1. Introduction

Fiber lasers, besides being highly useful industrial tools with many unparalleled advantages over other bulky sources, have become experimental platforms for studying various pulsing phenomena as well as the related dynamics. These are facilitated by the unique properties of fiber resonators, including easy-access to strong-enough nonlinearities, manageable group velocity dispersion (GVD) and even higher orders of dispersions, flexibility in polarization evolution manipulation, etc. As benefited, many widely different pulse types and pulse-pulse interactions have been realized in fiber lasers, especially those based on passive mode-locking that can flexibly and even fully explore the complex interactions among gain, saturable absorption, dispersion and various nonlinear effects [1].

Solitons exist in fiber lasers with all or net anomalous cavity dispersions. However, they are only able to carry pulse energies no more than 0.1 nJ in typical single-mode fiber resonators due to the well-known area-theorem. For overcoming the limited pulse energy with solitons, dispersion-managed solitons (i.e., stretched pulses) [2–4], similaritons [5,6], and dissipative solitons [7–9] have been proposed mainly through dispersion-management of fiber resonators. Pulses with over tens of nanojoule energy have been directly produced from fiber lasers by employing the dissipative soliton mode-locking.

For further increasing the pulse energy directly produced in a fiber laser resonator, recent years much attention has been paid to a particular mode-locking mechanism named dissipative soliton resonance (DSR) ever since it was proposed [10]. It was predicted that the DSR should be able to produce infinitely large pulse energy from fiber resonators with appropriate parameter managements [10–12]. Experimentally, 10 µJ single pulse energy with DSR has been produced directly from a fiber laser oscillator [13]. External amplification has scaled up the average power of DSR pulses from tens of milliwatts to over 100 W without any pulse breaking [14].

The DSR pulse profile is typically a square wave with two steep edges and a flat top. Nevertheless, some gain-related top-tilted profiles were also observed both experimentally and numerically [15]. Moreover, recently we observed a type of h-shaped pulse in thulium-doped fiber (TDF) lasers [16,17]. This kind of pulse exhibits much similar properties with typical DSR pulse that the pulse peak clamping (PPC) effect can intensively shape the pulse profile when the pump power is high enough. However, besides that, much differently the h-shaped pulse has a sharp leading edge that is not fully restricted by the PPC effect. As a recently discovered type of pulses, the detailed applications are still awaiting further explorations. One useful attempt can be found in [18], where the authors built a TDF amplifying system seeded with h-shaped pulses. Then they used the micro-joule level h-shaped pulse source to pump an HDF oscillator and realized gain-switched pulse output. Thus, as a nanosecond pulse, after amplification the h-shaped pulse can find applications that are alike to other pulses with similar durations that obtained through various methods, like gain-switching, Q-switching, and mode-locking. Those might include material processing, laser cutting, etc. Considering the particular pulse profile, it can also find applications where complex temporal characteristics are required.

It is also noted that our previously observed h-shaped pulses, as well as the one demonstrated by H. Luo et al [18], were all realized in the anomalous dispersion regime. In such a regime, the h-shaped pulse shows wide spectral bandwidth and high stability. Benefiting from those, the pulse duty circle (PDC) of h-shaped pulse can be adjusted through the cavity birefringence management in combination with polarization state (PS) manipulation [16], while the pulse maintains breaking-free. One interesting issue is whether the h-shaped pulse can be obtained in the normal dispersion regime. It is as-well interesting to explore the pulse dynamics if the h-shaped pulse exists. One even further issue is if there is some method to reshape this particularly shaped pulse profile.

In this paper, we demonstrate, for the first time, that the h-shaped pulse can indeed exist in the normal dispersion regime but possesses quite different characteristics and evolution properties compared to what in typical anomalous dispersion regime.

2. Experimental setup

A figure-of-eight (f-8) TDF laser is used as the platform to study the h-shaped pulse in the normal dispersion regime, as schematically shown in Fig. 1. The TDF laser comprises a nonlinear amplifying loop mirror (NALM) and a main unidirectional ring cavity (URC). A 1570.4 nm master oscillator power-amplifier (MOPA) system is used as the pump source. In the MOPA, the seeding source is a distributed feedback laser diode (DFB-LD) with emission linewidth less than 100 kHz, which can be further power-boosted up to ∼4.8 W by a subsequent erbium-ytterbium fiber amplifier (EYFA).

 

Fig. 1. Experimental setup of the TDF laser.

