  The design of optical resonant systems for controlling light at the nanoscale
is an exciting field of research in nanophotonics. While describing the
dynamics of systems with few resonances is a relatively well understood
problem, controlling the behavior of systems with many overlapping states is
considerably more difficult. In this work we formulate a form of time dependent
coupled mode theory based on complete and orthogonal modes, which project
Maxwell's dynamics into a set of spatio-temporal equations that retain both the
simplicity and the exactness of traditional coupled mode theory studied for
optical waveguides. We developed a fast and effective computational method that
extracts all the characteristics of a multi-mode resonant system, including the
full density of states, the modes quality factors, the mode resonances and
linewidths from a single first principle simulation. This approach can be used
to study both analytically and numerically the complex dynamics of systems with
many overlapping resonances in ensembles of resonators of any geometrical shape
defined in materials with arbitrary responses.
