Kilometre-scale, kilowatt average power, single-mode laser delivery through hollow core bre: overcoming nonlinear limits of glass bre

High power laser delivery with near-diffraction-limited beam quality, widely used in industry for precision manufacturing, is typically limited to tens of metres distances by nonlinearity-induced spectral broadening inside the glass-core delivery fibres. Anti-resonant hollow-core fibres offer not only orders-of-magnitude lower non-linearity, but also loss and modal purity comparable to conventional beam-delivery fibres. Using a single-mode hollow-core nested anti-resonant nodeless fibre (NANF) with 0.74-dB/km loss, we demonstrate delivery of 1 kW of near-diffraction-limited continuous wave laser light over an unprecedented 1-km distance, with a total throughput efficiency of ~80%. From simulations, more than one order of magnitude further improvement in transmitted power or length should be possible in such air-filled fibres, and considerably more if the core is evacuated. This paves the way to multi-kilometre, kW-scale power delivery – not only for future manufacturing and subsurface drilling, but also for new scientific possibilities in sensing, particle acceleration and gravitational wave detection.

For CW lasers, the main limitations arise from SBS and SRS, where SBS typically dominates for narrow-linewidth sources, while SRS is the leading effect for kW-level average power sources such as YFLs due to their intrinsic broadband linewidth 9,10 . For example, a standard single-mode fibre (SMF) designed for operation around 1 µm has a core diameter of less than 10 µm typically, which restricts the transmission of a 1-kW CW single mode beam to well below 10 m if significant SRS is to be avoided. While various methods for increasing the SRS threshold by suppressing the Stokes wavelength have been shown, more substantial efforts have gone into enlarging the mode area, since this can reduce all the aforementioned silica fibre non-linearities (except self-focusing) 10 .
However, the step-index core of an SMF can only be enlarged to approximately 16 µm while preserving single-mode (SM) operation and acceptable bend loss, and larger core sizes will lead to multimode guidance 3 . As a strategy to increase the mode area without undesired inter-modal beam instabilities, researchers have turned to alternative fibre designs. Photonic crystal fibres (PCFs) employ a wholly different guidance mechanism and thus have a less constrained relationship between core size and modal content 11 . Chirally-coupled core fibres 12 and HOM delocalised fibres 13 introduce loss mechanisms which selectively affect higher order modes (HOMs) to produce effectively SM operation. While such methods have demonstrated effectively SM operation in straight fibres with core diameters exceeding 100 µm, practical requirements for low bending loss in installations involving flexible and/or bent fibres restrict the core size to values closer to 50 µm.
Exploiting these ideas enables the transmission of near-diffraction-limited beams with significantly reduced nonlinearity, but few works have demonstrated kW-level power delivery over fibre lengths exceeding a few tens of meters. In ref 14 , fundamental mode propagation in a 60-µm core multimode (MM) step-index fibre enabled 100-m transmission of a 1-kW CW laser without onset of SRS, with a beam quality of M 2 =1.3. Similarly, a 5-kW beam with M 2 =1.3 was transmitted over a 20-m MM stepindex fibre with a 600-µm 2 effective mode area 15 . In refs 16,17 , a 3-mode PCF with an effective area of 2500 µm 2 was used to transmit 10 kW over 30 m and 1 kW over 300 m, although at the cost of a somewhat degraded output beam quality in the range M 2 =1.7-2.5 and with the need to impose large minimum bend diameters (~1 m) to ensure acceptable bend losses. Whilst these are impressive achievements, it is evident that single-mode solid-core fibres are operating close to their fundamental beam delivery limits. To transmit these powers over longer distances, or to further increase the delivered power levels, it is essential to look at radically new optical fibre technologies.

Power Delivery in Hollow-Core Fibre
In hollow-core fibres (HCFs) light travels inside a hollow core surrounded by a silica glass structure 18 .
