Mid-infrared (mid-IR) ultrafast μlaser sources are becoming increasingly attractive for a variety of applications ranging from spectroscopy to medical surgery.1^–5 In recent years, the mode-locked fluoride fiber laser (MLFFL) has emerged as a simple and cost-effective way to generate mid-IR ultrafast laser, as a compact, high-efficiency platform that features excellent beam quality. Femtosecond soliton mode-locking has been realized from fluoride fiber lasers near a wavelength of 3μm using the nonlinear polarization rotation (NPR) technique.6^–9 These soliton mode-locked lasers generally have a nanojoule-order pulse energy and peak power of the order of 10 kW. However, many mid-IR applications, such as supercontinuum generation and material modification, require a higher pulse energy and peak power,10^–12 which are challenging to achieve in MLFFLs.

As fluoride fibers exhibit anomalous group velocity dispersion (GVD) in the mid-IR range, MLFFLs generally work in a soliton mode-locking regime through a balance between nonlinearity and anomalous dispersion. In a soliton mode-locking regime, the accumulated excessive nonlinear phase will cause soliton break-up, limiting the pulse-energy scaling according to the soliton area theorem. One feasible strategy to overcome this limitation is to manage intracavity dispersion. In conventional silica fiber lasers, the sign and amount of GVD can be conveniently engineered by ion doping or by designing structures in silica fibers. Thus mode-locked silica fiber lasers can operate in a wide range of regimes, such as stretched-pulse mode-locking, dissipative soliton, and similariton.13^–16 These regimes intrinsically operate in the chirped-pulse mode in the cavity, resulting in less nonlinear phase accumulation and supporting a high pulse energy and peak power. Current state-of-the-art mode-locked silica-fiber lasers support a pulse energy of the order of microjoules and a peak power of the order of megawatts with the help of dispersion management.17 However, unlike silica fiber, fluoride fiber engineering remains an open problem, and current techniques cannot support the GVD engineering of fluoride fibers. It is critical to solve the dispersion-management problem of MLFFLs for pulse-energy and peak-power scaling.

In MLFFLs, fluoride fibers several meters long generally have a large anomalous dispersion (∼−105fs2) at an operation wavelength of 2.8μm.6^–9 It is nearly impractical to compensate for such a large anomalous dispersion using general bulk materials with normal GVD. However, we find that semiconductor material possesses a huge normal GVD near the absorption edge, which results from the rapid change of refractive index. For example, germanium (Ge) has an infrared bandgap (0.66 eV) and absorption region near 2μm; in the near absorption edge of 2.8μm, it has a huge GVD of +1685fs2/mm [Fig. 1(a)]. Such a GVD is more than 20 times that of fluoride fiber, which means that Ge rod a few centimeters in length is sufficient to manage the intracavity dispersion of MLFFLs. The combination of high transmission in the mid-IR range [Fig. 1(b)] and large positive GVD near the absorption edge makes such a semiconductor a reliable and practical method of dispersion management for MLFFLs.

In the present work, by utilizing the huge normal GVD generated near the absorption edge of Ge for dispersion management, we first realized breathing-pulse mode-locking in an Er-doped fluoride fiber laser. The pulse-energy-limitation effect was mitigated in the breathing-pulse mode-locking regime. The breathing-pulse MLFFL produced a pulse energy of 9.3 nJ and a pulse duration of 215 fs with a record peak power of 43.3 kW, which reaches the level of state-of-the-art mid-IR femtosecond optical parametric oscillators in the spectral region around 3μm.20^,21 This work paves the way for the pulse-energy and peak-power scaling of mid-IR MLFFLs.

The mode-locked Er:ZBLAN fiber laser (Fig. 2) was pumped by a 970-nm laser diode pigtailed to a 105/125-μm fiber with a numerical aperture of 0.22. A set of lenses consisting of planoconvex lens L1 (f=10mm) and aspheric lens L2 (f=12.7mm) was used to couple the pump beam into the double-clad Er:ZBLAN fiber. The Er:ZBLAN gain fiber had a length of 2.3 m and 6 mol.% Er doping with a core diameter of 16.5μm and cladding diameter of 200μm. The two ends of the fiber were 8-deg angle-cleaved to suppress parasitic oscillation. Mode-locking operation was initiated and sustained through NPR using an isolator, a half-wave plate, and a quarter-wave plate. To reduce the mode-locking threshold in the experiment, we controlled the intracavity pulse propagation along the pump-light direction. An output coupler (OC) with 40% transmission was positioned after the gain fiber. Three Ge rods with different lengths (L=2, 3, and 6 cm, corresponding to net cavity dispersions of −0.158, −0.141, and −0.090ps2, respectively) were prepared for dispersion management. The Ge rod introduces almost no insertion loss or nonlinear effect, which is beneficial to investigate the influence of dispersion on the dynamics of the mode-locked fiber laser. In particular, the huge GVD of Ge at the wavelength of 2.8μm facilitates intracavity dispersion management using a short Ge rod.

