Abstract

Here we demonstrate intracavity frequency-doubling of an ultra-compact (cavity length < 20 mm) Pr3+:LiYF4 (YLF) orbital Poincaré laser, in which the fundamental modes are represented on an equivalent orbital Poincaré sphere (eOPS) and a singularities hybrid evolution nature sphere (SHENS). The generated ultraviolet (UV, 320 nm) output carries orbital angular momentum (OAM), and it typically exhibits an optical bottle beam with a 3-dimensional dark core, formed of a coherent superposition of eigen Laguerre-Gaussian (LG) modes. Such ultraviolet structured light beams with OAM offer many advanced applications from microscopy to materials processing.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Structured light beams with orbital angular momentum (OAM) [13], i.e. optical vortices, carry a ring-shaped spatial form due to their helical wavefronts with on-axis phase singularity characterized by a topological charge, ℓ. An equivalent orbital Poincaré sphere (eOPS), in which the eigen states are two orthogonal Laguerre-Gaussian (LG) modes with topological charges ±ℓ, enables the pictorial and geometric representation of full possible structured light fields with OAM [48]. Helical-Ince–Gaussian (HIG) beams, formed by the coherent superposition of even and odd Ince–Gaussian (IG) modes [9,10] with a relative phase of π/2, and further exotic structured light fields with OAM states owing to the multi-singularities, dubbed vortex lattices (or vortex crystals) [11], can also be pictorially and geometrically represented on a singularities hybrid evolution nature sphere (SHENS) [12].

These structured light beams represented on eOPS and SHENS (we here call them OAM modes), have been extensively studied in a myriad of fundamental sciences and advanced applications, such as optical trapping and manipulation [1316], quantum information and communication [1720], super resolution microscopy [2123], and chiral microfabrication [2427]. Going beyond these conventional applications, ultraviolet (UV) structured light beams with high photon energy will further offer ultrahigh density optical data storage with the freedom of OAM [28], nano-bioimaging, and chiral nano/microfabrication [29], in particular, with the aid of plasmonic metasurfaces [30].

Wavefront modulation elements, such as spiral phase plates [31] and spatial light modulators (SLMs) [32], are commonly used to produce OAM modes in the visible and near-infrared regions; however, there are few wavefront modulation elements in the UV region. Instead of these elements, an alternative is the direct generation of LG modes from a laser cavity [33] with the use of a ring-shaped pumping geometry [34], centrally damaged cavity mirrors [35], and thermal lensing of the laser medium [36], with or without the aid of nonlinear frequency conversion.

In recent years, the direct generation of a UV (325 nm) LG mode has been demonstrated from a He-Cd gas laser using an output coupler (OC) with an engineered damage spot [37]. The generation of a tunable UV (332–344 nm) LG mode has also been achieved from a green vortex mode laser pumped continuous-wave (cw) optical parametric oscillator (OPO) based on MgO-doped stoichiometric periodically poled LiTaO3 (MgO:sPPLT) in combination with intracavity sum-frequency generation (SFG) between the green pump and the Gaussian resonant signal in BiB3O6 (BIBO) [38]. These systems consist of a gas-phase gain medium or many bulky components; therefore, they are rather large-scale and less robust. When using the damaged OC, it is difficult to obtain stable and reliable LG mode operation due to thermal effects and further damage to the mirror itself at high pump powers. Furthermore, it is difficult to generate versatile OAM modes except for the specific LG modes. Therefore, compact and robust UV structured light sources with versatile OAM modes have not yet been established.

Here, we propose an ultra-compact UV structured light source (cavity length less than 20 mm) formed of an intracavity frequency-doubled, laser diode pumped Pr3+:LiYF4 (Pr:YLF) laser [3941] with an off-axis pumping geometry and without any additional mode selection elements, such as a damaged-spot mirror or a spiral phase plate. The system enables the generation of red (640 nm) versatile OAM modes, including LG modes, HIG modes, and vortex lattices, represented on the eOPS and the SHENS. We here call this system an orbital Poincaré laser. The system also produces UV structured light beams with OAM, imprinted with fundamental OAM modes. This frequency-doubled orbital Poincaré laser system is expected to open the door towards new advanced bioimaging and microfabrication technologies.

