Abstract
Magnetic field control of light is among the most intriguing methods for modulation of light intensity and polarization on subnanosecond timescales. The implementation in nanostructured hybrid materials provides a remarkable increase of magnetooptical effects. However, so far only the enhancement of already known effects has been demonstrated in such materials. Here we postulate a novel magnetooptical phenomenon that originates solely from suitably designed nanostructured metaldielectric material, the socalled magnetoplasmonic crystal. In this material, an incident light excites coupled plasmonic oscillations and a waveguide mode. An inplane magnetic field allows excitation of an orthogonally polarized waveguide mode that modifies optical spectrum of the magnetoplasmonic crystal and increases its transparency. The experimentally achieved light intensity modulation reaches 24%. As the effect can potentially exceed 100%, it may have great importance for applied nanophotonics. Further, the effect allows manipulating and exciting waveguide modes by a magnetic field and light of proper polarization.
Similar content being viewed by others
Introduction
The magnetooptical activity of a magnetized medium is mainly described by its gyration g in the nondiagonal terms of the permittivity tensor^{1}. Effects that are quadratic in magnetization M are also determined by the magnetizationinduced changes of the diagonal elements of the permittivity tensor (Methods). For materials of cubic symmetry, g is proportional to M. In bulk, these terms lift the degeneracy of electromagnetic modes with respect to light polarization, inducing a splitting between orthogonally circularly or linearly polarized modes. This splitting gives rise to the Faraday or Voigt magnetooptical effects^{1}. In a spatially confined medium, the electromagnetic mode structure is more complex. Further, an external magnetic field can modify frequencies and distributions of the modes giving rise to a multifaceted phenomenology^{2,3,4,5}. An additional degree of freedom opens up in metaldielectric nanocomposites^{6,7} as well as periodic magnetic structures with the period close to the wavelength of a mode^{8,9,10,11,12,13,14,15}.
Periodic structures with metallic and dielectric constituents—plasmonic crystals—can support surface plasmon polaritons along with waveguide modes^{16}. Magnetoinduced changes of sample transmittance and reflectance due to cyclotron resonance were predicted for plasmonic crystals containing perforated nonmagnetic materials with a Drude ac conductivity tensor^{17,18}. However, this effect requires rather large external magnetic fields exceeding 1 Tesla. Much smaller values of a control magnetic field are feasible if the plasmonic crystal includes magnetic materials, which is referred to as magnetoplasmonic crystal (MPC). Such an MPC provides outstanding magnetooptical properties as evidenced by significant enhancements of the Faraday and transverse Kerr effects^{19,20,21,22,23,24,25,26,27,28,29,30}. The mostly pronounced enhancement of the magnetooptical effects was found for MPCs containing a perforated noble metal stacked on a magnetic dielectric film^{27,28,29,30}. Because of their constituents, such MPCs have a large specific Faraday rotation due to the magnetic dielectric and small optical losses due to the nanostructured noble metal. Physical origin of such an enhancement is related to the excitation of the surface plasmon polaritons and waveguide modes of the MPC, which, on the one hand, leads to resonances in the transmittance and reflectance spectra that are sensitive to the magnetic field and, on the other hand, increases the effective length of light interaction with the magnetized medium.
Here we demonstrate that apart from enhancing established magnetooptical effects, MPCs can also be used to generate novel phenomena. In particular, we report about a new magnetophotonic effect in the longitudinal magnetization configuration by which the MPC transparency is resonantly increased by about 24%. The effect may be increased even further by using materials with better magnetooptical quality, making it attractive for applications in modern telecommunication devices.
Results
Eigenmodes of the MPC
We consider an MPC consisting of three layers. From bottom to top the layer sequence is (Fig. 1a): a nonmagnetic dielectric substrate, followed by a magnetic dielectric layer, and a thin gold film stacked on top. The latter is periodically perforated by parallel slits with period d. The lower refractive index of the substrate relative to one of the magnetic layer ensures the existence of guided optical modes in the magnetic layer.
