Magnetic polaritons

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Due to recent development in metamaterials, Localized magnetic polaritons (MPs) have been recently shown as a physical mechanism for extraordinary optical transmission in some artificial nanostructures [1-3]. Some of the phenomena observed previously in periodic gratings can be well described by the excitation of MPs. Diamagnetism is responsible for the magnetic response in split-ring and U-shape structures for metamaterials, as shown in Fig. 1. According to Lenz’s law, when a time-varying magnetic field is introduced perpendicular to the plane of the structure, an oscillating current will be produced in the metal structure that creates an induced magnetic field. Such a diamagnetic response can also occur in a short-strip (or short-rod, short-wire) pair, as shown in Fig. 1(d), since anti-parallel currents are induced in the strips.

Figure 1. Common structures that serve as “magnetic atoms”. (a) The split-ring resonator, (b) single split-ring resonator, (c) U-shape resonator, (d) short-wire, short-rod, or short-strip pairs, (e) fishnet structure.


Even in a 1D deep grating, when the magnetic resonance condition is satisfied, strong absorption and enhanced transmission can occur at specific frequencies. Figure 2 illustrates the effect of MP for a slit array. The induced current flow, shown as red arrows, in the 1D grating can be modeled by an equivalent LC circuit model shown in Fig. 2(b). The contour plot of 1-R, or the sum of the transmittance T and absorptance α, as a function of ω and kx is shown in Fig. 2(c). The radiative properties of considered structure are calculated with RCWA and the predicted resonance frequency from the LC model for MP1 is illustrated as triangles. Excellent agreement between the LC model and the RCWA results further confirms the mechanism of magnetic resonance. The bright bands indicate usually a strong transmission, but can also be associated with a strong absorption, due to the resonance behavior of SPPs or MPs. The inclined line close to the light line, which is then folded due to the Bloch-Floquet condition in the gratings, is associated with the excitation of SPP at the Ag-vacuum interface. The SPP dispersion relation and the effect of folding by gratings have been discussed in the previous section. Several relatively flat dispersion curves correspond to the fundamental, second, and third modes of MPs and are marked as MP1, MP2 and MP3 in the figure. The frequency of higher order MPs is approximately an integer times the fundamental resonance frequency of MP1. The bending and truncation of MP2 is due to the interaction with the SPP. The flatness of MP dispersion curves indicates their unique feature as directional independence. The directional independence of MPs can be understood by the diamagnetic response, as the oscillating magnetic field is always along the y-direction no matter what incident angles is for TM waves. It should be noted that, the cavity-like resonance or coupled SPPs were previously proposed to explain the resonance phenomenon in simple gratings, but only MPs can quantitatively account for the geometric effects on the resonance conditions [1].


Figure 2. Effect of magnetic polaritons (MPs) on the radiative properties of a single grating (slit array): (a) Schematic of a deep grating; (b) the equivalent LC circuit model; (c) Contour plots of the sum of absorptance and transmittance (i.e., 1–R) for a Ag grating with period Λ = 500 nm, h = 400 nm, and b = 50 nm. Triangle marks indicate the frequency of the fundamental mode predicted by the LC circuit model [1].


Another potential application of the MPs is the construction of coherent thermal emission sources. It has been demonstrated that a nanostructure consisting of a periodic metallic strips separated by a thin dielectric layer over an opaque metal film [2,3]. The coupling of the metallic strips and the film induces a magnetic response that is characterized by a negative permeability and positive permittivity. On the other hand, the metallic film intrinsically exhibits a negative permittivity and positive permeability in the near infrared. This artificial structure is equivalent to a pair of single-negative materials. By exciting surface magnetic polaritons, large emissivity peaks can be achieved at the resonance frequencies and are almost independent of the emission angle. The resonance frequency of the magnetic response can be predicted by an analogy to an inductor and capacitor circuit. Furthermore, phonon-assisted MPs have also been predicted and to exhibit similar features as metallic gratings or slit arrays [4].


References

[1] Wang, L. P., and Zhang, Z. M., 2009, “Resonance Transmission or Absorption in Deep Gratings Explained by Magnetic Polaritons,” Applied Physics Letters, 95, p. 111904.

[2] Lee, B. J., Wang, L. P., and Zhang, Z. M., 2008, “Coherent Thermal Emission by Excitation of Magnetic Polaritons between Periodic Strips and a Metallic Film,” Optics Express, 16, pp. 11328-11336

[3] Zhang, Z., Park, K., and Lee, B. J., 2011, “Surface and Magnetic Polaritons on Two-Dimensional Nanoslab-Aligned Multilayer Structure,” Optics Express, 19, p. 16375.

[4] Wang, L. P., and Zhang, Z. M., 2011, “Phonon-Mediated Magnetic Polaritons in the Infrared Region,” Optics Express, 19, pp. A126–A135.