# Efficient energy extraction and improved pulse quality of a Mamyshev ultrafast fiber laser with a Fabry-Perot output coupler

Riccardo Gotti, Sara Pizzurro, Antonio Agnesi, Antonin Moreau, Julien Lumeau, Federico Pirzio

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## To cite this version:

Riccardo Gotti, Sara Pizzurro, Antonio Agnesi, Antonin Moreau, Julien Lumeau, et al.. Efficient energy extraction and improved pulse quality of a Mamyshev ultrafast fiber laser with a Fabry-Perot output coupler. Optics and Laser Technology, 2025, 192, pp.113504. 10.1016/j.optlastec.2025.113504. hal-05213399

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Submitted on 18 Aug 2025

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Full length article

# Efficient energy extraction and improved pulse quality of a Mamyshev ultrafast fiber laser with a Fabry-Perot output coupler

Riccardo Gotti<sup>a, *</sup> <sup>ID</sup>, Sara Pizzurro<sup>a ID</sup>, Antonio Agnesi<sup>a,b ID</sup>, Antonin Moreau<sup>c</sup>, Julien Lumeau<sup>c</sup>, Federico Pirzio<sup>a ID</sup>

<figure><img src="image_4.png" /></figure>

## ARTICLE INFO

### Keywords:

Yb:doped fiber lasers

Ultrafast lasers

Mode-locked lasers

Mamyshev oscillators

Pulse compression

## ABSTRACT

Ultrafast Mamyshev Oscillators (MOs) can generate sub-50-fs pulses with over 1-MW peak power, but easy and efficient output coupling preserving pulse quality remains unexplored. We designed a symmetric Fabry-Perot (FP) output coupler with SiO₂/Nb₂O₅ layers to minimize satellite pulses and improve pulse quality when combined with a commercial super-Gaussian bandpass (BP) filter. Implemented in a 1030 nm Yb-fiber MO, this scheme reduced pulse duration from 48 fs (BP filter only) to 40 fs after compression, suppressing autocorrelation satellites by a factor ~3 while preserving the same energy level. These results confirm that FP-based output coupling enables a clean and efficient pulse extraction in MOs.

## 1. Introduction

In the last decade, Mamyshev Oscillators (MOs) have attracted significant interest as ultrafast fiber laser configurations reaching the so-called Gain Managed Non-linear Amplification (GMNA) [1,2] regime. In such condition, MOs have been demonstrated capable of sustaining large non-linear phase shifts (~100 π), generating high-quality sub-50-fs pulses overcoming the 1-MW peak power level with all-fiber designs [3,4]. Owing to such performance, these oscillators are highly promising for various applications, spanning from fundamental physics laser studies to medical and industrial applications [5]. A major hurdle when working with MOs is the reliable starting of the mode-locking regime, which typically requires either pump power modulation [6] or external seeding from another mode-locked fiber laser [7,8], or with a simpler and cost-effective approach, from sub-nanosecond microchip solid-state lasers [9–12].

The working principle of MOs is based on intense self-phase modulation (SPM) and the use of relatively narrowband spectral filtering at offset wavelengths to avoid continuous wave (CW) oscillation [13]. In ultrafast laser architectures comprising also self-similar lasers, dissipative solitons together with MOs, typically a fraction of the fiber amplifier's output power is extracted from the cavity, either by using a half-wave plate and polarizer [3,14], or by filtering out the broader

