  We present and validate a semi-analytical quasi-normal mode (QNM) theory for
the local density of states (LDOS) in coupled photonic crystal (PhC)
cavity-waveguide structures. By means of an expansion of the Green's function
on one or a few QNMs, a closed-form expression for the LDOS is obtained, and
for two types of two-dimensional PhCs, with one and two cavities side-coupled
to an extended waveguide, the theory is validated against numerically exact
computations. For the single cavity, a slightly asymmetric spectrum is found,
which the QNM theory reproduces, and for two cavities a non-trivial spectrum
with a peak and a dip is found, which is reproduced only when including both
the two relevant QNMs in the theory. In both cases, we find relative errors
below 1% in the bandwidth of interest.
