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Abstract
We report on an all-fiber 200 W widely tunable GHz electro-optic (EO) frequency comb operating in the nonlinear regime. The EO comb pulses at 1030 nm are initially pre-compressed to sub-2 ps, then power amplified to 2.5 W, and finally boosted to 200 W in a newly designed large-mode-area, Yb-doped photonic crystal fiber. Continuously tunable across 12-18 GHz, the picosecond pulses experience nonlinear propagation in the last amplifier, leading to output pulses compressible down to several hundreds of femtoseconds. To push our system deeper into nonlinear amplification regime, the pulse repetition rate is further reduced to 2 GHz, enabling significant spectral broadening at 200 W. Characterization reveals sub-200 fs duration after compression. The present EO-comb seeded nonlinear amplification system opens a new route to the development of high-power, tunable GHz-repetition-rate, femtosecond fiber lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultrashort laser pulse generation and amplification in optical fibers have attracted massive attention in both industry and scientific research. Compared to solid-state systems, ultrafast fiber lasers provide several well-known advantages such as efficient single-pass amplification, possible all-fiber integration, high beam quality to cite a few. Besides, they also enhance nonlinear and dispersive effects, which result in many exotic phenomena and unique features. So far, mode-locking represents the most common way to generating ultrashort pulses in fibers, based on which, different techniques have been spun off, including saturable absorbers [1], nonlinear polarization evolution [2], Mamyshev oscillators [3]. In mode-locked fiber oscillators, the pulse repetition rate varies usually from tens to hundreds of MHz, limited by the physical cavity length. Reaching multi-GHz repetition rates remains challenging but is compulsory for various applications, for example, advanced material processing [4], coherent optical pulse stacking [5], ultrafast optical ranging [6], and optical communications [7]. To this end, pushing the limit of the fiber cavities’ lengths has been proven feasible for few-GHz pulse generation [8–10]. Besides, high-harmonic mode-locking also represents a viable technique [11,12]. Scaling the repetition rate to higher GHz level, however, in such ways often leads to longer pulses of tens of picoseconds which are undesirable for certain applications.
In contrast to passively forming ultrashort pulses in mode-locked oscillators, electro-optic (EO) frequency combs, represent a new kind of ultrafast fiber lasers based on active EO modulation in single-pass configuration [13–15]. Compared to existing mode-locking techniques, the repetition rate of an EO comb can be accurately set and continuously tuned at multi-GHz level using a radio-frequency (RF) synthesizer. Additionally, the carrier-envelope offset frequency is directly related to the single-frequency seed laser as well as the RF and can be stabilized by locking the seed laser. Besides, the quasi-linearly chirped pulses generated from an EO comb can be easily handled for further power amplification and pulse compression. Concerning the temporal properties of EO combs, compressed 15 fs pulses (with sub-cycle timing jitter) have been obtained from such an EO comb at 10 GHz after nonlinear spectral broadening [13]. Picosecond EO comb pulses continuously tunable across 11-18 GHz [14] and with further frequency division down to few-GHz level [16] have also been demonstrated. In the spectral domain, EO combs at $\sim$1 $\mu$m and $\sim$1.5 $\mu$m have enabled supercontinuum generation spanning the visible and near-infrared (IR) [17,18]. Frequency conversions to deep ultraviolet [19] and tunable mid-IR [20] have also been realized. However, in terms of output power, previously reported EO combs mainly stay at multi-watt level. The potential for high-power amplification is still to be explored.
In this paper, we report on the first demonstration of high-power nonlinear amplification of an ultrafast EO comb up to 200 W in an all-fiber configuration. Operating across 12-18 GHz repetition rates, the pulses from the EO comb are first spectrally shaped and compressed down to sub-2 ps near the Fourier-transform (FT) limit. They are then amplified to 2.5 W in conventional amplifiers and finally boosted to 200 W in a newly designed Yb-doped large-mode-area (LMA) photonic crystal fiber (PCF). Gain accompanied by self-phase modulation (SPM) in the last amplifier leads to output pulses compressible to hundreds of femtoseconds. Frequency division down to 2 GHz is further implemented to increase the pulse peak power, pushing the all-fiber amplification process deeper into nonlinear regime, and allowing to generate pulses compressible down to sub-200 fs.
