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Abstract
Multicolor visible high-order Bessel (Bessel-vortex) beams which have a helical wavefront and a long confocal length have garnered significant interest for applications in materials processing and biomedical technologies. In this paper, we demonstrate the direct generation of multicolor (523, 605 and 637 nm) Bessel-vortex beams from a Pr3+-doped water-proof fluoro-aluminate glass (Pr3+: WPFG) fiber laser with an intracavity lens which induces chromatic and spherical aberration. The handedness of the generated Bessel-vortex beam is selectively controlled through lateral displacement of the intra-cavity lens.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical vortices possess a helical wavefront, an on-axis phase singularity, a doughnut-shaped spatial intensity profile and carry orbital angular momentum (OAM) which can be quantified by its topological charge ℓ [1,2]. High-order Bessel beams (Bessel-vortex), which are eigenstates of the electro-magnetic equation in cylindrical coordinates with variable separation, are examples of optical vortices [3–5]. These types of optical vortices have been studied as examples of non-diffractive optical vortices which exhibit characteristics of deep-penetration and self-healing [6,7]. Furthermore, when these Bessel-vortex beams undergo spatial Fourier transformation, they produce so called “perfect vortices” which have size-invariant properties and maintain high magnitude OAM [8].
Bessel-vortex beams enable the demonstration of a range of novel techniques in applications such as optical trapping and manipulation [9,10], laser nano/microfabrication [11], direct 2D/3D printing via laser-induced forward transfer [12], ultra-high resolution microscopy [13] and underwater, ultrahigh-capacity quantum/optical telecommunications [14], and atomic guiding [15].
Bessel-vortex beams can be generated using a number of approaches, with perhaps the most common methods being the use of a spatial light modulator (SLM), a digital micromirror device, and a spiral phase plate with an axicon lens [16–20]. It should be noted that while these methods are effective at generating Bessel-vortex beams, they are not conducive to the generation of high-power beams (due to the low damage threshold of the beam-forming elements). These methods are also only capable of modulating the wavefront of the incident laser beam, and hence degradation of the mode purity may occur.
The direct generation of optical vortex modes as an eigenfunction of a laser cavity is an alternative way to generate high quality optical vortices which avoids the use of external beam forming elements [21,22]. Direct generation methods include pumping the laser gain medium with a doughnut-shaped pump beam and off-axis pumping of the laser cavity [23–26], using an intra-cavity lens [27,28], using an intracavity SLM [29], and using reflectivity-modified and polarization-selective photonic crystal mirrors [30]. However, there are few studies on the direct generation of Bessel beams even from passive resonators, which requires an intracavity axicon lens or an intracavity spherical aberrated lens with high diffraction loss [31,32]. Furthermore, there is no report, to the best of our knowledge, on the direct generation of Bessel-vortex beams from active laser cavities.
In recent years, Pr3+ doped water-proof fluoro-aluminate glass (Pr:WPFG) fibers have seen significant use as a laser material with high gain [33], especially for the development of cost-effective blue GaN-laser diode pumped ultra-compact visible (cyan, green, orange, red and deep red) solid-state lasers [34]. We and our-coworkers have demonstrated the generation of Laguerre-Gaussian (LG) modes, that is paraxial eigenstates, from a Pr:WPFG fiber laser with the use of a standard microscope slide as an interferometric output coupler [35].
In this paper, we significantly expand on our prior work and demonstrate, for the first time, the direct generation of Bessel-vortex modes with OAM, from a diode-pumped Pr:WPFG laser with a spherically aberrated intracavity lens, in which an optical-needle shaped caustic with a long depth of focus feeds back to the fiber core via output coupler (OC) reflection. We also address the multicolor (523, 605 and 637 nm) laser operation of Bessel-vortex beam owing to chromatic aberration of the intracavity spherical lens.
2. Experiments
A Pr:WPFG fiber was formed of AlF3-YF3-CaF2-BaF2 system fluoride glasses without alkali metals (the removal of alkali metals significantly improves the waterproof property of the fluoride glass), and thus, it exhibits an excellent water-proof performance (>500 times higher water-resistance as that of commercial ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN)) [33]. Also, the optical loss of the fiber was measured to be 0.1 dB/m, and this value is almost the same as that of ZBLAN fiber. The Pr:WPFG fiber has four absorption bands at 444, 468, 480, and 590 nm in the visible region, thus allowing the GaN blue laser pumping. The Pr:WPFG fiber showed strong emission at 482 nm (light blue), 523 nm (green), 605 nm (orange), 637 nm (red), and 719 nm (deep-red) wavelengths (Fig. 1(a)). Fluorescence lifetime of 635 nm emission in the Pr:WPFG fiber was typically measured to be 51.3 µs. Note that the Pr:WPFG fiber exhibits rather broad absorption and emission bands owing to the inhomogeneous broadening effects in the glass.
