Femtosecond (fs) lasers have attracted much interest in numerous applications, including spectroscopy, medical surgery, metrology, and material processing. Especially, fs lasers enable material processing with minimized thermal damage on materials by ablation, offering high-precision micro-processing of brittle materials (for example, glass, OLED, and TFT displays) with excellent quality [1–4]. However, they suffered from low productivity due to low pulse energy. Power scaling of fs lasers can increase productivity, but at the expense of high complexity and high cost. To overcome this limitation, material processing incorporating a fs laser with a multi-gigahertz (GHz) repetition rate was recently proposed [5–11]. In the GHz regime, the delay between the fs laser pulses is less than the thermal relaxation time, so thermal accumulation in the target material by fs laser burst-pulse deposition induces a temperature rise, leading to a reduced ablation threshold [9–12]. Compared to single-pulse laser processing, the reduced energy deposited by the burst-pulse of a multi-GHz repetition rate fs laser prevents instantaneous overheating damage on a target material by sophisticated temperature control. Moreover, the average power is multi-giga times the energy of a single pulse, so increasing the number of pulses in a burst is the simplest way for power scaling and, hence, burst-pulse energy scaling. The straightforward way to achieve fs laser operation at a multi-GHz repetition rate is to employ a passively mode-locked laser resonator of a very short cavity length. Both fiber-based and bulk solid-state mode-locked lasers have demonstrated multi-GHz fs laser operation in laser resonators with cavity lengths ranging from a few centimeters to less than tens of centimeters. However, these have suffered from instability in mode-locking and a relatively low output power due to low gain [13–17]. A modified regenerative amplifier seeded by a relatively high-repetition-rate mode-locked oscillator (over a few tens of megahertz) successfully demonstrated flexible GHz intra-burst laser operation [18, 19], but requires a complex configuration incorporating a Pockels cell and careful free-space optical alignment. The most popular method is to employ a repetition rate multiplier consisting of two cascaded fiber-based couplers with a 50/50 splitting ratio [9–11, 20]. This scheme doubles the rate of the original intra-burst repetition rate, making it possible to generate multiples of the rate on demand by using the number of multipliers needed.

Here, we report a high-power Yb-doped fs fiber laser at a repetition rate of 1.83 GHz. By employing a 5-stage repetition rate multiplier, we increased the repetition rate of the mode-locked master oscillator from 57.1 MHz to 1.83 GHz. The 1.83 GHz pulse train was amplified in a two-stage Yb-doped fiber amplifier, leading to >100 W of fs-pulse laser output. In addition, we have theoretically investigated the change of a pulse width due to the propagation of an ultrashort pulse in fiber multipliers and Yb-doped fiber amplifier stages and compared it with the experimental result, which to the best of our knowledge is the first report to the gigahertz-repetition-rate fs-pulse fiber laser system with >100 W output power.

The schematic diagram of the experimental setup is shown in Fig. 1. Our fs laser system is comprised of a mode-locked seed source, a 5-stage repetition rate multiplier, two Yb-doped fiber amplifier stages, and a pulse compressor. As a seed source, we used a mode-locked Yb-doped fiber laser centered at 1030 nm, which is commercially available (FPL-M4UFF-HAY-01; Calmar laser, CA, USA). The seed laser had 100 mW of pulsed output with a pulse duration of 1.5 ps at a repetition rate of 57.1 MHz. The spectral bandwidth (full width at half maximum, FWHM) is ~21 nm. Two isolators were spliced after the seed source to protect it and the mode field adapter (MFA) was used to match the fiber core of the seed source to that of the following fiber multiplier. Then, the output was coupled to a 5-stage repetition rate multiplier, generating 2⁵ multiples of the initial repetition rate of the seed laser, resulting in 1.83 GHz. Each multiplier had a Mach-Zehnder interferometer configuration with two fiber arms of different lengths, and the signal was split and combined by two 2 × 2 fused-fiber couplers with a splitting ratio of 50/50. The passive fiber lengths of the multiplier arms were carefully determined so that the pulses from one arm were later than those from the other for half of the incident pulse interval. The polarization-maintaining (PM) single-cladding passive fiber used for the multipliers had a core of 10 µm in diameter surrounded by a cladding of 125 µm in diameter. The signal multiplied up to a repetition rate of 1.83 GHz was coupled to the pre-amplifier stage after an isolator. The signal power incident on the pre-amplifier was only ~19 mW due to the insertion losses of the multipliers and the isolators.

Figure 1. Schematic diagram of the experimental setup. ISO, isolator; MFA, mode field adapter; LD, laser diode; HRF, horizontal roof mirror; VRF, vertical roof mirror.

