Open Access
Add to BibSonomy
Abstract
In this work, we propose a practical solution to visible vortex laser emission at 532 nm based on second harmonic generation (SHG) in a well-designed waveguide-grating structure. Such an integrated structure is fabricated by femtosecond laser direct writing (FsLDW) in an LBO crystal. Confocal micro-Raman spectroscopy is employed for detailed analysis of FsLDW-induced localized crystalline damage. By optical excitation at 1064 nm, the guiding properties, SHG performance, as well as vortex laser generation of the waveguide-grating hybrid structure are systematically studied. Our results indicate that FsLDW waveguide-grating emitter is a reliable design holding great promise for nonlinear vortex beam generation in integrated optics.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photon carries spin angular momentum (SAM) and orbital angular momentum (OAM), which are associated with the polarization and the spiral phase wavefronts, respectively [1,2]. Vortex beam, which contains the spiral phase factor exp(ilθ) in its complex amplitude expression, is a typical OAM beam possessing a spiral wavefront, where l denotes the topological charge (TC), θ denotes the azimuthal angle, and lħ denotes the orbital angular momentum of each photon, respectively [3,4]. In 1992, Allen et al. demonstrated that the vortex beam with an annularly distributed light field contains a phase singularity and zero intensity at its center [5]. Theoretically, the OAM carried by the optical vortex has an infinite number of eigenstates, thus significantly extending the dimensionality of information storage and transmission compared to Gaussian beams. Such a unique feature makes optical vortex beams very promising for research in optical communication, quantum information, manipulation of tiny particles, and optical imaging [6–10]. Several approaches and designs, including mode converter, spiral phase plates (SPPs) [11], q⁃plate [12], computational holography [13,14], and metasurfaces [15,16], have been well established for vortex beam generation. In particular, the fork grating which serves as a method that enables the generation of vortex beam array [17]. As compared to a single beam, the vortex beam array broadens the volume in the field of optical communication. Generally, the devices intended for the vortex beam generation tend to be oversized, rendering them inconvenient for applications in integrated optics [18,19]. As a comparison, the fork grating with a simple structure can apply to the generation of the vortex beam in different wavelengths by adjusting its period, and the overall size of the grating could be reduced to micrometer scale, which facilitates the photonic integration with other micro-optical components in the integrated optics [20–23].
Femtosecond laser direct writing (FsLDW), as a micro-/nano-fabrication technology, allows the direct definition of on-demand nanostructures with 3D geometric features and tailored photonic functionalities in transparent materials [24–28]. In particular, FsLDW-defined fiber-like depressed cladding waveguides have aroused great interests as a compact cavity for low-threshold lasing and high-efficiency nonlinear optical frequency conversion [29–33]. In addition, the morphology of circular cladding waveguides in principle enables fine connection with the commercial fibers to construct “fiber-waveguide-fiber” integrated photonic systems. [34–37]. Previously, a number of excellent approaches to generating vortex lasers have been reported. Miao et al. propose an InP-InGaAsP based semiconductor microlaser and implement a single-mode vortex laser [38]. Chen et al. realize the generation and manipulation of the vortex laser by devising a metasurface fork grating [39]. A double-ring fiber can also be employed for the generation of vortex laser, and Huang et al. utilize this method to generate OAM beams [40]. Hayenga et al. combine an active microring resonator with an S-shaped waveguide to fabricate the first tunable OAM microring cavity laser [41]. While all of these methods are efficient for generating vortex lasers, several of them are high-cost to manufacture and have cumbersome fabrication processes. Some of the schemes are more appropriate for implementation in semiconductors, and are challenging to apply in crystals and not user-friendly for integration. However, FsLDW presents an alternative option for the fabrication of the integrated optical devices in crystals [42–45]. Based on cladding waveguides in laser crystals, Zhuang et al. developed a waveguide-grating emitter that is compact and efficient to generate the vortex laser arrays at 1064 nm [46]. Nevertheless, in the available relevant reports, the waveguide-grating emitters operate almost exclusively in the infrared wavelength, experimental demonstrations in the visible wavelength remain missing. Vortex laser in the visible wavelength gains considerable attention and enjoys a wide range of applications in laser printing, quantum technology [47,48], high-resolution laser imaging [49,50], and underwater laser communication [51,52]. Consequently, waveguide-grating emitters that can generate visible vortex lasers are highly required.
