Efficient treatment of stacked metasurfaces for optimizing and enhancing the range of accessible optical functionalities

Abstract

We present, discuss and validate an adapted S-matrix formalism for an efficient, simplified treatment of stacked homogeneous periodically structured metasurfaces operated under normally incident plane wave excitation. The proposed formalism can be applied to any material system, arbitrarily shaped metaatoms, at any frequency and with arbitrary subwavelength periods. Circumventing the introduction of any kind of effective parameters we directly use the S-parameters of the individual metasurfaces to calculate the response of an arbitrary stack. In fact, the S-parameters are the complex parameters of choice fully characterizing the homogeneous metasurfaces, in particular with respect to its polarization manipulating properties. Just as effective material parameters like the permittivity and the permeability or wave parameters like the propagation constant and the impedance, the stacking based upon S-matrices can be applied as long as the individual layers are decoupled with respect to their near-fields. This requirement eventually sets the limits for using the optical properties of the individual layers to calculate the response of the stacked system -this being the conceptual aim for any homogeneous metasurface or metamaterial layer and therefore the essence of what is eventually possible with homogeneous metasurfaces. As simple and appealing this approach is, as powerful it is as well: Combining structured metasurface with each other as well as with isotropic, anisotropic or chiral homogeneous layers is possible by simple semi-analytical S-matrix multiplication. Hence, complex stacks and resonators can be set up, accurately treated and optimized with respect to their dispersive polarization sensitive optical functionality without the need for further rigorous full-wave simulations.

Polarization Conversion Effect in Biological and Synthetic Photonic Diamond Structures

“…Our intuitive understanding is supported by general mathematical considerations on how symmetry affects the transmission and reflection of D‐structures: For C 3 symmetry in conjunction with a mirror plane, as for light propagation in 〈111〉 directions, the response is always polarization independent (diagonalizable Jones matrix in reflection with identical eigenvalues). For propagation along 〈100〉 directions there is only single mirror symmetry, hence one obtains two distinct linear eigenpolarizations (of a diagonalizable Jones matrix in reflection with two distinct eigenvalues)—and only for excitation with those polarizations we obtain copolarization.…”

A simple transfer-matrix model for metasurface multilayer systems

“…To this end we rearrange the scattering S-matrices of metasurfaces, i.e., the inputoutput relations that can be extracted from any other suited and dedicated simulation tool, into transfer matrix method form. This approach is similar to the work of Menzel et al and Sperrhake et al, who developed S-matrix based models to analyze the polarimetric behavior of metasurface stacks [51,52].…”

“…In essence this construction can be viewed as casting the S-matrix of a metasurface (relating outgoing to incident fields) into a transfer matrix (relating fields on either side of the interface to each other. This approach is hence strongly related to the metasurface S-matrix formalism of Menzel and Sperrhake et al [51,52].…”

“…Since one must then account for two polarizations, this requires a 4×4 transfer matrix approach to allow for the polarization cross coupling effects. This would bring the proposed method on par with the S-matrix multilayer approach for metasurface stacks developed by Menzel and Sperrhake et al, who focused specifically on polarimetric applications [51,52]. A more fundamental limitation of our approach is that it cannot deal with propagating and evanescent diffraction orders.…”

Empowered Layer Effects and Prominent Properties in Few‐Layer Metasurfaces

“…r ij and t ij are the polarization‐dependent reflection and transmission coefficients at individual interfaces, which can be derived from numerical simulations of the isolated functional layers. If there are more than two stacked functional layers in a few‐layer metasurface, we can still obtain the overall response of the metasurfaces by simple semi‐analytical S‐matrix multiplication . One typical phenomenon related to multiple wave interference is the Fabry–Pérot (FP) resonance.…”