  The phenomenon of bound state in the continuum (BIC) with infinite quality
factor and lifetime has emerged in recent years in photonics as a new tool of
manipulating light-matter interactions. However, most of the investigated
structures only support BIC resonances at very few discrete points in the w~k
space. Even when the BIC is switched to a quasi-BIC(QBIC) resonance through
perturbation, its frequency will still be located within a narrow spectral band
close to that of the original BIC, restricting their applications in many
fields where random or multiple input frequencies beyond the narrow band are
required. In this work, we demonstrate that a new set of QBIC resonances can be
supported by making use of a special binary grating consisting of two
alternatingly aligned ridge arrays with the same period and zero-approaching
ridge width difference on a slab waveguide. These QBIC resonances are
distributed continuously over a broad band along a line in the w~k space and
can thus be considered as one-dimensional QBICs. With the Q factors generally
affected by the ridge difference, it is now possible to choose arbitrarily any
frequencies on the dispersion line to achieve significantly enhanced
light-matter interactions, facilitating many applications where multiple input
wavelengths are required, e.g. sum or difference frequency generations in
nonlinear optics.