2. Experimental setup
The experimental setup for the 200 W multi-GHz EO comb system is depicted in Fig. 1(a). The EO comb comprises a single-frequency diode laser at 1030 nm, two EO phase modulators and one Mach-Zehnder modulator (MZM). All the modulators are driven by amplified RF signals in phase, derived from a RF synthesizer. We set the frequency of the synthesizer in the range of 12-18 GHz in this experiment. Thus, the EO comb delivers chirped pulses of tens of picoseconds at 12-18 GHz repetition rate. The relative intensity noise and phase noise of the EO comb have been investigated previously [14]. Following the EO comb, another MZM sharing the same RF synthesizer is further used to divide the pulse repetition rate. Frequency division by any integer number is enabled by using a binary-controlled RF divider. The output from the MZM is amplified to 30 mW by a core-pumped Yb-doped fiber amplifier (YDFA) (6/125 $\mu$m) and then sent into a programmable pulse shaper. The pulse shaper trims the spectrum of the EO comb and compensates the chirp in the pulses, so that we obtain clean Gaussian pulses near FT limit at the output. Considering the optical losses in the pulse shaper, we use another similar core-pumped YDFA to linearly amplify the power back to 30 mW.
Fig. 1. (a) Experimental setup for the all-fiber 200 W EO comb system. BPF, band-pass filter; DM, dichroic mirror; M, mirror with high reflectivity. (b) Micrograph of the used Yb-dope photonic crystal fiber.
For further amplification, we use a band-pass filter centered at 1030 nm to lower the ASE level and send the pulses into a cladding-pumped YDFA (10/125 $\mu$m). The active fiber length is 1.5 m with its end spliced to a short mode-stripper followed by a fiber isolator. The output power from the isolator is fixed to 2.5 W, which in turn serves as a seed for the last YDFA. While the first two YDFAs are made of commercial gain fibers, the last one involves a newly developed Yb-doped PCF. The PCF has a hexagonal core with a mode field diameter of $\sim$24 $\mu$m [21]. Figure 1(b) shows the micro-structure of the PCF. Germanium and boron dopants ensure both the polarization preservation and, together with the low-index polymer coating, the wave guidance. Different from air-hole PCFs, the micro-structure of this PCF is formed and filled with silica. This new feature of the PCF alleviates technical issues encountered before such as fiber-end cleaning, fusion-splicing, and cleaving. The EO comb seed is combined with three pump diode lasers at 976 nm and mode matched to the Yb-doped PCF. The PCF is 1.9 m long, coiled and water-cooled on an aluminum optical breadboard. The output fiber tip is angle cleaved at 8$^{\circ }$ to avoid back reflection. With up to 357 W combined pump power, we generated 200 W output power. The 200-W beam is collimated to free space using a lens and extracted from the residual pump using a dichroic mirror. For characterizing the output beam, we pick up a $\sim$4$\%$ reflection of the whole power using an uncoated silica wedge and send it into a compact compressor where the beam passes through a single diffraction-grating four times. The configuration of our compressor is similar to [22], except that we use a transmission grating of 1739 grooves/mm instead of a reflection one.
3. Results and discussion
3.1 200 W EO comb operating at 15 GHz
In the experiment, we first set the EO comb frequency at 15 GHz and the frequency division module off. Figure 2(a) displays the EO comb spectra with and without spectral shaping, measured using an optical spectrum analyzer. Before entering the pulse shaper, the EO comb spectrum exhibits a typical rectangular shape with 2.35 nm bandwidth. In the pulse shaper, we applied a Gaussian filter on top of the original spectrum so that the output shaped spectrum has a near-Gaussian shape with a reduced 3 dB bandwidth of $\sim$0.9 nm. The oscillations observed on the measured spectra represent the barely resolved 15-GHz-spaced comb lines limited by the resolution of the optical spectrum analyzer. We also optimized the dispersion provided by the pulse shaper to obtain the shortest pulse duration at the output. The autocorrelation (AC) traces of the pulses compressed by the pulse shaper are displayed in Fig. 2(b). Without a Gaussian filter, the AC trace has a full-width-at-half-maximum (FWHM) duration of 1.9 ps with a low-intensity pedestal. The Gaussian spectral filtering broadens the AC trace, extending the width to 2.2 ps (close to FT limit), and removes the wing pedestal leading to clean sub-2 ps compressed pulses.