2. Experimental setup

Figure 1 shows a schematic of the experimental setup for the UV structured light source. The Pr:YLF laser crystal used in this experiment has a strong absorption band in the blue (ca. 442 nm) region, which allows efficient diode-pumping, and it exhibits strong visible emissions including green (523 nm), orange (607 nm), red (640 nm), and dark-red (720 nm), with the strongest emission at 640 nm due to the 3P03F2 transition. The Pr:YLF laser crystal was a 5 mm long a-cut crystal with 0.5 at% Pr3+ doping and a 4×4 mm2 aperture, and it was wrapped with indium foil and mounted inside a copper holder connected with a water-cooled chiller to maintain its temperature (ca. 15 °C). The crystal had an input facet with high reflection (R=99.8%) for 640 nm and anti-reflection for 442 nm, and its output facet was anti-reflective for 640 nm. Also, note that both crystal facets had no specific coating for 320nm. A blue InGaN single-emitter laser diode (Nichia Co., NDB7K75) was used as a pumping source, of which the wavelength was tuned to match the absorption band of the Pr:YLF crystal. The diode output exhibited an astigmatic multi-mode spatial form; therefore, it was collimated by an aspheric lens (L1; f1=4.5 mm) and a cylindrical lens (CL; fCL=250 mm). The output was focused to be an elliptical spot with radii wpx=41 µm and wpy=30 µm in the horizontal and vertical directions (these values were experimentally optimized to generate versatile OAM modes), respectively, on the front surface of the crystal by a lens (L2; f2=35 mm). It should be noted that a half-wave plate was used to make the diode polarization parallel to the crystal orientation direction (c-axis) to yield the maximum absorption.

 figure: Fig. 1.

Fig. 1. Schematic illustration of experimental arrangement used for the intracavity frequency-doubled Pr:YLF laser with an off-axis pumping geometry. This system simultaneously produced a 640 nm OPB mode and its imprinted 320 nm output. Li: lens; M: mirror; CL: cylindrical lens; λ/2: half-wave plate; Pr:YLF: laser crystal; BBO: nonlinear crystal; OC: output coupler; WS: wavelength separator; Dump: residual pump power dumper; CCD: CCD beam profile (the laser cavity structure used in our experiment is shown in inset).

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The laser cavity consisted of the input facet of the Pr:YLF crystal and a concave OC (curvature radius: 300 mm) with high reflection (R=99.5%) for 640 nm and high transmission (T>95%) for 320 nm. The OC was further mounted on a 2-dimensional translation stage to allow displacements with 0.5 µm steps along the x- and y- axes (Δx=0.5 µm, Δy=0.5 µm) to enable the generation of versatile spatial modes. The cavity length was fixed to be ca. 17 mm (as small as possible). This cavity configuration, in which the cavity mode radius (wl=97 µm, estimated using LADCAD software) was larger than the pump spot sizes of wpx and wpy in both the x and y directions [42], satisfies the tightly focused condition. A β-BaB2O5 (BBO) crystal [43,44] with high nonlinearity and high transmission in the UV region was used for intracavity frequency-doubling. The crystal was cut for type-I phase-matching (θ=37.4°, ϕ=90°) between 640 nm and 320 nm, and it was 1 mm long with a 6×6 mm2 aperture and anti-reflection coating for both 640 nm and 320 nm. The BBO crystal was also mounted on a 3-dimensional rotational stage to satisfy the critical phase matching between the fundamental red (640 nm) and frequency-doubled UV (320 nm) outputs. The BBO crystal was placed 7 mm from the laser gain medium, and the fundamental mode radius was then estimated to be approximately 100 μm onto the BBO crystal. The generated fundamental, frequency-doubled, and the residual pump diode outputs were separated by a fused silica transmission grating (200 lines/mm) and pinholes. The beam propagation of the red and ultraviolet outputs was then investigated by employing a conventional CCD beam profiler (Spricon Co., SP907).

3. Experimental results and discussions

3.1 Orbital Poincare sphere

Fundamental and frequency-doubled outputs from the laser cavity were investigated in terms of the OC displacement. Figure 2 summarizes the experimentally obtained spatial forms of the fundamental and frequency-doubled outputs at various off-axis positions of the OC. An on-axial aligned cavity should force the laser to operate at the lowest eigenmode Gaussian mode for fundamental and frequency-doubled outputs; therefore, the position of the OC was defined to be (x=0, y=0). When the displacements of the OC were (x=±31, y=0) μm (or (x=0, y=±45) μm), the laser produced a HG10 (or HG01) fundamental mode. It should be noted that the unavoidable elliptical spatial profile of the pump beam induced experimentally unequal displacements of the OC in the x- and y- directions to achieve the same order HG modes.

 figure: Fig. 2.