Lithium triborate (LBO) crystal is a type of nonlinear optical crystal with outstanding frequency-conversion performance in the visible and even ultraviolet bands [53,54]. With a broad transmission band, a high laser damage threshold, and moderate nonlinear optical coefficients, the LBO crystal can be combined with the FsLDW to fabricate a variety of nonlinear optical devices such as harmonic generators, optical parametric oscillators, and amplifiers [55,56]. Thus, LBO is an ideal platform for fabrication of a waveguide-grating emitter and a visible vortex laser source. The distinct advantage of the emitter lies in its micrometer-scale dimensions, enhancing convenience and adaptability for applications of visible vortex lasers across diverse scenarios [57–61].
In this work, a waveguide-grating emitter for generating the second harmonic (SH) of the visible vortex laser array at 532 nm is fabricated in LBO by FsLDW. The waveguide section is a hybrid structure consisting of a straight cylinder cladding waveguide coupled with a cone-frustum cladding waveguide. The vortex laser performance of the hybrid waveguide is investigated by exploring the relationship between the generated SH signals along different polarizations and the launched power. Afterward, the SH vortex laser array is recorded, which is in good agreement with the simulation results. Eventually, the SH efficiency of the vortex array in each diffraction order is calculated and compared. Our work demonstrates that the waveguide-grating emitter is a feasible generation device for the SH vortex laser array that can be implemented in integrated optics.
2. Experiment details
Figure. 1 illustrates the schematic diagram of the waveguide-grating emitter in LBO crystal (with the cutting directions of θ = 90° relative to the z-axis, φ = 11.4° relative to the y-axis for the o1064 + e1064→e532 process). The dimensions of the crystals employed in this work are 7(X) × 10(Y) × 2(Z) mm3 (X, Y, Z denote the directions marked in Fig. 1, not the crystal axis) with three faces optically polished. A linearly polarized femtosecond laser (with a central wavelength of 800 nm, a pulse width of 110 fs, and a repetition rate of 1 kHz) emitted by an amplified Ti: Sapphire femtosecond laser system (Astrella, Coherent Inc., USA) is applied to the preparation of the depressed cladding waveguide and the fork grating. Figure 1(a) displays the microscopic image of the fork grating fabricated at the output end-face of the waveguide. The fork grating is produced by focused femtosecond laser (with a pulse energy of 35.4 nJ) through a microscope objective lens (50×, N.A. = 0.55) onto the end face of the LBO crystal. While fabrication, the position of the sample is controlled by a 6-axis motorized stage, the scanning speed is set to 0.02 mm/s, and the length (the dimension vertical to the X-Z surface) of each point in the grating is designed to be 2 µm as controlled by a laser shutter. As can be obviously seen in Fig. 1(a), the center of the fork grating is arranged at the waveguide output-facet center, so that the SH signal generated from the waveguide can be completely diffracted through the fork grating. Simultaneously, the grating adopts a two-dimensional structure (lX = + 1, lZ = 0) with a period of 3.9 µm in both directions in order to provide a feasible solution for the multi-channel SH signal emission.
Fig. 1. Schematic diagram of the femtosecond laser directly writing the waveguide-grating emitter. (a) The microscopic image of the fork grating at the waveguide output end-face. The scale bar is 10 µm. (b) The top view of the waveguide output end-face and the fork grating. (c) The cross-section view of the waveguide input end-face.