In absence of an external magnetic field, the magnetic layer is demagnetized (Fig. 1a). Then the eigenmodes hosted by the MPC are surface plasmons as well as waveguided transverse magnetic (TM) or transverse electric (TE) waves. The TM and TE modes are mostly localized in the magnetic layer. Nevertheless, they are (especially the TM mode) sensitive to the permittivity of the adjacent metal and therefore also have plasmonic character. The TM and TE modes have three nonzero field components (Fig. 1b) and , respectively. The periodic perforation of the gold layer leads to Bloch wave character of these modes and to their leakage into the surrounding air so that the modes have a significant role for the optical farfield response of the structure. Indeed, these modes cause resonances with nonsymmetric Fanoshape in the transmittance T and reflectance R spectra^{31}.
The TM and TE modes can be excited by the incident light with momentum component if momentum conservation is fulfilled: , where , κ is the mode wavenumber and m is an integer. In addition, the incident light wave must have the proper polarization so that it has at least one component along the electromagnetic field of the mode. For example, a TE mode can be excited only if the incident wave has a E_{y} field component, which is satisfied for TEpolarized illumination (E field is along the slits).
An external DC magnetic field B, applied along the xaxis, magnetizes the magnetic layer of the MPC longitudinally (Fig. 1c) so that nondiagonal terms of the tensor appear: ɛ_{yz}=−ɛ_{zy}=ig. Their presence transforms the modes into ‘quasiTM’ and ‘quasiTE’ modes (Fig. 1d). Besides the TM components, the quasiTM mode also contains TE components: . Vice versa, the quasiTE mode acquires TM components: . Because all six field components are nonzero for both modes, those modes can be excited by the incident light of any polarization.
For normal incidence of the TMpolarized (E is perpendicular to the slits) light experimentally studied here, the excited waveguide modes have the E_{x} and H_{y} components of even parity in x, as inherent in the incident radiation. These modes are quasiTM and quasiTE ones with the following form of Bloch–Fourier series expansion:
where U^{TM/TE} are Fourier amplitudes of Bloch envelopes for principal components of the quasiTM/quasiTE modes, F(κ, z) and G(κ, z) are defined by the parameters of the magnetic layer waveguide (Methods). According to equation 1, the admixed components of the modes are proportional to g and, consequently, to the magnetization.
The appearance of the admixed field components can also be understood in terms of the TM–TE mode conversion taking place in the longitudinally magnetized waveguide due to the circular birefringence^{3}. However, this reasoning becomes cumbersome for the case of a standing wave. Moreover, for symmetry reasons, no transformation of light polarization occurs in the far field for normal incidence.
Longitudinal magnetophotonic intensity effect
The mode wavenumber of the quasiТM and quasiTE modes in the longitudinally magnetized structure changes according to (Methods):
For typical values of g, the shift of Fano resonances induced by these changes is relatively small and therefore would result only in small modifications of the transmittance/reflectance spectra.
A considerably larger effect is expected to come from the magnetizationinduced changes of the field distributions of the modes. The key point in that respect is that because of the appearance of the TM components in the quasiTE mode, this mode can be excited by light of TM polarization. The excited quasiTE mode takes a fraction of the incident optical energy, changing the overall absorbed energy by ΔA. Equation 1 implies that the quasiTE mode amplitude is proportional to the gyration g. Consequently, ΔA g^{2}, and because of energy conservation, the changes in transmittance ΔT and reflectance ΔR are also quadratic in g. For zeroth order of diffraction, the considered magnetooptical intensity effect can be described by the relative difference between the transmittance coefficients T_{M} and T_{0} of the magnetized and the demagnetized structure: observed at the TEmode eigenfrequencies. Because the longitudinal magnetization of the MPC also modifies the field of the TM modes by inducing TE components, one should expect intensity variation at the TMmode resonances as well.