This property can reduce nonlinear impairments to almost insignificant levels and thus enable transmission of average-and peak-power levels far beyond the limitations of silica-core fibres.
Research and development of HCFs is currently experiencing significant progress, with a large focus on anti-resonant guiding HCFs (AR-HCFs) [19][20][21][22] . The guided mode in this fibre type can have an overlap with the glass structure as low as 10 -4 -10 -5 , which practically eliminates the nonlinear contribution of silica. State-of-the-art AR-HCFs also offer effectively single-mode guidance and ultra-low propagation loss, comparable to or even below the Rayleigh scattering loss limit of silica [23][24][25][26][27] . The unique combination of low loss and negligible nonlinearity offered by AR-HCF presents an as yet unexplored opportunity to transmit ultra-high power levels over long distances without nonlinear signal distortion. Previous works have mostly focused on the transmission of high peak power short pulses over AR-HCF, achieving intensities even higher than the damage threshold of silica, but typically over fibres of a few tens of metres at most 28,29 . Experiments on high average power, neardiffraction-limited CW transmission in AR-HCFs have achieved substantial output power levels 30,31 , even exceeding 1 kW 32 . However, the propagation lengths demonstrated in these studies were no longer than a few metres -a power and distance combination also achievable with conventional glass fibres.
In this work, thanks to advances in AR-HCF fibre technology, we demonstrate, for the first time, performance well beyond that fundamentally possible in solid core fibres: the transmission of a 1-kW average power CW beam with near-diffraction-limited quality over a 1-km long AR-HCF. An input coupling efficiency of 95% and a propagation loss through the fibre of 0.74 dB/km, comparable to the Rayleigh scattering loss limit of pure silica, enabled nearly 80% of the laser source power to be delivered at the fibre output in a near-diffraction-limited beam.

Fibre characterisation
The AR-HCF used in this work is a 6-element NANF of 1-km length, fabricated using the stack-fuseand-draw method 33 . A scanning electron microscope (SEM) image of the uncoated NANF crosssection is shown in Fig. 1a. The NANF was designed to operate in the 2 nd anti-resonance window around 1064 nm 24 . The core diameter is 31 µm, the average membrane thickness is 780±10 nm and 765±5 nm for the inner and outer tubes, respectively, and the cladding diameter is 225 µm. The fibre is coated with a single ~50 µm layer of high-index polymer. The total length of the drawn NANF was 1010 m. However, a small region with defects in the middle of the fibre causing excessive local scattering was identified and cut out, resulting in two separate fibre lengths of 712 m and 289 m. These were then reconnected by fusion splicing using a standard arc-fusion splicer, with a splice loss estimated to be no more than 0.1 dB. Although the fibre was drawn using inert pressurization gas, free diffusion from the open ends over a period of several months has most likely resulted in its core being filled with a gas mixture close to atmospheric composition during the experiments 34 . Fig. 1b shows a cutback spectral loss measurement performed on the resulting 1001-m spliced NANF, together with the simulated total loss and dispersion of the same fibre (cf. Methods). There is very good agreement between the simulated and experimental loss curve in the region 1000-1100 nm.
The higher experimental loss around 1120 nm is attributed to water vapour absorption in the core, which does not impact our experiment and could be purged out if needed. At the laser wavelength of 1075 nm, the propagation loss is 0.74 ± 0.05 dB/km. The output beam quality from the 1-km NANF was determined by an M 2 measurement in a separate setup using a low-power 1064-nm laser diode (LD) (see Methods). Three consecutive measurements resulted in an M 2 value of 1.10±0.01 and 1.07±0.01 for the horizontal (x) and vertical (y) directions, respectively (one of the measurements is shown in Fig. 1c). This indicates that as a result of the large higher-order mode losses and low intermodal coupling typical of this fibre type 21 , the output light is in the NANF fundamental mode (with mode field diameter of ~22 µm) and has near-diffractionlimited beam quality (a near-field image is shown in Fig. 1d). neutral density filter, x20: microscope objective with x20 magnification, CAM: camera. b photo of the 1-km NANF. c Thermal camera image of the beginning of the coated NANF fibre following the stripped input section at P in = 1.38 kW. d Near-field camera images (CAM) of the 1-km NANF output beam at three output power levels (P out = 27 W, 174 W and 1086 W).