The fork grating is designed as a two-dimensional grating containing a fork grating along the X-direction and a splitting grating along the Z-direction. The optical field distribution of generated single-mode waveguide SH modulated by the fork grating can be expressed as:
The waveguide section within the waveguide-grating emitter is comprised of two distinct sections: a straight cylinder and a cone-frustum waveguide. The former has a diameter of 20 µm and is placed at the waveguide input end-face, as depicted in Fig. 1(c). The aperture angle of the waveguide with the diameter of 20 µm is measured. Also after the following equation the refractive index change of the waveguide can be calculated:
where Θm is the aperture angle, Δn ≈ 3 × 10−3 is the refractive index change between the waveguide region and the track region. During the fabrication process, the pulse energy applied to both parts is fixed at 122.5 nJ with a scanning speed of 0.5 mm/s. The mode of the laser at the output end-face of the waveguide is heavily dependent on the mode at the input section [63]. Thus, employing a narrower diameter effectively confines the laser to a quasi-single mode, concurrently restricting the SH signal emitting from the straight cylinder cladding waveguide. The length of the cone-frustum cladding waveguide is set to 1.8 mm, a critical parameter for expanding the diameter of the single-mode SH signal. Meanwhile, a deliberate unprocessed area with a distance of 70 µm separates the cladding waveguide and fork grating, which is depicted in Fig. 1(b), is designed to enhance the performance of the SH vortex laser by optimizing the mode-matching between the waveguide SHG and fabricated fork grating. From Fig. 1(a), as can be obviously observed, the diameter of the waveguide is slightly smaller than the size of the fork grating. When the laser propagates 70 µm after being emitted from the waveguide, the size of the laser spot can be calculated to expand to 55 µm. This alignment proves advantageous for diffraction, optimizing the interaction between the laser beam and the grating structure.3. Results and discussions
Measurement of Raman spectra by a confocal micro-Raman spectroscopy system can reveal the modification of the LBO crystal induced by FsLDW, which guides us to gain the localized material modification mechanism. Figure. 2(a) illustrates the Raman spectra of two different regions around the fork grating area (i.e., the bulk and the track). Apparently, the peaks of Raman shift at 330, 414, 461, 542, 596, 638, and 754 cm−1 can be identified. According to previous reports, the basic structural unit of the LBO crystal is the triborate group (B3Ø7, Ø = bridge oxygen), a six-membered ring containing two BØ3 planar triangles and one BØ4 tetrahedron [64]. The strongest peak located at 754 cm−1 is attributed to the symmetric breathing vibration of the B3Ø7 ring. The peak of Raman shift at 596 cm−1 is associated with the bending vibration of the intra-ring B-O bonds and the peak at 542 cm−1 is ascribed to the stretching vibration of the BØ4 tetrahedron of the ring. Furthermore, the intensity variation of the three peaks, as prominently depicted in Fig. 2(a), offers a clear and representative illustration. Notably, the intensity in the bulk region significantly exceeds that in the track region, underscoring the extent of lattice damage inflicted by the femtosecond laser during the fabrication of the fork grating in LBO crystal. Additionally, when examining the intensity of peaks in the two regions situated at 542 cm−1, a conspicuous red-shift in the peak of the track region relative to the bulk region becomes evident. Especially for the characteristic peak of the B3Ø7 group, this suggests that the certain extrusion and compression of the lattice in LBO crystal must be carried out by stretching the B-O bonds along with the laser processing. The microscopic mechanism of localized material modification by FsLDW can likewise be concluded in Figs. 2(c) and 2(d). Raman spectra imaging involves an image drawn on a two-dimensional plane with the intensity of the individual Raman peaks in the Raman spectrum. Raman peaks at different positions indicate different phonon modes, which in turn reflect the bonds in the crystal. Moreover, the changes of the Raman signal frequency shift can respond to the expansion and compression of the crystalline lattice in a straightforward way. Raman spectra imaging can visualize the variations of Raman signals in a definite region, and the images of the Raman peaks at different positions are more capable to provide an explicit response to the effect of the laser on different bonds. These figures comprehensively map the Raman signal intensity and frequency shift throughout the grating region, focusing on the central wavenumber at 754 cm−1. The frequency shift signals at 330 cm−1 and 414 cm−1 are relatively weak and it is impractical to draw two-dimensional figures, which verifies that the localized material modification is primarily caused by laser-induced damage in the B-O band.
Fig. 2. (a) The Raman spectra of the fork grating measured by the confocal-Raman microscope. Purple and yellow lines are the spectrum collected from the bulk region and the track, respectively. (b) The Raman spectra of the depressed cladding waveguide. Yellow, red, and blue lines are the spectrum collected from the waveguide region, the bulk region, and the track, respectively. (c), (d) Raman mapping images of the fork grating with channels of the intensity and frequency shift of the peak at 754 cm−1. (e) Raman mapping image of the waveguide with channel of the intensity of the peak at 754 cm−1.
The discernable variation of the Raman signals of the three different regions (i.e., the bulk, the waveguide, and the track) of the depressed cladding waveguide displayed in Fig. 2(b) is distinguished from that of the fork grating in Fig. 2(a). The Raman signal evolution at the track, illustrated in Figs. 2(b) and (e), manifests solely as intensity variation, devoid of any frequency shift. This observation suggests a comparatively weaker modification in the track at the waveguide region when juxtaposed with the track at the fork grating area, a design choice inherent in this hybrid structure. The heightened modification of the track at the grating area is purposefully designed to amplify the diffraction efficiency, enabling effective diffraction of the inherently weak second harmonic (SH) signal. Conversely, the waveguide, composed of the fusion of two distinct waveguides, is susceptible to the development of cracks in the connecting region between these two segments, potentially impacting the overall guiding performance.
