Characterization and generation of high-power multi-axis vortex beams by using off-axis pumped degenerate cavities with external astigmatic mode converter

Multiaxial super-geometric mode laser

Structured light was usually studied by two-dimensional (2D) transverse eigenmodes. Recently, the three-dimensional (3D) geometric modes as coherent superposed states of eigenmodes opened new topological indices to shape light, that optical vortices can be coupled on multiaxial geometric rays, but only limited to azimuthal vortex charge. Here, we propose a new structured light family, multiaxial super-geometric modes, enabling full radial and azimuthal indices coupled to multiaxial rays, and they can be directly generated from a laser cavity. Exploiting combined intra- and extra-cavity astigmatic mode conversions, we experimentally verify the versatile tunability of complex orbital angular momentum and SU(2) geometry beyond the limit of prior multiaxial geometric modes, opening new dimensions to revolutionize applications such as optical trapping, manufacturing, and communications.

Investigating the generation and propagation evolution of orange optical vortices using continuous-wave KGW Raman lasers with astigmatic mode transformations

Various high-order orange beams (HOBs) at 588 nm are produced via off-center pumped Nd:YVO₄/KGW Raman lasers. We experimentally confirm that the HOBs can be fairly sustained at the incident pump power of 2.88 W, where the average output powers are overall from 300 mW to 160 mW with increasing the off-center displacements from 0.14 mm to 0.21 mm. The HOBs are further transformed by using an astigmatic mode converter to generate a variety of structured lights with optical vortices. Moreover, theoretical wave functions are analytically derived to characterize the propagation evolution of the converted HOBs. The experimental patterns for all propagating positions are excellently reconstructed by the derived wave functions, and the evolution of phase structures is numerically calculated to manifest the robust optical vortices.

Astigmatic hybrid SU(2) vector vortex beams: towards versatile structures in longitudinally variant polarized optics

Structured light with more controllable degrees-of-freedom (DoFs) is an exciting topic with versatile applications. In contrast to conventional vector vortex beams (VVBs) with two DoFs of orbital angular momentum (OAM) and polarization, a hybrid ray-wave structure was recently proposed [Optica 7(7), 820-831 (2020)], which simultaneously manifests multiple DoFs such as ray trajectory, coherent state phase, trajectory combination, besides OAM and polarization. Here we further generalize this exotic structure as the astigmatic hybrid VVB by hatching a new DoF of astigmatic degree. Importantly, the transverse topology varies with propagation, e.g. a linearly distributed hybrid trajectory pattern can topologically evolve to a circularly polygonal star shape, where the number of singularity changes from zero to multiple in a single beam. The propagation-dependent evolution can be easily controlled by the astigmatic degree, including as a vector vortex state such that different astigmatic trajectories have different polarizations. We experimentally generate such beams from a simple laser with a special astigmatic conversion by combined spherical and cylindrical lenses, and the results agree well with our theoretical simulation. With our new structured light, the propagation-multiplexing multi-DoF patterns can be controlled in a single beam, which can largely extend related applications such as high-dimensional large-capacity optical communication, laser machining, and particle trapping.

Orbital angular momentum mode detection of the combined vortex beam generated by coherent combining technology

Coherent beam combining (CBC) technology has distinct advantages in generating high power vortex beam. In this paper, a circularly arranged coherent beam array (CBA) with discrete vortex phases is constructed to generate vortex beams. We demonstrated that the combined vortex beam (CVB) generated by the CBA is a multiplexing vortices optical field, which sidelobe is the coaxial interference pattern of these spiral harmonic components. Using the designed Dammam vortex grating (DVG), the orbital angular momentum (OAM) spectrum of the CVB is detected. Moreover, taking the target OAM mode purity of the CVB as the evaluation function of active phase control system, we realized the closed-loop phase control of the CBA and obtained the phase-locked output of the CVB.

