Open Access
Add to BibSonomyAbstract
Magnetoplasmonic crystals (MPC) composed of a 1D gold grating on top of a magnetic garnet layer made by a combined ion-beam etching technique are studied. We demonstrate that this method allows to make high-quality MPC. It is shown that MPC with a 30–40 nm thick perforated gold layer provides an effective excitation of two surface plasmon-polariton modes and several numbers of waveguide modes in the garnet layer. An enhancement of the transversal magneto-optical effect up to the value of 10−2 is observed for all types of resonant modes, that propagate in the magnetic layer, due to magnetic-field control over the mode excitation which is promising for future photonic devices.
© 2014 Optical Society of America
1. Introduction
Magnetoplasmonic crystals (MPC) attract much attention due to their unique and pronounced ability to control the light flow. [1–8]. One of the efficient MPC compositions is the combination of a dielectric magnetic film with a thin perforated metal layer on top [4–8]. It was demonstrated that MPC of such a type supports the resonant excitation of surface plasmon polaritons (SPP) with a relatively long SPP propagation length and reveals a strong magneto-optical response introduced by garnet films. This allows for a magnetic field control over the SPP excitation at the metal/garnet interface. An important point here is that the quality of the interfaces between the adjacent metal and dielectric layers should be smooth and free of defects. This restricts the number of accessible techniques for the MPC fabrication.
In most of the papers cited above the electron beam lithography followed by a lift-off technique or combined with the reactive ion etching by an Ar+ plasma were used to make the Au/garnet MPC on a gallium gadolinium garnet (GGG) substrate. It was shown that such a structure supports the excitation of the SPP modes localized on two metal surfaces, as well as the waveguide (WG) modes in the dielectric slab. The necessity in use of a template limited the variety of structures that have been studied; besides, it is worth noting that up to now the MPC with the gold layer no less than 70 nm have been reported. In this paper we present the results on the experimental studies of optical and magneto-optical response of Au/garnet/GGG MPC series with different parameters, such as the dielectric material, layers thickness and perforation period, made by combined ion-beam etching technique, which allows to produce high-quality periodic magnetoplasmonic crystals with 30–40 nm thick gold layer. We show that the structures support multiple modes excitation followed by the enhancement of the magneto-optical effects. This leads to the possibility of transparency control in wide spectral range by tuning a corresponding mode.
2. Resonant modes in MPCs
A schematic view of studied MPCs along with the experimental geometry are shown in Fig. 1. MPC consists of a garnet layer situated between a GGG substrate and a perforated gold film. The dispersion relation for the SPP and WG modes for a MPC of such a type can be derived [10, 11] within a three-layer model, in which the perforated gold layer is regarded as a continuous film characterized by an effective permittivity [5, 9], while the bulk values of the permittivity are used for the description of air, garnet and the GGG substrate.
Fig. 1 Scheme of the MPC: magnetic layer (3) grown on a GGG substrate (4) and covered by a perforated gold layer (2). Magnetic field is parallel to the stripes, wave vectors of the incident wave (k) and modes (kspp, kwg) propagating along x are shown together with the coordinate system. The inset shows the SEM image of the top view of the sample.
As the perforated metal layer is a periodic structure with the period d along the X-direction, it supports a resonant excitation of the electromagnetic modes with the wave vector kx(ω) if the quasi phase-matching condition k0 sinθ + mD = kx is satisfied (k0 = ω/c is the wave vector of the incident light, D = 2π/d the reciprocal lattice vector, θ the angle of incidence and m ∈ Z the order of the corresponding mode).
