3.3. NUMERICAL RESULTS 35
Figure 3.7: FDTD grid for non-coincident case, E
z
corner components.
At x = P
x
and y = P
y
E
n+1
z
n
x
+ 1,n
y
+ 1,k
= E
n+1
z
(1,n
y
+ 1,k)× e
jk
x
P
x
. (3.21)
The above procedure provides the six FDTD updating equations for the case of the non-
coincident skewed shift. These updating equations can be used to update the electr ic and magnetic
fields in any region in the computational domain (boundary and non-boundary).
3.3 NUMERICAL RESULTS
In this section, numerical results generated using the new algorithm are presented. The FDTD code
was developed using MATLAB [19]. All the test cases were executed using the same computer
(Intel Core 2 CPU 6700 2.66 GHz with 2 GB RAM). These results demonstrate the validity of
the new algorithm for determining reflection and transmission properties of periodic structures with
arbitrary skewed grids. The first example is an infinite dielectric slab excited by TM
z
and TE
z
plane
waves. The second example is a dipole FSS, where the structure is analyzed with special skewed
angles that can be simulated using the normal FDTD/PBC, and the third example is a JC FSS.The
results obtained from the skewed FDTD code are compared with results obtained from an analytic
solution, the axial FDTD method, and Ansoft Designer.

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