光电工程

基于Bi₂Se₃的被动调Q波导脉冲涡旋激光器

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王玺融 , 孙文青 , 孙晓莉 ^*^,^*

光电工程 | 科研论文 2026,53(7): 260082-1

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光电工程 |科研论文 2026 , 53 (7) : 260082 -1

基于Bi₂Se₃的被动调Q波导脉冲涡旋激光器

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王玺融 (2005-)，男，山东大学基地班24级本科生，研究方向为飞秒激光直写光波导器件。E-mail：wxr112905@outlook.com wxr112905@outlook.com

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孙文青 (2000-)，女，博士研究生，研究方向为离子束材料改性及其光子与光电器件研究。E-mail：15169831710@163.com 15169831710@163.com

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孙晓莉 (1993-)，女，教授，博士研究生导师，研究方向为离子束材料光学改性、低维光电子及光子器件、超快激光技术。E-mail：xlsun@sdu.edu.cn xlsun@sdu.edu.cn

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孙晓莉 (1993-)，女，教授，博士研究生导师，研究方向为离子束材料光学改性、低维光电子及光子器件、超快激光技术。E-mail：xlsun@sdu.edu.cn xlsun@sdu.edu.cn

王玺融, 孙文青, 孙晓莉^*^,^*

作者信息

山东大学物理学院，山东济南 250100

通讯作者:

孙晓莉，xlsun@sdu.edu.cn

作者简介:

作者贡献

王玺融，孙文青：研究资料的收集、分析，实验的设计与完成，论文写作；孙晓莉：指导论文选题、论文修改。

王玺融 (2005-)，男，山东大学基地班24级本科生，研究方向为飞秒激光直写光波导器件。E-mail：wxr112905@outlook.com wxr112905@outlook.com

孙文青 (2000-)，女，博士研究生，研究方向为离子束材料改性及其光子与光电器件研究。E-mail：15169831710@163.com 15169831710@163.com

孙晓莉 (1993-)，女，教授，博士研究生导师，研究方向为离子束材料光学改性、低维光电子及光子器件、超快激光技术。E-mail：xlsun@sdu.edu.cn xlsun@sdu.edu.cn

Passively Q-switched Nd:YAG waveguide vortex laser using Bi₂Se₃ saturable absorber

Xirong Wang, Wenqing Sun, Xiaoli Sun

Affiliations

School of Physics, Shandong University, Jinan, Shandong 250100, China

Corresponding Author:

xlsun@sdu.edu.cn

出版时间: 2026-07-25 doi: 10.12086/oee.2026.260082

文章导航

摘要

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采用飞秒激光直写技术在Nd:YAG晶体中制备圆形包层波导，以化学气相沉积法制备的拓扑绝缘体三硒化铋 (Bi₂Se₃)作为可饱和吸收体，成功实现被动调Q涡旋激光的稳定运转。通过显微成像、微拉曼光谱及端面耦合测试，证实所制备圆形波导具有优良的几何形貌与导光性能。对Bi₂Se₃薄膜的非线性光学特性进行实验表征，测得其调制深度为8.6%，饱和强度为26.25 GW/cm²。在1 μm波段系统研究并对比了连续波与调Q模式下的激光输出性能，结果表明，该圆形波导具备优异的热稳定性，在不同泵浦功率水平下均能维持高质量的涡旋光斑分布。当吸收泵浦功率为850 mW时，激光输出性能达到最优：最短脉冲宽度为39 ns，最高重复频率为9.1 MHz，最大单脉冲能量可达4.42 nJ。