Power delivery demonstration
The experimental setup for the power delivery tests (see Methods) is shown in Fig. 2a, while a photo of the two spliced sections forming the 1-km NANF is shown in Fig. 2b. The laser source emits a CW beam of wavelength 1075nm and beam quality factor M 2~1 .1. The beam is coupled into the NANF under test using two lenses, chosen to achieve the highest possible coupling efficiency (CE) into the fundamental mode of the fibre and thus reduce the risk of thermal damage to the fibre coating from stray light that is not guided in the core. Thermal lensing effects in the coupling optics 35 compensated by gradually shifting the NANF input tip as the input power was increased, thus enabling maintenance of a high CE (around 95%) up to power levels well above 1 kW (see Methods).
The power delivery results for the 1-km NANF can be seen in Fig. 3a. The left axis shows the output power (P out ) vs the input power into the fibre (P in ), and the right axis shows the corresponding throughput efficiency (TE=P out /P in ). The thermal lensing compensation approach allows a high coupling efficiency to be maintained at all power levels, ensuring a nearly constant TE of almost 80% (a total loss of 0.97 dB). By subtracting the propagation loss of 0.74 dB as determined from the cutback measurement, a coupling loss of 0.23 dB is obtained, corresponding to a CE of nearly 95%.
This is close to the maximum CE of ~98% that can be in principle achieved between a Gaussian beam and the mode of a second-window NANF 36 , and is one of the highest CEs reported to date for a hollow core fibre, to the best of our knowledge. The highest output power of P out = 1086 W is obtained for an input power of P in = 1377 W, corresponding to a TE = 79%. The small 1% drop observable at the highest input powers is likely due to a small input beam distortion from uncompensated thermal lensing. The coating temperature after the initial stripped section of the NANF was monitored using a thermal imaging camera. A linear increase in the temperature vs input power was observed, reaching a stable value of ~72 °C at the highest input power of P in = 1377 W, see thermal camera image in Fig. 2c. This temperature is well below the damage threshold of the coating, which should withstand values in excess of 100 °C. For further power scaling beyond this point, improvements to the coupling setup such as use of higher purity lens substrates and cladding light extraction should be adopted, as discussed in Supplementary information.

Fig. 3. Power delivery performance of the 1-km NANF. a
Left axis: NANF output power (P out ) vs NANF input power (P in ). Right axis: throughput efficiency (TE=P out /P in ). Note, the step-like increases in TE occur when applying the thermal lensing compensation method. b Experimentally measured input and output spectra at P in = 218 W (P out = 174 W) and P in = 1377 W (P out = 1086 W). c Simulated output spectra, based on the same experimentally measured input spectra and P in values as shown in b (plotted also in c for reference). Fig. 3b shows the output spectrum of the NANF at a relatively low input power level of P in = 218 W (P out = 174 W) and at the highest input power level tested of P in = 1377 W (P out = 1086 W). The NANF output spectra are plotted together with the corresponding input spectra (measured separately to the power delivery experiment). Note that the spectral envelope of the laser output increases in width as a function of power, which is attributed to nonlinearity within the laser system itself. Note also that the smaller irregular features on the laser spectrum are not repeatable when turning the laser off and on. As can be seen in Fig. 3b for P in = 1377 W, a small but noticeable red-shift of the output spectrum (~1 nm) is observed with increasing power. To investigate its origin, light propagation through the NANF was modelled using the generalised non-linear Schrödinger equation  Fig. 3c and exhibit a very good agreement with the experimental spectra in Fig. 3b at the same power levels. A nearly identical redshift of the spectral envelope can be observed, which our simulations identify as corresponding to the Raman response of the atmospheric air within the core. Due to the small overlap between optical mode and glass membranes (calculated to be 4×10 -5 of the total power for this fibre), the glass nonlinearity is found to play no role at these power levels and distances. We also measured the near-field of the NANF output using the camera and imaging setup shown in Fig. 2a. The recorded mode profiles at P out = 27 W, 174 W and 1086 W are shown in Fig. 2d. No change was observable in the NANF output mode profile as a function of power. Because the measurement setup was situated inside a safety enclosure, it was not practically feasible to carry out an M 2 beam quality factor measurement. However, the separate M 2~1 .1 measurement performed using a low-power 1064-nm LD (see Fig. 1c), together with the unaltered mode profile at all power levels in the power delivery test (see Fig. 2d), strongly indicate that a near-diffraction limited output beam quality with a comparable M 2 -value is achieved also at 1 kW.

