Open Access
Add to BibSonomy
Abstract
In this paper we explore the application of low-loss multimode anti-resonant hollow-core fiber (MM-AR-HCF) in the delivery of nanosecond laser pulses at 1 µm wavelength. MM-AR-HCF with large core offers a rich content of low-loss higher-order modes which plays a key role in the efficient coupling and transmission of high-power laser of low beam quality. In the experiment, laser pulses of an average pulse energy of 21.8 mJ with 14.6 ns pulse width (corresponding a peak power of 1.49 MW) are transmitted through MM-AR-HCF of 9.8 m length without damage. 85% transmission efficiency is achieved where the incident laser beam suffers a low beam quality with M2x and M2y of 2.18 and 1.99 respectively. Laser-induced damage threshold (LIDT) of MM-AR-HCF was measured to be 22.6 mJ for 85% transmission efficiency, which is 7 times higher than that for a multimode silica optical fiber with a large core of 200 µm.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-power lasers have found increasing applications in many industrial fields, such as laser cutting, welding and additive manufacturing [1–4]. Optical fiber based laser power delivery is known for its light weight, flexibility, robustness and low cost, which overcomes many constraints of using bulky laser sources in the practical industrial applications and scientific researches.
In high-power pulse laser delivery, solid-core silica fibers are difficult to achieve high peak power due to the limitation of laser-induced damage threshold (LIDT) [5,6]. There were researches that attempted to reduce power density through larger core diameter, but multi-mode guidance of the fiber results in low output beam quality [7,8]. The single-ring anti-resonant hollow-core fiber (AR-HCF) emerged in 2011 is featured by the large hollow core design and the negative-curvature core wall, providing a nearly free-space-like guidance for the laser delivery [9,10]. The modal overlap between the field of fundamental mode and the solid material of cladding is reduced to 10−4 and below, which brings in low optical nonlinearity, low dispersion and high LIDT [11,12]. Owing to the ultralow modal overlap, AR-HCFs present low and flat dispersion profile across the whole low-loss spectral window whereas [13]. AR-HCFs have been demonstrated in the high-power and high-field laser delivery in the spectral region from the deep ultraviolet to the mid-infrared [14–16]. Near diffraction-limited kilowatt-level high-power laser delivery over hundred meters have been verified [17–20].
By tuning the cladding design, the leakage loss of mode can be significantly increased owing to the phase-matching condition [21–23]. In this case, higher-order modes (HOMs) in AR-HCF could strongly coupling with certain cladding modes, so that the quasi single-mode guidance can be achieved even in a short piece of meters [24]. It is noted that most AR-HCF designs reported present the quasi-single mode guidance [24–26], therefore nearly all demonstrated high-power AR-HCF delivery experiments necessitate a fairly good beam quality of laser source with M2 less than 1.5 [16–20].
In the delivery of high-power laser with low beam quality, large amount of HOMs power leaks into the cladding at the coupling end, resulting in low transmission efficiency and easily cause laser-induced damage (LID) due to the high power density in the cladding [27]. To cater for the delivery of high-power laser beam of low beam quality, the concept of multimode anti-resonant hollow-core fiber (MM-AR-HCF) has been proposed. In 2019, Winter and colleagues fabricated a MM-AR-HCF with a core diameter of 164 µm and an outer diameter of 360 um [28]. By enlarging the diameter ratio of core over cladding, the phase-matching condition can be tuned so as to bring down the attenuations of certain HOMs of low rank [29]. However, such a large core diameter significantly increases bending loss [30]. In 2022, for high-power industrial laser delivery, Shere et al. proposed two designs of MM-AR-HCF with 10 and 24 nested cladding capillaries, respectively [31]. Their nested cladding design is beneficial to bring down the bending loss but on the other hand makes it a challenge to maintain the distribution uniformity of ten and more nested capillaries of smaller diameters. Recently, Wu et al. fabricated and characterized a low-loss MM-AR-HCF with 18 fan-shaped resonators in the cladding for 1 µm spectral region [32]. The touching capillaries support each other and such stable cladding design makes it easier to extend the number of capillaries where the distribution uniformity could be well maintained. With a smaller core diameter of 66 µm, the relative low bending loss was expected while the multimode guidance property was maintained, which was verified by S2 method.
