  The paper aims to apply the inverse scattering transform to the defocusing
Hirota equation with fully asymmetric non-zero boundary conditions (NZBCs),
addressing scenarios in which the solution's limiting values at spatial
infinities exhibit distinct non-zero moduli. In comparison to the symmetric
case, we explore the characteristic branched nature of the relevant scattering
problem explicitly, instead of introducing Riemann surfaces. For the direct
problem, we formulate the Jost solutions and scattering data on a single sheet
of the scattering variables. We then derive their analyticity behavior,
symmetry properties, and the distribution of discrete spectrum. Additionally,
we study the behavior of the eigenfunctions and scattering data at the branch
points. Finally, the solutions to the defocusing Hirota equation with
asymmetric NZBCs are presented through the related Riemann-Hilbert problem on
an open contour. Our results can be applicable to the study of asymmetric
conditions in nonlinear optics.
