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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.

We experimentally observe asymmetric electromagnetic field profiles along two-dimensional chiral metamaterials. The asymmetric field profiles depending on the chirality and the operation frequency have been reproduced well by the numerical simulation. Around a chiral meta-atom, distribution of a Poynting vector is found to be shifted asymmetrically. These results are explained in terms of an analogy with the side-jump mechanism in the electronic anomalous Hall systems.

This study observes microwave beam splitting dependent on circular polarizations through nonuniform chiral metamaterials. Nonuniform chiral metamaterials with a gradation in refractive index are constructed using chiral meta-atoms that exhibit optical activities at microwave frequencies. Microwave scattering far-field patterns by the nonuniform chiral metamaterials demonstrate a deflection of microwaves, which transmit in a direction perpendicular to the refractive index gradient. Furthermore, circularly polarized microwaves with opposite ``spins of light'' go their separate ways in the nonuniform chiral metamaterials. This phenomenon is an optical analog of the Stern-Gerlach effects for electrons.