In order to investigate the guiding performance of the waveguide, a Q-switched solid-state Nd:YAG laser (with a central wavelength of 1064 nm, a pulse duration of 5.2 ns, and a repetition rate of 3.62 kHz) is employed for the SH signal excitation. Figure 3 displays the characteristics associated with the SH signal without passing through the fork grating after emission from the waveguide. To begin with, a typical spectrum documenting the properties of the fundamental (at 1064 nm) and SH (at 532 nm) wave is readily visible in Fig. 3(d). Where the blue line represents the spectrum of the fundamental wave at 1064 nm and the red line stands for the spectrum of the SH wave at 532 nm. The central wavelength of the SH wave at 532 nm has a full width at half maximum (FWHM) about 2 nm. When the input fundamental wave power is fixed at 284 mW, all-angle polarization dependent of SH power emitting from the waveguide is captured in Fig. 3(c). The output power at TM polarization is considerably higher than that at TE polarization. This immediate consequence suggests that the fundamental wave at TM polarization can excite a higher-power SH wave. The distinctive polarization of the output power at 532 nm can be attributed to various factors, primarily stemming from two aspects. Partly, the crystal itself has a certain selectivity for the transmission of the fundamental (at 1064 nm) and SH (at 532 nm) wave under different polarizations. Additionally, the waveguide, in part, modulates the propagation of the laser within, thereby exerting a definite influence on the polarization characteristics.
Fig. 3. The properties of the waveguide generating the SH wave at 532 nm. (a), (b) Output power of the SH wave (at 532 nm) as a function of the fundamental wave (at 1064 nm) power at TM and TE polarization, respectively. The insets are the modal profiles of output laser under TM and TE polarizations. The scale bar is 50 µm. (c) The output power of the SH wave (at 532 nm) from the waveguide for all-angle polarization. (d) The spectra of the fundamental wave at 1064 nm (blue line) and the SH wave at 532 nm (red line).
The output power and corresponding conversion efficiency of the SH wave at 532 nm emitted from the waveguide under TM and TE polarizations are presented in Figs. 3(a) and 3(b), respectively. Notably, it is evident that the output power of the SH wave (at 532 nm) at TM and TE polarizations is functionally related to the launched power. Concurrently, the SH efficiency peaks at 4.79% when the output power at TM polarization reaches 13.6 mW, and 2.44% when the output power at TE polarization reaches 6.93 mW.
With the purpose of identifying the diffraction capability of the fork grating for the SH wave at 532 nm, the output diffraction far-field distribution of the waveguide-grating is calculated by the finite-difference time-domain (FDTD) algorithm and displayed in Fig. 4(b). The results unmistakably showcase the SH wave diffracted by the grating, forming a distinctive 3 × 3 vortex array in the far field. Furthermore, in the direction vertical to the “fork shape” of the grating, an annular intensity distribution is generated with zero intensity in the center as the distinctive characteristic of the vortex beam. The simulation results of the diffraction field provide compelling evidence supporting the rationality of the designed structural parameters for the fork grating.
Fig. 4. (a) Schematic diagram of the experimental setup for generating and measuring the vortex SH wave. L: a cylindrical lens for measuring the TC; CCD: camera. (b) FDTD results for the far field of the output diffraction. (c)-(j) The intensity profiles of far-field output SH wave at 532 nm and the focus point obtained by the cylindrical lens in the (−1, + 1), (0, + 1), (+1, + 1), (-1, 0), (+1, 0), (−1, −1), (0, −1) and (+1, −1) diffraction orders.
