Magnetoplasmonic Quasicrystals

ANDREY N. KALISH,1,2 ROMAN S. KOMAROV,2 MIKHAIL A. KOZHAEV,1,3 VENU GOPAL ACHANTA,4 SARKIS A. DAGESYAN,2 ALEXANDER N. SHAPOSHNIKOV,5 ANATOLY R. PROKOPOV,5 VLADIMIR N. BERZHANSKY,5 ANATOLY K. ZVEZDIN,1,3 VLADIMIR I. BELOTELOV,1,2,* 1Russian Quantum Center, Skolkovskoe shosse 45, Moscow 121353, Russia 2Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia 3Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov str. 38, Moscow 119991, Russia 4Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai 400005, India 5Vernadsky Crimean Federal University, Vernadsky Ave. 4, Simferopol 295007, Russia *Corresponding author: [email protected] Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX

Nanostructured magneto-optical materials sustaining optical resonances open very efficient way for light control via magnetic field, which is of prime importance for telecommunication and sensing applications. However, usually their response is narrowband due to its resonance character. Here we demonstrate and investigate a novel type of the magnetoplasmonic structure, the magnetoplasmonic quasicrystal, which demonstrates unique magneto-optical response. It consists of the magnetic dielectric film covered by a thin gold layer perforated by slits forming a Fibonacci-like binary sequence. The transverse magneto-optical Kerr effect (TMOKE) acquires controllable multiple plasmon-related resonances resulting in a magneto-optical response in a wide frequency range. The broadband TMOKE is valuable for numerous nanophotonics applications including optical sensing, control of light, all-optical control of magnetization etc. On the other hand, TMOKE spectroscopy is an efficient tool for investigation of the peculiarities of plasmonic quasicrystals.

usually metallic alloys and they provide high hardness, low friction 1. INTRODUCTION coefficient, low heat conductivity and wide optical absorption bands. Among potential applications of quasicrystals there are two-phase materials containing steel with high strength and plasticity at high Since 1970s quasicrystalline structures have attracted attention of temperatures, coatings, for example, for frying pans, and solar energy researchers. They were experimentally discovered by Shechtman et al. absorbers and reflectors [2]. [1], for which he was awarded the Nobel Prize in Chemistry in 2011. The concept of quasicrystals has been implemented in plasmonics as Quasicrystals are non-periodic but ordered structures [2]. Contrary to well [4-12]. Study of plasmonic structures has been of prime interest for the periodic crystalline structures, they do not possess translational the last decade regarding control of plasmonic modes and near-field symmetry but long-range ordering is present. For periodic structures manipulation [13,14], design of optical properties [15], high sensitivity the reciprocal lattice is given by equidistant set of reciprocal vectors. to surrounding media [16,17], all-optical light control [18-20], and Thus for one-dimensional periodicity of period d the reciprocal vectors ultrafast magnetism [21,22]. Plasmonic quasicrystals in the form of G are given by G=(2π/d m)e, where e is the unit vector along the metal-dielectric nanostructures with quasicrystal pattern that supports periodicity direction and m is an integer. Unlike periodic structures, the excitation of surface plasmon-polaritons (SPP) were designed. Due to quasiperiodic ones are characterized by discrete but non-equidistant discrete non-equidistant reciprocal space and rotational symmetry of reciprocal lattice and corresponding unusual diffraction patterns. The quasicrystals, larger number of resonances associated with SPP modes example of one-dimensional quasicrystalline pattern is the Fibonacci appear and therefore such structures demonstrate a broadband optical binary sequence [3]. It is constructed by the infinite specific sequence of response. Moreover, it is polarization-independent for the 2D structures ‘0’ and ‘1’ numbers. [7]. The advantage of quasicrystalline structures over periodic and non- Two-dimensional quasicrystalline structures can possess rotational periodic ones is that they possess rich and designable reciprocal lattice symmetry Cn of the orders prohibited for the periodic structures, such that governs the optical diffraction and dispersion of the eigenmodes, as n = 5, 7 and higher orders. An example of that is Penrose tiling that and therefore offers designable broadband optical response [23]. It possesses C5 rotational symmetry [4]. Quasicrystalline substances are comes from the fact that the reciprocal lattice is strongly dependent on geometrical parameters of the structure, while for the periodic structures it is defined solely by the period. However, the potential of quasicrystalline structures for