The development of the femtosecond fiber lasers with pulse repetition rates in the gigahertz regime is of interest and has been driven by the optical frequency combs, nonlinear bioimaging, optical communications, and material processing^[1–5]. By employing a high-repetition-rate laser operated at a wavelength of 1035 nm, the ablation-cooled material removal can be implemented, and the technique reduces the needed laser pulse energies for ablation and increases the efficiency of the removal process^[6]. Scaling the average power in a high-energy pulse amplifier system, high-repetition-rate ultrashort pulse lasers operated in the 1 µm wavelength range play an essential role in the stacking of a pulse train, where the pulse amplification relies on constructive interference of sequential pulses from a pulse train^[7,8]. Harmonic mode-locking^[9–11] and self-mode-locking^[12], methods based on pulse repetition multiplication external to the cavity^[13,14], are capable of achieving up to sub-THz pulse repetition rates. However, fundamental mode-locking is more reliable for some certain applications owing to its high spectral purity and stability. During the last two decades, candidates of active media providing optical gain for gigahertz fundamental repetition rates have been restricted to semiconductors^[15–17], rare-earth- (RE) doped ceramic/crystals^[18–20], Ti:sapphire crystals^[21,22], and glass fibers^[23–26]. In contrast, the laser setup constructed with active fibers, i.e., fiber lasers, stands out for its compactness, lack of susceptibility to misalignment, and efficient thermal dissipation. Liu et al. reported a femtosecond Yb3+-doped fiber laser (YDFL) with a repetition rate of 750 MHz and a maximum power of 150 mW, which is mode locked by a nonlinear amplifying loop mirror technique^[27]. In 2022, Yang et al. realized an ultralow timing jitter of 130 as (integrated from 10 kHz–1 MHz) from an 840-MHz nonlinear polarization evolution mode-locked fiber laser^[24]. Despite the efforts to enhance the characteristics, repetition rates in these ring-cavity fiber lasers are typically no more than 1 GHz. As for linear resonant-cavity YDFLs, multi-gigahertz repetition rates have been reported both in theories and experiments^[27-30].

At higher pulse repetition rates, the tendency for Q-switched mode-locking will unavoidably increase^[31,32]. The pulse instability, two types of pulsation resulting from gain- and soliton-induced pulse breathing in a GHz-repetition-rate passively mode-locked fiber laser, was numerically investigated^[33]. In addition, saturable absorber (SA)-based mode-locked fiber lasers with high repetition rates can easily suffer from temperature-dependent polarization dynamics because the fiber birefringence varies with the ambient temperature^[34], and subsequent polarization components interact with each other through nonlinear polarization coupling^[35]. In 2021, Lin et al. found that by twisting the no-PM gain fiber the soliton dynamics could be induced from linearly polarized solitons (LPSs) to polarization rotation vector solitons in the high-repetition-rate ultrafast fiber laser ^[36]. Hitherto, multi-gigahertz fundamentally mode-locked fiber lasers with PM architectures have been rarely reported. In 2022, Ou et al. demonstrated a 1.12-GHz repetition-rate YDFL using a PM gain fiber and free-space components in a ring cavity^[37]. By employing a piece of Er3+-heavily doped glass fiber, Song et al. reported a 1.03-GHz PM fiber laser, which represented an output power of 550 µW with a corresponding optical-to-optical efficiency of 0.3%^[38].

Herein, we demonstrated a 1.3 GHz passively mode-locked all-fiber YDFL with an all-PM architecture. To the best of our knowledge, this is the first PM fiber laser with a >1GHz repetition rate operating in the 1 µm wavelength range. The optical spectral shapes of the LPSs can be controlled by rotating the fast axis of the fiber optical pigtail of the designed dispersive dielectric mirror (DDM). Benefitting from the optimized systemic parameters of the centimeter-scale laser cavity, the optical-to-optical efficiency for the LPSs reached 29%.

