Realization of the Tellegen Effect in Resonant Optical Metasurfaces

Abstract

The nonreciprocal magnetoelectric effect in Tellegen materials enables exotic phenomena such as axion-modified electrodynamics and fosters the development of magnet-free nonreciprocal media. As the nonreciprocal counterpart to the well-known chiral electromagnetic response, it offers a parallel framework in which many concepts developed for chiral materials can be translated to Tellegen media, potentially unlocking new avenues for fundamental studies and applications. Although predicted over 75 years ago and observed in only a handful of natural materials with very low strength, the strong optical Tellegen effect has remained experimentally elusive. Here, we report the first experimental demonstration of a resonant optical diagonal Tellegen effect in a metasurface, showcasing a response that is 100 times greater than that of any known natural material. This optical metasurface, consisting of randomly distributed cobalt-silicon nanoscatterers with strong shape anisotropy, utilizes spontaneous magnetization to achieve a robust Tellegen effect without the need for an external magnetic field. In addition to the Tellegen response, the metasurface exhibits both gyroelectric and gyromagnetic effects, contributing to nonreciprocal cross-polarized light reflection. We introduce a technique to independently extract the amplitudes of these three effects using conventional magneto-optical single-side-illumination measurements. The observation of the resonant Tellegen effects in the optical frequency range may lead to the experimental observation of axionic electrodynamics and compact bias-free nonreciprocal optical devices.

Figures (4)

• Figure 1: Optical Tellegen metasurface design. (a) Illustration of the metasurface with optimized optical Tellegen meta-atoms consisting of cobalt (top) and silicon (bottom) parts. The metasurface is illuminated from opposite directions by normally incident light (a slight oblique incidence is depicted for visual clarity). The gradient color indicates that the reflected and transmitted light contain both co- and cross-polarized components. The inset depicts a close-up image of the meta-atom with close to single-domain vertical magnetization ${\bf M\mit}_{\rm s}$ in the cobalt. It also shows the high-frequency magnetic field distribution inside the nanocone when illuminated by a standing wave with an electric field antinode positioned at the center of the meta-atom. The field distribution is calculated at a free-space wavelength of 830 nm and reveals an $x$-oriented magnetic dipole moment ${\bf m\mit}$ induced solely by the incident $x$-polarized electric field through the isotropic (diagonal) Tellegen effect. (b)--(e) Simulated complex polarizabilities of the metasurface in (a), normalized by the free-space impedance $\eta_0$.
• Figure 2: Extraction of the independent gyrotropic, gyromagnetic, and Tellegen effects in a general nonreciprocal metasurface using magneto-optical measurements. (a)--(c) Three equivalent metasurfaces with identical meta-atoms and the same average surface densities on top of alumina spacers of three different thicknesses $h_1=0$ nm, $h_2=60$ nm, and $h_3=120$ nm. The metasurface are illuminated from the top by a normally incident light, and the Kerr rotation $\theta$ and ellipticity $\epsilon$ are extracted (an oblique incidence is depicted only for visual clarity). (d) The complex amplitudes of the coefficients introduced in Eq. \ref{['eq:Rcr']} plotted as functions of the free-space wavelength $\lambda$ and the alumina spacer thickness $h$. These coefficients quantify the contributions of the gyroelectric, gyromagnetic, and Tellegen effects to cross-polarized light reflection.
• Figure 3: Fabricated Tellegen metasurface and its characterization. (a)--(b) SEM images of one of the fabricated Tellegen metasurfaces with dielectric spacer thickness of $h=60$ nm (top and tilted views). The inset in (b) presents a zoomed-in image of a single meta-atom, artificially colored to visualize the cobalt and silicon parts with the averaged geometrical parameters of the nanocone used in full-wave simulations: $h_{\rm Si}=20$ nm, $h_{\rm Co}=104$ nm, $D_{\rm Si}=90$ nm, and $D_{\rm Co}=84$ nm. The averaged half-apex angle of the nanocone is $85^\circ$, which reflects the degree of tip rounding due to the hole-mask colloidal lithography process. (c) Schematic illustration of the polar magneto-optic Kerr effect (MOKE) experimental setup. Detailed information about the setup is available in the Methods section. (d)--(f) Experimental and simulated magneto-optical Kerr spectra for the three fabricated metasurfaces under an external magnetic field fixed at $B = 1.3$ T. Here, the positive-value magnetic field denotes the direction from the base of the meta-atom to its apex. The simulated spectra correspond to periodic metasurfaces with geometric parameters averaged from the fabricated samples. (g)--(i) The gyroelectric, gyromagnetic, and Tellegen polarizabilities extracted from the data in (d)--(f).
• Figure 4: Simulated results for purely Tellegen material systems. (a) A thin (50 nm) silicon nitride membrane with two identical Tellegen metasurfaces shown in Fig. \ref{['fig1']}(a) being deposited on its both sides. The membrane is illuminated from opposite directions by normally incident light (an oblique incidence is depicted for visual clarity). (b) Simulated complex collective polarizabilities of the membrane in (a), normalized by the free-space impedance $\eta_0$. (c) Kerr rotation angle and Kerr ellipticity for the membrane in (a) calculated for forward and backward light illuminations. (d) Isotropic Tellegen colloid consisting of randomly oriented nanocones inside water. The colloid exhibits the same magneto-optical Kerr effect regardless of the illumination direction. (e) Effective bulk Tellegen parameter of the colloid. (f) Kerr rotation angle and Kerr ellipticity for the colloid in (d).