Mode-locked operation was first conducted without dispersion management. Since fluoride fiber exhibits an anomalous GVD around 2.8μm, the mode-locked laser operated in a soliton regime through a balance between nonlinearity and anomalous dispersion. Under a launched pump power of 7.7 W, stable continuous-wave mode-locking was achieved [Fig. 3(a)]. The radio-frequency spectrum shows a high signal-to-noise ratio of 70 dB at a fundamental frequency of 75.5 MHz [Fig. 3(b)]. The mode-locked pulse had a duration of 190 fs, assuming a sech2 profile [Fig. 3(c)]. Despite the strong absorption by vapor in the atmosphere, Kelly sidebands can be identified in the spectrum [Fig. 3(d)], indicating soliton mode-locking. In the soliton regime, the mode-locked Er:ZBLAN fiber laser delivered a maximum pulse energy of 5.6 nJ. While further increasing the launched pump power in the experiment, the output pulse energy remained almost constant until multiple pulsing occurred [Fig. 4(d)].

In order to mitigate the limitation in pulse energy, we propose to manage the intracavity dispersion and promote the laser to the breathing-pulse mode-locking regime. An infrared-bandgap semiconductor with a huge normal GVD at 2.8μm is utilized to compensate for part of the anomalous dispersion in the fluoride fiber laser. Since the net dispersion of the laser is negative, the output pulse is a transform-limited femtosecond pulse. After the OC, the pulse is first stretched in the semiconductor, then compressed in the front part of the fiber, and finally evolves into a soliton pulse near the exit of the fiber. Owing to the coexistence of normal and anomalous dispersion elements in the laser, the intracavity pulse is stretched and compressed successively in a round trip, acting as a breathing pulse. The breathing pulse effectively reduces nonlinear phase accumulation in the laser compared with soliton mode-locking. Thus higher pulse energy can be generated in a breathing-pulse mode-locked laser.

Guided by this breathing-pulse mode-locking concept, we conducted a mode-locking experiment of the Er:ZBLAN fiber laser. In the mode-locked laser, a Ge rod was used to compensate for partial intracavity dispersion, promoting the laser to the breathing-pulse regime. In the soliton regime without a Ge rod, the output pulse energy remains unchanged while increasing the pump power, as shown in Fig. 4(d). After dispersion compensation, the limitation effect of pulse energy is mitigated. At a fixed launched pump power of 7.7 W, the output pulse energy increases from 5.6 to 8.0 nJ with the increase of Ge rod length [Fig. 4(a)]. Meanwhile, the output pulse duration increases from 190 to 290 fs because the self-phase-modulation-induced spectral broadening effect becomes weak [Figs. 4(b)–4(c)]. In the breathing-pulse regime, since the pulse is stretched and compressed successively in the cavity, the accumulated nonlinear phase shift is significantly reduced compared with the soliton regime. The reduction of the accumulated nonlinear phase shift mitigates the pulse-energy-limitation effect. As we increase the launched pump power, the output pulse energy is further increased, as shown in Fig. 4(d). A maximum pulse energy of 9.3 nJ is achieved under a launched pump power of 11 W. As the intracavity pulse energy and peak power increase, the self-phase-modulation-induced spectral broadening effect becomes stronger, whereby the output pulse duration gradually decreases [Fig. 4(d)]. Eventually, 215-fs pulses with a pulse energy of 9.3 nJ are achieved directly from the breathing-pulse mode-locked Er:ZBLAN fiber laser [Fig. 4(e)], with a record peak power of 43.3 kW at 2.8μm. Further increasing the peak power will pose a risk of damage to the end face of the fluoride fiber. A higher peak power might be achieved by splicing a protective end cap to the fluoride fiber.

Here, the employed Ge rod only compensates for a part of the anomalous dispersion of the entire fluoride fiber. The soliton-shaping effect still exists at the end of the fluoride fiber. According to the spectral width of 41.6 nm in the mode-locking spectrum [Fig. 4(f)], we calculate the time-bandwidth product of the output pulses as 0.347, which is close to the transform-limited value. Intracavity net anomalous dispersion enables the generation of transform-limited pulses, avoiding extra pulse compression outside the cavity.