The electromagnetic fields in a three-layer structure can be written in the form
where , F = Hy for the TM mode and F = Ey for the TE mode, the subscript i denotes the layers in the structure. Taking into account that these fields satisfy the Maxwell equations and the boundary conditions, one can obtain the following dispersion relation for the resonant modes: where κi = kzi/εi for the TM-mode and κi = kzi for the TE mode. Solution of this equation with respect to kx gives the dispersion relations kx(ω) for the propagating modes. The dispersion relations for the WG modes are obtained if the gold layer, garnet and the substrate are considered as media 1, 2, 3, correspondingly. To derive the SPP dispersion one should take air, gold and garnet as the media 1, 2, 3 correspondingly. In the assumption that the Au layer is thicker than the skin-layer (k2h ≫ 1), the dispersion relation for the SPP modes can be separated into two independent ones. They correspond to the SPP excitation on 1/2 and 2/3 interfaces with where i, j denote the corresponding layers.In the layer magnetized along y direction (transversal magnetization) the permittivity tensor ε̂ has additional components εxz = −εzx = igy, where gy is the y-component of the gyration vector. In such a medium a plane TM wave E = (exEx + ezEz) exp [i(ωt − kxx − kzz)] propagates without polarization rotation, thus only TM mode will be considered below, which corresponds to p-polarized light in our geometry. The Eq. (2) gives the following dispersion relation for the TM modes in the case of a magnetic dielectric slab:
Similarly to the case of a non-magnetized dielectric layer, the dispersion relation for the SPP modes can be splitted into two independent ones for thick metal layer. The dispersion relation for the SPP on the Au/garnet interface becomes magnetization dependent:
where μ = (−ε1ε2)−1/2(1 −ε2/ε1)−1. As both Eqs. (3), (4) depend on the magnetization of the structure My, the resonant conditions can be shifted by changing the magnetization. Therefore magnetization-induced effects in MPC transmittance (reflectance) can be observed in the vicinity of the SPP or WG modes excitation.3. Experimental results
In the experiment, we studied the optical properties of four 1D MPCs made by a modified combined ion beam etching technique described in detail elsewhere [13, 14]. In brief, high power focused ion-beam was used to make periodic narrow slits in the Au film. The slits were 25 nm wide and did not reach the bottom of the layer, so that the remaining Au film prevented the damage of the underlying garnet. After that, finishing low energy oxygen ion-beam etching was applied to remove delicately the remaining Au layer at the grooves bottom and to increase their width up to required values. Good gold adhesion on the garnet surface was supported by few successive cycles of gold deposition sputtering and etching [13]. The samples were fabricated as 100μm×100μm pixels that consisted of periodic arrays of gold stripes on top of either a 600 nm thick (YLuBi)3(FeGa)5O12 (YIG) layer (sample 1) or a 2200 nm thick (BiTm)3Fe5O12 (BIG) layer (samples 2÷4), the grating periods being 730 nm, 695 nm, 730 nm and 820 nm for samples 1÷4 correspondingly. The thickness of the gold layer was 40 nm (sample 1) and 30 nm (samples 2÷4), the slits were 100 nm wide. Optical spectra were measured using a setup based on a stabilized halogen lamp; the light beam passed through a spatial filter and a polarizer, and was focused in a spot of 50 μm in diameter. Transversal magnetic field of 3 kOe was applied (along y-axis, see Fig. 1). SEM image of sample #1 is shown on the inset in Fig. 1.
Figure 2 shows the angular-frequency transmission spectra of the MPCs with different periods for the p-polarized incident light; panel (a) shows the spectrum for the sample#1 (YIG-based MPC), panels (b)–(d) correspond to the MPCs #2–4 on BIG layer. All the spectra reveal many transmission minima that shift linearly as the angle of incidence or the wavelength is changed. It was checked that these peculiarities are absent either for s-polarized incident light or for a homogeneous continuous garnet film, which proves that they are attributed to the propagating TM excitations in a spatially periodic structure.
Fig. 2 Angular-frequency transmittance spectra of the MPCs. Sample #1 with YIG slab and 730 nm grating period (a), samples #2–4 with BIG layer and periods 695, 730 and 820 nm (b)–(d) correspondingly. The lines show the theoretical dispersion curves given by Eq. (2): solid lines for SPP and dashed lines for the WG modes.
The dispersion curves λ(θ) for the WG and SPP modes were obtained by the numerical solution of Eq. (2) together with the phase-matching condition for different numbers m and were compared with the experimental transmission spectra (Fig. 2, solid and dashed lines correspond to the dispersion of SPP and WG modes, respectively; m denotes the modes number). One can see that the experimental spectra correlate well with the dispersion curves for the SPP modes with m = ±2 excited at the Au/garnet interface (solid black lines) and the SPP mode with m = ±1 at the Au/air interface (white lines).
Moreover, the spectra reveal pronounced transmission branches that correspond to two series of WG modes with m = ±2 (dashed lines). They reveal sharper resonances than the SPP ones and their spectra agree quite well with the theoretically predicted. The modes with other m numbers are out of the accessible wavelength region. Due to the smaller thickness of the garnet layer the number of the observed WG modes is smaller for the YIG-based MPC.
Transversal intensity magneto-optical effect (TIMOE) was studied in transmission through the MPC structure. It can be characterized by the magnetic contrast, δ =(I(M) − I(−M))/I(0), where I(±M) is the intensity of the transmitted radiation measured for the opposite directions of the magnetization, and I(0)=(I(M) + I(−M))/2. The setup sensitivity allowed to measure the δ values with the accuracy of ∼ 4 × 10−4.
Figure 3(b) and Fig. 4 show 2D angular-frequency TIMOE spectra for the samples #1,3 correspondingly. For comparison, we show the calculated dispersion curves for the two types of SPP and for the WG modes for each of the MPC. For both samples one can see a strong enhancement of the magnetic contrast in the vicinity of the SPP excitation on Au/garnet interface, its maximum value being 0.5% and 1% for the samples #1 and #3 correspondingly. A pronounced increase of TIMOE corresponds also to the waveguide modes excitation, while the values of the contrast in those spectral regions are lower and do not exceed 0.2 % and 0.5% for the YIG- and BIG-based samples. The stronger TIMOE enhancement in the sample #2 is attributed to smaller gold thickness and, hence, different energy distribution between the modes.
