1. Introduction

Modelocked femtosecond Yb-fiber lasers presently find numerous applications and compete successfully with their solid state counterparts, such as Ti:Sa oscillators. Different laser cavity designs and mode-locking principles have been demonstrated (see e.g. [1, 2]), however only a few of the Yb-fiber lasers were realized in a truly all-fiber, i.e. monolithic format [3]. Also, fiber-end delivery of nJ-level femtosecond pulses with high polarization stability has not been demonstrated so far by monolithic fiber lasers, to the best of our knowledge.

Modelocking stability is yet another critical issue, which is not often commented upon in the literature. Nevertheless, modelocking stability is a key parameter for most laser applications, specifically for applications where further amplification of the laser is required.

Modelocked lasers operate in two modelocking regimes - stable modelocking with minimal pulse-to-pulse intensity fluctuations, and Q-switched modelocking, where spontaneous increase in pulse intensity leads to depletion of the inversion in the active medium by a few laser pulses followed by subsequent inversion recovery. Therefore, the Q-switched modelocked laser output intensity will be chaotically time-modulated by the gain depletion-recovery dynamics. This results in enormous pulse-to-pulse intensity fluctuations at relatively constant time-averaged output intensity of the laser, i.e. some of the pulses will have giant peak intensities. As a result, Q-switch-modelocked lasers are prone to fast degradation of cavity elements, and their amplification often leads to destruction of amplifier components. Also, Q-switching lasers are obviously not suitable for such applications as medicine and metrology, where high control over the laser performance is needed.

An important distinction should be made between the Q-switching and Q-switched modelocking processes. The former process may lead to longer pulses with very narrow bandwidth, but it will not be supported by the laser having a rapidly-reacting saturable absorber, that will still enforce axial mode synchronization, and therefore short pulses. Only stable or Q-switch modelocking, both producing short pulses with higher bandwidth, are physically possible in such lasers.

Below we will demonstrate a self-starting, fully monolithic linear cavity all-PM-fiber solution for a nJ-level fs laser which is stable against the Q-switched modelocking regime in a wide range of intracavity pulse energies. This is achieved by using a combination of a narrow-band fiber Bragg grating (FBG) and a semiconductor saturable absorber mirror (SESAM) with high modulation of reflectivity.

2. Operational principles and theoretical modelling

The full laser system consists of a modelocked oscillator, a series of pre-amplifiers, a power amplifier, and a spliced-on hollow-core photonic crystal fiber (HC-PCF), in which the output laser pulse is compressed down to femtosecond duration with low loss and a high degree of polarization stability. The oscillator involves a linear cavity consisting of polarization-maintaining single mode (PM SM) passive and Yb-doped fibers, confined between a SESAM and FBG, as shown in Fig. 1. Pumping of the oscillator by single mode 976 nm laser diodes (LD) is performed via a 980/1060 nm polarization-maintaining wavelength division multiplexer (PM WDM). The laser signal is outcoupled via a polarization-maintaining 20/80 filter coupler (PFC).

The SESAM supports the intensity fluctuations in the laser cavity, so that the signals with higher peak intensities will experience lower cavity loss. This results in a situation where pulsed operation of the laser is preferable, and thus self-starting modelocking is achieved. On the other hand, since a spontaneous increase in the pulse peak intensity as a result of pulse-to-pulse intensity fluctuations within the modelocked pulse train will still lead to lower cavity loss due to the nature of the SESAM, these fluctuations may lead to a chaotic Q-switched modelocking regime of the laser.

 

Fig. 1. General layout of the laser. FBG - fiber Bragg grating, SESAM - semiconductor saturable absorber mirror, WDM - 980/1060 nm wavelength division multiplexer, PFC-20/80 polarization filter coupler, LD - pump laser diode at 976 nm, PISO - polarization-maintaining isolator, PM SM - polarization-maintaining single-mode fiber. PM HC-PCF-polarization-maintaining hollow-core photonic crystal fiber, OS - optimized splice. Inset: oscilloscope reading of the modelocked pulse train.