Fig. 2. Spatial fundamental modes and the corresponding frequency-doubled outputs.

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The laser further enabled the generation of both HG10 and HG01 modes with the desired relative phase ϕ (=-π/2–π/2), simply by adjustment of the off-axial displacement of the OC along both the x- and y-directions. Operation at a positive (or negative) first-order vortex mode (ℓ=±1) with a ring-shaped spatial form was achieved to form a coherent superposition of the HG10 and HG01 modes with ϕ=-π/2 or π/2, as evidenced by a pair of upward (downward) and downward (upward) Y-shaped fringes produced by a lateral shearing interferometer with the transmission grating (20 lines/mm) (Fig. 3(a)). The x and y displacements of the OC were then measured to be ±31 μm and ±45 μm, respectively.

 figure: Fig. 3.

Fig. 3. Assignment of topological charge (magnitude and sign) for the experimentally generated fundamental and frequency-doubled outputs. (a,b) Experimental Y-shaped fringes formed by a laterally shearing interferometer of the left-handed and right-handed fundamental outputs. Second row: Spatial forms of frequency-doubled outputs focused by a cylindrical lens.

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The HG and LG families generated from the laser cavity can be systematically represented on the OPS. The structured modes on the OPS are connected by geometrical path which can be represented by mathematical equation. The first order OAM mode field SG1,1(θ, ϕ), formed of a coherent superposition of LG modes with positive and negative topological charges of ±1, is given by the following expression [4].

$$S{G_{1,1}}({\theta ,\phi } )= L{G_1}\textrm{cos}\left( {\frac{\theta }{2}} \right)'\cdot {e^{ - \frac{{i\phi }}{2}}} + L{G_{ - 1}}\textrm{sin}\left( {\frac{\theta }{2}} \right)\cdot {e^{\frac{{i\phi }}{2}}},\; \; $$
where LG±1 is the LG mode with a topological charge of ℓ=±1, and θ and ϕ are the azimuthal and axial angles, respectively, and it is represented as LG, HG and HLG (Hermite-Laguerre-Gaussian) modes for the first order eOPS using the terms of θ and ϕ connected with a geometric phase (Fig. 4). For instance, the LG modes with ℓ=±1 are plotted at the north and south poles on the eOPS. The HG modes are also plotted on the equatorial plane of the eOPS, in which the HG10 and HG01 modes are represented at ϕ=0 and π.

 figure: Fig. 4.

Fig. 4. Generated fundamental (640 nm) and frequency-doubled (320 nm) structured light fields are mapped on eOPSs.: (a) Structured light fields represented on eOPSs along the principal axes (b) Structured light fields represented on eOPSs along a single complete geometric path.

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The system allowed appropriate control of the geometrical phase difference between the simultaneously lasing LG±1 modes simply by tuning the off-axis position of the OC, thereby generating full fundamental OAM modes as an eigenmode. The fundamental modes obtained experimentally are theoretically well supported, and they can be plotted on the eOPS, as shown in Fig. 4. Such fundamental OAM modes were imprinted on the frequency doubled outputs, thereby creating unique UV structured light beams.

The UV outputs can also be plotted on the second order eOPS, as shown in Fig. 4. The threshold pump power for intracavity SHG was then measured to be 1.8 W. For instance, the topological charge of the frequency-doubled output should also be doubled, due to the nature of nonlinear wave-mixing [4547]. Therefore, the corresponding UV output also exhibited an annular spatial form with a relatively large dark core, which indicated a topological charge ℓ of ±2, as evidenced by a rightwards (or leftwards) inclined triple-lobed mode focused by the cylindrical lens (Fig. 3(b)). The fundamental and frequency-doubled output powers at a maximum diode pump power of 3 W were then measured to be 5 mW and 3 mW, respectively.

The resultant frequency-doubled LG modes can be plotted at the north and south poles as LG modes with ℓ=±2 on the second-order eOPS. The frequency-doubled HG10 (or HG01) mode is also plotted as a HG20 (or HG02) mode at ϕ=0 (or π), though the generated UV outputs generally include an undesired Gaussian mode by the nonlinear wave-mixing process. Furthermore, the frequency-doubled HLG modes can be plotted using θ and ϕ, the azimuthal and axial angles. Several frequency-doubled HLG modes are represented on the eOPS at (π/4,0), (3π/4,0), (π/4, 3π/2) and (3π/4, 3π/2), as shown in Fig. 4(b).