Micro-structured hollow-core fibers including photonic-bandgap hollow-core fibers (PBG-HCFs) and Kagome hollow-core fibers (Kagome-HCF) have demonstrated advantages of delivery of Q-switched nanosecond laser pulses over traditional solid-core fibers in terms of higher LIDT. In 2004, Shepard et al. firstly applied a 7-cell PBG-HCF to successfully transmit nanosecond pulses of 0.37 mJ [33]. In 2007, the delivery of higher pulse energy of 1.025 mJ was demonstrated in a 19-cell PBG-HCF [34]. Later, Beaudou et al. used Kagome-type HCFs in the delivery of Nd: YAG laser pulses and the transmitted pulse energy was up to 1.3 mJ and 4 mJ in 2011 and 2012, respectively [35,36]. In 2013, a quasi-single-mode AR-HCF was firstly explored in the transmission of nanosecond laser pulses. For a laser source with M2 of 1.2, delivery of 1.1 mJ pulse energy was achieved with a coupling efficiency of 92%, while for a laser with M2 of 5∼6, laser induced damage at the incident end was observed when the incident pulse energy exceeded 3.2 mJ [27]. In 2014, Dumitrache et al. demonstrated the nanosecond laser delivery by Kagome HCF, pulse energy of 35 mJ (30 ns pulse width) and 7.5 mJ (12 ns pulse width) were transmitted with transmission efficiency of 85% [37]. More details are referred to Table 1.
Table 1. Delivery of nanosecond laser pulses by micro-structured hollow-core fibers
In this paper, we demonstrate the damage-free delivery of nanosecond pulses with energy of 21.8 mJ and a corresponding peak power of 1.49 MW. At the output of MM-AR-HCF, M2 of transmitted beam is found to be reduce from about 2 to 1.7. LIDT at the incident end of MM-AR-HCF measures an average pulse energy of 22.6 mJ that is about 7 times of a commercial multimode silica fiber with a large core of 200 µm in diameter.
2. Properties of MM-AR-HCF
2.1 Attenuation of MM-AR-HCF
The MM-AR-HCF was fabricated using the stack-and-draw technique with a core diameter of 66 µm and an outer diameter of 193 µm. The cladding is composed of 18 fan-shaped capillaries. Such cladding geometry makes the control of fiber structural uniformity easier in the drawing compared to nodeless cladding type, especially in cases with a large number of cladding capillaries, e.g. MM-AR-HCFs. While it also enables a larger area ratio of core region to cladding hole than the “ice-cream-cone” shaped cladding, which is helpful to inhibit resonant coupling between HOMs and cladding modes [29]. The average core wall thickness is 350 ± 5 nm where the corresponding first resonant wavelength is calculated to be 740 ± 11 nm [38]. The attenuation is measured by cutback method using a tungsten lamp source. The light was coupled into the tested fiber by butt-coupling with a few-mode silica fiber (40 µm core diameter), which inevitably generated HOMs excitation at the coupling end. Due to the higher leakage loss of HOMs compared to fundamental mode [30], the ratio of HOMs to fundamental mode in the cutted part increases with the times of cutback, resulting in differences between several attenuation results. As shown in Fig. 1, the measured attenuation from four times of cutback at 1064 nm was 0.038 dB/m, 0.044 dB/m, 0.050 dB/m and 0.076 dB/m respectively. More details on the characterization of bend loss and mode content of MM-AR-HCF can be found in [32] where the geometry of cladding maintained almost the same.
2.2 Numerical aperture of MM-AR-HCF
The numerical aperture (NA) of multi-mode silica fiber is defined by sine of the output mode pattern’s divergence half angle, which also applies to AR-HCF [27,39,40]. Divergence half-angle of output mode pattern of MM-AR-HCF is measured by scanning the 1/e2 modal radius of far field pattern emitted at the fiber end along Z axis. As shown in Fig. 2(a), A superluminescent diode (Thorlabs, S5FC1050P) is used as the light source with the central wavelength at 1061 nm and full width at half maxima of 50 nm. For different coupling conditions, LP01-like mode, LP02 -like mode and unclarified field distribution are excited and their NAs are measured as 0.029, 0.032 and 0.045 respectively. Small NAs indicates high brightness of delivered laser beam maintained at the output end which may bring convenience for applications, e.g. laser machining and welding.