关键词

飞秒激光直写 / 波导激光 / 被动调Q / Bi₂Se₃ / 涡旋激光

Abstract

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Objective

Vortex beams, characterized by a spiral phase wavefront and a central phase singularity, carry orbital angular momentum (OAM). The infinite orthogonal states provided by OAM offer a new degree of freedom for manipulating optical fields, showing tremendous potential in high-capacity spatial division multiplexing communications, optical micromanipulation, and quantum information processing. Compared to continuous-wave (CW) vortex beams, pulsed vortex lasers with high peak power hold significantly greater application value in nonlinear optical frequency conversion and laser micromachining. However, traditional pulsed vortex lasers generally rely on bulky solid-state crystal resonators or complex spatial optical paths, making it difficult to meet the urgent demands of modern photonics for device miniaturization and high stability. Furthermore, high-power pumping in bulk crystals induces severe thermal lensing effects, which drastically distort the fragile spatial phase of vortex beams. To achieve compact and highly stable pulsed vortex sources, dielectric optical waveguides act as an ideal platform. The micrometer-scale geometric structure of the waveguide endows the device with an extremely high surface-to-volume ratio, which significantly enhances the heat dissipation capability of the system. In terms of pulse generation, passive Q-switching using two-dimensional saturable absorbers (SAs) is highly favored due to its compact footprint. Topological insulators, particularly bismuth selenide (Bi₂Se₃), feature a Dirac-cone electronic band structure and exhibit remarkable broadband nonlinear optical responses with large modulation depths. This study aims to propose and demonstrate a highly stable, compact passively Q-switched waveguide vortex laser by combining a femtosecond laser direct written (FsLDW) Nd:YAG waveguide with a high-quality Bi₂Se₃ SA grown by chemical vapor deposition (CVD).

Methods

A circular depressed-cladding waveguide was fabricated in a 1 at.% Nd³⁺-doped YAG crystal using the FsLDW technique. The fabrication utilized a Ti:sapphire regenerative amplifier delivering 120 fs pulses at a central wavelength of 795 nm with a repetition rate of 1 kHz. Parallel low-refractive-index damage tracks were inscribed to form a circular cladding boundary with a radius of 15 μm, perfectly preserving the original luminescence properties and lattice quality of the crystalline core. The geometric morphology and guiding characteristics were verified via optical microscopy and micro-Raman spectroscopy. Concurrently, a high-quality Bi₂Se₃ thin film was synthesized on a CVD method. Atomic force microscopy (AFM) and Raman spectroscopy were employed to characterize its morphology and structural properties. The nonlinear optical absorption parameters of the Bi₂Se₃ film were quantitatively evaluated using an open-aperture Z-scan technique driven by a 1030 nm femtosecond fiber laser. A compact laser resonator was subsequently constructed. An 808 nm continuous-wave Ti:sapphire laser served as the pump source, coupled into the waveguide via a spherical plano-convex lens. The Bi₂Se₃ film was inserted into the cavity as the SA. Notably, a spiral phase plate (SPP) with a topological charge of 1 was utilized as the output coupler. Compared to spatial light modulators or liquid crystal q-plates, the pure dielectric SPP possesses an exceptionally high laser damage threshold, directly generating the vortex beam while ensuring the robustness of the cavity.

Results and Discussions

The AFM measurements indicate that the average thickness of the synthesized Bi₂Se₃ film is approximately 16 nm. The Z-scan experimental results and subsequent nonlinear transmission fitting reveal that the Bi₂Se₃ SA exhibits an excellent modulation depth of 8.6% and a saturation intensity of 26.25 GW/cm² at 1 μm, indicating its strong capability for pulse modulation. In the laser performance evaluation, stable CW and passive Q-switching operations around 1064 nm were systematically compared under both TE and TM polarized pumping. After inserting the Bi₂Se₃ SA, stable Q-switched pulse trains were generated. The pulse temporal characteristics evolved typically with the increase of absorbed pump power. Specifically, at an absorbed pump power of 850 mW, the laser yielded the optimal pulsed performance: the shortest pulse width compressed to 39 ns, and the highest repetition rate reached 9.1 MHz. The corresponding maximum single-pulse energy was calculated to be 4.42 nJ. The recorded pulse trains exhibited uniform amplitude and high temporal stability without distinct amplitude fluctuations. Furthermore, the near-field intensity distributions captured by a CCD camera demonstrated a typical annular (donut-shaped) hollow profile, confirming the high generation quality of the vortex beam. More importantly, comparing the beam profiles at low and high pump powers, the annular contour showed no obvious distortion or degradation. This phenomenon provides strong evidence that the unique geometric structure of the circular waveguide effectively mitigates the thermal lensing effect through rapid transverse heat dissipation. Theoretical estimations further confirm that the maximum intracavity peak pulse energy fluence (1.3 mJ/cm²) is well below the physical damage threshold of the Bi₂Se₃ film (3.18 mJ/cm²).

