  Beyond the scope of space-coding metasurfaces, space-time digital
metasurfaces can substantially expand the application scope of digital
metamaterials in which simultaneous manipulation of electromagnetic waves in
both space and frequency domains would be feasible. In this paper, by adopting
a superposition operation of terms with unequal coefficient, Huygens principle,
and a proper time-varying biasing mechanism, some useful closed-form formulas
in the class of large digital metasurfaces were presented for predicting the
absolute directivity of scatted beams. Moreover, in the harmonic beam steering
scheme, by applying several suitable assumptions, we have derived two separate
expressions for calculating the exact total radiated power at harmonic
frequencies and total radiated power for scattered beams located at the
end-fire direction. Despite the simplifying assumptions we have applied, we
have proved that the provided formulas can still be a good and fast estimate
for developing a large digital metasurface with a predetermined power intensity
pattern. The effect of quantization level and metasurface dimensions on the
performance of power manipulating as well as the limitation on the maximum scan
angle in harmonic beam steering have been addressed. Several demonstrative
examples numerically demonstrated through MATLAB software and the good
agreement between simulations and theoretical predictions have been observed.
By considering the introduced restrictions in the manuscript, this method can
be implemented in any desired frequency just by employing phase-only
meta-particles as physical coding elements. The author believes that the
proposed straightforward approach discloses a new opportunity for various
applications such as multiple-target radar systems and THz communication.