Fig. 1. (a) The measured transmission spectrum of MM-AR-HCF from 900 nm to 1300 nm. (b) The measured attenuation of MM-AR-HCF from 900 nm to 1300 nm by cutback method. (c) Scanned electronic microscopy picture of MM-AR-HCF. The core diameter is 66 µm and capillary wall thickness is about 350 nm.
Fig. 2. (a) Schematic of experiment to measure the NA of MM-AR-HCF. L1 and L2 are microscopic objective lenses; R1 and R2 are silver mirrors (with average reflection R > 97%@1064 nm); A CCD camera is mounted on a single-axis translation stage to record the far-field patterns of emission from MM-AR-HCF along Z axis. (b) Modal diameters of far-filed patterns as functions of z position. 8 meters of MM-AR-HCF is used. Corresponding far-field images at the output end of MM-AR-HCF which are: (c-1) LP01 -like mode, (c-2) LP02 -like mode, (c-3) Unclarified mode pattern. Microscopic objective lenses L1 (f = 2.97 mm) and L2 (f = 18.6 mm) are used to couple with the fundamental mode of MM-AR-HCF, thus excited LP01-like mode. LP02-like mode is excited by adjusting focus length of L1 to 4.51 mm and L2 to 15.29 mm, and the unclarified field distribution is excited by applying transverse stress on the fiber.
3. Experimental study of MM-AR-HCF delivery of nanosecond laser pulses
3.1 Experiment setup
Figure 3 illustrates the schematic of laser delivery experiment by using MM-AR-HCF. A Q-switched Nd: YAG nanosecond pulse laser source (Continuum Surelite SL I-10) is used. The laser output is a linearly polarized elliptical beam with long and short axes of 5.147 mm and 3.312 mm at the exit of laser, M2x is 2.18 and M2y is 1.99. The temporal width of pulse is 14.6 ns and the repetition rate is 10 Hz. In the experiment, the laser power coupled in MM-AR-HCF can be continuously adjusted by rotating the half-wave plate (HWP) before the polarizer. The beam characterization unit includes beam splitters, spectrometer, photodetector and CCD to synchronously measure the output beam characteristics.
Fig. 3. Setup of nanosecond pulse laser delivery experiment. R1, R2 and R3 are Nd: YAG Laser Line Mirrors with reflection > 99.5%; L1 and L2 are plano-convex lenses with f1 = 75 mm, f2 = 50 mm; Samper 1 and 2 are beam splitters with 90:10 ratio; HWP: half wave plate; PBS: polarization beam splitter. Energy Meter 1 (Thorlabs, ES120C), Energy Meter 2 (Ophir, PE25BF-C). Two ends of MM-AR-HCF are sealed in custom-built gas-cells for vacuuming. Inserted image are far field pattern of laser source and fiber output.
A 9.8 m MM-AR-HCF is used in the laser delivery which is loosely rewound on an iron plate with a bend radius of 30 cm, which additional losses caused by bending can be ignored [32]. To prevent the damage from the air ionization induced by laser pulses [36], both MM-AR-HCF ends are sealed in the custom-built gas cells and vacuumed. Both internal pressure in the gas cells were maintained around 1.02 mbar in the experiment.
Coupling end of MM-AR-HCF is sealed in Gas-Cell 1, which is mounted on 3-axis stage (Thorlabs, MAX313D). The optimal coupling state was achieved by adjusting 3-axis stage to get the highest output pulse energy while ensuring Gaussian-like distribution of output beam. For high power laser delivery by MM-AR-HCF, deviation of coupling state leads to increase of HOMs excitation, thus deteriorate transmission efficiency, LIDT and output beam quality.