Fig. 2. (a) Unshaped (red) and shaped (blue) spectra of the EO comb at 15 GHz. (b) ACs of the unshaped (red) and shaped (blue) pulses of the EO comb after compression by the pulse shaper.
With the compressed clean pulses injected into the following cladding-pumped YDFA, we adjusted the pump power to obtain 2.5 W output power after a short mode stripper and a fiber isolator, and then characterized the amplified output pulses before the final amplifier. Figure 3(a) shows the measured spectrum at the output of the pre-amplifier. The initial spectral shape is conserved with the exception of a pedestal raising above 1033 nm however limited at the −40 dB level. The corresponding AC traces of the output pulses at 15 GHz are displayed in Fig. 3(b). The AC duration is slightly increased to 2.4 ps but can be compressed to 2.1 ps when using a grating compressor. These measurements imply that the 15 GHz EO comb pulses experience little SPM together with normal dispersion in the cladding-pumped pre-amplifier stage.
Fig. 3. Characterization of the output of the cladding pumped pre-amplifier. (a) Measured spectrum of the EO comb. Inset: Measured spectrum displayed in linear scale. (b) Measured ACs of the EO comb pulses. Blue: direct output; Red: compressed using a grating compressor.
In the last YDFA stage, the 2.5 W EO comb pulses are combined with the pump lasers through fusion splicing, ensuring an all-fiber configuration of the whole system. We first performed power scaling measurement targeting 200 W output power as shown in Fig. 4(a). The linear increase of the output power versus the pump corresponds to a slope efficiency of 57$\%$. With a combined pump power of 357 W, we measured 200 W amplified picosecond pulses after removal of the residual pump. The spatial beam profile of the output at 200 W was captured using a CCD camera, showing a regular single-mode distribution and the absence of transverse mode instabilities or fiber modal degradation. The spectrum and AC of the output were also characterized as displayed in Fig. 4(b). At 200 W, the shaped EO comb spectrum is broadened by SPM showing a dual-peak profile with extension to longer wavelengths. The corresponding 3 dB bandwidth increases to 2.7 nm. For characterizing the pulses, as described above, we extracted $\sim$4$\%$ of the full power using a silica wedge and sent it into a compact grating compressor unable to withstand the full power. The compressed pulses were then measured by an autocorrelator. It is notable that the diffraction grating of the compressor has polarization-sensitive loss and the output pulses comprise a main polarization with most of the power and an orthogonal one due to polarization crosstalk in fibers. We rotated the polarization of the output beam using a half-wave plate, so that only pulses at the main polarization are compressed, ensuring reliable AC measurements. The measured AC trace has a FWHM duration of 950 fs. As a comparison, the FT limited pulse and its AC trace based on the measured spectrum are also calculated, giving an ideal pulse duration of 480 fs and AC duration of 720 fs.
Fig. 4. (a) Power scaling of the final YDFA and spatial beam profile of the output at 200 W. (b) Measured spectrum of the EO comb at the output of the final YDFA. Inset: Measured AC of the compressed pulses at 15 GHz at the output of the final YDFA ($\sim$4$\%$ of the full power sent into the compressor), together with the AC of the FT limited pulses.