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In order to stabilize and dispersion-manage the cavity, we employ a uniform narrow-band FBG. Stronger pulses in optical fibers undergo substantial self-phase modulation, which leads to an increase in the spectral bandwidth of the pulse. Thus, the excess energy of the pulse will be spectrally redistributed to the shorter and longer wavelength sides of the pulse spectrum with respect to its central wavelength. Therefore, if the laser cavity includes a narrow-band FBG serving as an end mirror, the excess pulse energy resulting from a strong intensity fluctuation will not be reflected back into the cavity, and will leave the cavity past the FBG.

Bragg gratings, even uniform ones, also have positively and negatively chirping spectral regions. Thus, apart from enforcing the central wavelength of the laser, a FBG can be used as a means of dispersion management in the cavity, balancing the effect of pulse propagation through the long positively chirping single-mode fibers. We have performed numerical modelling of our laser based on the approach presented in [5]. This model is based on the nonlinear Schrödinger equation for fiber propagation and rate equations for the gain and saturable absorber. The fiber lengths in the model corresponded to those in the actual laser cavity, as described in the following section. The SESAM modulation depth and saturation fluence were assumed to be 24% and 70 µJ/cm² respectively, also corresponding to the experimental parameters. The FBG was modelled as a uniform grating with a maximal reflectivity of >0.99, and a reflectivity band FWHM of 0.7 nm. It is noted that the experimentally fabricated FBG was not strictly uniform, so the modelling only provides an approximate description of the experimental results. The combined action of SESAM and narrow-band FBG on the total cavity loss is illustrated in Fig. 2. In Fig. 2(a), separate contributions of the SESAM and FBG are shown.

 

Fig. 2. (a) Reflectivity of SESAM and FBG as a function of the respective incident pulse energy. (b) Combined reflectivity of SESAM and FBG as a function of the energy of the pulse incident on SESAM.

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While SESAM provides growing reflectivity as a function of incident pulse energy, the FBG reflectivity decreases as a result of more self-phase modulation-generated spectral bandwidth of the pulses being lost from the cavity. The SESAM and FBG reflectivities are shown on different incident energy scales because SESAM absorption, 20% outcoupling of the laser pulse, and a single pass through the amplifier section occur in between the reflection events in each of these elements. It is noted that while the pulse energy fluctuates significantly over the course of a single round trip, the normalized pulse shape was found to have little variation between different points in the cavity. In Fig. 2(b) the combined reflectivity of SESAM and FBG is shown as a function of the pulse energy incident on the SESAM. It has a clear maximum at around 175 pJ incident pulse energy, which will correspond to 23 pJ of outcoupled pulse energy, taking into account losses in the SESAM. This maximum marks the lower stability limit of the laser in terms of incident pulse energy [5]. When the incident pulse energy reaches twice this value, i.e. 350 pJ, the conditions for the formation of double pulses in the cavity are achieved. When the combined reflectivity becomes lower than the product of maximal FBG reflectivity and unsaturated SESAM reflectivity (assumed to be 60% in these calculations), the laser is unstable towards the formation of a continuum wave coexisting with the modelocked pulse. The lowest of these threshold energies will correspond to the upper stability limit of the laser. We do not present the calculated results in this pulse energy regime because the numerics of the model [5] become unstable.

In Fig. 3, the detailed performance of the FBG as both a pulse energy stabilizer and an intracavity dispersion management element is illustrated. We note here, that the full laser cavity with all its elements (i.e. FBG, active and passive fibers, outcoupler, and SESAM) is used in these calculations, and the steady state in the numerical model has been reached where the temporal and spectral behavior of the laser pulse is only set by the intracavity pulse energy. The pulse energy dependencies of reflectivity and transmission spectra of the FBG are shown in Fig. 3(a,b) on a normalized 30 dB scale. One can see that while the FBG-reflected spectrum (Fig. 3(a)) slowly broadens and then stabilizes as the incident pulse energy grows, the FBG-transmitted spectrum (Fig. 3(b)) always demonstrates substantial spectral broadening. This indeed will lead to the optical limiting behavior of the FBG, as an ever higher fraction of the incident pulse energy will be dumped away from the cavity as illustrated in Fig. 2.