Digitally tailoring arbitrary structured light of generalized ray-wave duality

Structured lights, particularly those with tunable and controllable geometries, are highly topical due to a myriad of their applications from imaging to communications. Ray-wave duality (RWD) is an exotic physical effect in structured light that the behavior of light can be described by both the geometric ray-like trajectory and a coherent wave-packet, thus providing versatile degrees of freedom (DoFs) to tailor more general structures. However, the generation of RWD geometric modes requires a solid-state laser cavity with strict mechanical control to fulfill the ray oscillation condition, which limits the flexiblility of applications. Here we overcome this confinement to generate on-demand RWD geometric modes by digital holographic method in free space without a cavity. We put forward a theory of generalized ray-wave duality, describing all previous geometric modes as well as new classes of RWD geometric modes that cannot be generated from laser cavities, which are verified by our free-of-cavity creation method. Our work not only breaks the conventional cavity limit on RWD but also enriches the family of geometric modes. More importantly, it offers a new way of digitally tailoring RWD geometric modes on-demand, replacing the prior mechanical control, and opening up new possibilities for applications of ray-wave structured light.

Revolving and spinning of optical patterns by two coaxial spiraling elliptic beams in nonlocal nonlinear media

Rotating patterns can be produced by two coaxial spiraling elliptic beams in nonlocal nonlinear media. The two constituent beams carry the orbital angular momentum (OAM), which has the same or opposite signs. The resultant patterns exhibit revolving and spinning rotations similar to the Sun-Earth system. The revolving-typed rotation comes of the overall OAM, while the spinning-typed rotation results from the respective OAM of the constituent beam. A kind of soliton patterns can stably exist, for which a vortex is nested centrally in the rotating square-shaped optical envelope and four peaks appear at four corners. The centrally nested vortex splits into two single vortex for r≠1, with r being the power ratio between the two constituent beams. The two single vortexes align vertically for r<1 and horizontally for r>1, and their spacing increases with |r-1|. The theoretical results give a possibility of the transforming from cross-phase-typed OAM into the helical-phase-typed OAM, which may find potential applications in beam shaping and controlling. In addition, the square optical envelope may exhibit advantages in the integration of optical components.

Periodic-trajectory-controlled, coherent-state-phase-switched, and wavelength-tunable SU(2) geometric modes in a frequency-degenerate resonator

We report a method to realize the periodic trajectory controlling, coherent-state phase switching, and wavelength tuning of SU(2) geometric modes (GMs) in a frequency-degenerate resonator (FDR). FDR is a resonator in which the ratio of transverse and longitude modes frequency spacing is a simple rational number, which would lead to a laser wave-packet in a SU(2) coherent state related to a periodic ray trajectory. We demonstrate that the periodic trajectory can be switched with coherent-state phase changing from 0 to π (or π to 0) by simply controlling the position of gain medium in the same FDR. For the period-of-four state, the geometries are switched between "W" and "M" shapes. For the period-of-three state, those are switched between "IV" and "VI" shapes. Moreover, because a special crystal Yb:CALGO with extremely broad emission band is used as the gain medium, our SU(2) GMs have the wavelength-tunable property in contrast to the conventional single-frequency GMs. The center wavelength can be tuned with the range of about 10 nm by adjusting the pump power. These effects can further enrich the various applications of structured light manipulation.

Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes

We report, for the first time to the best of our knowledge, a truncated diffraction with a triangular aperture of the SU(2) geometric modes and propose a method to detect the complicated orbital angular momentum (OAM) of an SU(2) wave-packet. As a special vortex beam, a nonplanar SU(2) mode carrying special intensity and OAM distributions brings exotic patterns in a truncated diffraction lattice. A meshy structure is unveiled therein by adjusting the illuminated aperture in the vicinity of the partial OAM regions, which can be elaborately used to evaluate the partial topological charge and OAM of an SU(2) wave-packet by counting the dark holes in the mesh. Moreover, through controlling the size and position of the aperture at the center region, the truncated triangular lattice can be close to the classical spot-array lattice for measuring the center OAM. These effects being fully validated by theoretical simulations greatly extend the versatility of topological structures detecting special beams.