intensities of the magneto-optically induced contribution for the individual dipoles forming the nanorod. In Figures 4(b)-(c) we present the real part of the magneto-optically induced dipoles for all point-like elements that compose the nanorod, for the most elongated one (see sketch in (a)) showing the internal layers of the rods for each polarization incidence. We show the cross induced dipoles (i.e. the half difference upon magnetic inversion +M to −M , where M is the magnetization at saturation), in Figure 4(b) the incident wave is polarized in the x−direction and thus ∆pyx = 0.5(py (+M ) − py (−M )) is represented, while in Figure 4(c) the incident wave is polarized in the y−direction and ∆pxy = 0.5(px (+M ) − px (−M )) is represented. Although not shown, it is important to mention that ∆pxx and ∆pzx , when the incidence is in x, or ∆pyy , and ∆pzy , when the incidence is in y, are not vanishing quantities, but do not contribute to the far field. This could lead to the conclusion that the analogue to the behavior of one single dipolar element might be not right, or at least it might be overstretched. However, the geometrical P average of the induced dipole, i. e. ∆P = (∆p) is zero except for ∆Pyx and ∆Pxy . What is more, ∆Pyx = −∆Pxy for all spectral range. This is the second important result, since this averaged dipole is the ultimate responsible to the point-like dipolar behaviour observed in far field.

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Figure 4: In (a) we present a sketch of the geometry depicting the actual aspect ratio employed in the calculation. (b)-(c) Spatial distribution of the real part of each magneto-optically induced dipole involved in the calculation, (b) along the y−direction for x−polarized incidence (∆pyx ), (c) along the x−direction for y−polarized incidence (∆pxy ) for a wavelength of 600nm and for a 130nm wide by 310nm long nanorod. To get into this idea, in Figure 5 (a) we show the spectral dependence of the modulus of the geometrical average of the magneto-optically induced dipole for the most elongated bar (oscillating in the y−direction when the incoming wave is x−polarized, ∆Pyx , and in the x−direction when incoming y−polarized, ∆Pxy ), normalized to its highest value. As ∆Pyx = −∆Pxy we only show one of them (red line). It can be seen that this dipole has two defined peaks at the same spectral locations as the polarization conversion curve shown in Figure 3 for the same geometry. In blue we show the corresponding far field generated by that averaged dipole located at r0 , also normalized to its highest value. This far field is basically the polarization conversion factor presented above. Notice that the spectral shape is identical to that of the exact the far field generated by the sum of the contribution of all 2 P dipoles Eexact = kǫ0 p Gff (rff , rp ). ff 11


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Figure 5: (a) Spectral dependence of the averaged magneto-optically induced dipole (red) and the corresponding absolute value of the far field (blue), both normalized to the maximum value for a 130nm wide by 310nm long nanorod. (b) Spatial distribution of the absolute value of y−component of the magneto-optically induced electromagnetic field at a plane 65nm above the nanorod (Ey component of the induced near field pattern) for an incident wave polarized along the long axis (x−direction) and a wavelength of 600nm. (c) The same but depicting the x−component of the magneto-optically induced electromagnetic field (Ex component of the induced near field pattern) when the incident polarization is along the short axis (y−direction). However, the different spatial distributions of the dipole intensities for each polarization is already pointing that the effective dipole view cannot be valid for all range of distances. We present here the third important result, showing that the single dipole picture breaks down whenever one abandons the far field and approaches the vicinity of the nanoparticle. In this near field range the details do matter. As an example, in Figure 5(b,c) we present the spatial distributions of the module of the magneto-optically induced y−component (|Ey | in (b)) and x−component ((|Ex | in (b)) of the electric field at a x − y plane 65nm above the particle for an incident wavelength of 600nm. Although the far field radiations of the induced dipole for both incidence directions are indistinguishable (blue curve), the near field is completely different. This different behavior will have direct consequences when the

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nanoparticle interacts with its neighborhood, since, depending on their relative position, the interacting elements would experience different fields. Therefore an adequately tailored near field pattern by means of a engineered particle would be paramount to obtain unprecedented performances in devices such as sensors, isolators or modulators, to name a few.