 

Fig. 3. Calculated spectra of the (a) pulses, reflected back into the cavity and (b) pulses, dumped away from the cavity by the FBG as a function of incident pulse energy. Spectral intensity is shown on a 30 dB scale, normalized to the maximum of the strongest reflectivity spectrum. (c) Linear power reflectivity and group delay dispersion of the FBG. (d) Calculated spectra of the pulses reflected back into the cavity (red) and dumped away from the cavity (green) by the FBG for the pulse energies of 166 pJ and 303 pJ. In (a),(b), and (d) the full laser cavity with all its elements is used for the calculations (see text).

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In Fig. 3(c) we show the calculated reflectivity and group delay dispersion (GDD) of the FBG. These FBG parameters are calculated assuming linear regime. The nonlinear properties of a FBG are insignificant here since its length is negligibly short. Even though this FBG is a uniform one, it is positively chirping (i.e. has negative GDD) on the shorter-wavelength part of its spectrum, and is negatively chirping (i.e. has positive GDD) on the longer-wavelength part of its spectrum. In the center of a reflection band the FBG is dispersionless. Thus, the longer-wavelength part of the FBG can be successfully employed for the dispersion compensation of otherwise positively chirping laser cavity. In fact, the accumulated fiber GDD over a full cavity round trip is as low as -0.15 ps/nm, which shows that the cavity dispersion is completely dominated by the grating GDD shown in Fig. 3(c).

 

Fig. 4. Calculated shapes of the outcoupled pulses of different pulse energies. Inset: pulse duration at FWHM as a function of the pulse energy.

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The spectra of FBG-reflected and FBG-transmitted laser pulses in the cavity are shown in Fig. 3(d) for two incident pulse energies. For the FBG-reflected (i.e. supported by the cavity) laser pulse, most of the spectral weight appears on the longer-wavelength, negatively-chirping side of the FBG reflectivity spectrum, with a pronounced peak appearing at the short-wavelength reflection edge. The spectrum resembles that of a soliton coupling to dispersive waves in the normal-dispersion region, a picture well known from soliton propagation close to a zero-dispersion point in fibers. Thus we demonstrated that the stable pulse formation in our laser is totally governed by the FBG performance. The satellite features in the spectrum are stronger than in the results of [5], due to slightly different assumed reflectivity of the FBG. The FBG used in the experiments described below had less uniform structure, with slightly reduced reflectivity over part of the bandwidth, and appeared to yield a much smoother output spectrum.

In Fig. 4 the calculated pulse shapes for the pulses of various energies are presented. The pulse always consists of a strong peak followed by a weak damped oscillating trail. This trail is formed by the spectral weight in the normal-dispersion region of the FBG. In the inset of Fig. 4 we present the pulse duration at FWHM of the main peak dependency on the pulse energy. It decreases with increasing pulse energy, as a result of more bandwidth being present in the stronger pulse. The decrease is weak, however, due to the strong bandwidth-limiting effect of the FBG. Indeed, the sub-nm bandwidth of the oscillator-generated pulses does not allow for generation of femtosecond pulses. The oscillator pulses are near-bandwidth-limited to picosecond duration, as shown in Fig. 4. In our approach, a higher bandwidth of the oscillator pulse was sacrificed for the excellent stability properties of the oscillator. Nevertheless, further amplification and consequent spectral expansion of a very stable oscillator pulse up to several THz of bandwidth is straightforward, as will be demonstrated below.

 

Fig. 5. (a) Normalized spectra measured at the output of the oscillator, end amplifier, and after 9.5 m of HC-PCF, i.e at the output end of the laser. HC-PCF group velocity dispersion (from [8]). (b) Intensity autocorrelation of the pulse measured after the end amplifier, and its Gaussian fit.

