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The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG0,2l vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4f system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam. [ABSTRACT FROM AUTHOR]

The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG0,2l vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4f system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam.

In laser-plasma interactions (LPI), the laser beam mode is a critical parameter when trying to explore new physical phenomena. Of the various spatial beam modes, the Laguerre-Gaussian (LG) mode with vortex phase has attracted considerable attention due to its unique features, including the ability to carry an orbital angular momentum. Due to this, it has been actively applied to LPI, which mainly utilize ultrashort intense laser pulses. However, existing transmissive phase-manipulating optical elements have several limitations when applied in LPI due to critical issues such as pulse broadening, attenuation, and beam shape–all of which have an influence on the beam quality, as well as, geometry, size, simplicity, and cost–all of which are related to processing technologies. In this paper, we present a series of procedures to obtain high-quality low-order (l = 1 and 2) LG vortex beams from large-sized off-axis reflective spiral phase plates (ORSPPs). The geometric designs for various surface structures, electromagnetic wave simulations in the extra-large domain, hybrid-mechanical processing technique attempted newly, and experimental demonstrations are involved. Experimental observations of LG intensity distributions and interference fringes were verified with the simulation results of Poynting vector, phase, and angular momentum densities. The beam quality of LG intensity distributions was analyzed quantitatively through the investigation of an annular zone formed from the uniformity of the stepped and continuous surface structures of ORSPPs. Furthermore, we numerically investigated the physical phenomena on the high-intensity angular momentum transfer from light to matter, considering ORSPP–driven low-order LG vortex laser pulses, by performing 3D particle-in-cell simulations.

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs’ difference between two vortex beams, and the twist direction relates to the sign of TCs’ difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence.

Within the framework of the generalized multi-particle Mie (GMM) theory, analytical solution to electromagnetic scattering of two interacting homogeneous uniaxial anisotropic spheres by a Laguerre–Gaussian (LG) vortex beam is investigated. The particles with different size and dielectric parameter tensor elements are arbitrarily configured. Based on the continuous boundary conditions at each sphere surface, the interactive scattering coefficients are derived. The internal and near-surface field is investigated to describe the propagation of LG vortex beam through the NaCl crystal. In addition, the far fields of some typical anisotropic medium such as LiNbO 3 , TiO 2 bispheres illuminated by an LG vortex beam are numerically presented in detail to analyze the influence of the anisotropic parameters, sphere positions, separation distance and topological charge etc. The results show that LG vortex beam has a better recovery after interacting with a spherical particle compared with Gaussian beam. The study in the paper are useful for the further research on the scattering and propagation characteristics of arbitrary vortex beam in anisotropic chains and periodic structure. [ABSTRACT FROM AUTHOR]

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs' difference between two vortex beams, and the twist direction relates to the sign of TCs' difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence. [ABSTRACT FROM AUTHOR]

• High-quality low-order Laguerre-Gaussian (LG) vortex beams from large-sized off-axis reflective spiral phase plates (ORSPPs) were obtained. • By performing 3D electro-magnetic wave simulations, the designs of ORSPPs were validated. • Stepped and continuous ORSPPs were manufactured by hybrid mechanical processing. • The uniformity of annular beam shape of LG vortex beams were analyzed by comparing the continuously and stepped ORSPPs. • 3D particle-in-cell simulations on the high-intensity angular momentum transfer were investigated as one of the main applications of low-order LG vortex laser pulses. In laser-plasma interactions (LPI), the laser beam mode is a critical parameter when trying to explore new physical phenomena. Of the various spatial beam modes, the Laguerre-Gaussian (LG) mode with vortex phase has attracted considerable attention due to its unique features, including the ability to carry an orbital angular momentum. Due to this, it has been actively applied to LPI, which mainly utilize ultrashort intense laser pulses. However, existing transmissive phase-manipulating optical elements have several limitations when applied in LPI due to critical issues such as pulse broadening, attenuation, and beam shape–all of which have an influence on the beam quality, as well as, geometry, size, simplicity, and cost–all of which are related to processing technologies. In this paper, we present a series of procedures to obtain high-quality low-order (l = 1 and 2) LG vortex beams from large-sized off-axis reflective spiral phase plates (ORSPPs). The geometric designs for various surface structures, electromagnetic wave simulations in the extra-large domain, hybrid-mechanical processing technique attempted newly, and experimental demonstrations are involved. Experimental observations of LG intensity distributions and interference fringes were verified with the simulation results of Poynting vector, phase, and angular momentum densities. The beam quality of LG intensity distributions was analyzed quantitatively through the investigation of an annular zone formed from the uniformity of the stepped and continuous surface structures of ORSPPs. Furthermore, we numerically investigated the physical phenomena on the high-intensity angular momentum transfer from light to matter, considering ORSPP–driven low-order LG vortex laser pulses, by performing 3D particle-in-cell simulations. [ABSTRACT FROM AUTHOR]