title: Semianalytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structures.
abstract: We present and validate a semianalytical 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 nontrivial 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.
authors.forename: Jakob Rosenkrantz
authors.initials: JR
authors.lastname: de Lasson
authors.forename: Philip Trøst
authors.initials: PT
authors.lastname: Kristensen
authors.forename: Jesper
authors.initials: J
authors.lastname: Mørk
authors.forename: Niels
authors.initials: N
authors.lastname: Gregersen