3.2 Bottle beam generation

As above mentioned, the generated UV outputs should include an undesired Gaussian mode. For instance, the frequency-doubled HG10 (or HG01) mode will be given by the HG102=HG20 + 2HG00 (or HG012=HG02 + 2HG00) mode; therefore, it was transformed into a twin lobed (like HG10 or HG01) mode in the near-field due to the Gouy phase shift. The frequency-doubled LG modes showed a ring-shaped near-field and a central bright spot far-field, manifesting an optical bottle beam property, due to the existence of the unexpected Gaussian mode, as reported in previous related works [48]. Figure 5 shows the UV output, which possessed a well-isolated 3-dimensional (3D) dark core surrounded by a bright ring within a distance of ±0.6zR from the near-field of the UV output (z=0). Such a UV bottle beam is expected to enable the development of scanning fluorescence microscopes and microfabrication with ultra-high 3D spatial resolution [49].

 figure: Fig. 5.

Fig. 5. Beam propagation of frequency-doubled output with an optical bottle beam property (zR is the Rayleigh length).

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3.3 Higher order structured modes

IG and HIG modes are also allowed in this high Q-cavity configuration by fine-tuning of the OC displacement. Their spatial forms were then imprinted on the frequency-doubled output. The experimental UV output exhibited almost the same IG and HIG near-fields as the fundamental mode, as shown in Fig. 6. Some experimentally obtained even and odd fundamental IG modes and their corresponding frequency-doubled outputs are summarized in Fig. 6. The spatial forms of the UV outputs are almost identical to those of the fundamental modes. In particular, interestingly, the generated fundamental and frequency-doubled square optical vortex modes (see figures at the left end of the lower row of Fig. 6), dubbed polygonal vortex beams [50], manifest quasi-frequency-degenerate state in laser cavity. The fundamental mode with spatially separated multiple first-order singularities is further generated and imprinted on the frequency-doubled output with multiple second-order singularities. Such exotic OAM modes with multiple singularities, represented on a SHENS should enable the realization of novel advanced technologies, such as the formation of multiple chiral nanoneedles. An optical vortex lattice with 4 or 6 phase singularities and a +’ shape mode (see the third and fourth column of Fig. 6) were further produced with this system by appropriate control of the off-axis position of the OC. Such structured light fields could further improve the performance of materials engineering.

 figure: Fig. 6.

Fig. 6. Experimentally generated fundamental and UV higher-order structured light fields.

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4. Conclusions

We have successfully demonstrated an ultra-compact UV structured light source based on an intracavity frequency-doubled Pr3+:YLF laser with an off-axis pumping geometry. This system enables the generation of fundamental first-order LG, higher-order IG, HIG modes and even optical vortex lattice simply by control of the off-axis displacement of the OC. The structured light fields generated can also be fully imprinted on the frequency-doubled UV output, which possesses the second-order OAM states, to realize the bottle beam property with a 3-dimensional dark core, and multiple phase singularities. This frequency-doubled orbital Poincaré laser system should be extended to produce further higher-order OAM modes by some minor modifications of the cavity configuration. Furthermore, this system can overcome the experimental artifacts that generally occur in UV applications. The orbital Poincaré laser source, formed of an intracavity frequency-doubled Pr3+:YLF laser, has the potential to generate dual-wavelength OAM modes, for example, (720 nm, 360 nm), (698 nm, 349 nm), (607 nm, 303.7 nm), (604 nm, 302 nm), (546 nm, 273 nm) and (522 nm, 261 nm) in a wide wavelength region. Further power scaling of the system without any damage of the laser crystal will be possible by employing an intracavity high reflection UV thin mirror.

Funding

Japan Society for the Promotion of Science fellowship (P19352); Japan Society for the Promotion of Science, KAKENHI (JSPS-KAKENHI) (JP16H06507, JP17K19070, JP18H03884); Core Research for Evolutional Science and Technology (JPMJCR1903).

Disclosures

The authors declare no conflicts of interest.

