  We study a single photon transmission through 1D N- qubit chain. The qubits
are supposed to be identical with equal distance between neighbors. We express
the transfer matrix of N- qubit chain in terms of Chebyshev polynomials, which
allows us to obtain simple expressions for the transmission and reflection
amplitudes for arbitrarily large N. If the distance between neighbor qubits is
equal to half wavelength, the transmission spectrum exhibits a flat bandgap
structure with very steep walls. We show that for odd N the tuning of the
excitation frequency of a central qubit gives rise to the appearance within a
bandgap of a narrow resonance with a full transmission. The position of the
resonance and its width can be controlled by the frequency of a central qubit.
We show that the formation of the bandgap and of the transmission resonance is
conditioned by the overlapping the widths of individual qubits which results
from the strong coupling between qubits and waveguide photons.