The pre-amplifier stage employed a double-clad PM Yb-doped fiber (Yb1200 10/125 DC-PM; nLight, WA, USA) as a gain medium, which had a Yb-doped core with a diameter of 10 µm (NA 0.08) and a pure silica inner-cladding with a diameter of 125 µm (NA 0.48). Pump light was provided by the fiber-coupled laser diode (LD) at 976 nm and was coupled via a pump/signal combiner. The absorption coefficient of the Yb fiber was 5.1 dB/m at 976 nm, but we used only ~1 m of the Yb fiber, which was relatively short. This was because the long length of the Yb fiber increases the re-absorption loss at a shorter wavelength regime, hindering robust amplification around 1030 nm. Figure 2(a) shows the amplified output power versus the incident pump power. The pre-amplifier yielded 2.2 W of output for 6.9 W of the incident pump power, corresponding to a slope efficiency of ~32%. The relatively low slope efficiency can be attributed to the short length of the Yb fiber (i.e. a low absorption efficiency of ~60%) and a low seed signal energy, lower than the saturation power of the Yb fiber, ~22 mW at 1030 nm. The amplified output signal centered at 1034 nm had a spectral bandwidth of 13.9 nm (FWHM), which is shown in Fig. 2(b) (black line). The pulse width was measured to be 14.1 ps with the aid of an autocorrelator (Pulsecheck NX 150; APE Angewandte Physik & Elektronik GmbH, Berlin, Germany).

Figure 2. Output characteristics for the pre-amplifier and the main amplifier. (a) Signal output power as a function of incident pump power for the pre-amplifier, (b) spectra of the amplified outputs from the pre-amplifier and the main amplifier, and (c) signal output power as a function of the incident pump power for the main amplifier.

Before the main amplifier, we spliced ~20 m of the single-cladding passive fiber with a 10 µm-diameter core to add a more positive chirp to the pulses [6, 7]. The main amplifier employed a double-cladding PM Yb-doped large-mode-area fiber (Yb1200-25/250DC-PM; nLights) with a Yb-doped core of 25 µm in diameter and 0.06 NA, and a pure silica inner-cladding of 250 µm in diameter and 0.48 NA. Two fiber-coupled high-power LDs wavelength-locked at 976 nm were used as the pump source. The absorption coefficient of the Yb fiber was ~13.4 dB at 976 nm, so a fiber length of ~1.8 m was selected for the main amplifier. The residual pump and cladding light were stripped by splicing a single-cladding fiber of ~ 0.3 m to the output side of the Yb fiber. The output end face of the fiber was angle-cleaved at ~9 degrees to prevent an unwanted feedback signal.

The output power from the main amplifier stage as a function of the incident pump power is shown in Fig. 2(c). The amplifier yielded a maximum output power of 125 W for an incident pump power of 202 W, corresponding to a slope efficiency of 61%. The measured output spectrum is also depicted in Fig. 2(b) (red line), showing that the center wavelength was shifted to 1037 nm from 1034 nm due to the stronger reabsorption at a shorter wavelength regime, but the FWHM spectral bandwidth was slightly increased to 16 nm. The pulse width was measured to be ~23 ps. The measured beam quality (M²) was 1.1 and the polarization extinction ratio (PER) of the amplified output was 14.4 dB at the maximum output power.

The amplified pulse output was compressed by a compressor, comprising a transmission holographic grating and two roof mirrors (Fig. 1), so the laser beam passed through the grating four times. The grating had 800 lines/mm, blazed at 1030 nm. The expression for the group delay dispersion (GDD) compensated by the compressor is [21, 22]

where λ is the center wavelength, L is the distance between the gratings, c is the speed of light, d is the line spacing, and ^θ_m is the m^th-order diffraction angle. The GDD of the incident pulse was ~820,663 fs², so the calculated distance between the grating and the roof mirror for the optimized pulse compression (i.e. half of L due to the folded configuration employing the transmission grating) was 12.2 cm, which was in good agreement with the experimental value of 12.1 cm. After four-passes through the grating, the pulse was compressed to ~290 fs, as shown in Fig. 3(a). The output power after the compressor was 102 W for an incident signal power of 125 W. The total compression loss was calculated to be ~18%, mostly due to the 4-pass transmission loss of the grating, ~4.5% per pass. The RF spectrum of the compressed output in Fig. 3(b) confirms that the repetition rate was 1.83 GHz with a high signal-to-noise ratio of >48 dB. The uneven peaks in the pulse train are caused by the imperfect 50/50 couplers. So, it can be improved by using a coupler with a better 50/50 splitting ratio. The peaks can also be made uniform by using a fast-response electro-optic modulator since the pulse train has a periodicity of 57.1 MHz, which is the repetition rate of the seed source. The symmetrical beam profile was well preserved in the compressor, as shown in Fig. 3(c), and the measured beam qualities were 1.3 on the x-axis and 1.04 on the y-axis. The high PER of the output beam was also preserved in the compressor, which had a value of 12 dB. Thus, it is confirmed that we have successfully operated a fiber-based fs laser MOPA system with a high power of >100 W at a high repetition rate of 1.83 GHz, while maintaining good beam quality and PER.