spectral component that is not passed through a band-pass filter [7]. The first method is inherently inefficient because it is impossible to completely dump the rejected spectral portion. Indeed, the selected narrow-band seed must retain enough energy to leverage SPM and sufficiently broaden the spectrum before reaching the next spectral offset filter, according to the operating principle of MOs. The second approach offers maximum efficiency, but the filter should ideally extract the spectral portion without degrading the spectral phase of the pulse, which is challenging considering the broad spectra involved. In all-fiber systems, this second approach has been pursued in one case using tailored designed short fiber Bragg gratings [15] which might be special components not readily available. On the other hand, in hybrid MO configurations, comprising both fiber and bulk optics components, a convenient and efficient way to realize such output coupling is through the reflection of the spectral portion from a bandpass (BP) filter placed after the gain medium [8,12]. Unfortunately, commercial BP filters are generally multi-cavity Fabry-Perot devices, lacking complete information about the complex spectral reflectivity. To address this issue, in this work we designed and tested a symmetric Fabry-Perot (FP) filter with SiO₂/Nb₂O₅ layers which, in combination with a super-Gaussian BP filter, yields efficient output coupling with minimal pulse satellites. By implementing this output coupling scheme in an externally seeded 1030 nm hybrid Yb-fiber MO, we reduced the compressed pulse duration from

<footnote><sup>a</sup> Dipartimento di Ingegneria Industriale e dell'Informazione, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy</footnote>

<footnote><sup>b</sup> Bright Solutions Srl, via degli Artigiani 27, 27010 Cura Carpignano (PV), Italy</footnote>

<footnote><sup>c</sup> Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, Marseille, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail address: riccardo.gotti@unipv.it (R. Gotti).</footnote>
48 fs (when the output coupling was made by the commercial super-Gaussian BP filter alone) to 40 fs. In addition, the satellite pulses were reduced to a factor of 3, still maintaining the same pulse energy. Our aim is not to outperform all-fiber lasers, but rather to demonstrate a simple and effective pulse extraction scheme that can be easily implemented in other ultrafast laser architectures, spanning from self-similar lasers to dissipative solitons to name a few, improving the pulse quality, in terms of compressed pulse duration and satellite pulses reduction, while preserving extraction efficiency.

## 2. Discussion

### 2.1. Fabry-Perot etalon design

The filter design, shown in Fig. 1a, consists of a symmetric FP structure made of alternating quarter-wavelength-thick layers of SiO₂ and Nb₂O₅, low (L) and high (H) refractive index materials respectively, deposited on a silica substrate with an antireflection coating on the opposite side. Of course, FP filters with similar performances could be designed with different dielectric materials. However, these two materials represent the most commonly used materials in the thin-film precision optics industry. Specifically, the FP structure includes four pairs of H-L quarter wavelength layers, a central H layer with optical thickness equal to four wavelengths (with a single resonance in the range of interest, 1000–1150 nm), and a symmetric four pairs of L-H quarter wavelength layers. This configuration was selected as one of the most promising among several designs considered, as discussed later. The FP filters were fabricated using plasma assisted electron beam deposition (Bühler SYRSUpro 710). High purity Nb₂O₅ and SiO₂ were used as the base materials and evaporated at a rate of respectively 0.25 and 0.5 nm/s. The depositions were assisted with argon and oxygen plasma thanks to advanced plasma sources directed towards the samples under coating. Thickness uniformity much better than 0.5% over the substrate aperture was guaranteed thanks to the rotation of the substrate holder as well as uniformity masks place right in front of it. In addition, an in-situ optical monitoring (Bühler OMS5000) at the central wavelength of the Fabry-Perot was implemented to secure minimal error on the thickness of each of the deposited layers (equivalent random thickness error of each layer below 1%). This ensured fabricating a component with close to theoretical performances.

The simulated reflectivity as a function of the wavelength for the FP is shown in Fig. 1b. Among the reflectivity minima, the one relevant to

<figure><img src="image_5.png" /><figcaption>Fig. 1. (a) Design of the FP filter and (b) its reflectivity function.</figcaption></figure>

the Mamyshev cavity is centered around 1064 nm, with a peak transmission of 97% (reaching 100% if we neglect back surface reflections) and with a full width at half-maximum (FWHM) of approximately 3 nm. The central wavelength can be tuned toward 1030 nm, by slightly tilting the filter as much as a few tens of degrees. As compared to typical stopband filter in MO [3,15], the FP alone is not sufficient to ensure suppression of the CW oscillation. Thus, to extract the pulse from the oscillator cavity after the active fiber we employ a combination of the FP with a commercial super-Gaussian BP filter, wavelength-matched and with 3.5-nm bandwidth. This ensures maximum efficiency of pulse extraction, an effective seeding of SPM and inhibits the CW regime.