Fig. 1. (a) Plot of the absorption and fluorescence spectra of Pr:WPFG. (b) Schematic of the experimental setup used for direct generation of Bessel-vortex beams in the visible wavelength range. (c) Generation of 0th and 1st order Bessel beams owing to spherical aberration of intracavity lens. (d) Wavelength control of Bessel beams owing to chromatic aberration of intracavity lens. (e) Schematic of the self-referenced shearing interferometer used for characterization of the generated Bessel-vortex beams.
The Pr:WPFG fiber (3000 ppm Pr3+ doping, fiber length: ∼40 mm) with a 8 µm core and a 125 µm clad diameters was used as the laser gain medium. It was pumped by a commercial GaN blue diode laser (PLPT9 450D_E A01, wavelength: 442 nm). Note that the emission bands of the Pr:WPFG fiber are broader than those of a Pr:YLF crystal [36–38]. The V value of the fiber was estimated to be 9.2, and thus supported the oscillation of high-order modes such as Bessel-vortex modes. The experimental setup of the system is presented in Fig. 1 (b). The output beam from the diode laser was elliptical due to strong astigmatism along the horizontal and vertical directions. Thus, the diode laser output was reshaped into a circular beam using relay optics comprised of an aspherical lens L1 (f1 = 15 mm), an achromatic lens L2 (f2 = 50 mm), a vertically-oriented cylindrical lens L3 (f3 = 50 mm), and a horizontally-oriented cylindrical lens L4 (f4 = -12.5 mm). This re-shaped pump beam was then coupled to the gain fiber using an aspheric lens L5 (f5 = 4 mm). The laser cavity was formed using the input facet of the fiber which was coated high reflecting (>99.9%) for 400-700 nm and high transmitting (∼98%) for 444 nm, and a flat OC with reflectivity of 94.4% for 523 nm, 97.1% for 605 nm, and 65% for 637 nm. The cavity length was fixed at 130 mm. A plano-convex spherical lens L6 (f6 = 4.5 mm) was placed within the laser cavity. This was used to both collimate the laser mode so as to maintain cavity stability and to induce spherical and chromatic aberration within the laser cavity. It should be noted that the convex face of the lens was oriented towards the fiber facet to maximize spherical aberration [39–41]. The laser mode is shaped to be a needle-shaped caustic with long depth of focus on a round trip via OC reflection owing to the strong spherical aberration of the intracavity lens, and it is then coupled well into the fiber core, thus allowing the selective laser amplification/oscillation of optical-needle shaped beam, such as Bessel beam. Also, the fiber core acts as an effective aperture, which enables the laser operation of multiple-ring-structured modes through diffraction effects (Fig. 1(c)).
The chromatic aberration of the intracavity lens (where the focal length is shorter for shorter wavelengths) acted as a wavelength selector [42] (Fig. 1(d)). As reported in our previous publication, the green (orange) laser mode has a lower coupling loss than the orange (red) laser mode. The fiber ∼ lens distance was determined to reimage (feedback well) the green/orange mode into the fiber core via OC reflection. The orange (red) mode was then defocused to be a larger size mode onto the fiber, thereby preventing the orange (red) mode operation. This wavelength selection technique allows the selective laser operation at the desired wavelength.
By varying the on-axis displacement D of lens L6, the order of the generated Bessel-vortex beam and the output wavelength could be varied. For reference, the displacement at which the 0th order Bessel-vortex beam at 637 nm was generated was referenced as 0 µm. As the displacement D became more negative (the displacement between L6 and the end of the fiber became smaller), the generated Bessel-vortex mode cycled between modes of different wavelength and order. This is highlighted in Fig. 2(a). The OAM of the generated Bessel-vortex modes was characterized using a self-referenced interferometer (schematic shown in Fig. 1(e)). The self-referenced interference fringes [43] of the generated 1st order Bessel-vortex beams are shown in Fig. 2(b). In each case, forked fringes indicate the presence of OAM, with the direction of the fork (up or down) indicating the sign of the OAM (the fork is highlighted in white as an aid to the eye). The sign of the generated Bessel-vortex beam could be selectively controlled by laterally displacing the intra-cavity lens in small increments (±1 µm).
Fig. 2. Images showing (a) spatial forms of the generated 0th and 1st order Bessel beams at various intracavity lens position D. (b) Wavefronts of 1st order Bessel beams measured using the self-referenced shearing interferometer. The green, orange, and red Bessel beams exhibit characteristics of 1st order vortices.
