  Cavity mode theory and analysis of open cavities and plasmonic particles is
an essential component of optical resonator physics, offering considerable
insight and efficiency for connecting to classical and quantum optical
properties such as the Purcell effect. However, obtaining the dissipative modes
in normalized form for arbitrarily shaped open cavity systems is notoriously
difficult, often involving complex spatial integrations, even after performing
the necessary full space solutions to Maxwell's equations. The formal solutions
are termed quasinormal modes which are known to diverge in space, and
additional techniques are frequently required to obtain more accurate field
representations in the far field. In this work we introduce a new
finite-difference time-domain technique that can obtain normalized quasinormal
modes using a simple dipole-excitation source and an inverse Green function
technique, in real frequency space, without having to perform any spatial
integrations. Moreover, we show how these modes are naturally regularized to
ensure the correct field decay behaviour in the far field, and thus can be used
at any position within and outside the resonator. We term these modes
"regularized quasinormal modes" and show the reliability and generality of the
theory, by studying the generalized Purcell factor of quantum dipole emitters
near metallic nanoresonators, hybrid devices with metal nanoparticles coupled
to dielectric waveguides, as well as coupled cavity-waveguides in photonic
crystals slabs. We also directly compare our results with full-dipole
simulations of Maxwell's equations without any approximations and show
excellent agreement.