Figure 3. Output characteristics of the compressed pulse. (a) Autocorrelator trace of the compressed pulse, (b) Radio frequency spectrum of the amplified output (the inset: the pulse train), and (c) change of the beam size near the waist position for the beam quality measurement (the inset: the beam profile at the waist).

In our system, the pulses propagate in a very long length of fibers (~45 m after the seed source), so the pulse broadening due to dispersion and nonlinear optical effects (especially, self-phase-modulation), is inevitable. Furthermore, gain-narrowing in the amplifier stages, accompanied by strong reabsorption in a shorter wavelength regime, also changes the pulse width. We simulated the evolution of the pulse duration in the fiber using the commercial software, RP Fiber Power (RP Photonics GmbH, Dürrheim, Germany). This software solves the following nonlinear Schrodinger equation for pulse propagation as follows [23, 24],

where A is the amplitude, β₂ is the group velocity dispersion, β₃ is the third order dispersion coefficient, T is the normalized time scale to the initial pulse width, γ is the nonlinear parameter, g₀ is the gain, Ω_ω is the gain spectral function, and Ω_T is the gain saturation function. Since we did not know all of the laser parameters including the dispersion and phase parameters of the seed source, we assumed that the temporal pulse profile and the spectrum of the seed source had a Gaussian shape to simplify the simulation of the pulse evolution. We used their measured values at FWHM as the initial values. The calculated pulse durations as a function of the fiber length were compared with the measured values by the autocorrelator in Fig. 4. Here, the measured values were compared with the theoretical values after the second isolator. The pulse width after the second isolator was measured to be ~6.4 ps, which was longer than ~1.5 ps of the seed pulse. We were unable to measure a pulse width from the third multiplier (i.e. the combining coupler of the third multiplier) to the input port of the pre-amplifier since the signal power was too low to be measured for the autocorrelator. Despite rough simulation, the simulated results were in good agreement with the experimental values. From the isolator to the input port of the pre-amplifier, the pulse width of the signal was broadened from 1.5 ps to 27 ps due to dispersion in the silica fiber. A strong SPM effect was observed since the measured spectral bandwidth was increased from 21 nm to 30 nm along the fiber. In the amplification stage, the pulse width was dramatically shortened from ~27 ps to ~14 ps. The measured spectral bandwidth was also decreased from 30 nm to 14 nm. These remarkable reductions in the pulse width and spectral bandwidth can be attributed to the gain narrowing effect accompanied by strong reabsorption of the Yb fiber in the short wavelength regime. This can be confirmed by the red shifts of the center wavelength from 1030 nm to 1034 nm and the shortest wavelength at the FWHM from 1012 nm to 1028 nm, while the longest wavelength remained at ~1042 nm. The amplified pulse after the pre-amplifier to the main amplifier experienced similar effects, i.e., pulse broadening in the delivery fiber and shortening in the Yb fiber amplifier, so the pulse duration was increased from ~14 ps to ~26 ps in the passive fiber and was then shortened to 23 ps in the main Yb-doped fiber amplifier. In the main amplifier, the difference between the theoretical and experimental values became larger than the pre-amplifier because the high peak power of the amplified pulse seemed to induce other nonlinear effects, such as cross-phase modulation, optical Kerr effect, and nonlinear birefringence [23]. However, the reduction in the pulse width is rather larger for the calculated values than for the measured values. A more sophisticated calculation, along with measurement of the pulse width before the amplifier, is therefore required to understand this phenomenon, which is ongoing. The pulse energy of the final amplified output was still low, 67 nJ, so higher output power and energy can be achieved by employing another amplifier configuration, such as a photonic crystal fiber with a larger core size and a solid-state amplifier, to minimize the detrimental nonlinear effects.

Figure 4. Theoretical calculation and experimental values of the pulse duration along the fiber. The first two points were the measured values after the isolator and the mode field adapter (MFA), respectively.

We have demonstrated high power operation of a fs laser and amplifier at a repetition rate of 1.83 GHz with a pulse duration of 290 fs. The ultrashort laser pulses multiplied by the 5-stage repetition rate multiplier were successfully amplified in the 2-stage Yb-doped fiber amplifiers, resulting in >100 W of fs laser output at a repetition rate of 1.83 GHz. Numerical simulation of the pulse duration along the fiber shows that the pulse width was mainly affected by pulse broadening due to dispersion, SPM, and reabsorption of the Yb-doped fiber in the short wavelength regime. The maximum output power was limited by the available pump power, but an amplifier design in combination with pulse stretching of the seed output should mitigate the detrimental nonlinear optical effects, offering the prospect of a GHz-rate fs laser power in the kilowatt regime.

Ministry of Trade, Industry & Energy (Technology Innovation Program no. 20017395).

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data underlying the results presented in this paper are not publicly available at the time of publication, which may be obtained from the authors upon reasonable request.