  We report a 1D planar optical waveguide with transverse distribution of
inhomogeneous loss profile, which exhibits an exceptional point (EP). The
waveguide hosts two leaky resonant modes; where the interaction between them in
the vicinity of the EP is controlled by proper adjustment of the inhomogeneity
in attenuation profile only. We study the adiabatic dynamics of propagation
constants of the coupled modes by quasi-static encirclement of control
parameters around the EP. Realizing such an encirclement with the inhomogeneous
loss distribution along the direction of light propagation, we report the
breakdown of adiabatic evolution of two coupled modes through the waveguide in
presence of an EP. Here, during conversion the output mode is irrespective of
the choice of input excited mode but depends on the direction of light
transportation. This topologically controlled, robust scheme of asymmetric mode
conversion in the platform of the proposed all-lossy waveguide structure may
open up an extensive way-out for implementation of state-transfer applications
in chirality driven waveguide-based devices.
