from Eq. (\[app:SCE\_fin\]) as a function of both Zeeman field $h$ and wave-vector $q$. The optimal wave-vector $q$ is then determined such that it maximizes the temperature at a given $h$, which is equivalent to minimize the Ginzburg-Landau free energy.

Following this procedure, the $(h_x,\, h_z,\, T)$-phase diagram is plotted (Fig. \[diag-theta\]) for different orientations of the field and for spin-orbit coupling $\alpha = 0.05\, v_\text{F}$ ($\alpha\,p_\text{F} = 100\,T_{c0}$). One can first observe the anisotropy induced by spin-orbit interaction: at fixed critical field (temperature), the critical temperature (field) increases when $\theta$ decreases, $\theta$ corresponding to the angle between the field and the wire (see Fig. \[schema\_system\]). This means that the superconducting phase is widened when the field tends to be normal to the SOC. As expected from Eq. (\[DL\_strong\_SOC\]), the purely parallel Zeeman field $h = h_z$ ($\theta = \pi/2$) or purely perpendicular $h = h_x$ ($\theta = 0$) to the spin-orbit field correspond to particular cases in which the linear term in $q$ in Eq. (\[DL\_strong\_SOC\]) vanishes.

When the field is longitudinal ($h_x = 0$), we get back to the FFLO case without SO, namely the modulated phase emerges at the tricritical point $(T^\star = 0.56\,T_{c0},\, h^\star = 1.07\,T_{c0})$. 