Discussion and conclusions
State-of-the-art AR-HCFs such as NANF are now capable of combining propagation loss comparable to or lower than solid silica fibres in a single transverse mode with negligible nonlinearity. This enables, for the first time, the power delivery of kW-class near-diffraction-limited beams over kilometre length scales, as demonstrated in this work.
To investigate the scalability of this result to even higher power levels or longer transmission distances, we have run numerical simulations under the reasonable assumption that Raman-induced spectral broadening remains the limiting factor (see Methods). An overview of the achievable fibre propagation length vs target output power for the NANF is shown in Fig. 4, where results are also compared to a conventional single mode step-index fibre (SMF) and to a state-of-the-art large core-area silica PCF designed for near-diffraction-limited power delivery 16,17 . The diagonal lines indicate the power-distance combination at which half the power is spectrally downshifted outside the original launch signal bandwidth by SRS. As can be seen, our experimental demonstration already represents a ~2.5 times improvement relative to that fundamentally achievable in the best large effective area glass-core fibres (1 kW over ~400m in the PCF). However, this is still well below the ultimate capacity of air-guiding fibres.
For example, our simulations (see Supplementary information) indicate that for a 1 kW target output power the present NANF could transmit over distances up to 6870 m with acceptable spectral distortions, 17 times longer than the PCF. At these transmission distances fibre loss starts to play a role, and if one were to use an improved NANF with 5-nested-tube and a measured record-low loss of 0.3 dB/km at 1060 nm (below the Rayleigh scattering loss limit of silica) 27 , the achievable distance would extend to 9640 m. For the transmission of a 10-kW beam, our simulations indicate that more than one kilometre would seem possible in the present NANF (~30 times longer than the PCF), limited only by Raman scattering in the atmospheric air inside the hollow core. These results would require more sophisticated launching and cladding light extraction techniques (see Supplementary information), but they do seem within the realm of possibility 17 . It is also worth noting that if air were to be evacuated from the core of the fibre, no nonlinear contribution from silica would be observed up to the 10 kW powers studied here -a potential route to achieving two or more orders of magnitude improvement in power or distance over what is possible with glass fibres. The availability of high power, near-diffraction-limited beams allows energy to be optimally directed to improve light-matter interactions, thus increasing energy-efficiency, process-control, functionality and speed. The order(s) of magnitude increase in the distances over which such beams can be delivered through hollow core NANFs can therefore be potentially disruptive in a variety of existing (this work) [15] [14] [16] [17] [32] [31] [30] and novel applications. For example, NANFs could be deployed to increase the distance between (single-mode) laser and workpiece, offering greater flexibility in the design of production lines and factory floors in future manufacturing 37 . Other laser processing opportunities arise where the target location is hazardous or difficult to access, such as for nuclear decommissioning 17,38 , or in subsurface laser drilling of rocks for oil and gas extraction, where it could provide a safer and more costeffective alternative to the use of charges and hydraulic fracturing, and where multi-kW powers and multi-km distances are required 39,40 .
