  Fundamental effects in nanophotonic resonance systems focused on singular
states and their properties are presented. Strongly related to lattice geometry
and material composition, there appear resonant bright channels and
non-resonant dark channels in the spectra. The bright state corresponds to high
reflectivity guided-mode resonance (GMR) whereas the dark channel represents a
bound state in the continuum (BIC). Even in simple systems, singular states
with tunable bandwidth appear as isolated spectral lines that are widely
separated from other resonance features. Under moderate lattice modulation,
there ensues leaky-band metamorphosis, merging modal bands and resulting in
offset dark states and reflective BICs along with transmissive BICs within a
high-reflectance wideband. Rytov-type effective medium theory (EMT) is shown to
be a powerful means to describe, formulate, and understand the collective
GMR/BIC fundamentals in resonant photonic systems. Particularly, the discarded
Rytov analytical solution for asymmetric fields is shown here to predict the
dark BIC states essentially exactly for considerable modulation levels. The
propagation constant of an equivalent EMT homogeneous film provides a
quantitative evaluation of the eminent, oft-cited embedded BIC eigenvalue. The
work concludes with experimental verification of key effects.