The FP design has been optimized by modelling reflection of pulses with a super-Gaussian spectral profile selected as a convenient approximation of the MO output in the GMNA regime. The spectral bandwidth was assumed of 50 nm (~30 fs Fourier-limited pulses), carrying an ideal linear chirp resulting in a pulse duration of about 5-ps, similar to the actual pulse duration measured before compression in the experiments. The aim of the simulation is to choose the filter configuration with fewer layers and with highest efficiency (considering also the combination with the BP filter), necessary to minimize satellite pulses after reflection. Indeed, the presence of satellite pulses strongly affects the output pulse quality by reducing the energy in the main pulse, an effect that can be clearly seen observing the presence of sidelobes in the second harmonic (SH) autocorrelation function (ACF) [12]. Table 1 presents the simulation results for several investigated FP structures, with the one highlighted in bold being the realized design. The simulations indicate that a central layer with a high refractive index (H) yields better results compared to designs with a low refractive index (L) in the central layer. For this reason, in Table 1 we show only the results for the former case. In the simulations, we considered an angle of incidence of approximately 5°, which facilitates efficient pulse extraction from the hybrid cavity. Additionally, we accounted for a relative amplitude of about 4% for the first secondary lobe of the pulse in the time domain, a consequence of the super-Gaussian spectral profile assumed in the model. The spectral profile used in the simulations is somewhat arbitrary, however it served as a simple benchmark to compare the results of different possible FP structures.

The selected FP design causes an increase in the satellite peak from 4% to 5% relative to the main pulse, still an acceptable value. In addition, we modeled some possible design solutions for a sharp-edge BP filter with an FWHM of around 3.5 nm and a super-Gaussian transmission window as the commercial filter available for our experiments. Here we considered the following BP structure: (HL)⁴ 12H (LH)⁴ L (HL)⁴ 16H (LH)⁴ L (HL)⁴ 16H (LH)⁴ L (HL)⁴ 12H (LH)⁴ 0.3H 1.3L. The reflectivity and phase profiles of both filters for the considered resonance around 1064 nm are reported in Fig. 2a. The importance of spectral filter shape in MOs has been described in [3]. The results are presented in Fig. 2b on a logarithmic scale, showing the ACF of the reflected pulse from a BP filter structure that closely matches the reflectivity profile of our filter, compared to the chosen FP design. In both cases the pulse reflected exhibits energy redistribution, with a portion shifting from the main peak to secondary satellites, but this

<caption>**Table 1**</caption>

Peak transmission, reflection efficiency and relative satellite pulse amplitude of different Fabry-Perot designs with H central layer. N1 and N2 are the number of layer pairs before and after the central thicker one (see Fig. 1), respectively.

<table><thead><tr><th>Central layer width</th><th>N1</th><th>N2</th><th>Peak transmission</th><th>Reflectivity outside transmission bandwidth</th><th>Satellite pulse contrast</th></tr></thead><tbody><tr><td>2λ</td><td>5</td><td>5</td><td>97%</td><td>95%</td><td>6%</td></tr><tr><td>2λ</td><td>7</td><td>5</td><td>73%</td><td>94%</td><td>6%</td></tr><tr><td>3λ</td><td>5</td><td>5</td><td>97%</td><td>96%</td><td>5%</td></tr><tr><td>3λ</td><td>5</td><td>4</td><td>73%</td><td>95%</td><td>5%</td></tr><tr><td>4λ</td><td>4</td><td>4</td><td>97%</td><td>94%</td><td>5%</td></tr><tr><td>4λ</td><td>5</td><td>5</td><td>97%</td><td>97%</td><td>5%</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** (a) Reflectivity (upper panel) and phase profiles (lower panel) of the BP and FP filters. (b) Calculated SH-ACF curves of reflected pulses, in logarithmic scale, from the synthetic BP approximating the amplitude reflectivity of the commercial device used in the experiments, and the design-optimized FP filter, respectively.</figcaption></figure>

