Mimicking Localized Surface Plasmons via Mie Resonances to Enhance Magnetic-Resonance-Imaging Applications

Metaphotonics, combining metamaterial (MM) and nanophotonic concepts, offers a unique platform for obtaining an unusual and/or advantageous electromagnetic response on a scale much less than the wavelength, although several practical applications are strongly hampered by the complexity of fabrication of MM devices and the intrinsic subwavelength inhomogeneous response of the MM composite. Recently, much research effort has been focused on the study of photonic devices for magnetic resonance imaging (MRI), one of the cornerstone diagnostics techniques in life science. In the MRI context, we introduce the use of magnetic surface excitations (magnetic localized surface plasmons) supported by a negative-magnetic-permeability MM sphere that results in a significant local enhancement of the MRI signal-to-noise ratio. Using the Mie resonance theory, we show that an increase in the signal-to-noise ratio boost can be obtained by replacing the MM sphere with a homogeneous high-permittivity one of the same radius. Overcoming some of the main MM limiting factors, our results suggest a simple approach for the realization of radio-frequency magnetic metadevices.

Figure 1

The MRI setup considered. A standard surface rf coil (with radius ${\rho }_0$ and radial width $w$), on the $z=0$ plane, is placed between the magnetic MM sphere (with radius ${\rho }_m$ and permeability ${\mu }_m$) and the cylindrical sample (with radius ${\rho }_s$, thickness $l_s$, and relative permittivity ${ϵ}_s$). ${\overrightarrow{B}}_0$ is a static homogeneous magnetic field applied along the $x$ axis and $d_m$ ($d_s$) is the minimum distance between the MM (the sample) and the rf-coil plane.

Figure 2

$|B_1^{(-)}|/{\mu }_0$ (blue line) and ${\mathrm{SNR}}^{(n)}$ (red line), evaluated inside the sample (at $\rho =0$ mm and $z=6$ mm), as a function of the real part of the permeability ${\mu }_m$, with our setting $\mathrm{Im}{\mu }_m=0.01$. Starlike markers highlight the first five local maximum values of ${\mathrm{SNR}}^{(n)}$. As a reference, the dashed dark lines show the permeability values allowing the existence of MLSPs for an isolated magnetic MM in a vacuum in the static limit, given by Eq. (5), with $L$ ranging from 3 to 7.

Figure 3

(a) $|B_1^{(-)}|/{\mu }_0$ and (b) ${\mathrm{SNR}}^{(n)}$ along the $z$ axis ($\rho =0$) for $\mathrm{Im}{\mu }_m=0.01$ and the five values of $\mathrm{Re}{\mu }_m$, corresponding to the MLSP resonances with $L=3$, 4, 5, 6, and 7. The dashed black line represents the case without the presence of the MM sphere.

Figure 4

(a) SNR map in the $(\rho ,z)$ plane for the configuration in Fig. 1 without the magnetic MM sphere. (b)–(f) ${\mathrm{SNR}}^{(n)}$ maps in the presence of the MM sphere for different values of $\mathrm{Re}{\mu }_m$ as in Fig. 3, with $\mathrm{Im}{\mu }_m=0.01$ and $\varphi =\pi /2$. The dashed black lines are contour lines for ${\mathrm{SNR}}^{(n)}=1$.

Figure 5

Same geometrical configuration as for Figs. 1–4. (a) $|B_1^{(-)}|/{\mu }_0$ and (b) ${\mathrm{SNR}}^{(n)}$ profiles as functions of $\rho$ inside the cylindrical sample ($z\ge 0.2$ cm, $\varphi =\pi /2$) for different $z$ values in the presence of the magnetic MM sphere with ${\mu }_m=-1.20+i0.01$ (solid black lines) or the dielectric sphere with ${ϵ}_d=1324+i1.65$ (dashed red lines), corresponding to the $L=5$ resonance. ${\mathrm{SNR}}^{(n)}$ maps for (c) the magnetic MM sphere and (d) the dielectric sphere in the $(\rho ,z)$ plane ($\varphi =\pi /2$). The dashed black lines are contour lines for ${\mathrm{SNR}}^{(n)}=1$, whereas the dashed white lines are contour lines for ${\mathrm{SNR}}^{(n)}=3$ and ${\mathrm{SNR}}^{(n)}=1.5$.

Figure 6

Same geometrical configuration as in Fig. 5 for UHDC spheres with $\mathrm{Re}{ϵ}_d=1200$ and radii ${\rho }_m=3.38$, 6.21, and 8.82 cm supporting the $L=1$, 3, and 5 resonances, respectively, at the Larmor frequency of $127.74$ MHz. (a) $|B_1^{(-)}|/{\mu }_0$ and (b) ${\mathrm{SNR}}^{(n)}$ at the point $z=2$ mm, $\rho =0$ mm as a function of the loss tangent $\tan \delta$. The solid black lines are the reference values evaluated without the UHDC sphere, the yellow area in (b) corresponds to ${\mathrm{SNR}}^{(n)}>1$, and the vertical dash-dotted black lines highlight the case $\tan \delta =0.04$ [53].

Figure 7

Same coil and sample geometrical configuration as in Fig. 6 for UHDC spheres with $\mathrm{Re}{ϵ}_d=3300$ and dielectric sphere radii ${\rho }_m=4.0$, 7.5, and 10.6 cm supporting the $L=1$, 3, and 5 resonances, respectively, at the Larmor frequency of $63.87$ MHz. (a) $|B_1^{(-)}|/{\mu }_0$ and (b) ${\mathrm{SNR}}^{(n)}$ at the point $z=2$ mm and $\rho =0$ mm as a function of the loss tangent $\tan \delta$. The solid black lines are the reference values evaluated without the UHDC sphere, the yellow area in (b) corresponds to ${\mathrm{SNR}}^{(n)}>1$, and the vertical dash-dotted black lines highlight the case $\tan \delta =0.05$ [53].

Figure 8

The SAR and the electric field distribution for unit current on the $(\rho ,z)$ plane at $3$ T with the same parameters as for Fig. 6 (a),(c) without and (b),(d) with the UHDC sphere for $\tan \delta =0.04$ and ${\rho }_m=8.82$ cm. The solid white line represents the sphere surface.

Figure 9

$|B_{1,\mathrm{eff}}^{(+)}|$ on the $(\rho ,z)$ plane ($\varphi =\pi /2$) at $3$ T with the same parameters as for Fig. 6 (a) without and (b) with the UHDC sphere for $\tan \delta =0.04$ and ${\rho }_m=8.82$ cm.