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In the NALM, the pump light is reflected and coupled into a piece of ∼75 cm long high-dopant TDF (SM-TDF-10P/130-HE, Coherent-Nufern, Co.) through a thin-film filter wavelength division multiplexer (FWDM). The TDF is highly Tm-doped in the fiber core, resulting in a strong pump absorption. Therefore we selected the length of 75 cm. A second FWDM is used after the TDF to eject any unabsorbed pump light from the fiber resonator. We noticed that, with merely Watts of incident pump power, the polymer coating of the TDF could be damaged due to strong thermal load that results from the intensive absorption and re-emission with the highly doped thulium ions in the fiber core. Thus, as shown, at the pump-launching end we use some thermally conductive silicone grease to coat around the polymer coating of ∼ 15 cm long TDF, by which the generated heat can be efficiently dissipated. The whole TDF laser system is placed on an aluminum plate. In the NALM, a three-paddle fiber polarization controller (FPC) with looped normal dispersion fiber (NDF) around three independent spools is used to adjust the intra-cavity local PS. The FPC is noted as FPC-1. Our main purpose in this paper is to investigate the h-shaped pulse characteristics operating in the normal dispersion regime. Thus, for adjusting the net cavity dispersion to a large normal value, we used a long piece of NDF. The NDF is a type of ultrahigh numerical aperture fiber (UHNA7, Coherent-Nufern, Co.), and the total length is ∼121.5 m. Meanwhile, for gaining adequate accumulative nonlinearity of the NALM and obtaining large enough nonlinear phase shift difference, the NDF is placed in the NALM, rather than in the URC.

The NALM is incorporated into the main URC through a 3-dB fiber optical coupler (FOC). In the URC, an isolator is used to enable the unidirectional propagation of the signal light, and a second FPC, noted as FPC-2, is used to adjust the local PS. The FPC-2 is a type of in-line polarization controller based on fiber squeezer. A FOC with 18/82 splitting ratio delivers ∼18% laser power from the URC.

We further attempt to use a piece of unpumped TDF to investigate the induced profile-reshaping effect on the h-shaped pulse. The length of the unpumped TDF was chosen based on the fact that it will not result in too much loss while the absorption-induced pulse profile modification is obvious. We try to place it at location (1) or location (2) through fusion-splicing, as noted in Fig. 1, to check if some location-related effect can be involved. The total roundtrip cavity length is ∼ 132.8 m (the length change due to the incorporation of the unpumped TDF could be ignored temporally). The net cavity dispersion is calculated as ∼4.46 ps² at 1.96 µm [19].

3. Results and discussion

Through varying the pump power and manipulating the intra-cavity PS, we obtained narrow bandwidth, h-shaped pulse generation in the net normal dispersion TDF laser, and also observed that it was highly circumstance-susceptible and could evolve into various other pulsing states, especially when the PS modulation was on-going. The pulse profile could even be reshaped via intra-cavity re-absorption, i.e., incorporation of some unpumped TDF. The details and related discussions are as follows.

3.1. Narrow bandwidth h-shaped pulse generation

The threshold pump power for continuous wave (CW) lasing was ∼1.85 W. Single pulse emission started when the pump power was increased to ∼2.38 W with appropriate polarization settings. The h-shaped pulse could maintain at least for several hours if no external perturbations occurred. Figure 2(a) plots several pulse profiles with different pump powers. As clearly seen, when the pump power from the MOPA system increased from ∼2.38 W to ∼4.80 W, the pulse duration broadened from ∼18.1 ns to ∼104.6 ns, the leading edge lowered down, and meanwhile the long flat central part remained roughly at a constant level. These characteristics were consistent with our previous observations [16,17], when the h-shaped pulses were obtained in the anomalous dispersion regime. All the temporal traces in this paper were measured by using an InGaAs photodetector (ET-5000, Electro-Optics Technology, Inc.) and a real time digital storage oscilloscope (DSO9104A, Agilent Technologies, Inc.). As we noted, some early results even showed that a tiny higher leading edge could even be noticed with some square wave DSR pulses [20–22]. But, as can be noted, here the leading edges of the obtained h-shaped pulses are much stronger than the followed trailing parts. That is why we name them as h-shaped pulses as what we did previously [16,17]. One might also notice that there is some resemblance between the h-shaped pulse and the reported soliton rains [23,24]. However, they should be different. The h-shaped pulse has a single and whole envelope, whereas the envelop of a train of soliton rains cannot be temporally resolved due to the temporal complexity and randomness. In spectrum, the h-shaped pulse is spectrally concentrated in a narrow band, whereas the spectrum of a train of solitons is typically accompanied with symmetrical Kelly sidebands [23,24].

