Inverse design of broadband epsilon-near-zero metasurface with nanoscale airtube superlattice based on the Bergman-Milton spectral representation

A metal-dielectric composite metasurface of the broadband epsilon-near-zero property is designed with the nanoscale airtube superlattice microstructure embedded in the metallic host. The design strategy rigorously starts from the theoretical analysis on the spectral representation of effective permittivity in quasistatic conditions for the Hashin-Shtrikman coated-cylinder microstructure, then improves in full-wave conditions for the nanoscale airtube superlattice microstructure. Through the computational simulations, the correctness and robustness of the strategy are verified and the broadband epsilon-near-zero property of the designed metasurface is demonstrated. Furthermore, the physical mechanism behind the broadband epsilon-near-zero property, including the potential application in broadband deep subwavelength electromagnetic wave tunneling, is also straightforwardly revealed.

Figure 1

Cross section of the four-meta-atom unit cell with (a) the Hashin-Shtrikman coated cylinder microstructure and (b) the nanoscale airtube superlattice microstructure in the broadband ENZ metasurface.

Figure 2

(a) Effective permittivity of the broadband ENZ unit cell with the Hashin-Shtrikman coated cylinder microstructure based on theoretical calculations (solid curves), the transmission and reflection coefficients retrieve algorithm (dashed curves), and the mode analysis (circles), respectively. (b) Profiles of the eigenmode at the frequency, where the effective permittivity is close to zero, displayed by the $z$ component of the magnetic field.

Figure 3

(a) Cross section of the period unit of the nanoscale airtube lattice. (b)–(h) Effective permittivity of the nanoscale airtube lattice based on theoretical calculations (solid curves) and the transmission and reflection coefficients retrieve algorithm (dashed curves), with the filling ratios of the air component from $f_{\mathrm{air}}=0.1$ to 0.7, respectively.

Figure 4

For the broadband ENZ unit cell with the nanoscale airtube superlattice microstructure of the cross sections $a_x\times a_y=10\mathrm{nm}\times 1\mathrm{nm}$ and $20\mathrm{nm}\times 2\mathrm{nm}$, (a), (c) the effective permittivity of the unit cell based on theoretical calculations (solid curves), the transmission and reflection coefficients retrieve algorithm (dashed curves), and the mode analysis (circles); (b), (d) the profiles of the eigenmode at the frequency, where the effective permittivity is close to zero, displayed by the $z$ component of the magnetic field.