  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has received renewed
interest recently due to the experimental indication of its presence in
CeCoIn$_5$, a quasi 2-dimensional (2D) d-wave superconductor. However direct
evidence of the spatial variation of the superconducting order parameter, which
is the hallmark of the FFLO state, does not yet exist. In this work we explore
the possibility of detecting the phase structure of the order parameter
directly using conductance spectroscopy through micro-constrictions, which
probes the phase sensitive surface Andreev bound states of d-wave
superconductors. We employ the Blonder-Tinkham-Klapwijk formalism to calculate
the conductance characteristics between a normal metal (N) and a 2D $s$- or
$d_{x^2-y^2}$-wave superconductor in the Fulde-Ferrell state, for all barrier
parameter $z$ from the point contact limit ($z=0$) to the tunneling limit ($z
\gg 1$). We find that the zero-bias conductance peak due to these surface
Andreev bound states observed in the uniform d-wave superconductor is split and
shifted in the Fulde-Ferrell state. We also clarify what weighted bulk density
of states is measured by the conductance in the limit of large $z$.