 

Fig. 2. (a) Temporal profiles of the h-shaped pulse with different pump powers; (b) typical measured output spectrum, (c) RF harmonics over a scan range of 50 MHz, and (d) RF beat note registered at the fundamental PRF, with ∼4.8 W pump power.

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Although no noticeable different evolution features could be observed from the temporal characteristics of the h-shaped pulse compared to that in the anomalous dispersion regime, considerable difference could be seen on the emission spectra. In the anomalous dispersion regime, one common feature of the h-shaped pulse spectrum is its broad bandwidth [16,17], i.e., typically with tens of nanometers. Figure 2(b) plots a typical output spectral profile with ∼4.8 W pump power. It was measured by using an optical spectrum analyzer (OSA, AQ75B, Yokogawa Test & Measurement Co.); the setting resolution was 0.05 nm. As seen, however, the emission spectrum showed a sharp and narrow profile with a peak wavelength of ∼1964.85 nm and a signal-to-noise ratio (SNR) of ∼56.41 dB. Due to the extremely narrow bandwidth, this high-resolution OSA was even unable to show the exact 3-dB bandwidth. Alternatively, only ∼0.84 nm could be evaluated by using the 10-dB bandwidth based on the measured data. This feature dramatically differs from the cases with anomalous dispersion regime, but it is similar to the DSR spectrum with net normal dispersion regime [15,25,26]. This indicates that the h-shaped pulse and DSR should share some common intrinsic mechanisms, although the h-shaped pulse typically exhibits a stronger pulse leading edge comparatively. The main contribution to the narrow spectrum with the h-shaped pulse should be the large net normal cavity dispersion. Presently we only noticed experimentally that a narrow band h-shaped pulse could be generated in normal dispersion regime, whereas an h-shaped pulse typically has broadband spectrum in anomalous dispersion regime. The reason why the normal dispersion could result in so much narrow a spectrum is still unclear and deserved to be further investigated. We suspected that, similar to DSR pulse generation in the normal dispersion regime, the h-shaped pulse is also resulted from the strong PPC effect in the normal dispersion regime. Additionally, the strong peak power clamping effect causes the narrow spectrum.

Figure 2(c) plots a train of RF harmonics over a scan range of 50 MHz. The equally spaced and damped modulating behavior upon these harmonic lines resulted from the long duration of the lower part of each h-shaped pulse. The modulation frequency of ∼9.5 MHz and the duration of the lower part of the corresponding h-shaped pulse of ∼104.8 ns roughly satisfied a well-known reciprocal relationship that has always been observed with DSR pulses [13,14,25]. Comparatively, the RF modulation depth for h-shaped pulse is evidently less than that for DSR pulse [13,14,25]. This is mainly due to that the leading edge of each h-shaped pulse does not contribute to this modulating behavior because of its much shorter duration; in fact, it can somehow weaken the modulation. Figure 2(d) plots the RF spectrum around the fundamental pulse repetition frequency (PRF) of ∼1.487 MHz. This gives an SNR of ∼50.5 dB. All the RF traces in this paper were measured by using the same photodetector for pulse measurement together with an RF spectrum analyzer (N9320B, Agilent Technologies, Inc.).

The measured output average power versus the pump power was depicted in Fig. 3, roughly following a linear evolution. The slope efficiency was ∼1.84% through linear fit. The maximum output average power was ∼54.2 mW. Thus, the maximum single pulse energy can be calculated as ∼36.45 nJ. From the roughly linear evolution, it could be expected that both higher output average power and larger pulse energy should be possible if a pump source with higher output power is available.

 

Fig. 3. Measured output average power versus pump power, with linear fit.

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3.2. Evolution into peak-depressed profiles and fully-split multiple-pulsing states

We had attempted to achieve different PDCs through PS manipulation and cavity birefringence management as what we did in [16], where we obtained various PDCs and achieved an ever-reported largest PDC of ∼98.2%. However, there was no evident tuning on the PDC (maximized PDC achieved is ∼15.6%) could be noted whether we simply adjusted the two FPCs or further incorporated ∼5 m polarization-maintaining fiber (PMF, PM980-XP, Coherent-Nufern, Co.) into the URC. This might indicate that the PDC tuning could only occur in anomalous dispersion regime where the h-shaped pulse has broadband spectral profile and high-enough circumstance stability. Similar wide tuning on the PDC based on PS manipulation was also observed in a color domain phenomenon with a large anomalous dispersion fiber laser in [27].