In order to confirm the pulse-breathing behavior along the cavity, the pulse evolution in the Er:ZBLAN fiber laser was investigated though numerical simulation in the time and frequency domains. The numerical simulation included the linear loss, dispersion map, Kerr nonlinear effect, saturable gain, and NPR action for reproducing the basic features of the experimental observations. The detailed simulation process can be found in Sec. 1 of the Supplementary Material. Figure 5 shows the evolutions of pulse duration, spectrum, and pulse energy with the position in cavity. When a near-transform-limited pulse passes through the Ge rod, it is stretched quickly by the normally dispersive Ge, resulting in a long pulse before amplification in the fluoride fiber. Because the low levels of loss and nonlinear effects in Ge can be neglected, the pulse energy and spectrum remain unchanged in the Ge rod. Consequently, the positively chirped pulse is amplified and compressed gradually in the anomalously dispersive fluoride gain fiber. At the end of the fluoride fiber, the compressed pulse evolves into a soliton through the balance of the anomalous dispersion and nonlinear effect in the fiber, the spectrum of which features Kelly sidebands [Fig. 5(b)]. Numerical simulation confirms the existence of pulse breathing along the cavity with a pulse breathing ratio of 6 [Fig. 5(a)], which significantly reduces the averaged peak power and avoids the excessive accumulation of nonlinear phase shift in the fiber. Consequently, the pulse energy can be linearly scaled up in the fiber without pulse break-up [Fig. 5(c)]. The irregular change of pulse duration in the Ge rod and fiber is attributed to the influence of third-order dispersion in these materials.

Dispersion management is the key to drive MLFFLs from the soliton to the breathing-pulse mechanism. Without dispersion management, the MLFFL generally operates in a soliton mode-locking regime, in which the pulse energy is limited by the soliton area theorem. In our case, the pulse energy is limited to 5.6 nJ in a soliton mode-locking regime. With dispersion management by means of a Ge rod, the MLFFL is no longer confined to a soliton regime. Dispersion-managed MLFFL transforms from soliton to breathing pulse regime, in which the intracavity pulse is stretched and compressed successively owing to the coexistence of normal and anomalous dispersion; the intracavity pulse finally evolves into a soliton pulse since the intracavity net dispersion remains negative. We recognize that the laser is still in the framework of dispersion-managed soliton because it is substantially a dispersion-managed cavity, but the breathing pulse is a new form of dispersion-managed soliton. The pulse-breathing effect significantly reduces nonlinear-phase-shift accumulation and relaxes the pulse-energy limitation in MLFFL. Pulse energy of MLFFL is scaled up to 9.3 nJ with a record peak power of 43.3 kW. Higher peak power is only constrained by damage risk of fluoride fiber end face. Provided that the fluoride fiber is spliced to a protective end cap and intracavity dispersion is further optimized, a higher pulse energy and peak power is expected to be generated from a breathing-pulse MLFFL. Although further increasing the normal dispersion to the net normal dispersion regime in the cavity, the mode-locked pulse evolves to the picosecond regime. For example, using a 20-cm Ge rod to compensate for the anomalous dispersion of a 3.0-m fluoride fiber at a net intracavity dispersion of +0.087ps2, a 1.78-ps pulse is achieved with a spectral bandwidth of 18 nm (see Fig. S1 in the Supplementary Material). In addition to dispersion management inside an oscillator, Ge can also be used as a reliable mid-IR dispersive component to stretch or compress pulses for the chirped pulse amplification with fluoride fibers in the future.

In conclusion, by utilizing the huge normal GVD generated near the absorption edge of Ge for mid-IR dispersion management, we realized breathing-pulse mode-locking, which mitigates the pulse-energy limitation in MLFFLs. The properties of Ge, including its low loss, large normal GVD, and easy installation, make it a reliable and practical dispersion management method for mid-IR rare-earth-doped (Er3+, Ho3+, and Dy3+) fluoride fiber lasers. With intracavity dispersion management, mid-IR MLFFLs are no longer confined to a soliton mode-locking regime. Here we demonstrated breathing-pulse mode-locking in an Er:ZBLAN fiber laser, in which the intracavity pulse is stretched and compressed successively, resulting in reduced nonlinear-phase-shift accumulation and permitting the generation of a high pulse energy. Finally, we achieved a pulse energy of 9.3 nJ and a pulse duration of 215 fs with a record peak power of 43.3 kW from a breathing-pulse mode-locked Er:ZBLAN fiber laser at 2.8μm. Our work paves the way for the pulse-energy and peak-power scaling of mid-IR MLFFLs, which will enable a wide range of applications, such as supercontinuum generation, material modification, medical surgery, and mid-IR ultrafast spectroscopy.