Conclusions In summary, we have explored the optical and magneto-optical response of optically anisotropic magnetoplasmonic elements with the shape of elongated nanorods. We have found that the magneto-optically induced polarization conversion of such anisotropic entities is independent of the incident wave polarization, when observed in the far field range. Thus when the resonances of the two main symmetry axis are brought apart by increasing the length of one of the axis, the overlap between them gives rise to a broad-band region of high polarization conversion, that manifest itself as an also broad-band region of magneto-optical activity. This magneto-optically induced polarization conversion presents strong differences depending on the observation point. The far field signature is found to be independent of the orientation of the incoming filed and thus the polarization conversion is equivalent to consider the geometrically averaged dipole. The near field, however, is very sensitive to the details of the excitation of the individual elements of the nanorod, and thus the spatial profile of the near field presents a strong dependence on the incoming polarization, thus allowing tailoring the near field response by an adequate design of the nanorods and their orientation with respect to the incident polarization state.

Methods Fabrication: The fabrication of the actual nanorods is carried out by a combination of hole mask colloidal lithography 24 and multiaxial evaporation in ultra-high vacuum. This process allows fabricating multicomponent structures of a wide variety of shapes with nanometer 13


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After deposition, sonication for 2 hours in an acetone bath removes the PMMA and the sacrificial gold layer, leaving the bare multicomponent rods on the substrate. As depicted in 6(b) the so obtained rods are expected to present rounded edges due to the circular shape of the holes in the template. The width of the rods (W) is determined by the diameter of the hole being thus independent of the oscillation amplitude, the length rod (L) is determined by the oscillation amplitude and the geometrical parameters of the template (mainly PMMA thickness), and the height (H) is controlled by the deposition time and its homogeneity along the rod is optimized by compensating the oscillation speed along the different steps of the oscillation cycle. Typically hundreds of oscillation cycles are performed in each deposition process to further insure the lateral homogeneity of the final structures. A representative AFM image of rods obtained this way is shown in Figure 6(c). The typical individual layer thicknesses for 20o incidence angle are 21nm Au / 5nm Co / 8nm Au / 2nm Ti. The obtained length vs width aspect ratios for the different deposition angles and the corresponding morphology for three specific cases are also shown in Figure 6(d). Experimental measurements: The transmission measurements were done using a M-2000 Woollam ellipsometer, whereas the reflectivity and polar Kerr spectra were obtained using a home made Polar Kerr spectrometer where light from a Xenon lamp source is dispersed by a monocromator. The resulting monochromatic light passes through a polarizer and a photoelastic modulator before reaching the sample. The reflected light is then analysed by a polarizer whose orientation can be change to obtain Rpp , Rss , rps , rpp , rsp and rss .

Acknowledgement Funding from the Spanish Ministry of Economy and Competitiveness through grant AMES MAT2014-58860-P is acknowledged. N. de Sousa thanks financial support from Spanish Ministerio de Economía y Competitividad (MINECO) project FIS2015-69295-C3-3-P.

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References (1) Khorasaninejad, M.; Aieta, F.; Kanhaiya, P.; Kats, M. A.; Genevet, P.; Rousso, D.; Capasso, F. Achromatic metasurface lens at telecommunication wavelengths. Nano lett. 2015, 15, 5358–5362. (2) Aieta, F.; Genevet, P.; Kats, M. A.; Yu, N.; Blanchard, R.; Gaburro, Z.; Capasso, F. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano lett. 2012, 12, 4932–4936. (3) Huang, L.; Chen, X.; Mühlenbernd, H.; Zhang, H.; Chen, S.; Bai, B.; Tan, Q.; Jin, G.; Cheah, K.-W.; Qiu, C.-W. Three-dimensional optical holography using a plasmonic metasurface. Nat. Comm. 2013, 4, 2808. (4) Kats, M. A.; Genevet, P.; Aoust, G.; Yu, N.; Blanchard, R.; Aieta, F.; Gaburro, Z.; Capasso, F. Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy. Proc. Natl. Acad. Sci. 2012, 109, 12364–12368. (5) Zhao, Y.; Alú, A. Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates. Nano lett. 2013, 13, 1086–1091. (6) Armelles, G.; Cebollada, A.; García-Martín, A.; González, M. U. Magnetoplasmonics: combining magnetic and plasmonic functionalities. Adv. Opt. Mat. 2013, 1, 10–35. (7) González-Díaz, J. B.; García-Martín, A.; García-Martín, J. M.; Cebollada, A.; Armelles, G.; Sepúlveda, B.; Alaverdyan, Y.; Käll, M. Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-optical Activity. Small 2008, 4, 202–205. (8) Chen, J.; Albella, P.; Pirzadeh, Z.; Alonso-González, P.; Huth, F.; Bonetti, S.; Bonanni, V.; Åkerman, J.; Nogués, J.; Vavassori, P. Plasmonic nickel nanoantennas. Small 2011, 7, 2341–2347.

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and Near-Field Broad-Band Magneto-Optical Functionalities Using

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