  We discuss the decay of a two-level system into an engineered reservoir of
coupled harmonic oscillators in the single-excitation manifold and propose its
optical simulation with an homogeneous chain of coupled waveguides where
individual elements couple to an external waveguide. We use two approaches to
study the decay of the optical analogue for the probability amplitude of the
two-level system being in the excited state. A Born approximation allows us to
provide analytic closed-form amplitudes valid for small propagation distances.
A Fourier-Laplace approach allows us to estimate an effective decay rate valid
for long propagation distances. In general, our two analytic approximations
match our numerical simulations using coupled mode theory and show
non-Markovian decay into the engineered reservoir. In particular, we focus on
two examples that provide enhancement or suppression of the decay decay rate
using flat-top or Gaussian coupling distributions.