As illustrated in Fig. 4(a), an experiment is designed to test the effectiveness of the waveguide-grating emitter in the generation of the SH vortex laser array at 532 nm. A microscope objective lens (10×, N.A. = 0.25) is employed to focus the fundamental wave (at 1064 nm) into the waveguide. A cylindrical lens (f = 50 mm) is applied to measure the topological charge (TC) of the SH vortex laser array, while the diffraction patterns are captured by a CCD collected in Figs. 4(c) to 4(i). Figures 4(c) to 4(i) encompass both the 2D and 3D views of the SH vortex laser array in the (-1, + 1), (0, + 1), (+1, + 1), (-1, 0), (+1, 0), (-1, -1), (0, -1), and (+1, -1) diffraction orders, with an annular-shaped intensity profile and the central intensity of zero, which aligns with typical features of vortex beams. The intensity distributions of the (0, + 1) and (0, -1) diffraction orders are just Gaussian modes owing to the fact that the fork grating (lX = + 1, lZ = 0) is designed to get the TC = 0-order in the Z-direction. The vortex beam features a spiral phase distribution in the transverse field, a property that results in the wave vector deviating from the direction of the propagation and a wave vector component that is orientated around the optical axis. When the vortex beam is focused by a cylindrical lens, the laser spot within the beam’s cross-section is divided into two symmetric parts with respect to the center of the optical field. This occurs due to the rotational wavevector component. The topological charge N of the vortex beam corresponding to the N + 1 of the asymmetric line focused by a cylindrical lens is indicated in the inset of Figs. 4(c) to 4(i). The intensity distributions of the vortex array in the Figs. 4(c) to 4(i) are essentially matched with the simulation results in Fig. 4(b), which confirms the feasibility of the waveguide-grating emitter in the generation of the SH vortex laser array.
Subsequent to the acquisition of intensity profiles for the vortex laser array in different diffraction orders, Fig. 5 systematically delineates the second harmonic (SH) signals and SH efficiencies at TM polarization. This representation illustrates the variation of the SH signals and the SH efficiencies in each diffraction order as a function of the launched power. The maximum SH signal and SH efficiency of 0.32 mW and 0.113%, respectively, in the (-1, + 1) diffraction order, as illustrated in Fig. 5(a). For a more visually intuitive presentation of the capability of the waveguide-grating emitter in generating the SH vortex laser array, Table 1 succinctly summarizes the diffraction efficiencies and the maximum SH efficiencies in each diffraction order. A closer inspection of Table 1 reveals that the difference in diffraction efficiency among various diffraction orders is relatively modest. The maximum diffraction efficiency in the (-1, + 1) diffraction order stands at 2.35%, while the minimum diffraction efficiency in the (+1, -1) diffraction order is 0.84%. The experimental results of the two diffraction orders (-1,0) and (+1,0) have relatively weak powers compared to those in the simulation, which is principally attributed to the following two reasons. On the one hand, the perfect Gaussian laser in the fundamental mode is adopted in the simulation, while in the actual experiment, the Gaussian laser inputted into the waveguide is not perfect, and at the same time, the waveguide has a certain modulation on the laser. On the other hand, there is the spatial walk-off effect in the LBO crystal itself, which would enhance the scattering in some of the diffraction order in the vortex laser array. Given that the quality of the vortex laser is crucial for evaluating the experimental results, compensatory measures are inevitably introduced during the actual experimental operation to address the deviations caused by these factors.
Fig. 5. The SH signal (the pink line) and the SH efficiency (the blue line) as the function of the launched power of the SH vortex laser array at 532 nm. The diffraction orders corresponding to (a) to (h) are (-1, + 1), (0, + 1), (+1, + 1), (-1, 0), (+1, 0), (-1, -1), (0, -1), and (+1, -1).
Table 1. Maximum SH efficiency and diffraction efficiency of the vortex SH wave
4. Conclusion
In brief, a waveguide-grating emitter is successfully fabricated by femtosecond laser direct writing (FsLDW) in LBO crystal. The microscopic mechanisms underlying femtosecond laser modification are explored through Raman spectra analysis. Our study not only characterizes the guiding performance of the waveguide for second harmonic (SH) wave generation at 532 nm under different polarizations but also demonstrates the emission of the SH vortex laser array at 532 nm via the hybrid structure. The results in our work strongly suggest the significant potential applications of the waveguide-grating emitter in the generation of the SH vortex laser array.
Funding
National Natural Science Foundation of China (12074223, 12274236); Natural Science Foundation of Shandong Province (2022HWYQ-047, ZR2021ZD02); Taishan Scholar Foundation of Shandong Province (tspd20210303, tsqn201909041); Shandong University.