A similarly defined intensityrelated effect, but of different origin, was studied in conventional magnetooptics of smooth ferromagnets, and was called orientational effect^{32,33}. However, for illumination polarized along the magnetization, the orientational effect vanishes^{33}. Therefore, the effect considered here has to be regarded as novel, with the most prominent feature being that the effect is exclusively caused by the excitation of eigenmodes of the nanostructured medium so that it may be termed ‘longitudinal magnetophotonic intensity effect’ (LMPIE).
Experimental demonstration
To provide a proofofprinciple demonstration of the effect, we fabricated several MPCs, and the highest value of the LMPIE is found for the sample based on a 1,270nm thick magnetic film of composition Bi_{2.97}Er_{0.03}Fe_{4}Al_{0.5}Ga_{0.5}O_{12}, possessing a large real part of gyration g=0.015 and a low absorption coefficient α=400 cm^{−1} (ref. 34) at 840 nm. The other prominent feature of this sample is that it was designed such that the dispersion curves of the principal TM and TE modes corresponding to m=2 intersect at the Г point (κ=0) of the Brillouin zone. As a consequence, both modes can be excited by normally incident light of the same frequency. The MPC has a gold grating with period d=661 nm, height h_{gr}=67 nm and slit width r=145 nm.
The LMPIE was observed in transmission (Methods). Intensities of the zerothdiffractionordertransmitted light for demagnetized and longitudinally magnetized MPCs were compared to determine the parameter δ that characterizes the LMPIE. First, we checked that no intensity modulation occurs for the bare magnetic film (Fig. 2a, green curve). Thereafter, we measured the LMPIE for the MPC illuminated with normally incident TMpolarized light and found that the longitudinally applied magnetic field resonantly increases MPC transparency by 24% at λ=840 nm (Fig. 2a). There are also resonances at about 825 and 801 nm, though their values are several times smaller. Numerical modelling results (blue curve in Fig. 2a) agree closely with the experimental data (Methods).
Properties of the LMPIE
The transmittance spectrum demonstrates three Fano resonances clearly related to excitation of TM modes whose spectral positions (shown by the black arrows in Fig. 2b) were calculated by the scatteringmatrix method (see Methods). The calculated spectral positions of the quasiTE modes indicated by the red arrows in Fig. 2a, on the other hand, confirm that excitation of these modes is responsible for the LMPIE peaks. A longitudinal magnetic field causes almost no shift of the Fano resonances but modifies their shapes substantially. That is why the LMPIE spectral lines have rather complex multiple peak character. An important feature of the designed MPC is that the TEmode resonance is tuned away from the transmittance minimum, allowing one to simultaneously have high transmittance (see for example, the negative peak of δ=−10.3% at λ=842 nm in Fig. 2a).
The LMPIE shows maximum values of about 24% at λ=840 nm where both quasiTE and quasiTM mode resonances are excited. Simultaneous excitation of the two orthogonal modes allows more efficient trapping of the TMpolarized illumination and its conversion into the quasiTE mode due to the applied magnetic field. This is also supported by the spatial distribution of the E field of the optical wave inside the magnetized MPC, calculated at the two quasiTEmode resonances (at 840 and 801 nm) (Fig. 3a). Coloured contour plot depicts E_{y}, which is one of the principal field components of the quasiTE mode. Squares of the quasiTEmode amplitude differ by a factor of 14, and the larger the amplitude of the TEmode, the larger the effect in the far field, that is, the LMPIE. In the case of a demagnetized MPC, the quasiTE mode vanishes demonstrating the nearfield aspect of the LMPIE, that is, switching on and off of the quasiTE mode by the external magnetic field (Fig. 3b).
At normal incidence, only the intensity of the transmitted light is sensitive to the MPC magnetization and there is no Faraday effect, that is, the polarization state of the transmitted light is unaltered. For moderate oblique incidence, the LMPIE remains present and the Faraday effect appears; however, the polarization rotation does not exceed 10^{−2} degree. The LMPIE takes largest values at the degenerate resonances of the quasiTE and quasiTM modes taking place at the angle of incidence θ=0°, λ=840 nm and θ=±2°, λ=830 nm (Fig. 4a).
