HFSS - Waveguide fed infinite array simulation - Floquet port

Dear all,
I am new in using HFSS, and I need to simulate an infinite array of circular waveguide disposed on an hexagonal lattice, working at 15.25 [GHz]. The radiating elements are covered by a layer of an anisotropic material. Such a test case is reported in the paper: S. Sajuygbe et al. "Wide angle impedance matching metamaterials for waveguide-fed phased-array antennas," IET Microw. Antennas Propag., 2010, Vol. 4, Iss. 8, pp. 1063–1072. (at pag. 1066 Fig. 2 there is the geometry whereas in Fig. 3 the obtained results). I attached the paper in following. View attachment Sajuyigbe.2010.pdf

At the beginning I implemented the model of the tutorial "Getting started with HFSS - Floquet Port" that considers an infinitely extended array of square waveguide lying on a square lattice. The model I made works properly. I tried to implement the model described in the aforementioned paper but without any success. So I am asking if someone is able to answer the following questions:

a) How to set the boundary conditions (BCs) ( master / slave ) ? I used three different master / slave BCs one couple for each pair of the sides of the hexagon.

b) How to set the Floquet Port? I defined the two vectors of equations:

v_1 = ½ * d * x
v_2 = ½ * d * ( ½*x + √3/2*y )

with d = 0.42 inches

the vectors are exactly half of the lattice vectors of the array. Is it correct?

c) Is it necessary to include in the model the layer of PEC surrounding the waveguide?

If you need more details about that problem, please do not hesitate to contact me.

Thank you in advance.

Dear all,
I find in literature an example very close to what I need to simulate, and I attach it. Following the instructions of the tutorials I used the following parameters to model the infinite array of circular waveguide:

1. PML layer instead of the Floquet Port with a load impedance on the top of the PML port defined as: 377*cos(theta) Ohm - (theta is the angle between the z-axis and the xy-plane as usual in standard spherical coordinates)

2. Master/Slave boundary conditions defined as pair on the lateral surface of an hexagon including the WAIM layer - and the PML

The tutorial works properly but I was not able to obtain the published results. However, after reading very carefully the paper I found the following sentence: "...In HFSS, the Yin (phi, theta) (or Gin (phi, theta) or S11 (phi, theta)) is obtained by referencing it to the aperture– air discontinuity and not the port assignment at the base of the waveguide." Do you have any idea how I can measure the S_11 referencing it to the aperture - air discontinuity instead of the classical S_11 computed at the base of the waveguide?

Thank you in advance for any suggestions.