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References

  • View by:

  1. L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref]
  2. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
    [Crossref]
  3. M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
    [Crossref]
  4. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
    [Crossref]
  5. D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
    [Crossref]
  6. M. R. Dennis and M. A. Alonso, “Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams,” Philos. Trans. R. Soc., A 375(2087), 20150441 (2017).
    [Crossref]
  7. R. Gutiérrez-Cuevas, M. R. Dennis, and M. A. Alonso, “Generalized Gaussian beams in terms of Jones vectors,” J. Opt. 21(8), 084001 (2019).
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  8. Y. Shen, Z. Wang, X. Fu, D. Naidoo, and A. Forbes, “SU (2) Poincaré sphere: A generalized representation for multidimensional structured light,” Phys. Rev. A 102(3), 031501 (2020).
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  12. Y. Shen, Y. Meng, X. Fu, and M. Gong, “Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince–Gaussian and Hermite–Laguerre–Gaussian modes,” J. Opt. Soc. Am. A 36(4), 578–587 (2019).
    [Crossref]
  13. B. Ada-Ioana and J. Glückstad, “Strategies for optical trapping in biological samples: aiming at microrobotic surgeons,” Laser Photonics Rev. 13(4), 1800227 (2019).
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  14. P. Meng, Z. Man, A. P. Konijnenberg, and H. P. Urbach, “Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems,” Opt. Express 27(24), 35336–35348 (2019).
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  15. Y. Liang, M. Lei, S. Yan, M. Li, Y. Cai, Z. Wang, X. Yu, and B. Yao, “Rotating of low-refractive-index microparticles with a quasi-perfect optical vortex,” Appl. Opt. 57(1), 79–84 (2018).
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  16. B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
    [Crossref]
  17. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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  18. A. Trichili, C. Rosales-guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Opticalcommunication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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  19. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
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  20. Y. Wen, I. Chremmos, Y. Chen, G. Zhu, J. Zhang, J. Zhu, Y. Zhang, J. Liu, and S. Yu, “Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems,” Optica 7(3), 254–262 (2020).
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  22. K. Otomo, T. Hibi, Y. Kozawa, and T. Nemoto, “STED microscopy—super-resolution bio-imaging utilizing a stimulated emission depletion,” Microscopy 64(4), 227–236 (2015).
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  23. Y. M. Sigal, R. Zhou, and X. Zhuang, “Visualizing and discovering cellular structures with super-resolution microscopy,” Science 361(6405), 880–887 (2018).
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  24. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
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  25. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
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  26. K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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  27. F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6(1), 21738 (2016).
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  28. X. Fang, H. Ren, and M. Gu, “Orbital angular momentum holography for high-security encryption,” Nat. Photonics 14(2), 102–108 (2020).
    [Crossref]
  29. T. Omatsu, K. Miyamoto, K. Toyoda, R. Morita, Y. Arita, and K. Dholakia, “A new twist for materials science: the formation of chiral structures using the angular momentum of light,” Adv. Opt. Mater. 7(14), 1801672 (2019).
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  30. X. Gao, R. Wan, J. Yan, L. Wang, X. Yi, J. Wang, W. Zhu, and J. Li, “Design of AlN ultraviolet metasurface for single-/multi-plane holography,” Appl. Opt. 59(14), 4398–4403 (2020).
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  31. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
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  32. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4(1), 2289 (2013).
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  33. T. Omatsu, K. Miyamoto, and A. J. Lee, “Wavelength-versatile optical vortex lasers,” J. Opt. 19(12), 123002 (2017).
    [Crossref]
  34. D. J. Kim, J. W. Kim, and W. A. Clarkson, “Q-switched Nd:YAG optical vortex lasers,” Opt. Exp. 24, 2129449–212454 (2013).
  35. A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
    [Crossref]
  36. M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, “Characterization of 1.06μm optical vortex laser based on a side-pumped Nd:GdVO4 bounce oscillator,” Appl. Phys. B 95(1), 69–73 (2009).
    [Crossref]
  37. Y. Uesugi, Y. Kozawa, and S. Sato, “Direct generation of the lowest-order vortex beam using a spot defect mirror in the ultraviolet region,” Opt. Lett. 45(7), 2115–2118 (2020).
    [Crossref]
  38. V. Sharma, G. K. Samanta, S. C. Kumar, R. P. Singh, and M. Ebrahim-Zadeh, “Tunable ultraviolet vortex source based on a continuous-wave optical parametric oscillator,” Opt. Lett. 44(19), 4694–4697 (2019).
    [Crossref]
  39. T. Gün, P. Metz, and G. Huber, “Power scaling of laser diode pumped Pr3+: LiYF4 cw lasers: efficient laser operation at 522.6 nm, 545.9 nm, 607.2 nm, and 639.5 nm,” Opt. Lett. 36(6), 1002–1004 (2011).
    [Crossref]
  40. X. Li, X. Yu, R. Yan, R. Fan, and D. Chen, “Optical and laser properties of Pr3+: YLF crystal,” Laser Phys. Lett. 8(11), 791–794 (2011).
    [Crossref]
  41. Y. Ma, A. Vallés, J. C. Tung, Y. F. Chen, K. Miyamoto, and T. Omatsu, “Direct generation of red and orange optical vortex beams from an off-axis diode-pumped Pr3+:YLF laser,” Opt. Express 27(13), 18190–18200 (2019).
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  42. N. Barré, M. Romanelli, and M. Brunel, “Role of cavity degeneracy for high-order mode excitation in end-pumped solid-state lasers,” Opt. Lett. 39(4), 1022–1025 (2014).
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  43. C. Chen, Z. Lin, and Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
    [Crossref]
  44. T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical boratecrystals: key materials for generation of visible and UV light,” Mater. Sci. Eng., R 30(1-2), 1–54 (2000).
    [Crossref]
  45. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
    [Crossref]
  46. D. G. Pires, J. C. A. Rocha, A. J. Jesus-Silva, and E. J. S. Fonseca, “Optical mode conversion through nonlinear two-wave mixing,” Phys. Rev. A 100(4), 043819 (2019).
    [Crossref]
  47. A. S. Rao, “Characterization of off-axis phase singular optical vortex and its nonlinear wave-mixing to generate control broad OAM spectra,” Phys. Scr. 95(5), 055508 (2020).
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  48. A. J. Lee, C. Zhang, T. Omatsu, and H. M. Pask, “An intracavity, frequency-doubled self-Raman vortex laser,” Opt. Express 22(5), 5400–5409 (2014).
    [Crossref]
  49. Y. Iketaki, H. Kumagai, K. Jahn, and N. Bokor, “Creation of a three-dimensional spherical fluorescence spot for super-resolution microscopy using a two-color annular hybrid wave plate,” Opt. Lett. 40(6), 1057–1060 (2015).
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  50. Y. Shen, Z. Wan, Y. Meng, X. Fu, and M. Gong, “Polygonal vortex beams,” IEEE Photon. J. 10, 1–16 (2018).