The LMPIE is quadratic in the longitudinal magnetization of the MPC, which is supported by a parabolic dependence of the effect on the external magnetic field B for B<30 mT (Fig. 4b). Though the saturation occurs for B=360 mT, the LMPIE is quite large even for much smaller magnetic fields. The saturation magnetic field could be diminished down to 10 mT if a magnetic film possessing easy inplane magnetic anisotropy is used instead.
Discussion
The measured magnetophotonic intensity effect with 24% modulation can be considered giant because its origin is secondorder in g. This becomes even more evident if compared with the orientational effect, which is also quadratic in g. For the same bare magnetic film, the orientational effect is negligible: δ~10^{−5} (as calculated for normal incidence and illumination polarized perpendicularly to M). For metallic ferromagnetics, it reaches maximum values of δ~10^{−3} (Krinchik and Gushchin^{33}).
The other MPC sample was based on Bi_{2}Dy_{1}Fe_{4}Ga_{1}O_{12} magnetic film of thickness h_{m}=873 nm. It has reduced magnetooptical quality (near the quasiTEmode resonance at λ=703 nm, g=0.0023 and α=820 cm^{−1}) (ref. 35). As a result, we measured peak value of δ as 0.85% only. It proves that the LMPIE is crucially dependent on the magnetooptical quality of the magnetic film. Thus, assuming an MPC with a magnetic layer of Bi_{3}Fe_{5}O_{12} having g=0.049 and α=580 cm^{−1} at 805 nm (ref. 36), our calculations demonstrate that the LMPIE can be optimized potentially, leading to δ exceeding 100%.
In summary, we demonstrated a new magnetophotonic effect in the longitudinal magnetization configuration for modulating the transparency of the nanostructured sample. Its experimentally observed value δ reaches 24%, which can be considered as a giant value. The modulation level can be increased even further by using materials with better magnetooptical quality, manifesting the relevance of the LMPIE for applications in modern telecommunication devices. Moreover, recent results on the inverse Faraday effect^{37} suggest that the LMPIE might be used for alloptical light modulation on subnanosecond timescales. On the other hand, the effect of mode switching is of great perspective for active plasmonics and metamaterials^{38,39}. For example, it might be used in optical transistors to allow efficient control of light propagation in magnetic waveguides through nonlinear interaction^{40} with the excited modes of the MPC.
Methods
Field and dispersion of the electromagnetic modes of the MPC
Optical properties of a medium magnetized along the xaxis are characterized by the permittivity tensor :
For magnetic dielectrics at optical frequencies, the following inequalities are fulfilled: b<<g<<ɛ_{2}, and the permeability μ is close to 1. The constants g and b are linear and quadratic in magnetization, respectively, which can be written in the form b=ag^{2}, where a is a magnetizationindependent coefficient. Consequently, the contribution of b causes only renormalization of the coefficients in the expressions describing the magnetooptical effect as compared with the case of b=0. Moreover, numerical modelling shows that the contribution of b to the effect is much smaller than the contribution by the g^{2} term. That is why in the following analysis we argue in terms of g, assuming that the contribution of b is implicitly taken into account in the corresponding coefficients.
