Abstract
The high-order Laguerre-Gaussian (LG) mode output from an end-pumped Nd:YVO<sub>4</sub> laser cavity with strong spherical aberration (SA) induced by short-focal-length lens is studied in this work. A long-focal-length lens L1 is used in the cavity to expand and collimate the beam, so that the beam incident on another short-focal-length lens L2 in the cavity undergoes a strong SA. Since the ring-shaped LG modes with different values of angular index <i>m</i> have different beam radii, the actual focal points of each order of beam are then spatially displaced. A flat output coupler (OC) is located near the focal point of L2, which is composed of a cat-eye retroreflector together with the lens. Such a retroreflector can provide only ideal retroreflection to the incident beam with a focal point exactly on the OC. Given the focal point displacements of the LG beams with different orders, such a mechanism can be used for implementing the transverse mode selection. The mode which has an actual focal point on the OC has a smaller loss than the other defocused modes. With an <i>a</i>-cut Nd:YVO<sub>4</sub> as laser crystal, scalar (linear-polarized) single-mode LG output with radical index <i>p</i> = 0 and angular index <i>m</i>>0 is obtained. The laser mode-order is selectable from LG<sub>0, ±10</sub> to LG<sub>0, ±33</sub> under 878.6-nm incident diode pump power of 1.03 W, by simply adjusting the distance between the OC and L2 in a range of 0.5 mm, when using lens L1 with <i>f</i> = 150 mm and lens L2 of <i>f</i> = 33.9 mm. It is found that sufficient SA which makes the optical paths of the neighboring modes well distinguishable is essential for single-mode operation of a wanted order of LG mode. However, too strong an SA can stop the high-order mode beam from oscillating, since the width and radius of the ring-shaped LG mode are an increasing function of indices <i>p</i> and <i>m</i>, which bring a stronger loss to the corresponding mode. Based on this analysis, we turn to a focal-length combination of <i>f</i><sub>1</sub> = 100 mm and <i>f</i><sub>2</sub> = 51.8 mm, to reduce the SA to a level suitable for further higher mode operation. A highest-order LG<sub>0, ±75</sub> is obtained by such an SA mode-selecting technique under fixed pump power of 1.03 W.
Highlights
Typical near- and Far-field beam patterns of the laser output when the output coupler M2 was located at different positions
Calculated focal point displacement induced by spherical aberration (SA) considering the radius of the ring LG beams
4) (Science and Technology on Electro-Optical Information Security Control Laboratory, Tianjin 300308, China) ( Received 16 August 2021; revised manuscript received 7 September 2021 )
Summary
图 2 不同角向指数 m 的 LG0, ±m 光束理论相对尺寸 Fig. 2. Calculated relative beam sizes of the LG0, ±m mode laser. 首先采用 焦距分别为 150 mm 和 33.9 mm 的透镜 L1 和 L2, 全反镜 M1 到透镜 L1 的距离 d1 以及透镜 L1 到 L2 的距离 d2 分别为 155 mm 和 20 mm. 然后减小输出镜 M2 与 透镜 L2 之间的距离, 记距离相对 TEM00 时的变 化量为 d. 光斑由环形和花瓣形光斑叠加的形态变为清晰的 单圈花瓣状分布, 且光斑的近场和远场能量分布 一致, 如图 3(e) 所示, 说明此时激光输出为单一 LG0, ±m 模式; 花瓣状的强度分布是由轨道角动量 分别为+m 和–m 的两种不同手性的模式相干叠 加而成, 通过查看花瓣之间暗点的数量, 可以确定 LG0, ±m模式的角向指数m, 图 3(e) 所 示 的 d = 1.30 mm 时的激光模式为 LG0, ±10. Typical near- and Far-field beam patterns of the laser output when the output coupler M2 was located at different positions (incident pump power 1.03 W). 图 4 激光器处于不同运转模式时的激光输出功率 (泵浦 功率 1.03 W) Fig. 4. Calculated focal point displacement induced by SA considering the radius of the ring LG beams
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