Model coordinates were then transformed to the local coordinate system applying identical transformation
to the common reference points on the models and in the geodesic data.
Note that we keep an identical transformation in the regions x' < [x.sub.0] and x > [x.sub.0]+d, and therefore they are still free space after the transformation.
The slab region [x.sub.0] < x <[x.sub.0] + d (filled with the null-space medium) is compressed in the y direction and the other regions (free space regions) are still undergoing an identical transformation. In the compressed region [x.sub.0] < x < [x.sub.0] + d, the coordinate grid x = [x.sub.c] (parallel straight lines) is still transformed to x = [x.sub.c] and the coordinate grid y = [y.sub.c] is transformed to y' = f (x', [y.sub.c]) (compressed lines) whose slope dy'/dx' = df /dx determines the local direction of the transformed grid.
for pairwise different complex numbers [[lambda].sub.1], [[lambda].sub.2], ..., [[lambda].sub.m], where [epsilon] is the identical transformation
and [theta] is the null transformation.
Note that people choose the identical transformation at the outer boundary of this kind of device, which is why such devices can only produce a local influence on electromagnetic waves.
We apply an identical transformation to the regions, excluding the region enclosed by [[GAMMA].sub.1] and [[GAMMA].sub.2].
At the input surface of our device, we have x' = x = 0, and thus y' = y and z' = z, which means an identical transformation
at the input surface of the device.
For example, we can simply compress a big volume to a small one while keeping the outside an identical transformation
to enhance the field (see Figures 1(a) and (b)), as proposed in [7,20].
Intermediate identical transformations
are omitted because of its triviality and to avoid excessive unwieldiness in the material presentation.