  We calculate the reflection and transmission probabilities in a
one-dimensional Fermi gas with an equal mixing of the Rashba and Dresselhaus
spin-orbit coupling (RD-SOC) produced by an external Raman laser field. These
probabilities are computed over multiple relevant energy ranges within the
pseudo-potential approximation. Strong scattering resonances are found whenever
the incident energy approaches either a scattering threshold or a quasi-bound
state attached to one of the energetically closed higher dispersion branches. A
striking difference is demonstrated between two very different regimes set by
the Raman laser intensity, namely between scattering for the single- minimum
dispersion versus the double-minimum dispersion at the lowest threshold. The
presence of RD-SOC together with the Raman field fundamentally changes the
scattering behavior and enables the realization of very different
one-dimensional theoretical models in a single experimental setup when combined
with a confinement-induced resonance.