Alternatively, however, we observed that the h-shaped pulse obtained in the net normal dispersion regime became highly circumstance-susceptible, especially to the intra-cavity PS. Some tiny change with the PS would induce considerable profile variation. Figure 4(a) captured a typical h-shaped pulse profile when the incident pump power was ∼4.15 W. However, with some slight PS adjustment, a tiny depressed dip could be observed as seen in Fig. 4(b). Figure 4(c) shows an h-shaped pulse profile embedded with three tiny dips. Even more and much deeper depressed dips could be obtained with finely manipulation of the intra-cavity PS, as seen from Figs. 4(d) to 4(g). Figure 4(g) can be seen as a fully burst-like emission.

 

Fig. 4. (a) through (g): Depressing temporal characteristics from a neat h-shaped pulse profile to a fully burst-like one; (h) typical output spectrum, (i) RF harmonics with a span of 100 MHz, and (j) RF beat note registered at the fundamental PRF, corresponding to the burst-like case shown in Fig. 3(g).

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As also noticed, the duration of the overall pulse package increased as more dips appeared, but the peak intensity roughly remained unchanged, indicating that the PPC effect always shaped the pulse package, except the leading edge. This peak-depressed behavior is similar to our previous observations with a DSR fiber laser [25]; the main difference comparatively is the high-rising sheer leading edge of the h-shaped pulse. Similarly, here the depressing process from the neat h-shaped pulse into an eventually burst-like emission was a competition process between the package-duration limitation with the PPC effect and the evolving toward split pulses facilitated by some locally anomalously dispersive fiber pieces.

Figure 4(h) shows a captured optical spectrum corresponding to the burst-like emission in Fig. 4(g). Much different from the neat and narrow spectral profile with the h-shaped pulse, here multiple spectral peaks appeared. These sharp peaks also varied slightly in intensity over time. Some energy exchanges among the neighboring sharp peaks could also be observed. Meanwhile, the spectral profile became much more structured. Compared with the RF characteristics of the h-shaped pulse, the modulation with the RF harmonics also became not so clear but irregular, as seen in Fig. 4(i). At the fundamental PRF, the RF spectrum [Fig. 4(j)] had an SNR of ∼57.74 dB, which was greater than that with the h-shaped pulse operation, partially attributed to the increased average output power, i.e., the increased energy of the pulse package due to the varied PS-related net laser gain.

Besides the incompletely split pulsing states in Fig. 4, we also observed some completely split cases, as seen in Fig. 5. Figure 5(a) shows two completely split, top-tilted pulses, and Fig. 5(b) shows 14 split pulses. A far-away-split multiple-pulse pattern could even be obtained as shown in Fig. 5(c). Figure 5(d) plots the corresponding output spectral profiles. As seen, one possible common feature is that all the spectra show complex structures compared with the neat and simple DSR spectral profile. Some similarly spectrum-varying characteristics could also be observed, similar to the spectral features shown in Fig. 4(d). The structured spectral profiles indicate the complex temporal characteristics. These completely split pulsing states mean that the h-shaped pulse formed in the net normal dispersion regime is more circumstance-susceptible than the DSR pulse with similar dispersion regime [25]. It should also be noted that the states shown in Fig. 5 were obtained at largely varied PS compared with those shown in Fig. 4. That is to say that to obtain the states from Figs. 4(a) to 4(g) only some slight adjustments of the two FPCs are required. However, if some states in Fig. 5 are attempted to be obtained from one in Fig. 4, some huge adjustments should be taken on the two FPCs.

 

Fig. 5. Evolution into other completely split multiple sub-pulses. (a) through (c): temporal characteristics; (d) the corresponding spectral characteristics.

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The various transformed pulsing states shown in Figs. 4 and 5 demonstrate that, in the net normal dispersion regime, the h-shaped pulse could only form within a narrow parameter space. Any parameter disturbances would result in dramatic changes on the pulse dynamics. Thus, one could conclude that a broad-bandwidth pulse can typically tolerate more disturbances and experiences only some moderate changes with parameters varying. Taking [16] for instance, only the PDC of a broadband h-shaped pulse could be tuned with PS manipulation; no evolution into other complex pulse state could be observed. However, a narrow bandwidth is typically highly susceptible to circumstance variations, like the h-shaped pulse here and the DSR pulse in [25]. These different behaviors are mainly resulted from different net cavity dispersion regimes: the net anomalous dispersion always tends to achieve a balance between GVD and self-phase modulation (SPM), whereas the net normal dispersion attempts to break the narrow parameter space of the stable single pulse operation.