magnetooptics has not been revealed yet. At the same time, magneto-optics is a powerful tool for manipulation and probing of optical properties of different materials and structures. In detail, vast research has been carried out during recent decade on the enhancement of magneto- optical effects in plasmonic structures [24-41]. Combining magnetooptics with plasmonics provides significant advance in magneto-optical properties. It was demonstrated that in systems containing bismuth iron-garnet films [42,43] conventional magneto-optical effects such as the transverse Kerr effect (TMOKE) are resonantly enhanced in magnetoplasmonic crystals [37,38], and also novel promising effects arise [39]. However, these effects are of resonant nature, related to the excitation of eigenmodes of the structure, such as cavity modes, SPPs, waveguide and quasi-waveguide modes etc. that leads to narrow spectral range of the magneto-optical response. In the present work, we propose and demonstrate an approach for forming a broadband magneto-optical response using one-dimensional magnetoplasmonic quasicrystals. We design and fabricate the magnetoplasmonic quasicrystal and measure its optical transmittance and the TMOKE and compare them to the case of periodic structure. We find that the TMOKE in a quasicrystalline structure has multiple- resonance character and, moreover, it is a sensitive tool for investigation Fig. 1. (a,b) Schematics of the experimentally studied one-dimensional of the quasicrystal spectral properties. magnetoplasmonic quasicrystal (a) and the magnetoplasmonic crystal (b). Golden stripes are on top of the magnetic dielectric film deposited 2. MAGNETOPLASMONIC QUASICRYSTAL SAMPLES on a substrate. (c) The Fourier transform of the experimentally studied AND EXPERIMENTAL SET-UP quasicrystal formed by Fibonacci-like sequence (red line) in comparison with the spectrum of the periodic crystal having the same The considered 1D magnetoplasmonic quasicrystalline structure is width of gold stripes as the quasicrystal (black line). (d) The Fourier formed by a metallic quasicrystal grating on top of the smooth magnetic transform of the experimentally studied quasicrystal formed by the dielectric layer on a substrate (Fig. 1(a)). The sequence of metal stripes Fibonacci-like sequence (red line) in comparison with the spectrum of and air slits of the grating can be described by symbols ‘1’ and ‘0’. Our the quasicrystal formed by the pure Fibonacci sequence (blue line). structure is based on the 1D binary Fibonacci sequence, where ‘0’ is Dashed horizontal lines indicate 25% level with respect to the highest substituted by ‘010’. The final formula of the structure is thus the peaks. following: Optical and magneto-optical spectra of the plasmonic quasicrystal ‘10101101010101101011010101011010101011010110101010110 samples were measured by the following experimental set-up. 10110101010110101010110101101010101101010101101011010 Tungsten halogen lamp is used as a light source. After the lamp light 101011010110101010110101010110101101010101101011…‘ passes through the fiber in order to obtain homogeneous point-like light (1) source, it is collimated with achromatic 75mm lens and focused onto the sample with another achromatic 35mm lens to a spot of about 200 μm Such structure was chosen to achieve rather large spectral density of in diameter. To perform the TMOKE measurements the sample is resonances. placed in uniform external magnetic field of 200 mT generated by The schematic of a part of the structure corresponding to the electromagnet in the direction along the gold stripes. After the sample, underlined blocks in Eq. (1) is shown in Fig. 1(a). For comparison we the light is collimated with 20x microobjective and detected with the also consider a periodic crystal that is described by sequence spectrometer. The spectrometer slit was oriented perpendicularly to ‘10101010101…’ (Fig. 1(b)). the gold stripes, so only light with perpendicular to gold stripes The metal grating of the experimentally studied samples was incidence plane was detected. Spectral and angular decomposed light fabricated by electron beam lithography of the thermally deposited 80- signal is detected by the spectrometer with CCD camera. nm-thick gold layer. The air slit width corresponding to single ‘0’ in the binary sequence is 80 nm and the metal stripe width corresponding to 3. FOURIER SPECTRA OF THE PLASMONIC single ‘1’ in the sequence is 600 nm. The magnetic dielectric is a bismuth substituted iron-garnet film of composition Bi1.5Gd1.5Fe4.5Al0.5O12 [46]. It STRUCTURES was fabricated by reactive ion beam sputtering on (111) gadolinium gallium garnet substrate. The thickness of the magnetic film was made Spectrum of the SPPs excited by the incident light in a plasmonic rather small, 80 nm, to exclude the waveguide mode excitation in the grating structure is determined by the reciprocal lattice vectors G which considered frequency range. Thus, only SPPs can be excited. enter the phase matching condition:

β  k||  G , (2)

where β is the SPP propagation vector, and k|| is the in-plane component of the incident light wave vector. The reciprocal lattice vectors G are found from the Fourier transform of the metal pattern as the coordinates in the reciprocal space of the Fourier transform peaks. Fig. 1(c) depicts calculated absolute values of the Fourier transforms of the quasicrystal (red line) and the periodic crystal (black line) patterns of the considered samples. The lowest peaks in the quasicrystal Fourier transform with amplitudes smaller than 0.01 a.u. can be neglected as they appear as a numerical calculation error. Moreover, low peaks do not contribute significantly to the excitation of eigenmodes, as the corresponding excitation efficiency is small. The reciprocal lattice for the quasicrystal is discrete and it is far denser compared to that of the periodic crystal. The discrete non-equidistant reciprocal lattice confirms that the structure is non-periodic but has some long-range order. The reciprocal vectors for the periodic crystal form a discrete equidistant lattice with their values Gm(per)=m⋅2π⁄d, where d is the period and m is an integer. For the considered parameters of the grating Gm(per)=m⋅9.24 μm-1. Due to equality of the width of the elements for both structures the reciprocal lattices correlate with each other. Namely, the reciprocal vectors of the quasicrystal lattice form bands that are located in the vicinities of Gm(per). Reciprocal lattices of quasicrystals can be tuned by adjusting their type of sequence. Fig. 1(c,d) shows Fourier spectra both for the experimentally considered structure (Eq. (1), red lines in (c) and (d)) and for the pure Fibonacci sequence (blue line in (d)). Spectral positions of the peaks and their amplitudes are different. In detail, in the range of the G vectors from 15 μm-1 to 20 μm-1 which produces resonances in the studied wavelength range from 750 nm to 1000 nm, the experimental sample has 3 peaks higher than 25%-level of the main peak. At the same time, the pattern based on the pure Fibonacci sequence provides only two such peaks (Fig. 1(d)). Another advantage of the experimentally Fig. 2. The dependence of transmittance (a,b) and the TMOKE (c,d) on considered structure is that the highest peaks are located closer to each the wavelength and the incident angle for the magnetoplasmonic crystal other, so their spectral density is larger than the one for the Fibonacci (a,c) and quasicrystal (b,d). Green lines show the calculated dispersion structure. Consequently, the quasicrystals formed by different types of curves for the surface plasmon polaritons. sequences have quite different Fourier transform and therefore the SPP Excitation of SPPs leads to Fano-shape resonances in transmittance. spectra. In the experimentally studied samples, main transmittance resonances are due to SPPs excited by the second diffraction order with 4. TRANSMISSION SPECTRA OF PLASMONIC G=18.48 μm-1 and G=19.01 μm-1, in the periodic and quasiperiodic QUASICRYSTALS structures, respectively (Fig. 1(c)). For the normal incidence it corresponds to the transmittance peaks at λ=820 nm (for the crystal, Fig. 2(a)) and λ=790 nm (for the quasicrystal, Fig. 2(b)). For the oblique Transmission spectra of the plasmonic samples demonstrate some incidence SPP resonances are split into low-frequency and high- resonant features which are dispersive with respect to the angle of frequency ones and demonstrate dispersion versus angle of incidence incidence (Fig. 2(a,b)). They are due to the SPPs propagating at the which is seen in Fig. 2(a,b) by peaks and dips following SPP dispersion interface between the magnetic film and gold grating as is confirmed by curve (green lines). Though the dispersion lines for the plasmonic the calculated dispersion of the SPP resonances (green dashed lines). quasicrystal predict more resonances in the range from λ=880 nm to The dispersion was calculated by Eq. (2) with propagation constant β0 λ=950 nm they are hardly seen in transmittance. As a result, taken from approximation of a smooth single-interface between two transmittance spectra for the crystal and its quasiperiodic counterpart 1/2 semi-infinite metal and dielectric media: β0=2π/λ [(εm εd)/(εm+εd)] , look rather similar. where εm and εd are dielectric constants of metal and dielectric, respectively, and λ is the vacuum wavelength. The dielectric constants were taken from [44] for gold and from [42] for magnetic dielectric. To 5. REVEALING PLASMONIC MODES IN QUASICRYSTALS take into account the finiteness of the magnetic film thickness, the FROM