effect is by far more pronounced in the case of the BP filter. The sharp edges of the BP filter compared to the soft spectral amplitude filtering of the FP is the main cause of the pulse quality deterioration by increasing the satellites' contribution. Indeed, Fig. 2.a suggests that the spectral phase of both filters is comparable outside the bandpass, hence no significant differences are expected from reflectivity phase. As mentioned in the Introduction, this led us to investigate FP designs as an alternative to commercial BP filters, to be used as a simple and convenient output coupler of the MO with a suitably designed spectral reflectivity profile.

## 2.2. Experimental setup

We tested the FP in an externally seeded Yb-fiber hybrid MO, with the basic configuration described recently in [12], and whose scheme is reported in Fig. 3. It consists of a 4-m Yb-doped double-clad fiber (n-LIGHT Yb1200-10/125DC) pumped by a 6-W multimode-fiber-coupled laser diode emitting at 976 nm (NA = 0.22, core 105 µm). The pump is coupled to the active fiber through a dichroic mirror and an achromatic two-lenses telescope (not shown in Fig. 3) with ~70 % coupling efficiency. The spectral filter F1 can be either a single super-Gaussian BP filter (Semrock LL01-1064, 95% peak transmission) with FWHM ~ 3.5

nm centered around 1037 nm, or the combination of the FP to test followed by the BP filter itself. In both configurations, F1 is used as the cavity output coupler. The transmitted portion from F1 is coupled into a 12-m PM single-mode fiber (PM-980-XP, ~60% coupling efficiency), serving as the single passive arm of the cavity. The filter F2 required by the MO architecture is realized by fiber coupling after reflection of a 600 grooves/mm diffraction grating (Thorlabs GR13-0610). The fiber-coupled spectrum has a Gaussian spectral profile (FWHM ~1.5 nm) centered around 1025 nm for optimal operation of the MO. A minimum offset filter separation of about 10 nm was necessary to prevent CW lasing up to the maximum available pump power. An optical isolator ensures unidirectional operation in the ring cavity, with a pulse repetition rate of approximately 10 MHz.

The mode-locking is started by injecting into the cavity, through a 10 % partially reflective mirror (PRM in Fig. 3), a degenerate four-wave mixing (DFWM) sub-ns seed pulse at 1030-nm with a scheme described in detail in [11,12].

The MO output power reaches a maximum value of 1.1 W before compression for the maximum incident pump power of ~6 W, in both cases using either the BP or the couple FP + BP filters respectively. More precisely, a slightly higher level of pump power (4%) is required in the latter case, proving that the designed FP can be practically as efficient as the commercial BP employed for output coupling.

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Scheme of the MO with the two different output coupling approaches. DM: Dichroic mirror anti-reflection coated at 976 nm and highly reflective at 1000–1100 nm. ISO: Optical isolator, range 1030–1080 nm, 4 mm aperture, (Electro-Optics Technology Inc.). PRM: partially reflective dielectric mirror (R = 10 % at 1030–1080 nm). FC: fiber collimators. F1: angle-tuned spectral filter and output coupler, switchable from only band-pass (BP) filter to Fabry-Perot (FP) filter followed by BP. F2: 600 grooves/mm reflective grating.</figcaption></figure>

## 2.3. Experimental results

Fig. 4a presents the output spectra of the MO when using the BP filter as the F1 output coupler, while Fig. 4b shows the spectra obtained with the FP as the output coupler followed by the BP filter. In both cases, the spectra were recorded for different output energies, measured after a folded single-grating Treacy compressor [16], with a transmission efficiency of approximately 65%. Once a pulse energy of about 110 nJ (corresponding to ~75 nJ after compression) is reached, any further increase of the pump power leads to the onset of Raman contribution around 1150 nm, which begins to destabilize the mode-locking oscillation and reduces pulse coherence.