Conclusions

A compact, highly thermally stable, passively Q-switched Nd:YAG waveguide vortex laser was successfully demonstrated. The integration of the FsLDW-customized circular depressed-cladding waveguide and the CVD-grown Bi₂Se₃ topological insulator effectively overcomes the thermal and physical bulkiness bottlenecks of traditional solid-state vortex lasers. The robust thermal management capability of the waveguide physically locks the high-order transverse mode, ensuring distortion-free annular vortex beam output even under intense pumping conditions. The experimental results verify the excellent nonlinear optical modulation properties and impressive thermal damage resistance of the Bi₂Se₃ film. This research provides a novel experimental paradigm and solid foundation for the development of miniaturized, highly stable all-solid-state pulsed vortex sources, paving the way for advanced on-chip photonic integrated circuits and optical manipulation systems.

Key words

waveguide laser / Nd:YAG / passive Q-switching / Bi₂Se₃ / vortex laser

引用本文

王玺融, 孙文青, 孙晓莉. 基于Bi₂Se₃的被动调Q波导脉冲涡旋激光器. 光电工程, 2026 , 53 (7) : 260082 -1 . DOI: 10.12086/oee.2026.260082

Xirong Wang, Wenqing Sun, Xiaoli Sun. Passively Q-switched Nd:YAG waveguide vortex laser using Bi₂Se₃ saturable absorber[J]. Opto-Electronic Engineering, 2026 , 53 (7) : 260082 -1 . DOI: 10.12086/oee.2026.260082

正文

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1　引　言

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涡旋光束携带独特的轨道角动量 (orbital angular momentum, OAM)，具有螺旋型相位波前与相位奇点，其中相位奇点处相位不确定且光强为零，使得涡旋光束整体呈现环状光强分布^[1-2]。其OAM模式所提供的无限正交态，为光场调控开辟了新维度，促使涡旋光在量子通信、OAM复用、涡旋传感等前沿领域展现出广阔的应用前景^[3-8]。目前，涡旋光束的生成主要通过腔外调控实现，常用器件包括螺旋相位板、空间光调制器、Q波片等^[9-11]。其中，将螺旋相位板作为输出镜是腔外生成涡旋光束的常用且有效的方法^[12-14]。相较于连续波 (continuous wave, CW)涡旋光，具有高峰值功率的脉冲涡旋激光在非线性光学频率转换、激光微加工等领域具有更高的应用价值。然而，传统脉冲涡旋激光器多依赖体积庞大的体块晶体、复杂的空间光路或较长的光纤结构，难以满足现代光子学对光源器件微型化、高度集成化及高稳定性的迫切需求^[15-20]。

波导结构作为构建紧凑型光子集成电路的核心平台^[21-22]，可有效限制光场传输，显著降低光束发散，延长光与物质的有效相互作用长度，进而实现低激光阈值、高斜效率的激光输出^[23-26]。此外，微米级波导的几何结构赋予器件极高的表面积/体积比，大幅提升了系统的散热能力，可有效抑制高功率泵浦条件下的热透镜效应^[27-28]。在各类波导制备技术中，飞秒激光直写 (femtosecond laser direct writing, FsLDW)技术凭借其优异的三维空间加工能力和广泛的材料适用性脱颖而出^[29-30]。其中，利用该技术制备的“包层波导”，光束主要在未受激光损伤的纤芯区域传输，可最大程度保留基质晶体原有的发光特性与晶格质量，在生成涡旋光等高质量结构光束方面具备独特优势^[31-32]。