3.2 Demonstration of frequency tuning and dividing
After demonstrating 200 W operation at 15 GHz, we further tuned the pulse repetition rate of the EO comb in the range of 12 to 18 GHz. Figure 5(a) and (b) present the characterized spectra obtained on both edges of the frequency range. Similar to the 15 GHz case, the spectra were Gaussian shaped before amplification. The shaped spectra as input at 12 GHz and 18 GHz are displayed in gray lines. Their corresponding input pulses are also compressed to near FT limit by the pulse shaper, having AC durations of 2.8 ps and 2.2 ps respectively. The longer duration at 12 GHz is due to a reduced spectral bandwidth as the comb line spacing is narrower while the modulation depth of the phase modulators is more or less constant. At 200 W, the output spectra are broadened with a tail extending to longer wavelengths, similar to the 15 GHz case. Focusing on the main spectral contribution, the spectrum at 12 GHz shows a double hump structure with 3 nm bandwidth while it is relatively flat with a 3.4 nm bandwidth at 18 GHz. The spectral shaping is essentially due to SPM and directly related to the pulse peak power. Therefore, assuming an initial pulse duration around 2 ps, stronger SPM is expected at 12 GHz as the pulses carry 50$\%$ more energy compared to 18 GHz. Still, the SPM modulated spectrum at 18 GHz is wider than at 12 GHz because of a larger initial bandwidth at 18 GHz and SPM broadening. These balanced effects lead to an output bandwidth almost constant over the whole 12 to 18 GHz. A $\sim$4$\%$ sample of the 200 W output power is compressed in the compact grating compressor and the output picosecond pulses are characterized by intensity autocorrelation for 12 and 18 GHz (insets of Fig. 5(a) and (b)). The pulses at 18 GHz have an AC duration of 840 fs (to be compared with the FT limited AC of 745 fs) while, at 12 GHz, it extends to 950 fs departing somehow from the FT limited AC of 760 fs with a deviation attributed to uncompensated non-linear phase accumulated in the long all-fiber amplifier chain.
Fig. 5. Measured input and 200 W output spectra of the EO comb at (a) 12 GHz and (b) 18 GHz. Insets display the corresponding ACs at the output of the final YDFA ($\sim$4$\%$ of the full power sent into the compressor), together with the ACs of the FT limited pulses.
In order to bring our 200 W EO comb deeper into nonlinear amplification regime, we reduced the repetition rate and consequently increased the energy and peak power. Starting from a native frequency of 18 GHz, we applied a division factor of 9, leading to a final repetition rate of 2 GHz. We first measured the output pulse train using a fast photodiode and a high-bandwidth sampling scope, as displayed in Fig. 6(a). With the line spacing reduced to 2 GHz, the comb is not anymore resolved by our optical spectrum analyzer, resulting in a smooth Gaussian-shaped input spectral profile, as shown in Fig. 6(b). The output spectrum at 200 W was also measured, exhibiting a significant nonlinear broadening effect, if compared to the 12-18 GHz cases. The measurement shows an extended spectrum ranging from 1020 nm up to 1060 nm with a 10 dB bandwidth of 20 nm. The B-integral, namely accumulated nonlinear phase shift, is estimated to be 4.5$\pi$ from the spectral fringes, while it is $\leq$1.5$\pi$ for 12-18 GHz. Contrary to previous demonstrations of high-power few-GHz femtosecond fiber sources [10,23] where chirped pulse amplification is implemented, we accumulate nonlinear phase in the amplifiers using pre-compressed input pulses with moderate peak power. The latter is responsible for enlarging the spectrum by SPM instead of undergoing spectral gain narrowing as expected in linear amplification. Consequently, this process allows to generate pulses compressible down to hundreds of femtosecond level. The continuous spectral extension towards longer wavelengths below 10 dB should be attributed to the dynamically evolving gain spectrum along the propagation axis in the final amplifier [24,25]. As proceeded previously, a fraction of $\sim$4$\%$ of the full output power was sent to the compact compressor for dispersion cancellation and characterization. To summarize, the picosecond pulses experience normal dispersion, SPM and dynamic gain in the chain of amplifiers and are finally compressed leading to an AC duration of 270 fs as shown on Fig. 6(c). Based on the measured output spectrum, we calculated the FT limited pulse and its AC trace, which were 118 fs and 170 fs wide respectively. In order to estimate the actual pulse duration, we assumed a Sech$^{2}$ line shape which fits the AC trace well. Under this assumption, we calculated a pulse duration of 175 fs. Besides, as the intensity of the AC trace declines quickly towards far wings, the energy outside of −2 ps to 2 ps becomes negligibly weighted for the whole pulse energy. Thus, considering an integration interval of −2 ps to 2 ps, we further calculated the root-mean-square (RMS) duration of the AC trace which is 239 fs and the RMS duration of the pulse which is 169 fs. Earlier studies suggest that even shorter pulses could be expected, with precise linear and nonlinear chirp management prior to amplification [26,27]. Last, we further disabled the Gaussian filter in the pulse shaper and used the original EO comb spectrum as input to demonstrate the importance of pre-shaping. Figure 6(b) shows the corresponding output spectrum in green. Clearly, it has less broadening effect and relatively noisy SPM peaks compared to the output spectrum with shaped input pulses. Without shaping, the input picosecond pulses with a significant temporal pedestal have evolved into a pulse breakdown regime after amplification to 200 W and compression, as shown in Fig. 6(d). The AC trace of FT limited pulses calculated from the spectrum is also displayed as a comparison. The higher intensity of the satellite pulses in the measured AC trace should be attributed to accumulated nonlinear chirps that could not be canceled by the grating compressor.