A schematic illustration of an all-PM YDFL with a 1.3 GHz fundamental repetition rate is shown in Fig. 1(a). An 8.8-cm-long PM Yb3+-doped fiber (PM-YDF, Corative YB 401-PM) was used as the gain medium in the Fabry–Pérot-type oscillator. A photograph of the cross section of the PM-YDF is illustrated in Fig. 1(b), showing the fiber core and the stress axis. The PM-YDF has 5/125 µm core/cladding diameters and a numerical aperture of 0.14. The small-signal gain coefficient and the group velocity dispersion (GVD) are 0.76 dB/cm and 238fs2/cm at a wavelength of 1040 nm, respectively. Protected by a PM-isolator (PM-ISO) operating at approximately 980 nm, a 976 nm/680 mW laser diode (LD) acts as a pump source through a PM wavelength division multiplexer (PM-WDM) to excite the PM-YDF. In the experiment, all of the fiber optical pigtails of optical devices are panda PM silica fiber (Corning PM980) [the photograph of the cross section is shown in Fig. 1(c)]. The PM-YDF was secured with epoxy in a zirconia ferrule with an inner diameter of 125 µm, and both end facets of the fiber assembly were polished flat. One end of the PM-YDF was butt-coupled to a DDM that was secured by the fiber optical pigtail. The pigtail of the DDM was spliced to the common port of the PM-WDM. The DDM was fabricated by alternately coating SiO2/Ta2O5 dielectric films onto a zirconia ferrule using a plasma sputter deposition system. The DDM exhibits a high transmittance of 98.8% at a pump wavelength of 976 nm, a reflectivity of 89.3%, and a GVD of −761fs2 at a wavelength of 1040 nm. As shown in Fig. 1(d), the DDM was deposited on the end facet of the PM-fiber ferrule. The opposite end of the PM-YDF was butted to a semiconductor saturable absorber mirror (SESAM) [Fig. 1(e)], which was sandwiched between the PM-YDF and the zirconia ferrule. The SESAM has a modulation depth of 5%, a non-saturable loss of 3%, a relaxation time of 1 ps, and a saturation fluence of 40μJ/cm2 at 1040 nm (Batop GmbH). The reflectivity and the GVD of the SESAM over the 1020–1060 nm wavelength intervals are illustrated in Fig. 1(f). At the laser wavelength of 1040 nm, the reflectivity and the GVD are 91.9% and 72.6fs2, respectively. The net GVD of the whole laser cavity is estimated to be 1404fs2.

The LPSs with a pulse repetition rate of 1.3 GHz were coupled out via the signal port of the PM-WDM, which was spliced to a 1040 nm PM-ISO. A pair of transmission diffraction gratings was set for de-chirping external to the cavity. The optical spectra were measured by an optical spectrum analyzer (Ando AQ6315B) with a resolution of 0.05 nm. The temporal waveform was detected by using a 25 GHz photodetector (PD) and a 6 GHz bandwidth digital oscilloscope (Tektronix TDS6604). The radio-frequency (RF) spectrum was detected by a signal analyzer (Keysight N9020A), and the noise characteristics of the PM oscillator was recorded by another signal analyzer (Rohde & Schwarz FSWP50). The pulse duration was measured by an autocorrelator (APE pulseCheck USB 50).

Figure 2 shows the measurements of the average output power of the 1.3 GHz all-PM mode-locked YDF laser as a function of launched pump power. The continuous wave (CW) laser oscillation started at a pump power of P=3.1mW, which is a considerably low value owing to the high-quality factor Q for the optimized cavity parameters. In the range of 3.1mW≤P≤30.3mW, the output power linearly increases. When P is above 30.3 mW, a regime of rectangular-shaped wave packet (RSWP) is attained, and the slope of the output power remains linear^[39]. Once P reaches 52.8 mW, self-started LPSs with a fundamental repetition rate of 1.3 GHz can be achieved. Note also that the maximal output power extracted from the miniature all-PM oscillator is 31.4 mW at the launched pump power P=109.1mW, corresponding to an optical-to-optical efficiency of 29%.