在波导激光器脉冲运转的实现方案中，基于可饱和吸收体 (saturable absorber‌, SA)的被动调Q技术因设计简洁、结构紧凑等优势受到广泛关注^[33]。近年来，二维材料凭借其宽带吸收特性与超快响应速度^[34-35]，在SA领域引发了广泛研究热潮。拓扑绝缘体作为一类具有狄拉克锥形电子能带结构的新型量子材料，展现出优良的宽带非线性光学响应，而三硒化铋 (Bi₂Se₃)作为拓扑绝缘体的典型代表，已成功实现1 μm波段的脉冲激光输出，成为脉冲激光产生领域极具竞争力的SA材料^[36-37]。然而，目前关于将FsLDW技术定制的晶体波导与Bi₂Se₃薄膜相结合，探索微型化脉冲涡旋激光产生机制与输出特性的相关报道仍较为匮乏。

基于此，本文构建了一种以Bi₂Se₃薄膜为SA的Nd:YAG 波导脉冲涡旋激光器。利用FsLDW技术制备Nd:YAG 包层光波导，结合化学气相沉积 (chemical vapor deposition, CVD)法制备的Bi₂Se₃薄膜，在1 μm波段实现了高热稳定性的被动调Q涡旋光束输出。在850 mW吸收泵浦功率下，获得了最短脉宽39 ns、最高重复频率9.1 MHz、单脉冲能量4.42 nJ的稳定脉冲序列，且器件在高功率运转过程中，涡旋光斑未出现明显热畸变。

2　器件制备与特性表征

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2.1　包层波导的制备与表征

本研究选用掺杂浓度为1 at.% Nd³⁺的Nd:YAG晶体作为基质材料，其尺寸为20 mm (x)×10 mm (y)×2 mm (z)，所有光学表面均抛光至光学级标准，为波导制备及后续导光性能测试提供了良好的基础。采用FsLDW技术在该 Nd:YAG 晶体中制备横截面直径为15 μm的圆形包层波导，制备过程所用飞秒激光器 (Spitfire，Spectra Physics，Santa Clara)的输出参数如下：中心波长795 nm，输出重复频率1 kHz，单脉冲能量1 mJ，脉冲宽度 120 fs，输出脉冲为线偏振态。飞秒激光经50×物镜 (数值孔径NA=0.65)聚焦于Nd:YAG晶体表面以下，最大聚焦深度可达150 μm。实验中将晶体样品固定于由计算机控制的三维平移台上，通过精确调控平移台相对于飞秒激光束的移动速度，使其稳定保持在500 μm/s，在晶体不同深度处写入平行排列的低折射率轨迹，从而构成圆形包层波导结构。FsLDW技术制备包层光波导的示意如图1(a)所示。

图1(b)为所设计圆形包层波导的横截面结构示意图，其输入端面与输出端面的包层半径均为15 μm，确保了波导结构的对称性与一致性。图1(c, d)分别为波导输入端面与输出端面的光学显微横截面图，从图中可清晰观察到包层的圆形轮廓，几何形貌规整，边缘清晰，表明所制备的包层波导具有良好的结构均匀性。

图1(e)是光波导输出端面的体材料、波导中心区域和激光损伤区域的微拉曼光谱图，图中测量了781 cm⁻¹附近峰的拉曼强度。结果表明，与体材料和波导中心区域相比，激光损伤区域的拉曼峰值强度分别降低了约12%和8%，表明激光直写轨迹处的晶格结构受到破坏，产生缺陷，导致了该区域折射率的降低。图1(f, g)与图1(h, i)表明，该波导在TE和TM偏振态下均能较好地限制光场，且出射光斑呈现出良好的基模分布，证实了所制备的包层波导具有优异的模式限制能力。