TMOKE SPECTRA presence of slits and the difference in magnetic chemical composition with respect to [42] εd was varied to obtain best fit with experimentally Since magneto-optical effects in plasmonic structures are enhanced observed spectral positions of optical resonances in both samples. The by the excitation of eigenmodes they can be used for investigation of the best correspondence was achieved when εd was multiplied by 0.95 for quasicrystals spectra. The impact of the magnetization M on the SPP the plasmonic crystal and by 0.91 for the plasmonic quasicrystal dispersion is given by [45]: compared to values from [42]. The difference in multiplicators comes from the difference in grating patterns, as the periodic and quasiperiodic β  β 1β [Mn], (3) crystals have different effective filling factors of metal. 0 0

where n is the surface normal, β0 is the mode propagation vector for zero magnetization, and α is the proportionality coefficient dependent on permittivities of dielectric and metal media. Here we keep only linear in M contribution. On the other hand, the TMOKE, if observed in transmitted light, compares intensity of the transmitted light T for the opposite directions of the transversal magnetization T(M) and T(-M) and is defined by δ=[T(M)-T(-M)]⁄T(0), where T(0) is transmittance through the non-magnetized sample. The magnetically induced change in dispersion gives rise to the enhancement of the TMOKE at the slopes of the plasmonic resonances in optical spectra. It happens because the spectral positions of plasmonic resonances are shifted by the transverse magnetization and therefore, at their slopes, where the absolute value of the transmittance derivative with respect to the wavelength reaches its maximum, large difference between transmittance for oppositely magnetized cases appears. According to Eq. (2), large density of the reciprocal lattice vectors produces multiplicity of plasmonic resonances and, therefore, of the TMOKE resonances. Experimentally measured TMOKE spectra are shown in Fig. 2(c,d). In contrast to the transmission spectra, they are quite different for the crystal and quasicrystal samples. It highlights high sensitivity of the TMOKE to the excitation of the eigenmodes of the structure. Let us consider them in detail. For the periodic crystal, the TMOKE spectrum demonstrates pronounced resonances at the slopes of the transmittance peaks and vanishes at normal incidence due to symmetry reasons (Fig. 2(c)). At the oblique incidence, two pronounced TMOKE peaks of opposite signs are observed at around λ=850 nm. They are related to the low-frequency and high-frequency branches of the plasmonic dispersion and their opposite sings are due to the Fig. 3. (a) The TMOKE spectrum for the incident angle of 2°. (b,c) The propagation of SPPs in forward and backward directions. The TMOKE schematically shown dependence of the SPP penetration depth on the reaches 2% at the extrema of the spectra. No noticeable TMOKE wavelength and the near-field of the excited SPPs for the response is observed for λ>900 nm. magnetoplasmonic crystal (b) and quasicrystal (c). Intensity of blue However, for the plasmonic quasicrystal the TMOKE demonstrates color indicates the SPP amplitude versus wavelength (horizontal axis) much richer response: three pairs of resonances appear. Apart from the and depth (vertical axis). Blue dashed line indicates depth in the first pair at around λ=820 nm (for small incidence angles) that is quite magnetic dielectric film at which the amplitude of SPP decreases by e similar to the resonances for the periodic structure at λ=850 nm, two times. other pairs appear at around λ=890 nm and λ=950 nm corresponding to G=16.76 μm-1 and G=15.39 μm-1 (see Fig. 1(c)). The resonance at The multiplicity of the excited plasmonic modes attracts attention λ=890 nm is well pronounced and provides the TMOKE as large as also because they possess different values of the penetration depth 0.8%. The last one is rather weak and the TMOKE doesn’t exceed 0.3% (Fig. 3). Estimations show that for the plasmonic resonances shown in though is still detectable above the noise level. For increasing angle of Fig. 3(a), the SPP penetration depth in the magnetic dielectric varies incidence the pairs of resonances split further and mix with their approximately from 70 to 100 nm. This fact opens new possibilities for neighbours. manipulation of the optical near field, 3D sensing, control of the inverse Fourier spectrum of the quasicrystal indicates that there are two magneto-optical effects and optically-induced magnetization. more reciprocal vectors of G=17.62 μm-1 and G=18.15 μm-1 in the After demonstration of the concept of magnetoplasmonic vicinity of G=18.48 μm-1 but they have relatively low Fourier amplitudes quasicrystals the next step is the