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Design of a Dichroic Transmissive Huygens' Metasurface Unit-Cell Presenting Refraction Angle Duality

Georgios Kyriakou, Giampaolo Pisano, Luca Olmi, Francesco Piacentini

Abstract

A purely transmissive Huygens' metasurface model under plane-wave illumination is used to derive circuit parameters describing a constituent unit cell, such that diverse refraction angles are attained at two distinct frequency bands. Various levels of accuracy of the circuit description approaching the analytical are possible by constraining certain numbers of parameters. This theoretical study is then tested by calculating the exact formulas of the two representations for the various strategies proposed. By using simulations of a candidate unit-cell, we then examine whether such circuit parameters correspond to rudimentary versions of the geometry of a so-called parallel 'dogbone' structure. A device of this type is intended as dual-band (dichroic), dual-angle beam refractor diverting an incoming beam at different directions in two different bands without reflections.

Design of a Dichroic Transmissive Huygens' Metasurface Unit-Cell Presenting Refraction Angle Duality

Abstract

A purely transmissive Huygens' metasurface model under plane-wave illumination is used to derive circuit parameters describing a constituent unit cell, such that diverse refraction angles are attained at two distinct frequency bands. Various levels of accuracy of the circuit description approaching the analytical are possible by constraining certain numbers of parameters. This theoretical study is then tested by calculating the exact formulas of the two representations for the various strategies proposed. By using simulations of a candidate unit-cell, we then examine whether such circuit parameters correspond to rudimentary versions of the geometry of a so-called parallel 'dogbone' structure. A device of this type is intended as dual-band (dichroic), dual-angle beam refractor diverting an incoming beam at different directions in two different bands without reflections.
Paper Structure (5 sections, 11 equations, 5 figures)

This paper contains 5 sections, 11 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Unit cell Impedance matrix structure and Second-order LC circuit approximation
  3. Preliminary Simulations and Circuit Parameter Fitting of Unit-Cell Geometry
  4. Conclusions
  5. Acknowledgment

Figures (5)

  • Figure 1: Schematic of the operating principle of a dual-band metasurface achieving transmission angle duality in two different frequency bands.
  • Figure 2: Relative error of the approximations $S_{11}\approx S_{11}^{\rm uc}$ (left panels) and $S_{12}\approx S_{12}^{\rm uc}$ (right panels). Various strategies are used, by means of the electric resonance position $\omega_e=n\omega_m,\ n\in\{1,2\}$ and the factor $\alpha$ used in Eqs. (\ref{['eq:Lm']}), (\ref{['eq:Le']}), (\ref{['eq:omegam_condition']}).
  • Figure 3: Relative error of the approximations $S_{11}\approx S_{11}^{\rm uc}$ (left panels) and $S_{12}\approx S_{12}^{\rm uc}$ (right panels) for $\omega_e=n\omega_m,\ n\in\{1,2\}$. The constraint of Eq. (\ref{['eq:omegam_condition']}) is not used here; it is instead chosen that $\theta_{t,l}=\theta_{t,h}-10^\circ$.
  • Figure 4: Parallel 'dogbone' unit cell geometry depicted in Ansys HFSS. The various strip lengths are denoted, in accordance with capolino2013. The darker region is filled with a dielectric material of $\epsilon_r=3.48$.
  • Figure 5: Left: $C_e$ across B1 (left axis, blue) and $L_m$ across B1 (right axis, orange) for 3 close values of A2, Right: $f_e, \ f_m$ across B1 for the same A1 values. Omitted values presented high fitting error.