Study on 1.9 μm structured lasers based on Ince–Gaussian modes superposition with multi-modulation by different directions off-axis dual-end-pump

Since P. Coullet first proposed an optical field with properties similar to hydrodynamic vortices in 1989 [1], optical vortices carrying orbital angular momentum have become a research hotspot for many years, and have promoted novel optical tweezers [2], multiplexing optical communication [3], quantum entanglement [4], [5], [6], metamaterial micro–nano machining [7] and other advanced fields of rapid development. In recent years, with the deepening of research, structured light has developed from traditional two-dimensional transverse fields to four-dimensional spatiotemporal structured light and multidimensional quantum states [8], and the spatial mode distribution of optical communication has expanded to more complex structured light [9]. The single-phase singularity vortex beam of Laguerre–Gaussian (LG) mode can no longer meet the requirements of the light source used in advanced research. Therefore, the realization of structured beam output with multi-phase singularities distribution will become the focus of research. At the same time, the characteristic wavelengths of vortex laser output focusing on applications in different fields are also further expanding. Compared with the common visible light and near-infrared (near 1 μm) laser output, the mid-infrared 2 μm band laser light source has great application potential in the field of free space optical communication (FSO) because it is located in the atmospheric window. If the wavelength division multiplexing (WDM) is further extended to complex tunable mode division multiplexing or space division multiplexing technology (MDM/SDM), this will greatly expand the capacity and speed of 2 μm laser space optical communication [10], [11].

At present, there are two primary approaches to generate a stable vortex array laser beam. The first approach is to use a well-designed two-dimensional phase plate [12] or a spatial light modulator (SLM) [13] to precisely phase modulate the output Gaussian fundamental mode beam to achieve customized laser output with a multi-phase singularities structure. The second approach is to use a vertical-cavity surface-emitting laser (VCSEL) called “vortex optical crystal” [14]. Through the precise design of the material microstructure, the vortex array beam output is realized based on the inherent optical nonlinearity of the laser. Due to the relatively low damage thresholds of core components, both methods do not have the potential to achieve high-power and high-energy structured beam output.

M. A. Bandres proposed a new complete family of transverse modes [15], the Ince–Gaussian (IG) modes, which is constructed in the elliptic coordinate system and realizes the unified and continuous transition of Hermite–Gaussian (HG) modes in the Cartesian coordinate system and Laguerre–Gaussian (LG) modes in the polar coordinate system. Y.J. Shen achieved the 15th-order HG modes output in the 1 μm band by means of off-axis pumping of Yb:CALGO crystal, and realized the conversion from HG modes to LG modes through an astigmatic mode converter (AMC) [16]. Similarly, we used the same technical method to realize the 1.9 μm topological charge number 20-order HG modes and LG modes output for the first time based on the off-axis pumping Tm:YLF crystal [17]. Y.J. Shen further realized the output regulation of Hermite–Laguerre–Gaussian (HLG) modes by adjusting the relative angle between the AMC and the output HG modes [18]. At the same time, another technical method was adopted to realize the astigmatic hybrid SU(2) vector vortex beams of the ray-wave duality based on geometrical optics, and the Greenberger–Horne–Zeilinger (GHZ) state was realized for the first time [19]. However, the research on these modes is based on the evolution process of a single output mode, and the superposition evolution of the two modes needs to be further analyzed. S. C. Chu proposed an unbalanced Mach–Zehnder interferometer with a Dove prism embedded outside the resonator [20], which theoretically simulates the conversion of even IG modes (IGp,pe modes) into vortex array laser beams output composed of a p × p number of well- aligned vortices.

In this work, the double IGp,pe modes superposition evolution output in a simple plano-concave resonator was achieved which used the different directions off-axis dual-end-pumped 1.9μm Tm:YLF laser. The superposition evolution process of double IGp,pe modes under the influence of various factors such as different order modes, rotation angle, phase difference, optical field intensity ratio, and ellipticity is established and analyzed theoretically. Based on this, the different directions off-axis dual-end-pump structure was designed. The experimental results show that the theoretical simulation and experimental results have a high degree of the agreement under the orthogonal superposition of IGp,pe modes. At the same time, the changes of different superposition phase differences when the same order IGp,pe modes are orthogonally superimposed, and the high-order IGp,m modes formed by the superposition evolution of IGp,pe modes under different rotation angles are experimentally studied. Thus, the feasibility of compound modulation of double IGp,pe modes by multiple factors is proved from theoretical and experimental studies. Finally, the 1.9μm Tm:YLF structure laser output with double IGp,pe modes multi-factor composite modulation superposition evolution within 10 orders is realized. When the 10-order IGp,pe modes are superimposed, the output power exceeds 5.7 W, and the conversion efficiency is higher than 17.5%. It provides potential application value for space division multiplexing expansion of high-power 2μm laser free space optical communication.

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