3.2 Characterization of coupling and transmission efficiencies
Figure 4(a) shows the laser transmission through the 9.8 m long MM-AR-HCF as function of the incident pulse energy. In the experiment, the output power of laser source is sampled and monitored to calibrate the incident and output powers of MM-AR-HCF. As the incident power rises, the transmission efficiency stays around 85%. The alternation of transmission efficiency for different incident power was measured stable within 1.5% through the experiment.
Fig. 4. (a) The measured averaged transmitted pulse energy over 9.8 m MM-AR-HCF length and calculated transmission efficiency as function of incident pulse energy. (b) The temporal measurement of laser transmission over 20 minutes for an averaged incident pulse energy of about 18 mJ. Output pulse energy of laser source slightly decreases over time.
Before damage, the maximum transmitted single pulse energy is recorded as 23.4 mJ with a peak power of 1.6 MW accordingly. The average of pulse energy over 30 seconds is 21.8 mJ in this case. Figure 4(b) shows the temporal measurement of laser transmission over 20 minutes for an average incident pulse energy of around 18 mJ. In laser delivery, due to the inability to accurately define guided mode content in the fiber, the attenuation of MM-AR-HCF and coupling efficiency cannot be accurately characterized. We also conducted laser delivery by 1 m MM-AR-HCF under the same experimental conditions and the optimized transmission efficiency is 92.5%, which is close to actual coupling efficiency.
3.3 Characterization of transmitted pulse widths and spectra
The measured temporal profiles of transmitted pulses are presented in Fig. 5 for incident pulse energy of 15.2 mJ. An InGaAs detector (Thorlabs, DET08CFC/M) and oscilloscope (Keysight, DSOX6002A) are used in the measurement. The full-width at half maxima of the Gaussian fitting of pulse profile is calculated as the pulse width. The laser pulse shows no significant broadening after being transmitted through 9.8 m MM-AR-HCF. The differences in pulse shape and width comes from the nature of Q-switched laser [41].
Fig. 5. Normalized temporal measurement of (a) incident and (b) output pulse profiles. The differences in pulse width and shape are caused by nature of Q-switched laser.
Fig. 6. Normalized optical spectra of laser pulses before and after transmission in the 9.8 m long MM-AR-HCF when the incident pulse energy is 18.69 mJ. Inset: zoom-in of spectrum at 1064 nm wavelength. Resolutions of spectrometers in use are 0.47 nm for Ocean and 6.77 nm for Ideaoptics.
The spectra of laser beam before and after transmission in the 9.8 m MM-AR-HCF are measured by spectrometers for an incident pulse energy of 18.69 mJ. The incident laser beam is measured by Ocean spectrometer (Maya 2000Pro), and the output by both Ocean and Ideaoptics Spectrometer (NIR25S) to scan the entire visible and near-infrared spectral regions. The measured output shown in Fig. 6 spectrum is very slightly broadened compared to incident spectrum. As implied in [18,42], self-phase modulation (SPM) and other nonlinear optical effects are likely to be negligible at such power level in an evacuated AR-HCF of 9.8 m length. We attribute the spectral broadening to the low resolution (0.47 nm) of spectrometer used for measurement.
3.4 Characterization of beam quality before and after transmission
The beam profiles before and after transmission in MM-AR-HCF were characterized by M2 measurement using the knife-edge method, the collimated parallel beam was focused by a long focal length convex lens with f = 250 mm. As Fig. 7(a) shows, the output of laser source has an elliptical profile of beam with M2x and M2y as 2.18 and 1.99 respectively. The beam quality at the output end of MM-AR-HCF is improved with M2x and M2y reduced to 1.70 and 1.75, indicate that MM-AR-HCF still has a certain HOMs filtering effect under the optimal coupling condition. After beam shaping by MM-AR-HCF, the output beam profile was improved to Gaussian-like distribution, which is beneficial for effectively focusing to achieve higher power density.
Fig. 7. The measured incident (a) and output (b) beam diameters near focus point. The distribution of beam diameter was obtained through hyperbolic fitting.