In the regime of the LPS operation, the peak wavelengths of the mode-locked spectra shift toward shorter wavelengths as the launched pump power increases from 64.1 mW to 103.5 mW, as shown in Fig. 3(a). Interestingly, in the process, the peak intensities gradually increase while the “pedestal” component on the edge of the short wavelength of the spectra [indicated by the dashed circle in Fig. 3(a)] obviously weakens and ultimately disappears for P=103.5mW. Moreover, the spectrum displays a peak wavelength of 1040 nm and a spectral width (FWHM) of 1.95 nm. Correspondingly, the measurement of the autocorrelation trace of the de-chirped LPS is shown in Fig. 3(b), indicating a pulse duration of 814 fs and assuming the intensity profile to be hyperbolic secant. Considering a 582-fs transform-limited FWHM pulse duration, the difference can be attributed to a slightly imperfect dispersion compensation. The measurements of the pulse train temporal behavior are shown in Fig. 3(c), illustrating output pulses separated by 783 ps, which corresponds to the fundamental repetition rate of 1.28 GHz. Figure 3(d) shows the radio-frequency spectrum of the all-PM oscillator recorded between 1.2762 GHz and 1.2782 GHz with a 20-Hz resolution bandwidth (RBW). A single peak at 1.28 GHz is observed and the background noise is suppressed by 76.5 dB.

For P=103.5mW, as shown in Fig. 4(a), the spectral shape of the LPS operation changed [relative to the one in Fig. 3(a)] by rotating the fast axis of the fiber optical pigtail of the DDM, equivalently rotating the angle θ of the fast axis of the DDM to the fast axis of the PM-YDF. The peak wavelength shifts to 1036.6 nm while a “pedestal” component arises on the edge of the long wavelength. In addition, the temporal waveform is shown in the inset of Fig. 4(b), indicating an almost identical intensity of each optical pulse. The RF spectrum measured with a resolution bandwidth (RBW) of 20 Hz in Fig. 4(b) illustrates a signal-to-noise ratio of 77.7 dB and demonstrates that the LPSs with this spectral shape are stable and free of Q-switching instabilities.

The reason for the controllable spectral-shape feature in the LPS laser can be concluded as follows: the radiation of the 1.3-GHz pulse train in the resonant cavity is extracted through the fiber–fiber interface from the PM-YDF direction and the PM silica (undoped) fiber direction [Fig. 1(a)]. In the all-PM architecture, each orthogonal component (Exo,Eyo) of the LPSs experiences a magnitude change when they pass through the interface and then enter the PM silica fiber because of the existing angle θ of the fast axis of the DDM to the fast axis of the YDF. If we add the emerging Exo′ and Eyo′ with the magnitude change, then the resultant polarization state can be modified by rotating θ. When the light further comes out of the PM-ISO (similar to an analyzer behavior), only the field component parallel to the slow axis will be allowed to pass through. The shape of the optical spectrum therefore relates to the intensity of an LPS passing through a PM-ISO, which can also be modified by the incident polarization state that depended on the angle θ.

We further measured the relative intensity noise (RIN) and the phase noise (PN) of the 1.3 GHz LPSs for P=103.5mW. While recording the data, the all-PM YDF oscillator did not feature enclosures or any other means to prevent ambient disturbances, such as temperature fluctuation. The RIN (blue curve) and the integrated RIN (green curve) are plotted in the same figure [Fig. 5(a)]. Integration from 10 Hz to 10 MHz results in an integrated RIN of 0.08%. The PN of the all-PM YDFL is shown in Fig. 5(b). The PN gradually decreases from −33dBc/Hz to −142dBc/Hz with an increase in an offset frequency from 10 Hz to 10 MHz. The integrated timing jitter is calculated to be 291 fs integrated from 1 kHz to 10 MHz.

In summary, a 1.3-GHz YDFL with an all-PM architecture has been demonstrated, and its output spectral shape can be controlled by rotating the angle of the fast axis of the PM-silica fiber of the DDM to the fast axis of the PM-YDF. Owing to optimal systemic parameters, the compact all-fiber PM oscillator exhibits a threshold pump power for a CW laser oscillation of 3.1 mW and an optical-to-optical efficiency for mode locking of 29%. Temperature-dependent polarization dynamics is effectively suppressed in the 8.8-cm all-PM laser cavity, and the relative RIN integrated from 10 Hz to 10 MHz was measured to be 0.08%. The fiber laser emitting high-repetition-rate LPSs described here is readily incorporated into the existing pulse-stacking amplification system as a reliable seed source using coherent addition.