The transmission window of the output coupler F1 is angle-tuned to be centered around 1037 nm, and its spectral dip is evident in both figures. However, in Fig. 4b, the dip is less pronounced due to the FP's transmission function, which is more Gaussian-like compared to the BP filter's super-Gaussian profile. As discussed in the last part of paragraph 1.1, this soft-aperture filter is the main cause of improvement in the compressed pulse duration and pulse quality. We will further illustrate the performance enhancement in Table 2 when comparing the theoretically expected values, obtained via IFFT with zero-constant spectral phase, with those retrieved experimentally.

The main advantage of using the FP and BP combination as the output coupler becomes evident when analyzing the SH-ACFs after compression. The results are summarized in Table 2, which reports the
<figure><img src="image_8.png" /><figcaption>Fig. 4. Experimental spectra for BP filter (a) and FP + BP filter (b) output coupler, as a function of the output pulse energy after the Treacy compressor.</figcaption></figure>

<table><caption>**Table 2**

Performance comparison between BP and FP + BP filter output coupling.</caption><thead><tr><th></th><th>Output energy after<br>compression (nJ)</th><th>Spectral widths at -3 dB<br>(nm)</th><th>Experimental compressed pulse<br>duration (fs)</th><th>Area ratio in the main<br>peak</th><th>Exp./IFFT pulse<br>duration</th></tr></thead><tbody><tr><td rowspan="5">BP as output coupler</td><td>24</td><td>57</td><td>54</td><td>89 %</td><td>1.38</td></tr><tr><td>36</td><td>70</td><td>51</td><td>89 %</td><td>1.5</td></tr><tr><td>48</td><td>80</td><td>48</td><td>92 %</td><td>1.55</td></tr><tr><td>60</td><td>84</td><td>47</td><td>93 %</td><td>1.62</td></tr><tr><td><strong>75</strong></td><td><strong>93</strong></td><td><strong>48</strong></td><td><strong>91 %</strong></td><td><strong>1.78</strong></td></tr><tr><td rowspan="5">FP + BP as output<br>coupler</td><td>25</td><td>50</td><td>54</td><td>90 %</td><td>1.35</td></tr><tr><td>36</td><td>58</td><td>45</td><td>92 %</td><td>1.22</td></tr><tr><td>48</td><td>69</td><td>42</td><td>93 %</td><td>1.27</td></tr><tr><td>60</td><td>73</td><td>40</td><td>95 %</td><td>1.29</td></tr><tr><td><strong>75</strong></td><td><strong>78</strong></td><td><strong>40</strong></td><td><strong>94 %</strong></td><td><strong>1.38</strong></td></tr></tbody></table>

spectral widths, compressed pulse durations, retrieved area of the main peak in the ACF from fitting, and the ratio between the experimentally measured pulse duration and the IFFT-derived duration assuming a flat spectral phase.

Although the spectral widths are approximately 15 % narrower and exhibit slightly different shapes when using the FP + BP output coupling scheme, the compressed pulse durations are systematically shorter. This brings them significantly closer to the IFFT theoretical limit and results in an overall improvement in the main peak area relative to the fit. In particular, the enhancement in pulse quality and the reduction of parasitic satellites are clearly demonstrated in Fig. 5, which shows the SH-ACFs at the maximum investigated output power and refers to the lines highlighted in bold in Table 2. Comparing Fig. 5a and Fig. 5b, the

