Terahertz Vortex Beam as a Spectroscopic Probe of Magnetic Excitations

Circularly polarized light with spin angular momentum is one of the most valuable probes of magnetism. We demonstrate that light beams with orbital angular momentum (OAM), or vortex beams, can also couple to magnetism exhibiting dichroisms in a magnetized medium. Resonant optical absorption in a ferrimagnetic crystal depends strongly on both the handedness of the vortex and the direction of the beam propagation with respect to the sample magnetization. This effect exceeds the conventional dichroism for circularly polarized light. Our results demonstrate the high potential of the vortex beams with OAM as a new spectroscopic probe of magnetism in matter.

Figure 1

Linearly polarized terahertz radiation is converted into vortex beam modes ${\overrightarrow{e}}_{\pm 1}$ using a combination of a Fresnel prism (FP) and an axicon. After passing through a two-bounce FP retarder, the linearly polarized light ${\overrightarrow{e}}_x\pm {\overrightarrow{e}}_y$ becomes circularly polarized ${\overrightarrow{e}}_{L,R}$. After passing through the axicon, the beam acquires a vortex phase ${\overrightarrow{e}}_{\pm 1}$ while losing its circular polarization.

Figure 2

Calculated radially independent electric fields and equal phase trajectories in the vortex beams. (a),(b) Projections of electric field for the ${\overrightarrow{e}}_{+1}$ and ${\overrightarrow{e}}_{-1}$ modes are shown in the $x\text{−}y$ plane. The white areas represent the intensity distribution of the vortex beam. The beam propagation direction $\overrightarrow{k}$ is along the positive $z$ axis. Decoupling of the vortex modes into the azimuthal and radial ones is also shown. (c) Spatial variation of the equal phase trajectories. ${\overrightarrow{e}}_{+1}$ and ${\overrightarrow{e}}_{-1}$ form the right-hand and left-hand spirals. The corresponding electric field vectors in the $x\text{−}y$ plane at $z=0$ and $\varphi =0$ are shown with red and blue arrows.

Figure 3

Energies of the LF, KK, and CF modes vs temperature. Experimental data for energies of the LF, KK, and CF modes are shown with solid symbols. Data from Ref. [39] obtained with conventional linearly polarized light are shown with dashed curves for comparison. The solid black curve is a guide for the eye.

Figure 4

Magnetic dichroism in transmittance spectra for circularly polarized light and vortex beams. (a) Normalized transmittance spectra for circularly polarized light ${\overrightarrow{e}}_R$ and ${\overrightarrow{e}}_L$, and for conventional linearly polarized light ${\overrightarrow{e}}_y$. The magnetization vector $\overrightarrow{M}$ is antiparallel to $\overrightarrow{k}$. (b)–(d) Normalized transmittance spectra for three temperatures and two orthogonal vortex beams ${\overrightarrow{e}}_{+1}$ (blue spectra) and ${\overrightarrow{e}}_{-1}$ (red spectra) measured for $\{\overrightarrow{k},{\overrightarrow{e}}_{\pm 1},\overrightarrow{M}\}$ with the magnetization vector $\overrightarrow{M}$ parallel to $\overrightarrow{k}$. (e)–(g) The same for the opposite directions of the light propagation with respect to the sample: $\{\overrightarrow{k},{\overrightarrow{e}}_{\pm 1},{\widehat{R}}_{y,180°}(\overrightarrow{M})\}$, with the magnetization vector $\overrightarrow{M}$ antiparallel to $\overrightarrow{k}$. All experimental data in (a)–(g) are normalized to that measured at $T=75\mathrm{K}$.

Figure 5

Schematics of the observed dichroic effects. Propagation of the wave front in the vortex beam is illustrated with color rendering. The closest distance between the same colors along the $z$ direction corresponds to the wavelength of light $\lambda$. (a) Vortex beam dichroism: $\{\overrightarrow{k},{\overrightarrow{e}}_{-1},\overrightarrow{M}\}\ne \{\overrightarrow{k},{\overrightarrow{e}}_{+1},\overrightarrow{M}\}$. (b) The same for the observed inversion of the selection rules for rotation of the magnetized sample that also resulted in the sign change for ${\rho }_{\pm 1}$. (c) Transformation between $\{\overrightarrow{k},{\overrightarrow{e}}_{-1},\overrightarrow{M}\}$ and $\{\overrightarrow{k},{\overrightarrow{e}}_{+1},-\overrightarrow{M}\}$ can be obtained by applying a mirror reflection that is perpendicular to $z$ and rotation around the $y$ axis, both for the whole experimental setup. The sample is shown with blue rectangles with green arrows for the sample magnetization direction $\overrightarrow{M}$. One of the sample faces is marked with a vertical brown line.