2020 (6)

Y. Shen, Z. Wang, X. Fu, D. Naidoo, and A. Forbes, “SU (2) Poincaré sphere: A generalized representation for multidimensional structured light,” Phys. Rev. A 102(3), 031501 (2020).
[Crossref]

Y. Wen, I. Chremmos, Y. Chen, G. Zhu, J. Zhang, J. Zhu, Y. Zhang, J. Liu, and S. Yu, “Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems,” Optica 7(3), 254–262 (2020).
[Crossref]

X. Fang, H. Ren, and M. Gu, “Orbital angular momentum holography for high-security encryption,” Nat. Photonics 14(2), 102–108 (2020).
[Crossref]

X. Gao, R. Wan, J. Yan, L. Wang, X. Yi, J. Wang, W. Zhu, and J. Li, “Design of AlN ultraviolet metasurface for single-/multi-plane holography,” Appl. Opt. 59(14), 4398–4403 (2020).
[Crossref]

Y. Uesugi, Y. Kozawa, and S. Sato, “Direct generation of the lowest-order vortex beam using a spot defect mirror in the ultraviolet region,” Opt. Lett. 45(7), 2115–2118 (2020).
[Crossref]

A. S. Rao, “Characterization of off-axis phase singular optical vortex and its nonlinear wave-mixing to generate control broad OAM spectra,” Phys. Scr. 95(5), 055508 (2020).
[Crossref]

2019 (8)

D. G. Pires, J. C. A. Rocha, A. J. Jesus-Silva, and E. J. S. Fonseca, “Optical mode conversion through nonlinear two-wave mixing,” Phys. Rev. A 100(4), 043819 (2019).
[Crossref]

V. Sharma, G. K. Samanta, S. C. Kumar, R. P. Singh, and M. Ebrahim-Zadeh, “Tunable ultraviolet vortex source based on a continuous-wave optical parametric oscillator,” Opt. Lett. 44(19), 4694–4697 (2019).
[Crossref]

Y. Ma, A. Vallés, J. C. Tung, Y. F. Chen, K. Miyamoto, and T. Omatsu, “Direct generation of red and orange optical vortex beams from an off-axis diode-pumped Pr3+:YLF laser,” Opt. Express 27(13), 18190–18200 (2019).
[Crossref]

