In this study, we explore the generation of high-order Laguerre?Gaussian (LG) mode vortex beams from a 914-nm Nd∶YVO₄ laser using spherical aberration within the laser cavity. Traditional methods for generating high-order LG modes typically require complex setups involving custom-designed optical components such as phase plates, spatial light modulators, and amplitude masks. However, these approaches are often expensive and difficult to adapt to various wavelengths. In this study, we propose a simpler and more cost-effective solution that utilizes a single spherical lens inside the cavity to introduce spherical aberration, enabling the selective generation of high-order LG modes in low-gain wavelength region. A flexible, easily adaptable method to produce LG_0,±m vortex beams with selective angular indices (m) over a large range is developed. We use only one lens in the cavity as opposed to two lenses in the former studies, which simplifies the cavity arrangement. A new model based on the cavity stability and pump overlap is developed to predict the relationship between the mode order and cavity parameters. This approach can be applied to a variety of scientific and industrial fields, such as optical manipulation, precision laser machining, and optical communications.

The experimental setup involves a 914-nm Nd∶YVO₄ laser with a cavity that includes a single short-focus spherical lens (L1), with a nominal focal length of 25.3 mm, to introduce spherical aberration. Given that the mode sizes of the LG_0,±m modes vary with their angular indices m, this aberration facilitates the mode discrimination and selection of high-order LG modes by affecting the focal lengths of the modes differently. The laser is end-pumped by a fiber-coupled 808-nm diode laser, and the cavity includes a concave mirror (M1), plane output mirror (M2), and spherical lens. Furthermore, the Nd∶YVO₄ crystal, which serves as the gain medium, has dimensions of 3 mm×3 mm×5 mm and a doping mass fraction of 0.15%. Given that the effective focal length of lens L1 varies for different orders of modes, the specific distance between lens L1 and output coupler M2 ensures that only laser modes with ring sizes exceeding a certain threshold remain stable within the cavity. In the family of stable modes, the smallest mode exhibits the largest overlap with the pump beam and oscillates. Therefore, mode selection can be realized by adjusting the distance between the lens and output mirror.

The experimental results show that the proposed method successfully generates LG modes with angular indices ranging from 8 to 34. At a pump power of 5.2 W, the laser initially produces a fundamental Gaussian mode. By gradually reducing the distance between the spherical lens and output mirror, the output transitions into a multimode. As the distance is further reduced, the output beam exhibits a hollow petal-like structure, indicating a single-mode high-order LG output. The highest mode order achieved is LG_0,±34 at a pump power of 8.1 W. With increasing mode order, the effective focal length decreases, causing the spherical lens to focus more tightly, which leads to the selective excitation of higher-order modes. The relationship between the mode order and cavity parameters is consistent with the calculated relationship based on the spherical aberration, beam size, and cavity stability. The far-field beam patterns show good uniformity, even for the highest angular indices, owing to the self-healing properties of LG modes, which aid in maintaining beam quality during propagation. However, the output power for higher-order modes decreases because of the reduced overlap between the pump beam and higher-order modes, leading to a lower conversion efficiency. Nevertheless, the laser system demonstrates excellent stability in high-order LG modes with minimal transverse mode fluctuations.

We demonstrate that high-order LG mode vortex beams can be generated from a 914-nm Nd∶YVO₄ laser using a single spherical lens to introduce spherical aberration in the cavity. This method provides a simple and cost-effective approach for generating high-order LG modes in flexible wavelength regions without the need for custom optical components. In the experiment, LG modes with angular indices, ranging from 8 to 34, are selectively generated by adjusting the position of the output mirror and focusing lens. The simplified cavity scheme and model facilitate the practical application of high-order LG lasers.