Enhanced magnetochiral effects at microwave frequencies by a single metamolecule

We have experimentally and numerically studied the directional birefringence of $X$-band microwaves by magnetochiral (MCh) effects of a single metamolecule under dc magnetic fields at room temperature. Phase and amplitude transmission coefficients from top and bottom, i.e., $S$ parameters of $S_{21}$ and $S_{12}$, are measured for the single metamolecule consisting of a copper chiral structure and ferrite cylinder in a waveguide. By applying a dc magnetic field, we observe a difference between $S_{21}$ and $S_{12}$, which is an emergence of the MCh effects with simultaneous space-inversion and time-reversal symmetry breaking. Numerical calculation based on a finite element method reproduces well the experimental results of the MCh effects. The MCh effect can be enhanced by using the magnetic resonance of the ferrite cylinder. Notably, numerical calculation predicts that the MCh effect is extremely enhanced by interacting magnetic resonance with a specific resonant structural optical activity, leading to a giant MCh effect. The giant MCh effect observed in the present study originates from the one-way transparency caused by the Fano resonance in the metamolecule.

Figure 1

(a) Photograph of MCh metamolecule (center). The diameter of the coin in the photo is 17.91 mm. Illustrations of Cu chiral meta-atom (left) and ferrite magnetic meta-atom (right). (b) Setup for numerical calculation. A metamolecule is put in the center of the WR-90 waveguide. Both sides of the waveguide are terminated with perfectly matched layers (PMLs).

Figure 2

Transmission $S_{21}$ (red curves) and $S_{12}$ (blue curves) amplitude spectra [(a)–(d)] and phase spectra [(e)–(h)] of a single MCh metamolecule under external dc magnetic fields of 0 mT [(a) and (e)], $+201$ mT [(b) and (f)], $+260$ mT [(c) and (g)], and $+400$ mT [(d) and (h)]. Chiral resonances are labeled $A,B,C$, and $D$, while magnetic resonance is labeled $E$. Insets illustrate enlarged spectra for $S_{21}$ (red) and $S_{12}$ (blue) of chiral resonance originally appearing at 9.1 GHz.

Figure 3

Differences in amplitudes between $S_{21}$ and $S_{12}$ from 8 to 14 GHz of an MCh metamolecule under dc magnetic fields from 0 to $\pm 400$ mT.

Figure 4

Differences in phases between $S_{21}$ and $S_{12}$ from 8 to 14 GHz of an MCh metamolecule under dc magnetic fields from 0 to $\pm 400$ mT.

Figure 5

Differences in calculated (a) amplitudes and (b) phases spectra between $S_{21}$ and $S_{12}$ between 8 and 15 GHz for an MCh metamolecule under dc magnetic fields from $+100$ to $+600$ mT. Magnetic resonance is labeled $F$, while chiral resonances are labeled $G,H$, and $I$.

Figure 6

Calculated differential spectra between $S_{12}$ and $S_{21}$ of amplitude (a) and phase (b) in the vicinity of ${\mu }_0{H}_{\mathrm{ext}}=+500$ mT. ${\mu }_0{H}_{\mathrm{ext}}$ is varied from 495 to 510 mT with steps of 5 mT.

Figure 7

Pseudocolor plot for differences in calculated phase between $S_{21}$ and $S_{12}$ in the range from 8 to 15 GHz. External dc magnetic fields vary from $+100$ to $+600$ mT.

Figure 8

Differences in calculated amplitude spectra between $S_{21}$ and $S_{12}$ between 9 and 12 GHz of (a) right- and (b) left-handed MCh metamolecules. External dc magnetic field varies from $+100$ to $+600$ mT with steps of 50 mT.

Figure 9

Poynting vector flow in the vicinity of magnetic resonance of ferrite magnetic meta-atom at (a) 14 GHz under $+400$ mT and (b) 13.15 GHz under $+500$ mT. The length of the cone is proportional to the Poynting vector amplitude. The insets illustrate the enlarged spectra of Fig. 5.

Figure 10

Electric field distributions of three chiral resonances under $+100$ mT. Resonance frequencies are 10.6 (a), 13.7 (b), and 14.5 GHz [(c) and (d)], respectively. Cones and pseudocolor plots indicate electric field vectors and intensities, respectively. Vector fields in the $y\text{−}z$ plane are illustrated in (a)–(c), whereas those in the $z\text{−}x$ plane are illustrated in (d). Insets illustrate electric charge distributions. Purple arrows in (d) are applied electric fields on the metamolecule, while green arrows are electric fields induced by charge distribution by electric charge on the chiral meta-atom.

Figure 11

Electromagnetic field distributions at 14.446 GHz under ${\mu }_0{H}_{\mathrm{ext}}=+505$ mT. (a), (c) Electric field vectors in the $z\text{−}x$ plane are indicated by red cones. Pseudocolor indicates electric field intensity. (b), (d) Pseudocolor of magnetic field intensity. Incident microwaves in (a) and (b) are from port 1, whereas that in (c) and (d) is from port 2.

Figure 12

Calculated amplitude spectra for $S_{21}$ (red) and $S_{12}$ (blue) of the MCh metamolecule between 13 and 15 GHz under ${\mu }_0{H}_{\mathrm{ext}}=+505$ mT. The amplitude spectrum of $S_{21}$ calculated only with magnetic meta-atom is plotted also by a green dashed curve as reference. Third chiral resonance frequency is indicated by a vertical black dashed line.