3.5 Comparison of laser-induced damages of MM-AR-HCF and large-core multimode silica optical fiber
As shown in Fig. 8 when transversely offset from the optimized coupling condition, LIDT was found significantly decreased. LID to the end of MM-AR-HCF is found even for an incident pulse energy as small as 3.3 mJ for approximately 10 µm transverse offset along X axis. For incident pulse energy of around 10mJ, LID occurred when applying about 3 µm transverse offset along X axis. For incident pulse energy over 15mJ, slightly offset would cause LID to overall structure of the end. For 85% transmission efficiency, LIDT of MM-AR-HCF is 22.6 mJ. The deviation from the optimal coupling condition will lead to an increase in the optical power density at the silica cladding, causing damage to cladding capillaries and further cutoff the laser delivery.
Fig. 8. Microscopic images of damaged MM-AR-HCF ends for incident pulse energies of (a) 3.3 mJ, (b) 4.1 mJ, (c) 9.8 mJ, (d) 11.5 mJ, (e) 17.5 mJ, (f) 22.6 mJ when the coupling condition deviates from the optimal.
In comparison, we replace MM-AR-HCF with a large-core multimode silica optical fiber (MMF) and optimize the coupling state by adjusting the 3-axis stage to achieve highest output pulse energy. The MMF (Xinrui, SIH200 22A) has a core diameter of 200 ± 2 µm, a cladding diameter of 220 ± 5 µm, and a numerical aperture of 0.22 ± 0.02. As the incident pulse energy reaches 3 mJ, some point damages and cracks are to be observed at the end of MMF, shown in Fig. 9(b). It is noted that such damages are often accompanied with sparks in the air near the fiber end. When the incident pulse energy rises to 4.8 mJ, the end of MMF would be completely destroyed, shown in Fig. 9(c). Previous studies have shown that the LIDT of multimode fiber is positively correlated with the core diameter [43,44]. Based on this premise we propose that LIDT of this MM-AR-HCF is 7 times higher than large-core silica multimode fiber.
Fig. 9. Microscopic images of MMF ends: (a) before damage (b) and (c) for an incident energy of 3 mJ and 4.8 mJ respectively. The red circle in (c) indicates the fiber end region before damage.
4. Conclusion
In this paper, a MM-AR-HCF is experimentally demonstrated in the laser beam delivery of medium-beam-quality nanosecond pulses at 1 µm wavelength. In spite of incident beam quality with M2 up to 2, about 85% transmission efficiency is still achieved. And after propagating through the 9.8 m MM-AR-HCF, the laser beam has M2 reduced to 1.7. LIDT of MM-AR-HCF is found to be around 7 times higher than that for a MMF with a larger core diameter. Our experiment implies promising potential of AR-HCFs in high-power laser delivery of various application requirement.
Funding
Shanghai Sailing Program (23YF1454400); STI 2030-Major Projects (2022ZD0212100); Key Technology Research and Development Program of Shandong Province (2021CXGC010202); National Natural Science Foundation of China (61935002, 62075200, 62127815); Chinese Academy of Sciences (ZDBS-LY JSC020).
Acknowledgment
We would like to thank Mr. Jinhu Zheng and Mr. Henan Shen for the assistance in the fiber drawing.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data used to produce the plots within this work are found in Ref. [45].
References
1. U. K. Tirlapur and K. König, “Targeted transfection by femtosecond laser,” Nature 418(6895), 290–291 (2002). [CrossRef]
2. Y. P. Kathuria, “Laser microprocessing of metallic stent for medical therapy,” J. Mater. Process. Technol. 170(3), 545–550 (2005). [CrossRef]
3. M. Farsari and B. N. Chichkov, “Two-photon fabrication,” Nat. Photonics 3(8), 450–452 (2009). [CrossRef]
4. B. Eckhard, M. Achim, L. Matthias, et al., “Innovations in high power fiber laser applications,” Proc. SPIE 8237, 823717 (2012). [CrossRef]
5. B. Richou, I. Schertz, I. Gobin, et al., “Delivery of 10-MW Nd:YAG laser pulses by large-core optical fibers: dependence of the laser-intensity profile on beam propagation,” Appl. Opt. 36(7), 1610–1614 (1997). [CrossRef]
6. A. Stakhiv, R. Gilber, H. Kopecek, et al., “Laser ignition of engines via optical fibers?” Laser Phys. 14, 738–747 (2004).