2.2　Bi₂Se₃饱和吸收体的特性分析

本实验所用Bi₂Se₃薄膜样品由深圳六碳科技有限公司提供，采用化学气相沉积法沉积于蓝宝石衬底上，为后续可饱和吸收特性测试及激光实验奠定了良好基础。Bi₂Se₃薄膜的拉曼光谱测试结果如图2(a)所示，在532 nm激光激发条件下，可清晰观测到70 cm⁻¹、130 cm⁻¹和174 cm⁻¹处的三个特征峰，其峰位与先前相关报道一致^[38]，证实了所提供Bi₂Se₃薄膜的晶体结构完整性。此外，光谱中84 cm⁻¹与250 cm⁻¹处出现的特征峰，源于激光照射过程中薄膜表面发生的轻微氧化反应。

采用原子力显微镜 (atomic force microscope‌, AFM)对Bi₂Se₃薄膜的厚度进行精准表征，表征结果如图2(b)所示，经统计分析得出薄膜平均厚度约为16 nm。结合Bi₂Se₃单层厚度约为1 nm的已知特性，可推测该样品的纳米片层数约为16层，为其可饱和吸收性能的评估提供了关键结构参数。此外，利用紫外/可见/红外分光光度计 (Cary 5000 UV Vis-NIR，Agilent Technologies)对Bi₂Se₃薄膜的线性光学吸收特性进行测试，结果如图2(c)所示；在考虑蓝宝石衬底的菲涅耳反射损失后，计算得到该薄膜在1064 nm波长处的吸光度约为0.38。

为评估所制备的Bi₂Se₃薄膜在1 μm波段调Q激光产生中的应用潜力，搭建了Z扫描测试光路，装置示意如图2(d)所示。测试所用激发光源为1030 nm掺镱飞秒光纤激光器 (FemtoYL-10，YSL Photonics，China)，该激光器输出脉冲的重复频率为25 kHz，脉冲宽度为400 fs，焦点处束腰半径为40 μm，可视为高斯光束，通过调节光路中的衰减片可灵活改变激发脉冲能量。图2(e)展示了激发脉冲能量分别为20 nJ、40 nJ、50 nJ和58 nJ时的开孔Z扫描实验结果及相应的拟合曲线。可以看出，所有曲线在焦平面附近均呈现尖锐且高度对称的峰值，表明Bi₂Se₃薄膜具有优异的饱和吸收效应，具有作为可饱和吸收体应用于1 μm波段调Q激光产生的潜力。采用三能级非线性吸收模型对归一化透过率曲线进行拟合，其拟合如式(1)所示：

$ T=\left[1-\dfrac{\Delta R\times {I}_{\text{s}}}{{I}_{\text{s}}+\dfrac{{I}_{0}}{1+{ (Z/{{Z}_{0}})}^{2}}}\right]\cdot \dfrac{1}{(1-\Delta R)} \;,$

(1)

式中：T是归一化透射率，Z是样品的Z轴位置，Z₀是激发光束的瑞利长度，I₀是激发脉冲峰值强度，I_s是饱和强度，∆R是调制深度。拟合得出Bi₂Se₃薄膜的调制深度为8.6%，饱和强度为26.25 GW/cm²。实验过程中，测得SA损伤阈值为3.18 mJ/cm²，对应的功率密度为7.95 GW/cm²。58 nJ引起的饱和吸收十分接近调制深度，此时对应的峰值功率密度为5.77 GW/cm²，仍小于损伤阈值对应的功率密度 (7.95 GW/cm²)。对于Bi₂Se₃薄膜而言，增加材料厚度可增大调制深度并降低饱和强度，从而更有利于调Q脉冲的产生。但与此同时，厚度的增加也会使体态占据主导，导致由光散射和晶体缺陷引发的非饱和损耗增加。综合权衡，本文所采用的厚度为16 nm的Bi₂Se₃薄膜兼具较大的调制深度，较低的饱和强度与较小的非饱和损耗，是实现1 μm波段调Q激光输出的理想SA。