Fig. 3 (a) TIMOE spectra measured for −3° and 3° angles of incidence, and (b) Angular-frequency TIMOE spectra of the magnetic contrast δ for the YIG-based sample #1, the lines show the theoretical dispersion curves given by Eq. (2): solid lines for SPP and dashed for WG modes.
Fig. 4 TIMOE angular-frequency spectra for the BIG-based sample 3; the lines show the theoretical dispersion curves by Eq. (2): solid lines for SPP and dashed for WG modes.
To make these statements more evident we showed the TIMOE spectra for θ = ±3° in Fig. 3(a). A strong maximum in the TIMOE contrast is observed at approximately 850 nm, which corresponds to the excitation of the SPP on the Au/garnet interface. The weaker maxima at the wavelengths 825 nm and 800 nm correspond to the excitation of the WG modes. Outside the Au/garnet and WG modes resonances the magnetic contrast is close to zero, the shape of the δ spectrum is consistent with the model of the magnetic field induced effects in MPC due to the SPP Fano resonance excitation [15,16].
It should be noted that both SPP and WG mode-driven enhancement of the MO effects are odd with respect to the angle of incidence and are not observed for θ =0°. This fact is a consequence of the symmetry transformations of the magnetization pseudovector M: transversal magnetic field (along y) breaks the reflection symmetry with respect to the ZOY plane and thus introduces difference for the waves with +kx and −kx.
4. Conclusion
Summing up, we have studied optical and magneto-optical properties of 1D magnetoplasmonic crystals fabricated by a new combined ion-beam etching technique. We demonstrate that this technology provides an excellent quality of all the interfaces in the gold grating with the thickness down to 30–40 nm, which is proven by a rich spectral response and excitation of high-order WG and SPP modes which are in good agreement with the theoretical predictions. An enhancment of the TIMOE contrast in the vicinity of the resonances is observed simultaneously for the SPP and the WG modes being 1% and 0.5% correspondingly, which exceeds typical values even for the ferromagnetic metals [17]. This tunable magnetic-field controlled behaviour in a wide spectral range can be a useful feature for various applications.
Acknowledgments
The financial support by RFBR grants 13-02-01102, 12-02-90039 is acknowledged.
References and links
1. G. Armelles, A. Cebollada, A. Garcıa-Martın, J. M. Garcıa-Martın, M. U. Gonzalez, J. B. Gonzalez-Dıaz, E. Ferreiro-Vila, and J. F. Torrad, “Magnetoplasmonic nanostructures: systems supporting both plasmonic and magnetic properties,” J. Opt. A., Pure Appl. Opt. 11, 114023 (2009). [CrossRef]
2. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. M. Garcia-Martin, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4, 107–111 (2010). [CrossRef]
3. A. A. Grunin, A. G. Zhdanov, A. A. Ezhov, E. A. Ganshina, and A. A. Fedyanin, “Surface-plasmon-induced enhancement of magnetooptical Kerr effect in all-nickel subwavelength nanogratings,” Appl. Phys. Lett. 97, 261908 (2010). [CrossRef]
4. V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6, 370–376 (2011). [CrossRef] [PubMed]
5. V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. V. Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013). [CrossRef] [PubMed]
6. M. Pohl, L. E. Kreilkamp, V. I. Belotelov, I. A. Akimov, A. N. Kalish, N. E. Khokhlov, V. J. Yallapragada, A. V. Gopal, M. Nur-E-Alam, M. Vasiliev, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Tuning of the transverse magneto-optical Kerr effect in magneto-plasmonic crystals,” New J. Phys. 15, 075024 (2013). [CrossRef]
7. J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013). [CrossRef] [PubMed]
8. L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).
9. A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: Experiment and theory,” Phys. Rev. B 70, 125113 (2004). [CrossRef]
10. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
11. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002). [CrossRef]
12. A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials, vol. 4 (Taylor and Francis, London, 1997). [CrossRef]
13. A. V. Bespalova, O. L. Golikovaa, S. S. Savina, A. I. Stognij, and N. N. Novitskiib, “Preparation of magnonic crystals with nanoislands by focused ion beam etching,” Inorg. Mater. 48, 1190–1192 (2012). [CrossRef]
14. M. Pashkevich, R. Gieniusz, A. Stognij, N. Novitskii, A. Maziewski, and A. Stupakiewicz, “Formation of cobalt/garnet heterostructures and their magnetic properties,” Thin Solid Films 556, 464–469 (2014). [CrossRef]
15. V. Belotelov, D. Bykov, L. Doskolovich, A. Kalish, and A. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” JETP 110, 816–824 (2010). [CrossRef]
16. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010). [CrossRef]
17. G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in the ultraviolet visible, and infrared parts of the spectrum,” JETP 26, 1080 (1968).
