Optical Magnetic Response in a Single Metal Nanobrick. Jianwei Tang, Sailing He, et al.

Transcription

1 Optical Magnetic Response in a Single Metal Nanobrick Jianwei Tang, Sailing He, et al. Abstract: Anti-syetric localized surface plasons are deonstrated on a single silver nanostrip sandwiched by SiC layers. By eploying the resonance of anti-syetric localized surface plasons, we enable single etal nanobricks to produce optical agnetis, in the blue and violet light range, as well as in a part of the ultraviolet light range. The physical echanis is explained. The agnetic response of a natural aterial is usually very weak, especially at optical frequencies, where people siply put agnetic pereability 1. However, with the help of etaaterials with artificial structures on sub-wavelength scales,, people have anaged to realize strong agnetic response fro icrowave frequencies to optical frequencies. In coon designs of etaaterials with optical agnetic response, the agnetis relies on the excitation of an anti-syetric plason resonance of a pair of coupled etal nanostrips (or other siilar geoetries, e.g. nanopillars, nanorods, etc.) [1, 2]. The anti-syetric plason resonance arises due to the coupling of the localized surface plasons of neighboring nanostrips within a pair. In general it is observed that only one fundaental plason resonance exists for the localized surface plason of a single etal nanostrip, which bjehaves like an electric dipole. When two etal nanostrips are positioned closely to each other, the fundaental plason resonance splits into two resonances, referred to as the syetric and anti-syetric resonances. The anti-syetric plason resonance behaves like a agnetic dipole and thus produces agnetis. Fro all the relevant works reported so far, one ay conclude that pairing etal nanostrips is necessary for a agnetic response. Such a conclusion is not true. In fact, with an appropriate design, a single etal nanostrip is also able to produce agnetis. In this work, we deonstrate anti-syetric localized surface plasons on a single etal nanostrip. By eploying the resonance of such an anti-syetric localized surface plason, we enable a single etal nanobrick to produce optical agnetis, in the blue and violet light range, as well as in a part of the ultraviolet light range. To deonstrate anti-syetric localized surface plasons on a single etal nanostrip, we sandwich every silver nanostrip (infinitely long as a 2D case) between two SiC nanostrips and let a plane wave with the electric field polarized in the x direction illuinate norally fro the top (Fig. 1). FIG. 1 Silver nanostrips sandwiched by SiC nanostrips and illuinated norally fro the top by a plane wave with the electric field polarized in the x direction. The thickness of the silver layer is t =15 n and the thickness of the SiC layer is t 30n. The width of the nanostrips is w 70n. The lattice constant of the periodic nanostrip array is p 300n. i

2 When the nanostrips are illuinated by the incident electroagnetic wave, localized surface plasons are excited on the two Ag/SiC interfaces. The localized surface plasons on the two interfaces interact with each other through the fields penetrated into the etal, which causes the plason resonance to split into syetric resonance (Fig. 2(b)) and anti-syetric resonance (Fig. 2(c)) as shown by the red transission spectru line in Fig. 2(a). For the syetric resonance, the electric field on the two surfaces of the silver nanostrip is in phase. This resonance is siply the kind of localized surface plason resonance coonly observed for a single etal nanostrip. For the anti-syetric resonance, the electric field on the two surfaces is out of phase. To the best of our knowledge, such an anti-syetric localized surface plason on a single etal nanostrip has never been reported before. This ay be due to the fact that the SiC layers are essential in order to achieve the anti-syetric resonance of our single silver nanostrip, as will be analyzed in detail later. If the strip width w is large (e.g., 140 n), the high order anti-syetric localized surface plason resonant odes will be revealed in the transission spectru. In the transission spectru we also find that the anti-syetric resonance is at a higher frequency than the syetric resonance. This is contrary to the case of a coupled pair of etal nanostrips, where the anti-syetric resonance is at a lower frequency than the syetric resonance. The key difference of the underlying echanis between these two cases is that for a single etal nanostrip the localized surface plasons on the two surfaces couple with each other through the field inside the etal ediu, while for a coupled pair of etal nanostrips, the localized surface plasons couple in the dielectric ediu. FIG. 2 (a) The transission spectra of our saples. For all the saples, p = 300 n, t i = 30 n, and w = 70 n. The thickness of the silver layer is t =15 n (black line), 20 n (red line), 30 n (green line) for the three saples. (b) The electric field and H z field distributions of the anti-syetric plason resonance. (c) The electric field and H z field distributions of the syetric plason resonance. For all the nuerical siulation in this paper, the perittivity of silver is obtained fro experiental data [3] and SiC is approxiately described as dielectric ediu with constant perittivity of 8. To investigate further the physical principle of the sandwiched silver nanostrip, we treat it as a 2-D IMI (insulator/etal/insulator) waveguide of finite length w as shown in Fig. 3(a) [4]. The thickness of the Ag layer is t, the thickness of the SiC layer is i t. The blue lines in Fig. 3(b) are the analytical dispersion curves for the two fundaental propagating odes of the IMI waveguide of infinite length. For siplicity, here the iaginary part of the perittivity of silver [3] is neglected. The upper dispersion curve corresponds to the odd propagating ode ( E x (z) is an odd function and H y (z) is even, as shown in Fig. 3(c)), and the lower curve corresponds to the even propagating ode (E x (z) is an