3　实验装置

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图3(a)展示了基于Bi₂Se₃可饱和吸收体的Nd:YAG脉冲涡旋激光的光路示意图。实验所用泵浦源为可调谐钛蓝宝石激光器，其输出光为线偏振态，中心波长精确调谐至808 nm，以匹配Nd:YAG晶体中Nd³⁺的吸收峰，提高泵浦效率。泵浦光经焦距为30 mm的球面平凸透镜CL1聚焦后，耦合进圆形包层波导。Nd:YAG圆形包层波导固定于五维调整架上，通过灵活调节波导空间位置，优化波导耦合效率。

平面镜IM作为谐振腔输入镜，在808 nm泵浦光波段的透过率为99.9%，可保证泵浦光高效入射；在1064 nm激光振荡波段的反射率大于99.9%，可减少腔内激光损耗，实现激光的高效振荡。螺旋相位板 (Spiral phase plate‌, SPP)的拓扑荷数设为1，透过率为99%，同时作为谐振腔输出镜和相位调控元件，直接对腔内激光进行相位调控，实现涡旋光输出。涡旋激光的模式分布与输出功率分别采用相机式电荷耦合器件 (charge-coupled device, CCD)光束质量分析仪和功率计 (Thorlabs，S145C)进行精准测量。未插入Bi₂Se₃薄膜时，激光器处于CW运转状态；Bi₂Se₃薄膜插入谐振腔后，实现脉冲激光输出。调Q脉冲序列通过低噪声InGaAs光电探测器 (Thorlabs，PDA10D2)进行探测，并且使用实时数字示波器 (Tektronix，MSO71604DX)记录脉冲波形及相关参数。

值得注意的是，得益于实验所用波导的较高增益，谐振腔仅需1%的输出反射率即可实现激光起振，因此可直接将螺旋相位板复用为输出镜。相比于采用独立的螺旋相位板，该一体化设计有效缩短了腔外光程，降低了插入损耗，进而提升了激光器的输出效率。这一低损耗、高集成度的方案，为构建紧凑型涡旋波导激光器提供了有利条件。

4　实验结果与讨论

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图3(b)与图3(c)分别展示了波导脉冲涡旋激光器在CW模式与被动调Q脉冲模式下，输出功率随吸收泵浦功率的变化规律。输出激光的中心波长均稳定在1064 nm，该波长对应于Nd³⁺从⁴F_3/2能级到⁴I_11/2能级的主要荧光跃迁。

在连续波模式运行时，当采用TE偏振光泵浦时，涡旋波导激光器的吸收阈值功率为169.7 mW，随着吸收泵浦功率的增加，输出功率逐渐提升，最大输出功率达到92.8 mW，对应的斜效率为13.75%；当采用TM偏振光泵浦时，器件的吸收阈值功率降至143.9 mW，最大输出功率提升至114.8 mW，斜效率达到15.39%，表明TM偏振泵浦条件下波导激光器性能更优。产生上述性能差异的主要原因在于所制备圆形包层波导的损伤轨迹截面并非理想圆形，而是长轴平行于TM偏振方向的椭圆形。这种椭圆形轨迹在构成波导包层时，于TM方向上排列更为致密，形成了更厚的低折射率包层，从而有效增强了光场限制作用并提升了传输效率；相反，在TE方向上则排列相对稀疏，低折射率包层更薄，导致轻微的模式漏光与能量损耗，进而制约了该偏振态下的器件整体输出性能。将Bi₂Se₃薄膜插入谐振腔后，实现被动调Q脉冲激光输出。在TE偏振光泵浦下，激光吸收阈值功率为138.6 mW，斜效率为5.24%，最大输出功率为35.1 mW；在TM偏振光泵浦下，吸收阈值功率为107.4 mW，斜效率为5.59%，最大输出功率为42.3 mW。

波导涡旋激光器在低泵浦功率下工作时，TE模和TM模的近场模式分布如图3(d, e) 所示。随着泵浦功率提高，TE模和TM模的输出光斑始终保持典型的环形中空分布，与涡旋光束的特征光斑形态一致，如图3(f, g) 所示。对比低功率与高功率条件下的光斑形态可见，光斑轮廓未因泵浦功率的提升而发生明显畸变或扩散，表明包层波导结构降低了高功率泵浦下的热透镜效应，具备优异的热稳定性。