Negative displacement (D = -53∼0 µm) of the intracavity lens enabled selective generation of red (637 nm), orange (605 nm), and green (523 nm) Bessel-vortex beams of 0th- or 1st-order. The generated Bessel-vortex beams were spatially and temporally stable for long observation times (several hours). Note that the green Bessel-vortex beam carried both negative and positive phase singularities (ℓ=±1), indicating the simultaneous laser operation of both positive and negative Bessel-vortex modes because of the relatively low laser gain at this wavelength. Power scaling of the generated Bessel-vortex beams was conducted, and the power-transfer curves are shown in Fig. 3. The maximum green, orange, and red Bessel-vortex output powers were measured to be 7 mW, 8.5 mW and 64 mW, respectively. The laser spectra of the system at maximum pump level were rather broader (1-2 nm (FWHM)) than that (<0.5 nm) of the Pr:YLF lasers [44], as shown in Fig. 3(b). The laser output power was temporally stable even during a long-time observation (30 minutes).
Fig. 3. (a) Plot showing the power scaling characteristics of the 637 nm (red), 605 nm (orange), and 523 nm (green), and 1st order Bessel (Bessel-vortex) beams. (b) The spectra of laser outputs under green, orange, and red operations.
3. Discussion
The generated Bessel-vortex beams were not diffraction invariant and propagated with low diffraction (beam divergence∼3 mrad). This diffraction was a consequence of the imperfect ring-aperture produced by the intracavity lens and spherical aberration [45–47], and can be understood by using space variant conical angle analysis. The space variant conical angle ${\alpha _c}(z )$ was estimated by fitting the experimental spatial form along the radial direction of the generated Bessel-vortex beam using a function of the form $I({r,z} )\propto {|{{J_1}({k{\alpha_c}(z )r} )} |^2}$, where r and z are the radial and propagation indices, respectively.
The theoretical space variant conical angle αc(z) in the aberrated lens is given by the following expression.
where rI and a are fitting parameters which were derived through iteratively fitting the theoretical curve to the experimentally determined spatial intensity profile of a 1st order Bessel-vortex beam (Fig. 4(a)). The fitting parameters $a$ = 0.1, and ${r_I}$ = 570 µm were derived and the experimental space variant conical angle for the generated red (637 nm) Bessel-vortex beam was modelled using Eq. (1). The numerically modelled beam propagation characteristics of the Bessel-vortex beam were in good agreement with the experimental results (Fig. 4).Fig. 4. Plots showing (a) experimentally (red) and theoretically (blue) derived spatial forms of a 1st order Bessel-vortex beam. This was used to determine the parameters rI and a at z = 50 cm. (b) Plot of the measured conical angle ac of a 637 nm (red) Bessel-vortex beam. (c), (d) Experimentally and theoretically derived propagation characteristics of a 637 nm (red) Bessel-vortex beam generated from the Pr:WPFG fiber laser.
In addition to the above investigations, the propagation characteristics of a generated Bessel-vortex beam was analyzed when the beam was partially perturbed. Here, the center of a generated Bessel-vortex beam was blocked using a black disc with a diameter of 280 µm. On propagation, the perturbed Bessel-vortex beam regained its spatial intensity profile (demonstrating self-healing) at a propagation distance of 20 cm. This property is shown in a sequence of spatial intensity profiles in Fig. 5, taken at propagation distances of 1 cm, 10 cm and 20 cm from the position of the black disc.
Fig. 5. Images showing the spatial intensity profile of a 637 nm Bessel-vortex beam partially perturbed by a black disc and taken at different propagation distances.
Bessel-vortex beams with a rather long depth of focus (10.2 times longer than that of a conventional Gaussian beam with the same spot radius in the near field) generated from this system still enable the forementioned applications.
4. Conclusion
We have demonstrated the direct generation of multicolor Bessel-vortex beams at 523, 605, and 637 nm from a diode pumped Pr3+:WPFG fiber laser which uses an intracavity spherical lens to induce spherical and chromatic aberration. The handedness of the generated red and orange Bessel-vortex beams could be controlled through slight lateral displacement of the intracavity lens. The diffraction and propagation characteristics of the Bessel-vortex beams were numerically analyzed using a space variant conical angle model.
The laser output power of the system was limited to be less than 100 mW, because of the limitation of pump power owing to the poor cooling of the gain fiber. Further power scaling up to watt level of the system will be possible towards the aforementioned applications by improvement of the pumping system including conductive cooling of the gain fiber.
The system will be also extended to generate higher-order LG/Bessel-vortex beams.
Further, the Pr3+ doped gain fiber exhibited rather higher laser gain and broadband emission bands (1∼2 nm) in comparison with Pr3+ doped laser crystals, thus allowing the development of compact sub-picosecond lasers with high efficiency in the future [48–51].
We believe that a multicolor Bessel-vortex laser source will be an enabling technology for the development of novel methods in advanced applications including 2D/3D microfabrication, ultra-high resolution microscopy and light-sheet imaging systems.
Funding
Core Research for Evolutional Science and Technology (JPMJCR1903); Japan Society for the Promotion of Science (JP22H05131, JP22H05138, JP22K18981, JP23H00270).
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.
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