T. Omatsu, K. Miyamoto, K. Toyoda, R. Morita, Y. Arita, and K. Dholakia, “A new twist for materials science: the formation of chiral structures using the angular momentum of light,” Adv. Opt. Mater. 7(14), 1801672 (2019).
[Crossref]

Y. Shen, Y. Meng, X. Fu, and M. Gong, “Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince–Gaussian and Hermite–Laguerre–Gaussian modes,” J. Opt. Soc. Am. A 36(4), 578–587 (2019).
[Crossref]

B. Ada-Ioana and J. Glückstad, “Strategies for optical trapping in biological samples: aiming at microrobotic surgeons,” Laser Photonics Rev. 13(4), 1800227 (2019).
[Crossref]

P. Meng, Z. Man, A. P. Konijnenberg, and H. P. Urbach, “Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems,” Opt. Express 27(24), 35336–35348 (2019).
[Crossref]

R. Gutiérrez-Cuevas, M. R. Dennis, and M. A. Alonso, “Generalized Gaussian beams in terms of Jones vectors,” J. Opt. 21(8), 084001 (2019).
[Crossref]

2018 (4)

2017 (4)

T. Omatsu, K. Miyamoto, and A. J. Lee, “Wavelength-versatile optical vortex lasers,” J. Opt. 19(12), 123002 (2017).
[Crossref]

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

M. R. Dennis and M. A. Alonso, “Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams,” Philos. Trans. R. Soc., A 375(2087), 20150441 (2017).
[Crossref]

M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
[Crossref]

2016 (4)

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

A. Trichili, C. Rosales-guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Opticalcommunication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6(1), 21738 (2016).
[Crossref]

2015 (2)

K. Otomo, T. Hibi, Y. Kozawa, and T. Nemoto, “STED microscopy—super-resolution bio-imaging utilizing a stimulated emission depletion,” Microscopy 64(4), 227–236 (2015).
[Crossref]

Y. Iketaki, H. Kumagai, K. Jahn, and N. Bokor, “Creation of a three-dimensional spherical fluorescence spot for super-resolution microscopy using a two-color annular hybrid wave plate,” Opt. Lett. 40(6), 1057–1060 (2015).
[Crossref]

2014 (2)

2013 (4)

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4(1), 2289 (2013).
[Crossref]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

D. J. Kim, J. W. Kim, and W. A. Clarkson, “Q-switched Nd:YAG optical vortex lasers,” Opt. Exp. 24, 2129449–212454 (2013).

A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
[Crossref]

2012 (2)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (3)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

T. Gün, P. Metz, and G. Huber, “Power scaling of laser diode pumped Pr3+: LiYF4 cw lasers: efficient laser operation at 522.6 nm, 545.9 nm, 607.2 nm, and 639.5 nm,” Opt. Lett. 36(6), 1002–1004 (2011).
[Crossref]

X. Li, X. Yu, R. Yan, R. Fan, and D. Chen, “Optical and laser properties of Pr3+: YLF crystal,” Laser Phys. Lett. 8(11), 791–794 (2011).
[Crossref]

2010 (1)

2009 (1)

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, “Characterization of 1.06μm optical vortex laser based on a side-pumped Nd:GdVO4 bounce oscillator,” Appl. Phys. B 95(1), 69–73 (2009).
[Crossref]

2005 (1)

C. Chen, Z. Lin, and Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
[Crossref]

2004 (2)

2000 (1)

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical boratecrystals: key materials for generation of visible and UV light,” Mater. Sci. Eng., R 30(1-2), 1–54 (2000).
[Crossref]

1999 (1)

1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Ada-Ioana, B.

B. Ada-Ioana and J. Glückstad, “Strategies for optical trapping in biological samples: aiming at microrobotic surgeons,” Laser Photonics Rev. 13(4), 1800227 (2019).
[Crossref]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Allen, L.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Alonso, M. A.

R. Gutiérrez-Cuevas, M. R. Dennis, and M. A. Alonso, “Generalized Gaussian beams in terms of Jones vectors,” J. Opt. 21(8), 084001 (2019).
[Crossref]

M. R. Dennis and M. A. Alonso, “Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams,” Philos. Trans. R. Soc., A 375(2087), 20150441 (2017).
[Crossref]

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref]

Arie, A.

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Arita, Y.

T. Omatsu, K. Miyamoto, K. Toyoda, R. Morita, Y. Arita, and K. Dholakia, “A new twist for materials science: the formation of chiral structures using the angular momentum of light,” Adv. Opt. Mater. 7(14), 1801672 (2019).
[Crossref]

Bandres, M. A.