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3. Experimental results

The oscillator cavity consisted of 2.3 m of Nufern PM Panda fiber [6], of which 0.3 m was Yb-doped [7] (see Fig. 1). This cavity length provides the oscillator repetition rate of 44.7 MHz. The cavity was confined between an FBG with the center of the reflection band at 1065 nm, and a SESAM with 24% saturable loss. We have also successfully tested several other cavity lengths, which resulted in the repetition rates ranging between 34 MHz and 80 MHz. We always observed stable modelocking without entering the Q-switching mode, that was maintained over the course of many hours long tests.

The central wavelength of 1065 nm was chosen to match the wavelength of minimum third-order dispersion in the Crystal Fibre A/S HC-1060-02 PM HC-PCF [8], which is used for monolithic compression of the output of our laser down to femtosecond pulse duration. PM HC-PCF are the fibers of natural choice for low-loss high-PM monolithic fiber laser pulse compression [9], since they demonstrate the unique combination of the properties needed for this task: (i) high anomalous dispersion and low third-order dispersion, (ii) low loss over a wide wavelength range, and (iii) low Kerr nonlinearity.

The oscillator showed stable self-starting and long-lasting modelocking in the range of pump powers of 30–45 mW provided by the single-mode laser diode operating at 976 nm. The oscilloscope-measured modelocked pulse train produced by the oscillator is shown in the inset of Fig. 1. At 32 mW of pump power, the output pulse energy of the oscillator was 20 pJ as measured after the low-insertion-loss polarization-maintaining isolator (PISO). This value is in a very good agreement with the theoretically predicted value for lower-energy modelocking stability limit of 23 pJ, which demonstrates a high numerical accuracy of our theoretical model [5].

The oscillator output was sequentially preamplified in a series of single-mode amplifiers up to the level of 600 pJ, before entering an end amplifier. Sequential preamplification was required in this case to bring the contrast between the laser emission around 1065 nm and amplified spontaneous emission (ASE) in Yb at around 1040 nm to the level of >30 dB before end amplification. The end amplification in yet another single-mode amplifier with a slope efficiency of 0.61 brought the output pulse energy to the level of 10.2 nJ at the amplifier pump power of 750 mW. At this final stage, the contrast between the laser output and ASE was reaching the values of >20 dB.

 

Fig. 6. (a) Calculated pulse shapes as a function of the HC-PCF length, on a linear intensity scale. Measured spectrum and deconvoluted pulse duration from Fig. 5 are used as an input for the calculation. (b) Calculated shapes of transform-limited pulse, and of shortest pulse resulting from the HC-PCF propagation model. The pulses are centered at zero time delay for clarity. (c) Measured intensity autocorrelation of the laser pulse after compression in 9.5 m of HC-PCF, and calculated intensity autocorrelations of transform-limited pulse, and of shortest pulse resulting from the HC-PCF propagation model, shown in (b).

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The laser output was launched into a 10 m-long piece of PM SM fiber, where the spectrum was broadened up to a bandwidth of 11 nm at FWHM due to self-phase modulation. The broadband output was then isolated in yet another PISO with an insertion loss of 2.7 dB, before launching it into the pulse-compression HC-PCF. In Fig. 5(a), the normalized output spectra measured at the output of the oscillator, after the PISO at the end of the spectral-broadening fiber, and at the output end of the laser after 9.5 m of pulse-compression HC-PCF are shown, along with the GVD of the HC-PCF. It can be seen that spectral broadening in the 10 m-long piece of PM SM fiber by a factor of >10 was achieved while still retaining an acceptable spectral shape. The spectrum of the laser pulse stays practically unchanged after the propagation through nearly 10 m of HC-PCF, which demonstrates a very low Kerr nonlinearity of such a fiber. The noncollinear autocorrelation of the isolated output of the laser before the compression is shown in Fig. 5(b). The shape of the autocorrelation signal is a near-perfect Gaussian with the FWHM of 15.7 ps. This corresponds to the deconvoluted [10] pulse duration at FWHM of 11.1 ps.