3 even function and H y (z) is odd, as shown in Fig. 3(d)). These two fundaental propagating odes in the IMI waveguide are due to the evanescent field coupling of the propagating surface plason polaritons at the two Ag/SiC interfaces. If the IMI waveguide is of finite length, reflections at the two terinations occur and the interference of the counter-propagating guided waves results in soe Fabry Pérot (F-P) resonances with standing-wave-like field distribution. Such a field distribution is siilar to the field distribution of the plason resonance of our sandwiched single silver nanostrip (studied earlier in Fig. 2): F-P resonance of the even propagating ode is siilar to the syetric localized surface plason resonance (see Fig. 2(c)), and F-P resonance of the odd ode is siilar to the anti-syetric resonance (see Fig. 2(b)). In this sense, the localized surface plason resonances of a single etal nanostrip can be viewed as F-P resonances of counter-propagating guided waves, which are partially reflected at the waveguide terinations [4]. Two requireents should be fulfilled for the waveguide to have a strong F-P resonance: first, the effective wavelength of the guided wave should atch the length of the waveguide (i.e., the length of the waveguide should be an integer of half effective wavelength); secondly, the reflections at the two terinations should be strong enough for the guided wave. The SiC cladding layers ake the dispersion curves of the two fundaental guided odes lower than the light line in SiC (solid black line in Fig. 3(b)), and thus far below the light line in air (dashed black line in Fig. 3(b)). Otherwise, the dispersion curves (purple lines in Fig. 3(b) for the silver waveguide without SiC cladding layers) will be close to the light line in air. Thus, with the SiC cladding layers the effective wavelength of the guided waves can be uch shorter than that in air, which akes it possible to support F-P resonance in a waveguide of sub-wavelength length (required for the hoogenization of the etaaterial). With such a short effective wavelength, the fields are tightly confined inside the SiC/Ag/SiC waveguide structure (see Fig. 3(c) and (d)). This guarantees the large reflection of the guided waves at the waveguide terinations. Although the SiC layers play roles for both syetric and anti-syetric localized surface plason resonances, we ephasize here that they are essential for the anti-syetric resonances, but not necessary for the syetric resonances. The silver thickness t is an iportant paraeter of the waveguide, as it is closely related to the coupling between the surface plasons at the two SiC/Ag interfaces. For a saller t (e.g., 15 n), the dispersion curves (red lines in Fig. 3(b)) of the even and odd odes are ore separated. For a larger t (e.g., 25 n), the dispersion curves (green lines in Fig. 3(b)) are closer to each other, until the two odes degenerate for a large enough t when the surface plasons at the two interfaces becoe decoupled [5]. We have also plotted the transission spectra for different t (15 n, 20 n, and 25 n) in Fig. 2(a). For a saller t, the anti-syetric resonances blue shift and the syetric resonances red shift; while for a larger t, the anti-syetric resonances blue shift and the syetric resonances red shift. This agrees with the dispersion curves shown in Fig. 3(b).

