  We investigate the single-photon scattering spectra of a giant atom coupled
to a one dimensional waveguide via multiple connection points or a continuous
coupling region. Using a full quantum mechanical method, we obtain the general
analytic expressions for the single-photon scattering coefficients, which are
valid in both the Markovian and the non-arkovian regimes. We summarize the
influences of the non-dipole effects, mainly caused by the phases accumulated
by photons traveling between coupling points, on the scattering spectra. We
find that under the Markovian limit, the phase decay is detuning-independent,
resulting in Lorentzian lineshapes characterized by the Lamb shifts and the
effective decay rates. While in the non-Markovian regime, the accumulated
phases become detuning-dependent, giving rise to non-Lorentzian lineshapes,
characterized by multiple side peaks and total transmission points. Another
interesting phenomenon in the non-Markovian regime is generation of broad
photonic band gap by a single giant atom. We further generalize the case of
discrete coupling points to the continuum limit with atom coupling to the
waveguide via a continuous area, and analyze the scattering spectra for some
typical distributions of coupling strength.