We have performed an optimized splice between the PM SM pigtail of the end PISO and a long piece of pulse-compression PM HC-PCF, using the procedure described in [9]. Such an approach allows for PM-SMF-to-HC-PCF splice loss of only 0.62±0.24 dB, and polarization extinction ratio (PER) of 19±0.68 dB. As was shown in [9], low splice loss is a key prerequisite in achieving high PM properties of the splice, and thus of the whole fiber assembly. The group birefringence of HC-1060-02 PCF, resulting from its slight core asymmetry, was measured to be Δn=1.65·10^-4, which ensures its high PM properties, as described in [9].

 

Fig. 7. (a) SEM image of the HC-PCF. Courtesy of B.J. Mangan, Crystal Fibre A/S. (b) Measured far-field profile of the laser mode on the logarithmic intensity scale. (c) Cuts through the maximum intensity area of the laser mode profile in vertical and horizontal directions on the linear intensity scale, and their Gaussian fits.

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In order to estimate the length of the HC-PCF needed to compress the pulse to the shortest possible duration, we performed a numerical modelling of the pulse propagation, using the measured pulse duration and spectrum as an input, and taking into account the GVD of the fiber, shown in Fig. 5(a). We have also assumed in this calculation, that only and the second-order dispersion is present in the original 11.1 ps - long pulse (linearly stretched pulse). The calculation results are shown in Fig. 6(a), as a function of HC-PCF length. This modelling provides the shortest resulting pulse duration when the HC-PCF reaches the length of 8.8 m, after which the pulse starts to acquire a net negative chirp.

A noncollinear autocorrelation of the compressed laser output at the end of a long piece of HC-PCF was measured, and a series of cutbacks was performed in order to achieve the shortest pulse duration. We have found that the shortest output pulse corresponds to 9.5 m of the HCPCF length, which is in reasonably good agreement with our theoretical prediction of 8.8 m. The pulse energy after the HC-PCF compression was found to be 4 nJ. The decrease of the pulse energy from 10.2 nJ, as measured right after the end amplifier, is caused mostly by the high insertion loss of the end PISO, whereas the combined HC-PCF loss, consisting of the splice loss and attenuation in HC-PCF, only reaches 1.35 dB.

In Fig. 6(b) the calculated shapes of transform-limited pulse, and of the shortest pulse resulting from the HC-PCF propagation model are shown. Their respective FWHM durations are 225 fs and 280 fs. The asymmetry of the HC-PCF compressed pulse shape, and its longer duration, is explained by the contribution of a higher-order dispersion of the HC-PCF (see Fig. 5(a)), which results in a small residual chirp of the pulse. In Fig. 6(c) we present a measured autocorrelation of the laser pulse compressed in 9.5 m-long HC-PCF, and the calculated autocorrelations of the transform-limited pulse, and of the shortest pulse resulting from the HC-PCF compression model. Their respective FWHM durations are 615 fs, 315 fs, and 394 fs.

We note here that the measured autocorrelation line shape could not be fitted with any parameterized function [10], and therefore the real pulse duration in this case can only be estimated by comparison with the autocorrelations of known pulse shapes. We have found, that the measured autocorrelation of the best-compressed pulse of 615 fs can be reasonably well reproduced by the calculated autocorrelation of the laser pulse, having 370 fs FWHM duration and originating from the same spectrum (not shown here). This pulse duration is somewhat longer than 280 fs, resulted from the numerical propagation model, although the HC-PCF lengths used in experiment and in theory, 9.5 m and 8.8 m, respectively, are quite close. We believe that the longer experimental pulse duration is due to the fact, that the original 11.1 ps long pulse at the entrance of the HC-PCF (see Fig. 5(b)) has acquired a certain degree of higher-order chirp during the spectral broadening stage, which was not taken into account in our HC-PCF compression modelling. Another possible reason for longer than expected autocorrelation of a measured pulse is the small deviations of GVD of the HC-PCF from the specified values [8], and by the GVD fluctuations along the fiber length, that also could not be accounted for in the calculations.

