  The dispersion surfaces of printed periodic structures in layered media are
efficiently computed using a full-wave method based on the periodic Method of
Moments (MoM). The geometry of the dispersion surface is estimated after
mapping the determinant of the periodic MoM impedance matrix over a range of
frequencies and impressed phase shifts. For lossless periodic structures in the
long-wavelength regime, such as lossless metasurfaces, a tracking algorithm is
proposed to represent the dispersion surface as a superposition of
parameterized iso-frequency curves. The mapping process of the determinant is
accelerated using a specialized interpolation technique with respect to the
frequency and impressed phase shifts. The algorithm combines a fast evaluation
of the rapidly varying part of the periodic impedance matrix and the
interpolation of the computationally intensive but slowly varying remainder.
The mapping is further accelerated through the use of Macro basis functions
(MBFs). The method has been first tested on lossless metasurface-type
structures and validated using the commercial software CST. The specialized
technique enables a drastic reduction of the number of periodic impedance
matrices that needs to be explicitly computed. In the two examples considered,
only 12 matrices are required to cover any phase shift and a frequency band
larger than one octave. An important advantage of the proposed method is that
it does not entail any approximation, so that it can be used for lossy
structure and leaky waves, as demonstrated through two additional examples.