side lobe amplitude relative to the central peak decreases from ~3 % to ~1 %, while the area beneath them in the ACF is reduced from 9 % to 6 % (the error in the estimation of the area is about ±0.02 %). This is in qualitative agreement with Fig. 2 which suggests that the FP output coupler offers superior performance in terms of pulse quality. The exact shape and intensity of sidelobes probably depends on the specific output spectrum (intensity and phase) from the fiber amplifier. Additionally, the compressed pulse duration decreases from 48 fs to 40 fs (the statistical error in the determination is about ± 0.05 fs), corresponding to a reduction of approximately 17 %, and an increase of 20 % in pulse peak power. In those two cases, the second-order dispersion required to compress the pulses are around -20000 fs² and -16500 fs², respectively. These results demonstrate the potential of using tailored FP

<figure><img src="image_9.png" /><figcaption>Fig. 5. SH-ACF of the pulse after compression at maximum incident pump power, in logarithmic vertical scale, for BP filter (a) and FP + BP filter (b) output coupling. The red curves are the corresponding fitting function of autocorrelations related to pulse intensity with sech² shape.</figcaption></figure>
etalon designs to efficiently extract pulses from the hybrid Mamyshev
cavity with a simple optical component while minimizing pulse quality
degradation after reflection.

3. Conclusion

We have demonstrated that using a symmetric Fabry-Perot filter in
combination with a commercial bandpass filter as an output coupler in a
hybrid Yb-fiber Mamyshev oscillator enables efficient and straightfor-
ward pulse extraction while improving pulse quality and reducing the
compressed pulse duration. The FP design was selected based on nu-
merical simulations of its transmission, reflectivity, and the spectral
phase of an ideal reflected pulse, focusing on configurations with a
minimum number of layers.

The FP structure and design method based on standard multilayer
matrix techniques and pulse modelling with FFT techniques are very
easy to implement with any modern programming language (we used
Matlab), while coating deposition can be realized with the most
convenient material technology available at specialized companies.

It is also worth noting that the FP filter and the wavelength-matched
sharp-edge BP filter could, in principle, be implemented on the same
substrate, thus realizing a single device for output coupling and sharp-
edge filtering.

Testing the combination of filters as an output coupler for a MO setup
available, we achieved a reduction in autocorrelation satellites from
~3% to ~1%, with respect to the main peak, and a ~17% decrease in
compressed pulse duration, reaching 40 fs, compared to using only the
BP filter as the output coupler. These results confirm the effectiveness of
our approach in improving the spectral filtering of the output coupled
pulses while maintaining high extraction efficiency. The FP filter can
also be used as an output coupler in other ultrafast fiber laser archi-
tectures employing some kind of spectral filtering, such as self-similar
and dissipative soliton lasers, to name a few.

CRediT authorship contribution statement

**Riccardo Gotti:** Writing – review & editing, Writing – original draft, Validation, Software, Investigation, Formal analysis, Data curation.
**Sara Pizzurro:** Writing – review & editing, Writing – original draft, Validation, Software, Formal analysis, Data curation.
**Antonio Agnesi:** Writing – review & editing, Writing – original draft, Validation, Super-vision, Resources, Project administration, Investigation, Funding acquisition, Formal analysis, Conceptualization.
**Antonin Moreau:** Writing – review & editing, Writing – original draft, Resources, Meth-odology, Investigation, Conceptualization.
**Julien Lumeau:** Writing – review & editing, Writing – original draft, Validation, Resources, Methodology, Formal analysis, Conceptualization.
**Federico Pirzio:** Writing – review & editing, Writing – original draft, Visualization, Su-pervision, Resources, Project administration, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

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.

Acknowledgment

The authors acknowledge financial support from the project
“ATTILA - Advanced room-Temperature THz hyperspectral Imaging
based on novel ultrafast fiber LASers" funded by the MIUR Progetti di
Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2022 - grant
20227849RL.

Data availability

Data will be made available on request.

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