  Recently, optical bound states in continuum in various passive photonic
crystals have been identified and similar structures incorporated with optical
gain have been reported to exhibit lasing. However, no explicit control over
the type of lasing BIC has been reported. In this work, we utilize all four
fundamental BICs related to the lowest energy Gamma-point of a square photonic
crystal lattice. We identify the associated topological charges from
experimentally obtained dispersions, finite element method simulations, as well
as from spherical decomposition method based on the microscopic polarization
currents in the photonic crystal plane. By tailoring the periodicity and the
hole diameter of the photonic crystal slab, we selectively bring each of the
four BIC resonances to a wavelength regime, where fluorescent IR702 molecules
overlaid with the photonic crystal provide sufficient gain for the onset of
lasing. We experimentally analyze all four observed lasing BICs by imaging
their far-field polarization vortices and their associated topological charges.
The results correspond excellently with the transmission results as well as the
simulation results in the absence of gain. Finally, we experimentally present a
case where the lasing signal reveals the coexistence of two BICs with opposite
topological charges, resulting in a unique polarization pattern. We believe our
results enable tailoring the properties, such as polarization winding and
topological charge of BICs, by a priori design and thus pave the way for a more
general utilization of their appealing properties.