Let us first consider the MPC structure in which the metal grating is substituted with a smooth metal. The solutions of the Maxwell’s equations corresponding to waveguide modes are found in the following form (the coordinate axes are shown in Fig. 1):
in the metal:
in the magnetic layer:
and in the substrate:
where , κ is the mode wavenumber, ɛ_{1} and ɛ_{3} are dielectric constants of the metal and substrate, respectively, ω is the frequency, c is the speed of light in vacuum, is the unit electric field vector corresponding to polarization denoted by (j), and coefficients A_{i}, B_{i} and K_{i} are to be found (see below). Note that the electromagnetic field in the magnetic layer consists of four plane waves with different polarization states, whereas in surrounding media, it contains both TE and TM components. For magnetic media γ and are found from the Fresnel equation:
where n denotes the refraction vector n={κ; 0; ±γ_{±}}. γ_{±} can be represented as γ_{±}=γ_{2}±Δγ_{±}(g), where and Δγ_{±} is a magnetooptical contribution. Taking into account the boundary conditions for E and H vectors at the metal/magnetic dielectric and magnetic dielectric/substrate interfaces, the following dispersion equation is obtained:
where , for the ‘quasiTM’ modes and η_{i}=γ_{i} for the ‘quasiTE’ modes, h_{m} is the magnetic layer thickness and Ψ(κ, ω) is determined by the optical and geometrical parameters of the structure (the expression for Ψ(κ, ω) is not presented because of its complexity). Excluding some specific cases when , where κ_{0} is the mode wavenumber for the demagnetized system (Φ(κ_{0}, ω)=0), and taking into account the smallness of g, it follows from equation 8 that the magnetic contribution to κ is quadratic in g:
which leads to equation 2: κ=κ_{0}(1+g^{2}), where .
The coefficients A_{i}, B_{i} and K_{i} in equation 4 are found by applying boundary conditions for E and H vectors at the two interfaces. Substituting those coefficients in equation 4 reveals that all six components of the electromagnetic field are nonzero, but the admixed components for either of the two modes vanish for g=0. In the linear in g approximation, one can find that the admixed components are proportional to g, whereas the principal components are magnetization independent:
for the ‘quasiTM’ modes:
for the ‘quasiTE’ modes:
For given magnetization direction, the functions (κ, z) and (κ, z) are odd in κ. The explicit formulas for (κ, z) and (κ, z) have rather complicated form and are not presented here.
The presence of the periodic array of slits in the metal layer makes the modes Bloch waves:
where U(x, z) is a periodic function of x and thus can be expanded in a Fourier series, so that:
where m is an integer and d is the grating period. If the slit width is rather small in comparison with the period, then the electromagnetic field distribution for each of the terms in equation 13 is not greatly affected by the slits, as the field is concentrated mostly inside the magnetic layer. It implies that their wavenumbers and therefore the Bloch wavenumber κ can be estimated by equation 2, and equations 10 and 11 also conserve their form for each term in equation 13 in the presence of the slits.
At κ=0, equation 13 for the principal components of the quasiTE and quasiTM modes takes the form:
Applying equations 10 and 11 for each term in equation 14, we derive the expressions for the admixed components:
Taking into account that (κ,z) and (κ,z) are odd in κ, we come to equation 1.
Fabrication
The MPC structure was fabricated by the following procedure. The magnetic layer of bismuthsubstituted rareearth iron garnet with composition Bi_{2.97}Er_{0.03}Fe_{4}Al_{0.5}Ga_{0.5}O_{12} was deposited on the gadolinium gallium garnet substrate by rfmagnetron sputtering of the composite 3.2Bi_{2}O_{3}+4Fe_{2}O_{3}+0.5Al_{2}O_{3}+0.5Ga_{2}O_{3}+0.03Er_{2}O_{3} oxide target in a 25mTorr Ar–O2 (4:1) gas mixture at a substrate temperature of 580 °C and rfpower density of 10 W cm^{−2}. The film synthesis was finalized with in situ postannealing at 550 °C for 10 min at 500 Torr of oxygen pressure^{34}. The epitaxial quality of the magnetic film was confirmed by Xray diffraction patterns. The film shows a uniaxial magnetic anisotropy and a mazelike domain structure of 1 μm typical domain width. The gold grating was fabricated by thermal deposition of a gold layer onto the iron garnet film and subsequent electron beam lithography combined with reactive ion etching by an Arion plasma. Grating period and slit width were determined from atomic force microscopy.