4 FIG. 3 (a) 2-D IMI (insulator/etal/insulator) waveguide of finite length w. Wave is guided in the x direction. The thickness of SiC layers is ti 30 n. (b) Dispersion curves of the waveguides. The red, blue and green lines are the dispersion curves of the waveguide with Ag layer thickness t 15 n, 20 n and 25 n, respectively. The solid and dashed black lines are light lines in SiC and air, respectively. The purple lines are the dispersion curves of the silver waveguide without SiC cladding layers. The electric field distribution (arrow plot) and agnetic field distribution (color contour plot) of (c) the even ode and (d) the odd ode. When we treat the localized surface plason resonances of the single etal nanostrip as F-P resonances of guided waves, the way of excitation/illuination is not involved in such a odal analysis. However, we know the way of excitation/illuination would influence soehow the localized surface plason resonance. First, the strength of a certain resonant ode depends on its capability of scattering the exciting/illuinating light. For exaple, for noral incidence of plane waves, the scattering capability of the first order syetric/anti-syetric resonance is larger than that of the third order syetric/anti-syetric resonance, while the second order can hardly scatter any norally incident plane wave. This agrees with the transission spectru in Fig. 2, where only odd nuber order resonances are excited and the higher odd nuber order resonances are weaker for both syetric and anti-syetric odes. Secondly, the way of excitation/illuination also influences the field distribution and resonant frequency of a certain resonant ode. This is due to soe retardation effects related to the finite structure size. For exaple, when we change the angle of incidence fro 0 (i.e., noral incidence) toward 90, the first order anti-syetric resonance would blue shift and the field distribution would also change slightly. Due to the retardation effect, the waveguide analysis can only give rough estiation of the resonant frequency of the sandwiched silver nanostrip. Having deonstrated anti-syetric localized surface plasons on a sandwiched single silver nanostrip (2D case), we can further eploy such anti-syetric localized surface plasons on a sandwiched single silver nanobrick (3D case) to operate as a agnetic etaaterial with optical agnetis. The inset in Fig. 4(a) shows an array of silver nanobricks sandwiched by SiC. The side length of each nanobrick (square shape) is 70 n, the lattice constant is 120 n, and the thicknesses of

5 the silver layer and SiC layer are 20 n and 30 n, respectively. For noral incident light with the electric field polarized along the x direction, the transission and reflection spectra are shown in Fig. 4(a). The effective pereability of the silver nanobrick array is retrieved fro the transission and reflection spectra [6], and is shown in Fig. 4(b). The Lorentz-type resonance in the dispersion spectra of the effective pereability confirs the optical agnetic response of the sandwiched single silver nanobrick. The transission spectra are further given for different lattice constants and the agnetic resonances are nearly in the sae spectra position as shown in Fig. 4(c). This verifies that the resonance is a local effect, where periodicity only influences the overall scattering aplitude. We further push the agnetic response to a shorter wavelength by reducing the thickness of the silver brick (Fig. 4(d)). Of course, the nanobricks are not liited to square shapes, other shapes, e.g., circular shapes, are also feasible, as long as the structure in the z direction is of IMI for. In suary, we have deonstrated for the first tie optical agnetic response in a single etal nanobrick. Our agnetic etaaterial allows a large agnetic response in the blue and violet light range, as well as in a part of the ultraviolet light range. This is also the first tie a single etal layer is introduced to give large agnetic response. Our single-etal-layer design ay stiulate new types of subwavelength agnetic resonators for applications in biosensing and optical iaging, etc. It also enriches the odes of localized surface plasons, i.e., the interactions between the light and etal particles. FIG. 4 (a) The transission (solid line) and reflection (dashed line) spectra of an array of square silver nanobricks sandwiched by SiC. (b) The real (solid line) and iaginary (dash-dotted line) parts of the retrieved effective pereability. (c) The transission spectra of the nanobrick saples with different lattice constants (120 n for the black line, 200 n for the red line, and 300 n for the green line). (d) The effective pereability spectra of the nanobrick saples with different silver thickness (10 n for the black line, 15 n for the red line, 20 n for the green line, and 25 n for the blue line).

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