Historically, scientists and engineers have focused their
studies on finding analytical models that allow accurate
modeling of the electromagnetic response of radiant devices. Commercial software based on numerical full-wave
techniques such as the finite element method (FEM) or the
finite-difference time-domain method (FDTD), among others,
allows simulating many different scenarios at the expense
of assuming a high computational cost, especially when the
radiant elements are sub-wavelength or when a complete
multi-modal description of the fields is required.
As an alternative, circuit models based on transmission
lines and lumped elements represent a great solution for
these proposes due to their low computational cost and their
physical insight. In fact, a circuital method is considered fully
analytical when it is unnecessary to extract any information
from external full-wave tools [1], [2]. However, the main
difficulty lies in finding equivalent circuits of the structure
under study [3].
This paper presents a multi-modal, fully analytical circuit
model for simulating (2+1)D spacetime-periodic modulated
structures. A closed formulation is proposed in terms of
Floquet-Bloch harmonic expansions, from which all parameters related to diffraction and scattering can be extracted,
providing information on the propagative or transient nature of
the spacetime harmonics. We already applied this formulation
in our previous works for simulating metastructures based
on spatial modulations [4] and (1+1)D spacetime modulations [5].
As an example, Fig. 1 and Fig. 2 depict a comparison
between the obtained results by the proposed theoretical
analysis and external tools for a 2D spatial case and (1+1)D
spacetime case, respectively.
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