All magnetooptical measurements were performed at room temperature. A halogen lamp was used as a white light source. The collimated light was focused on the sample with an achromatic doublet in conjunction with an adjustable iris to reduce the angle of the incoming light cone to <1°. The focused light spot on the sample was about 200 μm in diameter. The polarization of light with respect to the slits was adjusted with a Glan–Thomson prism. Magnetic fields up to 360 mT were applied in the MPC film plane and perpendicularly to the grating slits. The zerodiffraction ordertransmitted light was collimated by an achromatic lens and focused on the entrance slit of a spectrograph. The later has linear dispersion of 6.4 nm/mm and is equipped by a chargecoupled device camera, which provides an overall spectral resolution of 0.3 nm.
Numerical simulation
The electromagnetic modelling was performed using the Rigorous CoupledWave Analysis technique extended to the case of gyrotropic materials^{41}. The eigenfrequencies of the guided modes of the structure were determined by the scatteringmatrix method^{42}. For the modelling of the experimentally studied MPC with the Bi_{2.97}Er_{0.03}Fe_{4}Al_{0.5}Ga_{0.5}O_{12} ferromagnetic film, the permittivity ɛ and the gyration g were taken from experiment and from Dzibrou and Grishin^{36} (for example, at 840 nm, ɛ=6.440+0.012i, g=0.015−0.001i and b=4 × 10^{−5}). Dispersion of both quantities was taken into account. For the permittivity of gold, we used the experimental data from Johnson and Christy^{43}. To get optimal correspondence with the experimental data, the gold grating height h_{gr} and slit width r were varied during the electromagnetic modelling within their measurement errors. Best matching was found for h_{gr}=67 nm (experimentally found value of h_{gr} was 65 nm) and r=145 nm (experimentally found value of r was 149 nm).
Additional information
How to cite this article: Belotelov, V. I. et al. Plasmonmediated magnetooptical transparency. Nat. Commun. 4:2128 doi: 10.1038/ncomms3128 (2013).
References
Zvezdin, A. K. & Kotov, V. A. Modern Magnetooptics and Magnetooptical Materials IOP Publishing: Bristol and Philadelphia, (1997).
Bi, L. et al. Onchip optical isolation in monolithically integrated nonreciprocal optical resonators. Nat. Photon. 5, 758–762 (2011).
Dötsch, H. et al. Applications of magnetooptical waveguides in integrated optics: review. J. Opt. Soc. Am. B 22, 240–253 (2005).
Temnov, V. et al. Active magnetoplasmonics in hybrid metal/ferromagnet/metal microinterferometers. Nat. Photon. 4, 107–111 (2010).
Wu, Z., Levy, M., Fratello, V. J. & Merzlikin, A. M. Gyrotropic photonic crystal waveguide switches. Appl. Phys. Lett. 96, 051125 (2010).
Barthelemy, M. & Bergman, D. J. Faraday effect in composites. Phys. Rev. B 58, 12770–12781 (1998).
Bergman, D. J. & Strelniker, Y. M. Anisotropic ac electrical permittivity of a periodic metaldielectric composite film in a strong magnetic field. Phys. Rev. Lett. 80, 857–860 (1998).
Inoue, M., Khanikaev, A. B. & Baryshev, A. V. inNanoscale Magnetic Materials and Applications (eds Liu, J. P., Fullerton, E., Gutfleisch, O., Sellmyer & D. J.)627–660Springer Verlag: Dordrecht, (2009).
Fang, K., Yu, Z., Liu, V. & Fan, S. Ultracompact nonreciprocal optical isolator based on guided resonance in a magnetooptical photonic crystal slab. Opt. Lett. 36, 4254–4256 (2011).
Belotelov, V. I. & Zvezdin, A. K. Magnetooptics and extraordinary transmission of the perforated metallic films magnetized in polar geometry. J. Magn. Magn. Mater. 300, e260–e263 (2006).
Bonanni, V. et al. Designer magnetoplasmonics with nickel nanoferromagnets. Nano. Lett. 11, 5333–5338 (2011).
Banthi, J. C. et al. High magnetooptical activity and low optical losses in metaldielectric Au/Co/Au–SiO2 magnetoplasmonic nanodisks. Adv. Mater. 24, OP36 (2012).
