Non-Hermitian photonic lattices offer unconventional control over light evolution owing
to modal non-orthogonality and the resulting non-normal dynamical response. In this
work, we show that a uniform passive waveguide lattice with dissipation confined to
one or a few sites near an edge can exhibit an algebraic(nearly linear) decay of optical
power—an absorption law forbidden in orthogonal (normal-mode) dissipative systems,
where any superposition of eigenmodes yields purely multi-exponential attenuation. We
demonstrate that algebraic absorption arises when the input excitation is appropriately
tailored to exploit non-orthogonal modal interference, effectively channeling energy toward
the dissipative boundary. In particular, under the condition of coherent perfect absorption
(CPA) associated with a spectral singularity of the semi-infinite lattice, nearly complete
light absorption accompanied by algebraic decay of the optical power can be achieved.
Starting from the minimal configuration of a single lossy edge site, we derive compact
analytical expressions for the dynamics and identify the conditions under which linear-like
absorption emerges. We then extend the analysis to multiple edge-proximal lossy sites. Our
results show that simple dissipative photonic lattices, when driven by suitably prepared
input states, enable robust sculpting of absorption laws through non-normal dynamics,
providing a new route to programmable attenuation.