  This study suggests an idea that radiation in a periodic leaky-wave antenna
(PLWA) should be considered to be produced with the fundamental mode,
regardless of whether it is fast-wave or slow-wave. The idea is different from
the conventional PLWA theory, which considers it a fact that a PLWA produces
radiation with its fast-wave space harmonic when the fundamental mode is
slow-wave. To elaborate the idea, it is proved that there is not an
eigen-equation like Pythagorean theorem for the fundamental mode in PLWAs. Then
a non-uniform structure antenna is designed to show that slow-wave modes can
produce leaky-wave radiation. Again it is proved that the difference of the
phase constants between a slow-wave fundamental mode and its fast-wave space
harmonics has not any effect on the radiation pattern of a PLWA. Moreover, it
is clarified that the fundamental mode has a more definite physical
significance than space harmonics. Finally, a concept of generalized
fundamental modes is proposed without using Fourier expansion. The generalized
fundamental modes have the same phase and attenuation constants as any space
harmonics, and have physical significance as the conventional fundamental mode.
Therefore, it could replace the roles that the space harmonics used to play.