Acknowledgments
Y. Jia thanks the financial support of “Qilu Young Scholar Program” of Shandong University, China.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Wang, J.-Y. Yang, I. M. Fazal, et al., “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
2. M. J. Padgett, “Orbital angular momentum 25 years on [Invited],” Opt. Express 25(10), 11265–11274 (2017). [CrossRef]
3. A. E. Willner, K. Pang, H. Song, et al., “Orbital angular momentum of light for communications,” Appl. Phys. Rev. 8(4), 041312 (2021). [CrossRef]
4. J. Wang, J. Liu, S. Li, et al., “Orbital angular momentum and beyond in free-space optical communications,” Nanophotonics 11(4), 645–680 (2022). [CrossRef]
5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, et al., “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
6. Y. Chen, K.-Y. Xia, W.-G. Shen, et al., “Vector Vortex Beam Emitter Embedded in a Photonic Chip,” Phys. Rev. Lett. 124(15), 153601 (2020). [CrossRef]
7. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016). [CrossRef]
8. Z. Liu, S. Yan, H. Liu, et al., “Superhigh-Resolution Recognition of Optical Vortex Modes Assisted by a Deep-Learning Method,” Phys. Rev. Lett. 123(18), 183902 (2019). [CrossRef]
9. B. Gao, J. Wen, G. Zhu, et al., “Precise measurement of trapping and manipulation properties of focused fractional vortex beams,” Nanoscale 14(8), 3123–3130 (2022). [CrossRef]
10. M. Zhao, X. Liang, J. Li, et al., “Optical Phase Contrast Microscopy with Incoherent Vortex Phase,” Laser Photonics Rev. 16(11), 2200230 (2022). [CrossRef]
11. D. Gauthier, P. R. Ribič, G. Adhikary, et al., “Tunable orbital angular momentum in high-harmonic generation,” Nat. Commun. 8(1), 14971 (2017). [CrossRef]
12. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef]
13. M. Guillon, B. C. Forget, A. J. Foust, et al., “Vortex-free phase profiles for uniform patterning with computer-generated holography,” Opt. Express 25(11), 12640–12652 (2017). [CrossRef]
14. Y. Tian, L. Zhu, and M. Sun, “Enhancing computational holography with spiral phase coding,” Opt. Lett. 48(24), 6585–6588 (2023). [CrossRef]
15. F. Mei, G. Qu, X. Sha, et al., “Cascaded metasurfaces for high-purity vortex generation,” Nat. Commun. 14(1), 6410 (2023). [CrossRef]
16. V. C. Su, S. Y. Huang, M. H. Chen, et al., “Optical Metasurfaces for Tunable Vortex Beams,” Adv. Opt. Mater. 11(24), 2370101 (2023). [CrossRef]
17. S. Gao, Z. Chen, Y. Xiong, et al., “Nd: YSAG waveguide-grating vortex laser: design and implementation,” Opt. Express 31(19), 31634–31643 (2023). [CrossRef]
18. L. Xu, C. Wang, X. Qi, et al., “Femtosecond laser direct writing continuous phase vortex gratings with proportionally distributed diffraction energy,” Appl. Phys. Lett. 119(13), 131101 (2021). [CrossRef]
19. T. Wang, X. Xu, L. Yang, et al., “Fabrication of lithium niobate fork grating by laser-writing-induced selective chemical etching,” Nanophotonics 11(4), 829–834 (2022). [CrossRef]
20. J. Liu, H. Zhang, S. Ai, et al., “Femtosecond-laser micromachining fork gratings in LN crystal with different mechanisms,” Microwave and Optical Technology Letters 66(1), e33945 (2024). [CrossRef]
21. H. Wang, D. Wei, X. Xu, et al., “Controllable generation of second-harmonic vortex beams through nonlinear supercell grating,” Appl. Phys. Lett. 113(22), 221101 (2018). [CrossRef]
22. D. Wei, C. Wang, X. Xu, et al., “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10(1), 4193 (2019). [CrossRef]
23. Y. Yang, H. Li, H. Liu, et al., “Highly efficient nonlinear vortex beam generation by using a compact nonlinear fork grating,” Opt. Lett. 48(24), 6376–6379 (2023). [CrossRef]
24. X.-J. Wang, H.-H. Fang, Z.-Z. Li, et al., “Laser manufacturing of spatial resolution approaching quantum limit,” Light: Sci. Appl. 13(1), 6 (2024). [CrossRef]
