Asymmetric Transmission of Linearly Polarized Light at Optical Metamaterials

We experimentally demonstrate a three-dimensional chiral optical metamaterial that exhibits an asymmetric transmission for forwardly and backwardly propagating linearly polarized light. The observation of this novel effect requires a metamaterial composed of three-dimensional chiral meta-atoms without any rotational symmetry. Our analysis is supported by a systematic investigation of the transmission matrices for arbitrarily complex, generally lossy media that allows deriving a simple criterion for asymmetric transmission in an arbitrary polarization base. Contrary to physical intuition, in general the polarization eigenstates in such three-dimensional and low-symmetry metamaterials do not obey fixed relations and the associated transmission matrices cannot be symmetrized.

Figure 1

(a) Two sketches of the MM unit cell from different perspectives with the definition of the geometrical parameters: $l_1=l_2=290\mathrm{nm}$, $w_1=w_2=130\mathrm{nm}$, $h_1=h_2=40\mathrm{nm}$, $d=80\mathrm{nm}$. (b) Schematic of the experimental setup. Normally incident light was linearly polarized before propagating through the MM and subsequently analyzed by means of a second linear polarizer. (c) Normal view electron micrograph with false colors of the fabricated MM. The meta-atoms were completely embedded in an index-matched dielectric. Focused ion beam slicing reveals the two layers composing the MM. Green and red colors represent the nanowires and the $L$ structures in the top and bottom layer, respectively. The periods in both the $x$ and $y$ directions are 500 nm.

Figure 2

Squared moduli of the four $T$-matrix components of the MM. (a),(b) Measurements and (c),(d) simulations. (a),(c) The $k$ vector of the plane waves illuminating the MM was directed in (a), (c) positive and (b),(d) negative $z$ direction. Note that $t_{xy}$ and $t_{yx}$ interchange when $k$ is reversed.

Figure 3

Values for the asymmetric transmission $\Delta$ for linear (a) and circular (b) states as determined by the numerical data. The color of the lines indicates the particular input state. (c) Eigenstates of the polarization at different wavelengths. The rotation direction is indicated by increasing spot sizes.