Three-dimensional coherent optical waves localized on trochoidal parametric surfaces

Structured transverse modes governed by maximum entropy principle

Based on the birefringent effect of the gain medium, a diode-pumped Nd-doped vanadate laser with nearly hemispherical cavity is exploited to emulate the quantum Green functions of two-dimensional commensurate harmonic oscillators. By matching the theoretical calculations to the far-field patterns of lasing modes, the resonant transverse frequencies can be accurately determined up to extremely high orders. The Shannon entropy is further employed to calculate the spatial entanglement of the quantum Green function as a function the transverse frequency. From the resonant transverse frequencies, all lasing modes are confirmed to be in excellent agreement with the maximum entropy states. This discovery implies that the formation of lasing modes is relevant to the coupling interaction between the pump source and the laser cavity.

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers for free-space optical communication, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and data transmission by the conjugated modulation method, demonstrating lower error rates caused by center offset and coherent background noise, compared with OAM basis. Our work provides a potentially useful basis for the next generation of large-scale dense data communication.

Generating high-power Lissajous structured modes and trochoidal vortex beams by an off-axis end-pumped Nd:YVO4 laser with astigmatic transformation

High-power structured beams with the transverse morphologies as the Lissajous figures are generated by an Nd:YVO₄ laser under two-dimensional off-axis pumping. By fine-tuning the cavity length in the neighborhood around the condition of longitudinal-transverse coupling, different cases of accidental degeneracies from the intracavity astigmatism are achieved to lead the output emission to be various Lissajous modes with different transverse frequency ratios. The generated Lissajous modes reveals good power performance with slope efficiency up to 47% and optical-to-optical conversion efficiency to be higher than 37.5% at a pump power of 16 W. Moreover, by applying beam transformation via a single-lens astigmatic mode converter, the generated Lissajous modes are further converted into structured vortex beams with transverse patterns localized on the trochoidal curves. The transformed trochoidal vortex beams are confirmed to preserve well-defined mode structures even when the average output power has been scaled up to be higher than 4 W.

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.

High-power structured laser modes: manifestation of quantum Green's function

The distributions of resonant frequencies in an astigmatic cavity are theoretically confirmed to be analogously equivalent to the quantum energy structures of two-dimensional commensurate harmonic oscillators. In the first part [Opt. Lett.45, 4096 (2020)OPLEDP0146-959210.1364/OL.399251] of this two-part series study, the lasing modes were verified to reveal a variety of vortex array structures. Here, in the second part of this two-part series study, the lasing modes are confirmed to agree very well with the quantum Green's functions that correspond to a bundle of Lissajous figures in the high-order regime.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

Kaleidoscope vortex lasers generated from astigmatic cavities with longitudinal-transverse coupling

We propose an efficient and robust method to generate the kaleidoscope vortex beam by employing an astigmatic laser cavity with an extra-cavity cylindrical lens. The kaleidoscope vortex beam is arising from the superposition of Laguerre-Gaussian modes with the longitudinal-transverse coupling effect in the laser cavity. The superposed Laguerre-Gaussian mode leads to the formation of complex phase singularities and implies the participation of different optical orbital angular momentum involved in a single kaleidoscope vortex beam. We experimentally demonstrate that a series of kaleidoscope vortex beams with different symmetry are systematically achieved by using a simple setup. The output power of the laser is dependent on the cavity length. This approach is expected to create high-order optical vortex beams and pave the way for optical entanglement.

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.

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

The generalized geometric mode with several high-order Hermite-Gaussian (HG) beams localized on ray periodic orbits in the degenerate resonator is generated by an off-axis pumped Nd:YVO₄ laser, by performing beam transformation via an astigmatic mode converter, the generalized geometric modes are found that can be converted into the multi-axis vortex beams with the bundled-rings structures. Experimental results reveal that the generated multi-axis vortex beams can preserve quite stable beam structures even under high-power operation. Moreover, the radius of the bundled rings for the multi-axis vortex beams can be flexibly adjusted by the off-axis pumping to lead to vortex structures with easily controlled orbital angular momentum distribution. The good agreement between the experimental and theoretical results of propagation evolution for the astigmatic transformation of generalized geometric modes further verify the feasibility of using the proposed system to realize various high-powered, multi-center vortex beams with good reliability and predictability.

Generating orthogonally circular polarized states embedded in nonplanar geometric beams

We experimentally demonstrated the generation of orthogonally circular polarized states embedded in nonplanar geometric beams. Experimental results revealed that the production of circularly polarized beams, induced by crystal birefringence, is quantized. Numerical analyses of the polarization and the spatial morphology are consistent with the experimental results.

Generalized Bessel beams with two indices

We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such generalized beams has, in the paraxial zone, the same radial structure as Laguerre-Gaussian beams. We investigate the form of these new beams as well as their peculiar propagation properties.

Observation and analysis of single and multiple high-order Laguerre-Gaussian beams generated from a hemi-cylindrical cavity with general astigmatism

We experimentally verified that anisotropic Hermite-Gaussian modes can be generated from a hemi-cylindrical laser cavity and can be transformed into high-order Laguerre-Gaussian modes using an extra-cavity cylindrical lens. We further combined the Huygens integral and the ABCD law to clearly demonstrate the transformation along the propagation direction. By controlling the pump offset and the pump size in hemi-cylindrical cavities, we experimentally observed the unique laser patterns that displayed the optical waves related to the coherent superposition of Laguerre-Gaussian modes.

Two- and three-dimensional standing waves in a reaction-diffusion system

We observe standing waves of chemical concentration in thin layers [quasi-two-dimensional (2D)] and capillaries [three-dimensional (3D)] containing the aqueous Belousov-Zhabotinsky reaction in a reverse microemulsion stabilized by the ionic surfactant sodium bis-2-ethylhexyl sulfosuccinate (AOT) and with cyclo-octane as the continuous phase. The 3D structures are oscillatory lamellae or square-packed cylinders at high and low volume fractions, respectively, of aqueous droplets. These patterns correspond to oscillatory labyrinthine stripes and square-packed spots in the 2D configuration. Computer simulations, as well as observations in E. coli, give qualitative agreement with the observed patterns and suggest that, in contrast to Turing patterns, the structures are sensitive to the size and shape of the system.

Observation of lasing modes with exotic localized wave patterns from astigmatic large-Fresnel-number cavities

We investigate the lasing modes in large-Fresnel-number laser systems with astigmatism effects. Experimental results reveal that numerous lasing modes are concentrated on exotic patterns corresponding to intriguing geometries. We theoretically use the quantum operator algebra to construct the wave representation for manifesting the origin of the localized wave patterns.