design of plasmonic quasicrystalline (0.03 and 0.02, respectively) and, therefore, do not produce any notable structures in order to obtain desired optical response. Quasicrystalline resonances even in TMOKE. structures provide designable reciprocal lattice, i.e. the set of reciprocal Thus, the plasmonic quasicrystals offer multiplicity of the vectors and therefore, dispersion of eigenmodes, by means of adjusting plasmonically mediated TMOKE. Fig. 3(a) demonstrates it more clearly. geometrical parameters. In particular, plasmonic quasicrystals offer The TMOKE spectrum for the range of wavelengths from λ=750 to designable spectrum of magneto-optical response for light modulation, λ=1000 nm is shown for the incident angle of 2 degrees for the periodic which is prosperous for parallel light information processing at several and quasicrystalline structures. For the former only one pair of frequencies. resonances (marked by ‘P’) is observed while, the latter clearly exhibits Furthermore, the plasmonic quasicrystals are promising for two close pairs of resonances (‘Q1’ and ‘Q2’) and also the third weaker achieving other broadband magneto-optical effects related to the one (‘Q3’). It confirms that plasmonic quasicrystals allow much broader excitation of eigenmodes. If the structure supports waveguide modes magneto-optical response. then there are many resonances for TE and TM modes with the As we saw in Fig. 1(c,d) the quasicrystals formed by different type of resonant wavelengths close to each other. This condition is favorable for sequences have quite different Fourier transform and therefore SPP the enhancement of the Faraday effect, as the TE-TM conversion is the spectra. However, most of the resonances do not have large efficiency most effective. Besides that, the magnetization affects the waveguide and are hardly observable in transmission or reflection. At the same mode polarization that usually leads to the longitudinal time, measuring TMOKE allows to reveal these resonances and identify magnetophotonic effect (LMPIE) in plasmonic structures. The dense different quasicrystal patterns. dispersion of the waveguide modes might lead to multiple LMPIE resonances.

6. CONCLUSION

We have proposed and demonstrated a novel structure - magnetoplasmonic quasicrystal for getting significant magneto-optical effects in the broadband wavelength range. It is based on magnetic dielectric film and the gold film perforated with the subwavelength slits forming Fibonacci-like binary sequence. While transmission spectra of the periodic and quasiperiodic patterns are quite similar, the TMOKE spectra demonstrate significant difference. Namely, for the quasicrystal the magneto-optical response is much more abundant. It shows that TMOKE spectroscopy is an efficient tool for investigation of the peculiarities of plasmonic quasicrystals. Due to larger density of the discrete peaks in the Fourier transform of the quasicrystal the additional plasmonic resonances appear leading to multiple TMOKE resonances. In particular, instead of one resonance at λ=850 nm for the plasmonic crystal, three resonances at λ=820 nm, crystals with plasmonic nanostructures and nanoparticles,” Nanophotonics 7, λ=890 nm and λ=950 nm appear. As a result the structure acquires 1-38 (2018). pronounced broadband magneto-optical response in the wavelength 17. D. O. Ignatyeva, G. A. Knyazev, P. O. Kapralov, G. Dietler, S. K. Sekatskii, range from λ=780 nm to λ=980 nm. It makes the proposed structure and V. I. Belotelov, “Magneto-optical plasmonic heterostructure with very promising for numerous nanophotonics applications including ultranarrow resonance for sensing applications,” Sci. Rep. 6, 28077 (2016). optical sensing, control of light, all-optical control of magnetization etc. 18. J. Chen, Z. Li, S. Yue, and Q. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single Funding. Russian Foundation for Basic Research (16-52-45061); the slit,” Nano Lett. 11, 2933-2937 (2011). Russian Presidential Grant (MK-2047.2017.2); Department of Science 19. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching and Technology (DST), India; the Ministry of Education and Science of in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Expr. 19, the Russian Federation (3.7126.2017/8.9). 2910-2915 (2011). 20. A. Kar, N. Goswami, and A. Saha, “Long-range surface-plasmon-enhanced Acknowledgment. The work is supported by the Russian Foundation all-optical switching and beam steering through nonlinear Kerr effect,” Appl. for Basic Research (project 16-52-45061), the Russian Presidential Phys. B 123, 1 (2017). Grant MK-2047.2017.2, and Department of Science and Technology 21. D. Bossini, V. I. Belotelov, A. K. Zvezdin, A. N. Kalish, and A. V. Kimel, (DST), India. 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