25. Y. Lei, G. Shayeganrad, H. Wang, et al., “Efficient ultrafast laser writing with elliptical polarization,” Light: Sci. Appl. 12(1), 74 (2023). [CrossRef]
26. P. Wu, X. Jiang, B. Zhang, et al., “Mode-controllable waveguide fabricated by laser-induced phase transition in KTN,” Opt. Express 28(17), 25633–25641 (2020). [CrossRef]
27. Q. Chen, X. Huang, D. Yang, et al., “Three-Dimensional Laser Writing Aligned Perovskite Quantum Dots in Glass for Polarization-Sensitive Anti-Counterfeiting,” Adv. Opt. Mater. 11(10), 2300090 (2023). [CrossRef]
28. Y. Jia and F. Chen, “Recent progress on femtosecond laser micro-/nano-fabrication of functional photonic structures in dielectric crystals: A brief review and perspective,” APL Photonics 8(9), 090901 (2023). [CrossRef]
29. Y. Jia, S. Wang, and F. Chen, “Femtosecond laser direct writing of flexibly configured waveguide geometries in optical crystals: fabrication and application,” Opto-Electron. Adv. 3(10), 190042 (2020). [CrossRef]
30. Y. Xiong, S. Wang, Z. Chen, et al., “Femtosecond laser direct writing of compact Tm: YLF waveguide lasers,” Opt. Laser Technol. 167, 109786 (2023). [CrossRef]
31. Z.-S. Hou, J.-J. Cao, F. Yu, et al., “UV–NIR femtosecond laser hybrid lithography for efficient printing of complex on-chip waveguides,” Opt. Lett. 45(7), 1862–1865 (2020). [CrossRef]
32. J. Li, J. Yan, L. Jiang, et al., “Chiral Lithography with Vortex Non-diffracted Laser for Orbital Angular Momentum Detection,” Laser Photonics Rev. 1, 2301050 (2024). [CrossRef]
33. J. Li, J. Yan, L. Jiang, et al., “Nanoscale multi-beam lithography of photonic crystals with ultrafast laser,” Light: Sci. Appl. 12(1), 164 (2023). [CrossRef]
34. Z.-Z. Li, X.-Y. Li, F. Yu, et al., “Circular cross section waveguides processed by multi-foci-shaped femtosecond pulses,” Opt. Lett. 46(3), 520–523 (2021). [CrossRef]
35. F. Ye, Y. Yu, X. Xi, et al., “Second-Harmonic Generation in Etchless Lithium Niobate Nanophotonic Waveguides with Bound States in the Continuum,” Laser Photonics Rev. 16(3), 2100429 (2022). [CrossRef]
36. L. Wang, X. Zhang, and F. Chen, “Efficient Second Harmonic Generation in a Reverse-Polarization Dual-Layer Crystalline Thin Film Nanophotonic Waveguide,” Laser Photonics Rev. 15(12), 2100409 (2021). [CrossRef]
37. G. Li, W. Du, S. Sun, et al., “2D layered MSe2 (M = Hf, Ti and Zr) for compact lasers: nonlinear optical properties and GHz lasing,” Nanophotonics 11(14), 3383–3394 (2022). [CrossRef]
38. P. Miao, Z. Zhang, L Sun, et al., “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016). [CrossRef]
39. S. Chen, Y. Cai, G. Li, et al., “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016). [CrossRef]
40. W. Huang, Y. Xiong, H. Qin, et al., “Orbital angular momentum generation in a dual-ring fiber based on the phase-shifted coupling mechanism and the interference of supermodes,” Opt. Express 28(11), 16996–17009 (2020). [CrossRef]
41. W. E. Hayenga, M. Parto, J. Ren, et al., “Direct Generation of Tunable Orbital Angular Momentum Beams in Microring Lasers with Broadband Exceptional Points,” ACS Photonics 6(8), 1895–1901 (2019). [CrossRef]
42. Z. Wang, B. Zhang, Z. Wang, et al., “3D Imprinting of Voxel-Level Structural Colors in Lithium Niobate Crystal,” Adv. Mater. 35(47), 2303256 (2023). [CrossRef]
43. D. Wei, Y. Cheng, R. Ni, et al., “Generating Controllable Laguerre-Gaussian Laser Modes Through Intracavity Spin-Orbital Angular Momentum Conversion of Light,” Phys. Rev. Appl. 11(1), 014038 (2019). [CrossRef]
44. X. Xu, T. Wang, P. Chen, et al., “Femtosecond laser writing of lithium niobate ferroelectric nanodomains,” Nature 609(7927), 496–501 (2022). [CrossRef]
