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We investigate the single-photon scattering spectra of a giant atom coupledto a one dimensional waveguide via multiple connection points or a continuouscoupling region. Using a full quantum mechanical method, we obtain the generalanalytic expressions for the single-photon scattering coefficients, which arevalid in both the Markovian and the non-arkovian regimes. We summarize theinfluences of the non-dipole effects, mainly caused by the phases accumulatedby photons traveling between coupling points, on the scattering spectra. Wefind that under the Markovian limit, the phase decay is detuning-independent,resulting in Lorentzian lineshapes characterized by the Lamb shifts and theeffective decay rates. While in the non-Markovian regime, the accumulatedphases become detuning-dependent, giving rise to non-Lorentzian lineshapes,characterized by multiple side peaks and total transmission points. Anotherinteresting phenomenon in the non-Markovian regime is generation of broadphotonic band gap by a single giant atom. We further generalize the case ofdiscrete coupling points to the continuum limit with atom coupling to thewaveguide via a continuous area, and analyze the scattering spectra for sometypical distributions of coupling strength.

Coherent single-photon scattering spectra for a giant-atom waveguide-QED system beyond dipole approximation