Osada, M., HajdukovaSmidova, N., Akatsuka, K., Yoguchi, S. & Sasaki, T. Gigantic plasmon resonance effects on magnetooptical activity of molecularly thin ferromagnets near gold surfaces. J. Mater. Chem. C 1, 2520–2524 (2013).
Kuzmiak, V., Eyderman, S. & Vanwolleghem, M. Controlling surface plasmon polaritons by a static and/or timedependent external magnetic field. Phys. Rev. B 86, 045403 (2012).
Fan, F., Chen, S., Wang, X. H. & Chang, S. J. Tunable nonreciprocal terahertz transmission and enhancement based on metal/magnetooptic plasmonic lens. Opt. Express 21, 8614–8621 (2013).
Christ, A. et al. Optical properties of planar metallic photonic crystal structures: experiment and theory. Phys. Rev. B 70, 125113 (2004).
Strelniker, Y. M. & Bergman, D. J. Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field. Phys. Rev. B 59, R12763 (1999).
Strelniker, Y. M. & Bergman, D. J. Transmittance and transparency of subwavelengthperforated conducting films in the presence of a magnetic field. Phys. Rev. B 77, 205113 (2008).
Torrado, J. et al. Tunable magnetophotonic response of nickel nanostructures. Appl. Phys. Lett. 99, 193109 (2011).
Zharov, A. A. & Kurin, V. V. Giant resonant magnetooptic Kerr effect in nanostructured ferromagnetic metamaterials. J. Appl. Phys. 102, 123514 (2007).
Clavero, C., Yang, K., Skuza, J. R. & Lukaszew, R. A. Magneticfield modulation of surface plasmon polaritons on gratings. Opt. Lett. 35, 1557–1559 (2010).
Chetvertukhin, A. V. et al. Magnetooptical Kerr effect enhancement at the Wood’s anomaly in magnetoplasmonic crystals. J. Magn. Magn. Mater. 324, 3516–3518 (2012).
Grunin, A. A., Zhdanov, A. G., Ezhov, A. A., Ganshina, E. A. & Fedyanin, A. A. Surfaceplasmoninduced enhancement of magnetooptical Kerr effect in allnickel subwavelength nanogratings. Appl. Phys. Lett. 97, 261908 (2010).
Sapozhnikov, M. V., Gusev, S. A., Troitskii, B. B. & Khokhlova, L. V. Optical and magnetooptical resonances in nanocorrugated ferromagnetic films. Opt. Lett. 36, 4197 (2011).
Newman, D., Wears, M., Matelon, R. & Hooper, I. Magnetooptic behaviour in the presence of surface plasmons. J. Phys.: Condens. Matter. 20, 345230 (2008).
Kostylev, N. et al. Plasmonassisted high reflectivity and strong magnetooptical Kerr effect in permalloy gratings. Appl. Phys. Lett. 102, 121907 (2013).
Belotelov, V. I., Doskolovich, L. L. & Zvezdin, A. K. Extraordinary magnetooptical effects and transmission through metaldielectric plasmonic systems. Phys. Rev. Lett. 98, 77401 (2007).
Belotelov, V. I., Bykov, D. A., Doskolovich, L. L., Kalish, A. N. & Zvezdin, A. K. Giant transversal Kerr effect in magnetoplasmonic heterostructures: the scatteringmatrix method. J. Exp. Theor. Phys. 110, 816–824 (2010).
Belotelov, V. I. et al. Enhanced magnetooptical effects in magnetoplasmonic crystals. Nat. Nanotech. 6, 370–376 (2011).
Chin, J. Y. et al. Nonreciprocal plasmonics enables giant enhancement of thinfilm Faraday rotation. Nat. Commun. 4, 1599 (2013).
Luk’yanchuk, B. et al. The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 9, 707–715 (2010).
Carey, R., Thomas, B. W. J., Viney, I. V. F. & Weaver, G. H. Magnetic birefringence in thin ferromagnetic films. J. Physics D: Appl. Phys. 1, 1679 (1968).
