Non-Reciprocal Transmission/Diffraction through Plasmonic Grating above a Time-Varying Medium

Yakir Hadad Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas, USA Andrea Alu Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas, USA

Reciprocity is a desired property in many wave applications. Nevertheless, sometimes we would like to be able to violate reciprocity, and at the extreme to have elements such as isolators or circulators. This ability is rather mature at radio-frequencies where one usually utilizes the gyrotropic property of rare-earth materials in order to break the time-reversal symmetry between two counter-propagating waves in a structure. Unfortunately, a straightforward extension of the techniques used in radio-frequencies into the optical regime is challenging if not impossible due to the change in material properties at these frequencies. Therefore, a different methodology should be followed. According to Lorentz reciprocity theorem, a linear and time-invariant structure will be reciprocal if it is made of symmetric materials (ε=εT, μ=μT). Thus, in order to violate reciprocity, except for using gyrotropic materials, one may use either non-linear or time dependent materials.

In this work, we follow the latter approach and explore the problem of diffraction by grating above spatiotemporally modulated medium as a mechanism to obtain non-reciprocal transmission/diffraction. We will compare this problem to the case of diffraction through moving grating, as well as to the problem of spatiotemporally modulated surface impedance in a non-modulated environment [1]. First, we will analyze the detailed Green’s function in such media, unravels the medium’s inherent non-reciprocity of each wave spectrum component, either discrete (modes) or continuous (e.g. lateral waves). Then, we will apply the derived Green’s function to analytically describe the non-reciprocal coupling between plasmonic grating elements to ultimately establish the non-reciprocal response of the entire structure, observable in abnormal properties of reflection, transmission or diffraction. The localized and enhanced response of plasmonic elements boosts these effects and allows a realistic implementation at optical frequencies. The proposed concepts may have applications for optical non-reciprocal antennas with different radiation patterns in transmission and reception, as well as to realize surface-isolators for free-space waves and laser beams.

[1] Y. Hadad, D. L. Sounas, and A. Alu, “Space and time grating metasurfaces”, in preparation.

alu@mail.utexas.edu









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