Lasing From Bound States In The Continuum Based On Dye-TiO₂ Lattices

Vortex beams exhibit helical phase and spatially varying polarization,which can find applications in various fields such as high-resolution imaging,particle manipulation,classical and quantum communication.In recent years,as the interest in the direct generation of vortex beams continues to surge,lasers using bound states in the continuum（BICs）as optical feedback have received a lot of attention.Unlike other on-chip vortex micro-lasers involving spiral or ring components,the photonic crystal slab supporting BICs is planar and macroscopically homogeneous.BICs at theΓPoint in the first Brillouin zone in momentum space are usually called symmetry protected BICs,as these antisymmetric modes are incompatible with even symmetric plane wave and cannot radiate along the surface normal direction of the photonic crystal slab.Importantly,BIC has a topological property,which corresponds to the center of far field polarzation,and has an infinite quality factor.Therefore,it allows not only vortex emission,but also can realize large-area surface-emitting laser with low threshold.So far,photonic crystal slabs with different geometric shapes have been used for laser generation,including hole arrays,pillar arrays,and nanoparticle arrays made of dielectric,semiconductor,and metal materials,as well as various gain materials such as multiple quantum wells,perovskite,organic dye molecules,and colloidal nanoplates or quantum dots,The use of liquid dye gain materials on photonic crystal slabs is a flexible way to achieve efficient lasers,which provide separate control of the gain medium and the laser cavity.For dye gain BIC lasers,researchers have reported donut-shaped laser patterns（circular polarization pump）and discrete bright spot laser patterns（linearly polarized pump）.However,it is not clear how pump polarization affects the laser generation behavior of BIC dye laser.Furthermore,it has not been verified whether a single pump can generate multiple vortex beams.Here we study the vortex laser generation using a dye covered two-dimensional TiO₂square lattice.We fabricated square arrays of titanium dioxide nanoparticles on a quartz substrate,forming a photonic crystal slab with an area of approximately 1 cm×1 cm.The angle-resolved transmission spectra of the sample was measured,and the measured spectra were consistent with the simulated angle-resolved spectra.Four BICs were found in the wavelength range of 850 nm to 930 nm.After analyzing their mode profiles,it was found that these four BICs belong to different types.These different BIC modes can generate lasers simultaneously under pulsed pumping,and all can exhibit donut-shaped laser modes independent of the pump polarization,but the threshold is polarization dependent.In addition,we demonstrated the ability to generate multiple vortex beams through a single pump.The phase singularity of the emitted beam was confirmed through self-interference,and a pair of fork-shaped stripes was observed.These findings provide exciting prospects for compact and tunable light sources of vector vortex beams.