Krinchik, S. S. & Gushchin, V. S. Magnetooptical effect of change of electronic structure of a ferromagnetic metal following rotation of the magnetization vector. JETP Lett. 10, 24 (1969).
Khartsev, S. I. & Grishin, A. M. High performance latchingtype luminescent magnetooptical photonic crystals. Optics Letters 36, 2806–2808 (2011).
Vasiliev, M. et al. RF magnetron sputtered (BiDy)3(FeGa)5O12:Bi2O3 composite garnetoxide materials possessing record magnetooptic quality in the visible spectral region. Opt. Express 17, 19519–19535 (2009).
Dzibrou, D. O. & Grishin, A. M. Fitting transmission and Faraday rotation spectra of [Bi3Fe5O12/Sm3Ga5O12]^{m} magnetooptical photonic crystals. J. Appl. Phys. 106, 043901 (2009).
Kirilyuk, A., Kimel, A. V. & Rasing, T. h. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010).
Stenning, G. B. et al. Magnetic control of a metamolecule. Opt. Express 21, 1456–1464 (2013).
Cai, W. & Shalaev, V. Optical Metamaterials: Fundamentals and Applications Springer (2009).
Boardman, A. D., Hess, O., MitchellThomas, R. C., Rapoport, Y. G. & Velasco, L. Temporal solitons in magnetooptic and metamaterial waveguides. Photonic. Nanostruct. 8, 228–243 (2010).
Li, L. Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors. J. Opt. A: Pure Appl. Opt. 5, 345–355 (2003).
Tikhodeev, S. G., Yablonskii, A. L., Muljarov, E. A., Gippius, N. A. & Ishihara, T. Quasiguided modes and optical properties of photonic crystal slabs. Phys. Rev. B 66, 045102 (2002).
Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972).
Acknowledgements
The work was supported by the Deutsche Forschungsgemeinschaft, the Russian Foundation for Basic Research (No. 120233100, 120231298, 130201122, 110200681, 130712410, 130291334), the Russian Federal Targeted Program ‘Scientific and ScientificPedagogical Personnel of the Innovative Russia’. V.I.B. and A.N.K. additionally acknowledge support by Alexander von Humboldt foundation personal grant and Russian Presidential Fellowship (No. SP124.2012.5), respectively. A.M.G. acknowledges support from the Advanced Optics and Photonics Vetenskapsrådet Linné center.
Author information
Authors and Affiliations
Contributions
V.I.B., A.K.Z. and D.A.B. conceived and designed the experiments. A.M.G., S.I.K., M.N. E. A. and M.V. fabricated magnetic films. S.K., V.J.Y., A.V.G. fabricated the gold nanostructure on the magnetic film. L.E.K. and I.A.A. performed the experiments. A.N.K., D.A.B., V.I.B. and L.L.D. analysed the experimental data. V.I.B., M.B., A.K.Z., I.A.A., D.R.Y. and K.A. cowrote the paper. All authors discussed the results and commented on the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Rights and permissions
This work is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/byncnd/3.0/
About this article
Cite this article
Belotelov, V., Kreilkamp, L., Akimov, I. et al. Plasmonmediated magnetooptical transparency. Nat Commun 4, 2128 (2013). https://doi.org/10.1038/ncomms3128
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/ncomms3128
This article is cited by

Magnetooptical heterostructures with second resonance of transverse magnetooptical Kerr effect
Scientific Reports (2024)

Beam steering at the nanosecond time scale with an atomically thin reflector
Nature Communications (2022)

Theoretical investigation of optical properties and Faraday rotation of onedimensional periodic structure of magnetooptical material with a defect electrooptical material for the supported Tamm plasmon polaritons
Indian Journal of Physics (2022)

Role of avoided crossing and weak value amplification on enhanced Faraday effect in magnetoplasmonic systems
Communications Physics (2021)

Magnetically controllable metasurface and its application
Frontiers of Optoelectronics (2021)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.