45. Y. Yuan, X. Li, L. Jiang, et al., “Laser maskless fast patterning for multitype microsupercapacitors,” Nat. Commun. 14(1), 3967 (2023). [CrossRef]
46. Y. Zhuang, S. Wang, Z. Chen, et al., “Tailored vortex lasing based on hybrid waveguide-grating architecture in solid-state crystal,” Appl. Phys. Lett. 120(21), 211101 (2022). [CrossRef]
47. Q. Gu and X. Cui, “Self-bound vortex lattice in a rapidly rotating quantum droplet,” Phys. Rev. A 108(6), 063302 (2023). [CrossRef]
48. T. A. Yoğurt, U. Tanyeri, A. Keleş, et al., “Vortex lattices in strongly confined quantum droplets,” Phys. Rev. A 108(3), 033315 (2023). [CrossRef]
49. W. Tan, Y. Bai, X. Huang, et al., “Enhancing critical resolution of a ghost imaging system by using a vortex beam,” Opt. Express 30(9), 14061–14072 (2022). [CrossRef]
50. B. Wang, N. J. Brooks, P. Johnsen, et al., “High-fidelity ptychographic imaging of highly periodic structures enabled by vortex high harmonic beams,” Optica 10(9), 1245–1252 (2023). [CrossRef]
51. M. Khodadadi Karahroudi, S. A. Moosavi, A. Mobashery, et al., “Performance evaluation of perfect optical vortices transmission in an underwater optical communication system,” Appl. Opt. 57(30), 9148–9154 (2018). [CrossRef]
52. Q. Yan, Y. Zhang, L. Yu, et al., “Absorptive Turbulent Seawater and Parameter Optimization of Perfect Optical Vortex for Optical Communication,” Journal of Marine Science and Engineering 10(9), 1256 (2022). [CrossRef]
53. W. Sun, Y. Liu, C. Romero, et al., “Q-switched vortex waveguide laser generation based on LNOI thin films with implanted Ag nanoparticles,” Opt. Express 31(22), 36725–36735 (2023). [CrossRef]
54. Z. Zhang, L. Hai, S. Fu, et al., “Advances on Solid-State Vortex Laser,” Photonics 9(4), 215 (2022). [CrossRef]
55. J. P. Phillips, S. Banerjee, K. Ertel, et al., “Stable high-energy, high-repetition-rate, frequency doubling in a large aperture temperature-controlled LBO at 515 nm,” Opt. Lett. 45(10), 2946–2949 (2020). [CrossRef]
56. H. Zhou, J. Zhang, T. Chen, et al., “Picosecond, narrow-band, widely tunable optical parametric oscillator using a temperature-tuned lithium borate crystal,” Appl. Phys. Lett. 62(13), 1457–1459 (1993). [CrossRef]
57. S. Cui, N. Li, B. Xu, et al., “Direct generation of visible vortex Hermite-Gaussian modes in a diode-pumped Pr:YLF laser,” Opt. Laser Technol. 131, 106389 (2020). [CrossRef]
58. X. Lin, Q. Feng, Y. Zhu, et al., “Diode-pumped wavelength-switchable visible Pr3+:YLF laser and vortex laser around 670 nm,” Opto-Electron. Adv. 4(4), 210006 (2021). [CrossRef]
59. Y. Wang, J. Fang, T. Zheng, et al., “Mid-Infrared Single-Photon Edge Enhanced Imaging Based on Nonlinear Vortex Filtering,” Laser Photonics Rev. 15(10), 2100189 (2021). [CrossRef]
60. S. Avramov-Zamurovic, A. T. Watnik, J. R. Lindle, et al., “Designing laser beams carrying OAM for a high-performance underwater communication system,” J. Opt. Soc. Am. A 37(5), 876–887 (2020). [CrossRef]
61. H. Chen, P. Zhang, S. He, et al., “Average capacity of an underwater wireless communication link with the quasi-Airy hypergeometric-Gaussian vortex beam based on a modified channel model,” Opt. Express 31(15), 24067–24084 (2023). [CrossRef]
62. F. Li, C. Q. Gao, M. W Liu, et al., “Experimental study of the generation of Laguerre-Gaussian beam using a computer-generated amplitude grating,” Acta Phys. Sin. 57(2), 860–866 (2008). [CrossRef]
63. C. Romero, J. García Ajates, F. Chen, et al., “Fabrication of Tapered Circular Depressed-Cladding Waveguides in Nd:YAG Crystal by Femtosecond-Laser Direct Inscription,” Micromachines 11(1), 10 (2019). [CrossRef]
64. D. Wang, S. Wan, S. Yin, et al., “High temperature Raman spectroscopy study on the microstructure of the boundary layer around a growing LiB3O5 crystal,” CrystEngComm 13(16), 5239–5242 (2011). [CrossRef]