 

Fig. 8. Dependencies of spectral width at FWHM, and intensity autocorrelation duration of the laser pulse at FWHM on the end amplifier pump power.

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In Fig. 7 we show the SEM image of the HC-PCF fiber and the resulting far-field laser mode shape. The HC-PCF based on the 7-cell core design provides the near-single mode Gaussian output overlapped with a low-intensity hexagonal beam pattern in the far-field, which is typical for this type of fiber [8]. The cuts through the maximum intensity area of the mode shape made in horizontal and vertical directions of the mode image show near-perfect Gaussian shapes, with vertical-to-horizontal FWHM aspect ratio of 1.07. Interestingly the low-intensity hexagonal pattern has an apparent vertical-to-horizontal aspect ratio of <1, which is illustrated by the deviation from a Gaussian line shape in the low-intensity part of the horizontal direction cut. This weak mode ellipticity is a result of a slight asymmetry of the core typical for the air-guiding 7-cell core design fibers, which is also responsible for the high birefringence of the HC-PCF, leading to its strong PM properties [9].

The monolithic all-fiber laser, like the one described above, has only one user-accessible degree of tuning freedom: change in the power provided by the pumping laser diodes. In Fig. 8 we demonstrate dependencies of the resulting pulse autocorrelation duration, and its spectral bandwidth, both measured at FWHM, on the end amplifier pump power. 750 mW was the maximum achievable output power for the pump LD used in the amplifier. The compression HC-PCF was kept at the same length of 9.5 m as in the measurements shown above. One can see that the generated bandwidth grows linearly with increase in the pump power, whereas the resulting autocorrelation duration linearly decreases. This is precisely expected behavior for a chirped signal containing more and more bandwidth, propagating through an optical element with a fixed GDD. These linear dependencies demonstrate that the proposed laser design has a potential in scalability leading to both higher output pulse energies and shorter pulse durations, as well as a high degree of tunability in its performance by simply adjusting the pump power in the end amplifier. In particular, one can generate negatively prechirped pulses at the end of the laser, as a result of the higher pulse bandwidth provided by the stronger amplifier pumping. Thus, precompensation can be achieved for the positive chirp acquired in the optical elements following the laser output end. The chirp tunability limit will be reached when the pulse bandwidth reaches values at which the higher-order dispersion in HC-PCF acts more strongly on the spectral wings of the pulse, which will result in its inhomogeneous stretching. The spectral shape may also become a limiting factor at this stage, since more spectral fringes resulting from the self-phase modulation will result in the pronounced wings in the pulse, and in an overall more complicated resulting pulse shape.

4. Conclusions

In conclusion, we have demonstrated both theoretically and experimentally, a fully monolithic (i.e. without any free-space coupling), all-PM femtosecond laser with a very high stability against chaotic Q-switched modelocking. The oscillator is modelocked using a SESAM and is stabilized and dispersion-managed using a narrow-band FBG. The subsequent amplification of the oscillator output in a series of single-mode amplifiers, its spectral bandwidth expansion in a single-mode fiber, and monolithic compression in spliced-on PM HC-PCF provides pulses of around 370 fs duration and 4 nJ pulse energy, directly delivered from the fiber end with a high optical mode quality.

Our laser has a potential of scalability both in terms of higher pulse energies and shorter pulse durations, as well as in the chosen repetition rate (by adjusting the cavity length). It also offers a high degree of tunability in the resulting pulse energy, duration and chirp by simply adjusting the pump power in the final amplifier stage. A reasonably good agreement between theoretical predictions and experimental results is observed for such crucial parameters as the laser modelocking stability lower limit and the HC-PCF pulse compression performance.

Exceptional environmental stability of our laser suggests that it may be very promising as a compact and reliable seed source for the high power applications, such as novel Yb-doped amplifier systems based on Yb:KGW [11] and Yb:YAG [12] media.