It might also lead to new scientific opportunities in the trapping and acceleration of particles by radiation pressure. Guidance of particles in HCFs by radiation pressure has already been demonstrated 41 . The possibility of guiding "flying particle sensors" in km-long NANFs could enable sensing of various physical quantities with high positional accuracy at remote locations, e.g. in a radioactive environment 42 . Neutral particle acceleration by radiation pressure, for which Ashkin predicted velocities up to 3x10 6 m/s for micron-sized particles 43 , could be enabled by km-long, vacuum-pumped NANFs, wherein intensity levels could be kept low enough to avoid absorption and evaporation of the accelerated particle. Finally, with some cross-sectional enlargement, it is not unforeseeable that completely straight and vacuum-filled hollow-core fibres might one day be able to support the several hundreds of kW over several kilometres that would make them attractive for long path interferometry, e.g. for gravitational wave detection 44 .

Methods
Cutback measurement. For the cutback loss measurement, a free-space launch setup comprising two aspherical lenses was used to couple light into the 1-km NANF. Prior to the cutback procedure, such a short cutback length. Note however that chromatic aberration in the lenses imply a gradually higher excitation of higher order modes when moving away from 1064 nm, which can contribute to a fundamental mode loss overestimate since the cutback length may be insufficiently long to attenuate the higher order modes. Note also that the PM-980 launch fibre is no longer single-moded below 980 nm, hence exciting higher order modes in the NANF which may similarly lead to an overestimate of the fundamental mode loss (as can be observed in Fig. 1b). progressively shifted towards the lens, an approach that proved adequate for maintaining the CE at nearly 95% up to power levels well above 1 kW.
Power delivery, fibre arrangement. For reasons of fire safety during high power testing, the NANF is not kept on a combustible bobbin (e.g. plastic). Instead, it is rewound at low tension (20 g) into a free, self-supporting coil of diameter 32 cm and height 2 cm. This is achieved using a bobbin that can be dismounted after rewinding without affecting the fibre coil. Note that the two lengths of 712 m and 289 m constituting the 1-km NANF were wound into separate coils using this method, prior to splicing. While the loss at the splice point is small (estimated to less than 0.1 dB), it leads to heat accumulation in the protective splice sleeve, which was therefore kept submerged in water during the power delivery test to dissipate the heat and avoid damage.
Power delivery, output beam characterisation. The output power of the NANF is measured using a water-cooled power meter (PM: Gentech UP55C-2.5KW-HD-D0). The CW laser output power is recorded during the experiment using the internal power meter of the laser source. The corresponding input power to the NANF is determined from a separate reference measurement where the PM is placed after the coupling optics, yielding a reference measurement of the NANF input power as a function of the laser internal power meter value. The optical output spectrum of the NANF is measured by picking off some of the scattering from the power meter surface using a multimode fibre, connected to an optical spectrum analyser (OSA: Ando model AQ-6315A). The output mode of the NANF is monitored using the imaging system schematically shown in Fig. 2a. The total attenuation of the 4 wedges and ND filter is estimated to about 80 dB, with a polarisationdependent variation of about 1 dB. The camera exposure time is adjusted for each power to stay just below the detector saturation level. Note that the LB1723-B lens (f 3 ) is placed after W2 to avoid thermal lensing effects (following W2, the power is reduced by ~33 dB relative to the NANF output).
Note also that the transmitted beam through W2 is redirected to the PM using a mirror (this is not shown in Fig. 2a).
Numerical simulations. We used the same approach as ref 45  The fiber characteristics are modeled using a finite element method (FEM) mode solver (COMSOL) on the geometry of the fiber cross-section extracted from an SEM image for the air-filled NANF. This study provides the required information for nonlinear propagation modeling such as: full chromatic dispersion (material and waveguide dispersion), loss (confinement loss and macro-bend loss) and wavelength-dependent effective mode area. The total modeled loss presented in Fig. 1b additionally includes micro-bending loss, which is calculated by the power mode coupling method 46 applied on micro-bend induced perturbation. The combined total loss is in very good agreement with the measured cutback loss, as shown in Fig. 1b. The simulations indicate that the loss within the antiresonant passband is limited by macro-bending effects towards the shorter wavelengths and confinement loss towards the longer wavelengths.