图4展示了在不同泵浦功率下的调Q脉冲序列和单脉冲包络。可以看出，脉冲序列整齐且稳定，验证了Bi₂Se₃薄膜可饱和吸收体优异的光学性能与热稳定性。图5(a)与图5(b)分别展示了调Q涡旋激光器的脉冲宽度和重复频率随吸收泵浦功率的变化情况。随着吸收泵浦功率的增加，脉冲宽度从56 ns减小到39 ns，而重复频率则从6.3 MHz增加到9.1 MHz。进一步计算得出了调Q涡旋激光器单脉冲能量与吸收泵浦功率的关系，如图5(c)所示。结果表明，单脉冲能量随泵浦功率逐渐增加，在850 mW的吸收泵浦功率下，记录到的最高脉冲能量为4.42 nJ。值得注意的是，计算表明腔内最高单脉冲能量密度为1.3 mJ/cm²，未超过Bi₂Se₃的损伤阈值 (3.18 mJ/cm²)。导致该器件具备高重频特性的物理机制可归结为两点：一是波导结构相较于体块晶体能更有效地紧密束缚光场，结合晶体自身的高增益，使得在低泵浦功率下即可实现极高的腔内功率密度；二是Bi₂Se₃可饱和吸收体的调制深度较低，仅8.6%，易于实现快速饱和与恢复。上述低阈值的高功率密度与低调制深度的耦合效应，共同驱动了MHz量级高重频脉冲的激发。此类密集型脉冲序列在高速光通信、光时钟生成及光信号处理等领域具有不可替代的优势。结合波导结构的紧凑性与二维材料的易集成特性，该器件在未来微型化、低功耗光子集成回路中展现出巨大的应用前景。

为进一步定量表征所产生的涡旋光束，分别采用柱透镜聚焦法与正三角形光阑衍射法对其进行测量，并利用CCD相机记录相应的光强分布。理论上，拓扑荷数为|N|的涡旋光束经柱透镜聚焦后，会在焦平面处演化为|N|+1条亮纹；当N=+1时，亮纹沿反对角线方向排列，当N=−1时则沿对角线方向排列。实验中，涡旋光束在通过长通滤波片后，被焦距为3 cm的柱透镜聚焦，CCD记录的焦点处光强分布如图6(a)所示。图中清晰可见两条沿反对角线方向排列的亮纹，表明输出涡旋光束的拓扑荷数为+1。此外，涡旋光束穿过三角形光阑后会形成特殊的夫琅禾费衍射图样，其三角形轮廓的每条边上将呈现|N|+1个光斑。在CCD前方放置一个高为0.8 mm的正三角形光阑，所得衍射光强分布如图6(b)所示。该图样特征与理论高度吻合，进一步证实了该涡旋光束的拓扑荷数确为+1。

5　结　论

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本文使用飞秒激光直写技术在Nd:YAG晶体中制备了半径为 15 µm的包层波导，并利用CVD制备的Bi₂Se₃薄膜作为可饱和吸收体，实现了稳定的被动调Q涡旋激光输出。结合开孔Z扫描Bi₂Se₃薄膜的三阶非线性光学效应进行表征，其调制深度为8.6%，饱和强度为26.25 GW/cm²。实验结果表明，当吸收泵浦功率为850 mW时，脉冲激光的脉宽为39 ns，重复频率为9.1 MHz，单脉冲能量为4.42 nJ。该研究验证了Bi₂Se₃优异的三阶非线性光学效应和包层波导的导波特性，为实现结构紧凑、热稳定性优异的Nd:YAG波导脉冲涡旋激光器提供了实验依据。

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2026年第53卷第7期

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doi: 10.12086/oee.2026.260082

接收时间：2026-04-01
首发时间：2026-10-22
出版时间：2026-07-25

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收稿日期：2026-04-01
修回日期：2026-06-18
录用日期：2026-06-22

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山东大学物理学院，山东济南 250100

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孙晓莉，xlsun@sdu.edu.cn

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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