3.3. Intra-cavity profile-reshaping on the h-shaped pulse

Considering that the h-shaped pulse is highly circumstance-susceptible, we attempted to check whether the unclamped part, i.e., the leading edge, could be somehow suppressed via making changes on some cavity parameters. For that purpose, we propose that inserting a piece of unpumped TDF might be able to reshape the h-shaped pulse profile, which is equivalent to an addition of some further saturable reabsorption in the fiber resonator. This is based on the fact that the leading portion of a pulse would suffer from a stronger absorption compared to other subsequent portion of the pulse if it counters with a fiber absorber. We have observed that for a nanosecond pulse the leading edge could experience a greater amplification compared to other parts of the pulse when it went through a fiber amplifier [14]. Thus, conversely it could be estimated that for a nanosecond pulse the leading edge should be suppressed at first and would experience a greater decline than other parts of the pulse profile when it encounters a fiber absorber. Inserting the unpumped TDF in the cavity also allows the absorption of disturbing peaks in the pulses since thulium ions have three energy levels. Also, the position of the absorbing fiber should also be important because the contrast in the UR and the NALM between both propagative and counter-propagative waves is not the same. It can be expected that, due to the feedback property of the fiber laser oscillator, more significant suppressing effect should be possible in comparison to the single-pass propagation.

Considering that inserting a doped-fiber as an absorber modifies the parameters of the cavity somehow, we used only 13 cm unpumped TDF in the laser cavity, as shown in Fig. 1. Such a short piece of TDF resulted in some absorption, but only slightly modified the cavity dispersion. Thus, besides the minor modification on the net laser gain, other induced parameter changes are acceptable. Figure 6 plots the original h-shaped pulse profile (black), as well as the reshaped pulse profile when the TDF was placed at location (1) (red) and location (2) (blue), respectively, all with the same pump power of ∼4.15 W. It can be seen that, compared to the original pulse profile, the leading edge was mostly suppressed when the TDF was placed at location (1). Moreover, compared to the case with location (2), the pulse duration with location (1) was much closer to the originally unshaped pulse duration. This might be due to the bi-directional amplifying characteristics of the NALM. Thus, location (1) should be the most appropriate reabsorption location in order to suppress the leading edge of the h-shaped pulse. This can also be partially confirmed by the output average power. With the same pump power of ∼4.15 W, the output average power of the original h-shaped pulse was ∼41.8 mW, whereas it became ∼24.3 mW and ∼15.2 mW when the unpumped TDF was placed at location (1) and (2), respectively.

 

Fig. 6. Intra-cavity profile-reshaping on the h-shaped pulse. Black: the original h-shaped pulse profile with ∼4.15 W pump power; Red: the reshaped pulse profile when a piece of unpumped TDF was incorporated at location (1) as noted in Fig. 1; Blue: the reshaped pulse profile when the unpumped TDF was incorporated at location (2) as noted in Fig. 1.

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As could also be seen, despite the location dependence the overall pulse profiles in both cases experienced some amplitude decreases, however, the leading edge dropped most considerably. Thus, it could conclude that using a piece of unpumped active fiber as the absorber should be an effective approach to suppress the unclamped leading edge of an h-shaped pulse, and, in addition, the unpumped active fiber should be placed in the bi-directional gain loop, to reduce the tradeoff between pulse-profile reshaping and pulse-energy losing. Certainly, a different length of unpumped TDF can also be employed for such leading-edge-suppressing purpose. It can be expected that a longer (shorter) TDF would result in a stronger (weaker) suppression on the pulse leading edge.

4. Summary

In conclusion, we have reported on the circumstance-susceptible, narrow-bandwidth, h-shaped pulse generation and evolution in a TDF laser with net normal cavity dispersion, for the first time to our best knowledge. Despite some generally temporal evolution characteristics with the pump power, the h-shaped pulse could also evolve into various peak-depressed profiles and even some completely split pulse patterns. We further proposed an effective approach to suppress its leading edge and also investigated its location-related characteristics. Our results represent new investigations on particular profile, long duration pulses, demonstrating some related new features and evolution properties.