7. T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, et al., “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001). [CrossRef]
8. S. Joshi, N. Wilvert, and A. P. Yalin, “Delivery of high intensity beams with large clad step-index fibers for engine ignition,” Appl. Phys. B 108(4), 925–932 (2012). [CrossRef]
9. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, et al., “Demonstration of a waveguide regime for a silica hollow - core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011). [CrossRef]
10. M. Michieletto, J. K. Lyngso, C. Jakobsen, et al., “Hollow-core fibers for high power pulse delivery,” Opt. Express 24(7), 7103–7119 (2016). [CrossRef]
11. F. Poletti, “Nested antiresonant nodeless hollow core fiber,” Opt. Express 22(20), 23807–23828 (2014). [CrossRef]
12. W. Belardi, “Design and Properties of Hollow Antiresonant Fibers for the Visible and Near Infrared Spectral Range,” J. Lightwave Technol. 33(21), 4497–4503 (2015). [CrossRef]
13. R. Carter, W. Macpherson, P. Jaworski, et al., “Dispersion measurement of microstructured negative curvature hollow core fiber,” Opt. Eng. 55(11), 116106 (2016). [CrossRef]
14. F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 mu m spectral region,” Opt. Express 20(10), 11153–11158 (2012). [CrossRef]
15. F. Yu, M. Cann, A. Brunton, et al., “Single-mode solarization-free hollow-core fiber for ultraviolet pulse delivery,” Opt. Express 26(8), 10879–10887 (2018). [CrossRef]
16. X. Y. Zhu, F. Yu, D. K. Wu, et al., “Laser-induced damage of an anti-resonant hollow-core fiber for high-power laser delivery at 1 mu m,” Opt. Lett. 47(14), 3548–3551 (2022). [CrossRef]
17. Q. Fu, Y. D. Wu, I. A. Davidson, et al., “Hundred-meter-scale, kilowatt peak-power, near-diffraction-limited, mid-infrared pulse delivery via the low-loss hollow-core fiber,” Opt. Lett. 47(20), 5301–5304 (2022). [CrossRef]
18. H. C. H. Mulvad, S. A. Mousavi, V. Zuba, et al., “Kilowatt-average-power single-mode laser light transmission over kilometre-scale hollow-core fibre,” Nat. Photonics 16(6), 448–453 (2022). [CrossRef]
19. M. A. Cooper, J. Wahlen, S. Yerolatsitis, et al., “2.2 kW single-mode narrow-linewidth laser delivery through a hollow-core fiber,” Optica 10(10), 1253–1259 (2023). [CrossRef]
20. Q. Fu, I. A. Davidson, S. M. A. Mousavi, et al., “Hollow-core fiber: breaking the nonlinearity limits of silica fiber in long-distance green laser pulse delivery,” Laser Photonics Rev. 18(4), 2201027 (2024). [CrossRef]
21. C. Wei, R. A. Kuis, F. Chenard, et al., “Higher-order mode suppression in chalcogenide negative curvature fibers,” Opt. Express 23(12), 15824–15832 (2015). [CrossRef]
22. P. Uebel, M. Günendi, M. Frosz, et al., “Broadband robustly single-mode hollow-core PCF by resonant filtering of higher-order modes,” Opt. Lett. 41(9), 1961–1964 (2016). [CrossRef]
23. M. S. Habib, O. Bang, and M. Bache, “Low-loss single-mode hollow-core fiber with anisotropic anti-resonant elements,” Opt. Express 24(8), 8429–8436 (2016). [CrossRef]
24. F. Yu, M. Xu, and J. Knight, “Experimental study of low-loss single-mode performance in anti-resonant hollow-core fibers,” Opt. Express 24(12), 12969 (2016). [CrossRef]
25. A. Hartung, J. Kobelke, A. Schwuchow, et al., “Low-loss single-mode guidance in large-core antiresonant hollow-core fibers,” Opt. Lett. 40(14), 3432–3435 (2015). [CrossRef]
26. M. S. Habib, J. E. Antonio-Lopez, C. Markos, et al., “Single-mode, low loss hollow-core anti-resonant fiber designs,” Opt. Express 27(4), 3824–3836 (2019). [CrossRef]
27. P. Jaworski, F. Yu, R. Maier, et al., “Picosecond and nanosecond pulse delivery through a hollow-core negative curvature fiber for micro-machining applications,” Opt. Express 21(19), 22742–22753 (2013). [CrossRef]
28. B. Winter, T. A. Birks, and W. J. Wadsworth, “Multimode hollow-core anti-resonant optical fibres,” in Frontiers in Optics + Laser Science (Optica Publishing Group, 2019), paper JTu4A.18.