Fig. 6. (a) Measured pulse train at 2 GHz. (b) Measured shaped input spectrum and 200 W output spectra at 2 GHz with and without shaping. (c) Measured AC at the output of the final YDFA with shaped input pulses ($\sim$4$\%$ of the full power sent into the compressor), together with a Sech$^{2}$ fit and the AC of the FT limited pulses, at 2 GHz. (d) Measured AC at the output of the final YDFA with unshaped input pulses, together with the AC of the FT limited pulses, at 2 GHz. Inset: AC of unshaped input pulses with pedestal at 2 GHz.
4. Conclusions
In conclusion, we have demonstrated high-power nonlinear amplification of an ultrafast GHz EO comb up to 200 W in an all-fiber configuration. By controlling the RF synthesizer, we could operate the EO comb in a continuously tunable repetition rate range from 12 to 18 GHz. The output chirped pulses generated by the EO comb experience Gaussian-shaping, pulse compression to sub-2 ps and power amplification to 2.5 W in conventional fiber amplifiers. A newly designed polarization-maintaining, Yb-doped LMA PCF with silica micro-structure is further employed in the final amplification stage, increasing the output power to 200 W. For repetition rates in the 12-18 GHz range, the sub-2 ps input pulses propagate non-linearly in the final amplification stage, resulting in output pulses compressible down to few hundreds of femtoseconds. To further explore the repetition rate tunability and operate our system deeper into nonlinear amplification regime, we decrease the pulse repetition rate down to 2 GHz before amplification. With a higher pulse energy, the input picosecond pulses have enabled a significantly broadened output spectrum due to SPM and dynamically evolving gain spectrum in the final amplifier, resulting in a 10 dB bandwidth of 20 nm. The corresponding compressed output pulses are characterized by autocorrelation showing a deconvoluted and RMS pulse duration of 175 fs and 169 fs, respectively.
To our knowledge, the direct output of this system represents the first hundred-watt-level, ultrafast EO comb source at tunable GHz repetition rate. Further pulse compression proves the potential of the system for delivering GHz femtosecond pulses with over 100 W output power when using a proper high-power pulse compressor. The concept of EO comb seeded fiber amplifiers operating in the nonlinear regime also provides a new route to the development of high-power, tunable GHz-repetition-rate, femtosecond fiber lasers. In the future, possibilities such as burst-mode operation, further pulse shortening, exploration of other emission bands, frequency up- and down-conversion, as well as relevant applications are foreseeable.
Funding
Conseil Régional Nouvelle Aquitaine (2019-1R5M04); H2020 LEIT Information and Communication Technologies (H2020-ICT-2018); Aquitaine Science transfert (AST_AT_2018-043); Institut Universitaire de France; Agence Nationale de la Recherche (ANR-10-IDEX-03-02).
Acknowledgments
The authors acknowledge financial supports from the French National Research Agency (ANR) in the frame of "the investments for the future" Program IdEx Bordeaux – LAPHIA (ANR-10-IDEX-03-02), the Institut Universitaire de France, and European Union’s Horizon 2020 research and innovation programme under grant agreement No 825246 (Flexiburst).
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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