The silica PCF chosen for our comparison modelling (Fig. 4) is reported in refs 16,17 for record power delivery. For simplicity, the core, with an effective mode area of A eff = 2500 µm 2 , is assumed to support only the fundamental mode, although the actual PCF supports 3 modes. Due to the unavailability of accurate data, the propagation loss and chromatic dispersion were assumed to be dominated by the silica material parameters rather than the waveguide.
For the optical nonlinear response of atmospheric air, we have used a quasi-quantum model which includes an individual model for each gas component (for details and parameters, please refer to ref 45 ). The accuracy of this model is also verified independently in ref 47 for the femtosecond pulse regime. To include the nonlinear response of the glass in the modeling process, we used a multimaterial nonlinear response model by considering the relative power portion in the cladding glass and air core. This method captures the full nonlinear behavior of the fiber in a unified GNLSE, as described in ref 45 , which enabled us to study the effect of each material (i.e. air or glass) separately and provides accurate modeling results (as shown in Fig. 3b and 3c).
Modelling a CW laser using the GNLSE is a challenging task since a simple flat-top pulse does not accurately model a realistic CW laser and cannot reproduce the spectral broadening observed in our experiments. As shown in Fig. 3b, the measured spectrum of the CW laser has a broader spectrum in comparison to an ideal CW laser which is caused by random noise fluctuations 48 . This broadening can be modeled by a well-known phase-diffusion model in the input field envelope 49 : Here, is a phase fluctuation with zero ensemble average and is the fibre input power of the CW field. In the frequency domain, manifests itself as random fluctuations, denoted , of the central frequency of the CW laser 48 . In the simplest form, such frequency fluctuations ( ) can be considered as Gaussian white noise with zero mean and a variance of 2 which represents the full width at half maximum (FWHM) spectral linewidth of the CW laser 50 . The phase and frequency fluctuations are related by the following equation 48 : This definition of produces a CW field with a Lorentzian power spectrum 51 . Therefore, we adapted the phase-diffusion model to the measured FWHM spectral linewidth of our CW laser and reshaped the spectrum profile of the model to the experimentally measured one while preserving the total power of the laser. This method enabled us not only to include the experimentally measured CW laser in the GNLSE, but also to reproduce the NANF output spectrum with a very good agreement with the experimental results, as shown in Fig. 3b and 3c.
Here, ( , ) is the power spectrum at a propagation distance and is the optical frequency. The parameter ( ) quantifies the ratio of power transferred outside of the initial spectrum profile.
According to this definition, when ( ) is 0.5, the power is equally distributed between the initial spectrum profile and outlier frequencies. This is analogous to the definition of critical power for forward SRS in silica fiber where the power at the pump and Stokes wavelengths are equal, which can be approximated by = 16 ⁄ 8 . Here, is the effective core area, is the Raman gain coefficient, and = �1 − exp (− )�� is the effective interaction length where is the fibre loss at the pump wavelength. Hence, the condition ( ) = 0.5 is used to define the critical -or maximum allowable -spectral broadening in both air-filled NANF and silica-core fibres.
This condition is used to calculate and compare the maximum transmission length vs target output power for the fibre types shown in Fig. 4 (diagonal lines). A more detailed explanation of the procedure can be found in Supplementary information. Note that for the silica SMF in Fig. 4, the maximum transmission length was calculated from the above expression for using typical parameters for a standard, commercially available step-index SMF designed for operation around 1 µm (A eff = 30 µm 2 , α p = 0.67 dB/km, g R = 5×10 -14 m/W).