29. D. Bird, “Attenuation of model hollow-core, anti-resonant fibres,” Opt. Express 25(19), 23215 (2017). [CrossRef]
30. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964). [CrossRef]
31. W. Shere, E. N. Fokoua, G. T. Jasion, et al., “Designing multi-mode anti-resonant hollow-core fibers for industrial laser power delivery,” Opt. Express 30(22), 40425–40440 (2022). [CrossRef]
32. D. K. Wu, F. Yu, C. Wu, et al., “Low-loss multi-mode anti-resonant hollow-core fibers,” Opt. Express 31(13), 21870–21880 (2023). [CrossRef]
33. J. D. Shephard, J. D. C. Jones, D. P. Hand, et al., “High energy nanosecond laser pulses delivered single-mode through hollow-core PBG fibers,” Opt. Express 12(4), 717–723 (2004). [CrossRef]
34. J. Tauer, F. Orban, H. Kofler, et al., “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007). [CrossRef]
35. B. Beaudou, F. Gerome, G. Gaborel, et al., “Bench top milli-joule energy-level nanosecond pulse delivery through hollow-core fiber,” in Conference on Lasers and Electro-Optics (Optica Publishing Group, 2011), paper CThM2.
36. B. Beaudou, F. Gérôme, Y. Wang, et al., “Milli-Joule laser pulse delivery for spark ignition through kagome hollow-core fiber,” Opt. Lett. 37(9), 1430–1432 (2012). [CrossRef]
37. C. Dumitrache, J. Rath, and A. P. Yalin, “High power spark delivery system using hollow core kagome lattice fibers,” Materials 7(8), 5700–5710 (2014). [CrossRef]
38. N. M. Litchinitser, A. K. Abeeluck, C. Headley, et al., “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27(18), 1592–1594 (2002). [CrossRef]
39. A. Kudlinski, A. Cassez, O. Vanvincq, et al., “Double clad tubular anti-resonant hollow core fiber for nonlinear microendoscopy,” Opt. Express 28(10), 15062–15070 (2020). [CrossRef]
40. K. Pierściński, G. Stepniewski, M. Klimczak, et al., “Butt-coupling of 4.5 µm quantum cascade lasers to silica hollow core anti-resonant fibers,” J. Lightwave Technol. p. 1 (2021).
41. G. D. Goodno, Z. Guo, R. J. D. Miller, et al., “Investigation of β-BaB2O4 as a Q switch for high power applications,” Appl. Phys. Lett. 66(13), 1575–1577 (1995). [CrossRef]
42. L. B. Liang, J. Z. Guan, X. Y. Zhu, et al., “Delivery of nearly diffraction-limited picosecond laser pulses in the air-filled anti-resonant hollow-core fiber at 1 µm wavelength,” Photonics 10(4), 416 (2023). [CrossRef]
43. G. Mann, J. Vogel, M. Zoheidi, et al., “Breakdown limits of optical multimode fibers for the application of nanosecond laser pulses at 532 nm and 1064 nm wavelength,” Appl. Surf. Sci. 255(10), 5519–5522 (2009). [CrossRef]
44. G. Mann, S. Pentzien, and J. Krüger, “Beam diameter dependence of surface damage threshold of fused silica fibers and preforms for nanosecond laser treatment at 1064 nm wavelength,” Appl. Surf. Sci. 276, 312–316 (2013). [CrossRef]
45. M. Zhao, F. Yu, D. Wu, et al., “Data for "Delivery of nanosecond laser pulses by multi-mode anti-resonant hollow core fiber at 1 μm wavelength",” Science Data Bank (2024), https://doi.org/10.57760/sciencedb.14014