Barré, N.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Ben Salem, A.

A. Trichili, C. Rosales-guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Opticalcommunication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

Bokor, N.

Brunel, M.

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4(1), 2289 (2013).
[Crossref]

Cai, Y.

Chen, C.

C. Chen, Z. Lin, and Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
[Crossref]

Chen, D.

X. Li, X. Yu, R. Yan, R. Fan, and D. Chen, “Optical and laser properties of Pr3+: YLF crystal,” Laser Phys. Lett. 8(11), 791–794 (2011).
[Crossref]

Chen, Y.

Chen, Y. F.

Chremmos, I.

Chujo, K.

Clarkson, W. A.

D. J. Kim, J. W. Kim, and W. A. Clarkson, “Q-switched Nd:YAG optical vortex lasers,” Opt. Exp. 24, 2129449–212454 (2013).

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

Courtial, J.

Dennis, M. R.

R. Gutiérrez-Cuevas, M. R. Dennis, and M. A. Alonso, “Generalized Gaussian beams in terms of Jones vectors,” J. Opt. 21(8), 084001 (2019).
[Crossref]

M. R. Dennis and M. A. Alonso, “Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams,” Philos. Trans. R. Soc., A 375(2087), 20150441 (2017).
[Crossref]

Dholakia, K.

T. Omatsu, K. Miyamoto, K. Toyoda, R. Morita, Y. Arita, and K. Dholakia, “A new twist for materials science: the formation of chiral structures using the angular momentum of light,” Adv. Opt. Mater. 7(14), 1801672 (2019).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dudley, A.

A. Trichili, C. Rosales-guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Opticalcommunication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Ebrahim-Zadeh, M.

Fan, R.

X. Li, X. Yu, R. Yan, R. Fan, and D. Chen, “Optical and laser properties of Pr3+: YLF crystal,” Laser Phys. Lett. 8(11), 791–794 (2011).
[Crossref]

Fang, X.

X. Fang, H. Ren, and M. Gu, “Orbital angular momentum holography for high-security encryption,” Nat. Photonics 14(2), 102–108 (2020).
[Crossref]

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Fonseca, E. J. S.

D. G. Pires, J. C. A. Rocha, A. J. Jesus-Silva, and E. J. S. Fonseca, “Optical mode conversion through nonlinear two-wave mixing,” Phys. Rev. A 100(4), 043819 (2019).
[Crossref]

Forbes, A.

Y. Shen, Z. Wang, X. Fu, D. Naidoo, and A. Forbes, “SU (2) Poincaré sphere: A generalized representation for multidimensional structured light,” Phys. Rev. A 102(3), 031501 (2020).
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Figures (6)

Fig. 1.
Fig. 1. Schematic illustration of experimental arrangement used for the intracavity frequency-doubled Pr:YLF laser with an off-axis pumping geometry. This system simultaneously produced a 640 nm OPB mode and its imprinted 320 nm output. Li: lens; M: mirror; CL: cylindrical lens; λ/2: half-wave plate; Pr:YLF: laser crystal; BBO: nonlinear crystal; OC: output coupler; WS: wavelength separator; Dump: residual pump power dumper; CCD: CCD beam profile (the laser cavity structure used in our experiment is shown in inset).
Fig. 2.
Fig. 2. Spatial fundamental modes and the corresponding frequency-doubled outputs.
Fig. 3.
Fig. 3. Assignment of topological charge (magnitude and sign) for the experimentally generated fundamental and frequency-doubled outputs. (a,b) Experimental Y-shaped fringes formed by a laterally shearing interferometer of the left-handed and right-handed fundamental outputs. Second row: Spatial forms of frequency-doubled outputs focused by a cylindrical lens.
Fig. 4.
Fig. 4. Generated fundamental (640 nm) and frequency-doubled (320 nm) structured light fields are mapped on eOPSs.: (a) Structured light fields represented on eOPSs along the principal axes (b) Structured light fields represented on eOPSs along a single complete geometric path.
Fig. 5.
Fig. 5. Beam propagation of frequency-doubled output with an optical bottle beam property (zR is the Rayleigh length).
Fig. 6.
Fig. 6. Experimentally generated fundamental and UV higher-order structured light fields.

Equations (1)

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S G 1 , 1 ( θ , ϕ ) = L G 1 cos ( θ 2 ) e i ϕ 2 + L G 1 sin ( θ 2 ) e i ϕ 2 ,

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