${\mathrm{Nd}}^{3+}$-doped silica fiber (NDF) combines the excellent thermal and mechanical properties of silica glass and a rich content of absorption and emission laser lines of ${\mathrm{Nd}}^{3+}$, which finds wide application in ultrafast lasers and high-power lasers^[1,2]. The ${{}^4\mathrm{F}}_{3/2}\to {{}^4\mathrm{I}}_{11/2}$ transition of ${\mathrm{Nd}}^{3+}$ gives rise to a 1060-nm laser line with a long fluorescence lifetime, beneficial for lasing operation^[3]. Other laser lines of ${\mathrm{Nd}}^{3+}$ have also been studied, e.g. the ${{}^4\mathrm{F}}_{3/2}\to {{}^4\mathrm{I}}_{9/2}$ transition emitting at $\sim 900\mathrm{nm}$ wavelength finds applications in biological and medical research^[4]. Mode-locked lasing operation requires NDFs with lower loss and higher gain. However, obtaining a high gain in an NDF is challenging because of the agglomeration of highly concentrated ${\mathrm{Nd}}^{3+}$ ions in the silica glass. The development of the modified sol–gel method has proved to be an effective way to raise the doping concentration of the ${\mathrm{Nd}}^{3+}$ ions in NDFs^[5].

In recent years, the performance of NDFs in terms of lasing operations has improved rapidly. In 1987, Reekie et al. fabricated an NDF with a loss at 1.1 µm of a remarkable 1.7 dB/km. The absorption at the pump wavelength of 823 nm was 7.8 dB/m^[6]. In 1998, Cook et al. reported an NDF with an absorption at 800 nm of 275 dB/m and with the background attenuation (at 1275 nm) of 45 dB/km^[7]. In 2014, Motoichiro reported an NDF with a smaller core diameter of 12 µm and absorption at 810 and 1064 nm of 376 dB/m and 3.47 dB/m, respectively^[8]. In 2020, Wang et al. demonstrated a 1.0 dB/cm net gain in an NDF at 915 nm^[9].

The advancement of NDFs has led to the improvement of fiber laser performances. In 2007, Jelger et al. used a ${\mathrm{Nd}}^{3+}$-doped micro-structured large-mode-area fiber (1300 × 10⁻⁶) to build a continuous wave (CW) fiber laser, which realized a slope efficiency of 51 %, a stable output of 166 mW, and a drastically narrowed linewidth ($<0.07\mathrm{nm}$)^[10]. In 2014, Qian et al. reported an NDF-based oscillator featuring a W-type fiber operating at 930 nm. The chirped pulses with 2.2 nJ pulse energy that could be compressed to 126 fs were generated in a dispersion-managed (DM) cavity^[11]. In 2021, Yamasaki et al. fabricated an NDF by the zeolite method, and the additive mass fraction of ${\mathrm{Nd}}_2{\mathrm{O}}_3$ was 1.25%. They applied a 40-mm-long piece in a Q-switched mode-locked fiber laser at 1.06 µm with a 2.6 GHz fundamental repetition rate^[12]. In 2021, Mkrtchyan et al. reported an ${\mathrm{Nd}}^{3+}$-doped polarization-maintaining mode-locked fiber laser at 905 nm using two pieces of 1.3-m-long active fibers (CorActive ND 103-PM) with a rectangular-shaped dissipative soliton which had a 1.25 nJ energy and a 80 ps width^[4]. In 2022, Xu et al. reported an NDF-based (CorActive, Nd 103) ANDi fiber laser at 1.06 µm. A maximum average output power of 0.63 mW and a pulse duration of 1.22 ps were measured^[13]. In 2022, Zhang et al. reported the noise-like pulse generation in a mode-locked Raman laser at 0.93 µm using an NDF (CorActive, Nd 103)^[14]. In 2022, Zhang et al. demonstrated a femtosecond fiber laser at 0.9 µm with a repetition rate of 1.08 GHz and an output power of 1.75 W, and a pulse duration of 309 fs were obtained after external amplification and pulse compression^[15]. Table 1 compares the performance of several NDF-based mode-locked fiber lasers reported so far.

In this work, we demonstrate two all-fiber mode-locked fiber laser oscillators running at 1064 and 910 nm, respectively, using our homemade NDF as the gain medium. The ${\mathrm{Al}}^{3+}/{\mathrm{Nd}}^{3+}$ co-doped silica core glass was fabricated by the modified sol–gel method and the 4/125 µm NDF was drawn by the rod-in-tube method. Using our NDF, we achieve a maximum average output power of 18 mW with a pulse duration of 5.75 ps, a pulse energy of 1.14 nJ, a 7.2% slope efficiency at 1064 nm, a maximum average output power of 3.1 mW with a pulse duration of 877 ns, a pulse energy of 2.7 nJ, and a 1.44% slope efficiency at 910 nm.

The silica core glass with 18,300 × 10⁻⁶${\mathrm{Nd}}^{3+}$ doping concentration was prepared using the self-developed modified sol-gel method, which was described in detail in Ref. [3]. ${\mathrm{Al}}^{3+}$ with the content of 34,300 × 10⁻⁶ was added to suppress the agglomeration of ${\mathrm{Nd}}^{3+}$. Figure 1(a) shows the polished ${\mathrm{Nd}}^{3+}/{\mathrm{Al}}^{3+}$ co-doped silica rod with an outer diameter of 5 mm. The concentration distribution of ${\mathrm{Nd}}^{3+}$ in the glass rod is displayed in Fig. 1(b).

The glass rod was cut and polished into 2-mm-thick sheets to characterize their physical and spectral properties. Figure 1(c) shows the absorption of ${\mathrm{Nd}}^{3+}$ in the wavelength range of 200–1000 nm. The absorption cross section at the ${{}^2\mathrm{H}}_{9/2}+{{}^4\mathrm{F}}_{5/2}$ level was $1.02{\mathrm{pm}}^2$ located at 802 nm. The main emission peak of the ${{}^4\mathrm{F}}_{3/2}$ level is located at 1059 nm, as shown in Fig. 1(d). The effective emission linewidth is 45.3 nm, which is obtained by dividing the integral area of the emission spectrum by the maximum absorption intensity. The maximum value of the emission cross sections (${\sigma }_{\mathrm{emi}}$) at 1059 nm is calculated as $1.69{\mathrm{pm}}^2$^[16,17], and the second maximum value of the emission cross sections (${\sigma }_{\mathrm{emi}}$) at 905 nm is $0.82{\mathrm{pm}}^2$, which is higher than that of the ${\mathrm{Nd}}^{3+}$ -doped silica glass at 1059 nm prepared by other methods for similar compositions ($1.4–1.5{\mathrm{pm}}^2$)^[18]. The measured fluorescence lifetime of the silica glass at 1.06 µm is 380 µs. Meanwhile, the measured fluorescence lifetime at 0.9 µm is 389 µs due to self-absorption^[19]. Both are longer than the phosphate and silicate glass ($<350\mathrm{\mu s}$)^[20]. A longer fluorescent lifetime of ${\mathrm{Nd}}^{3+}$ indicates the suppression of the agglomeration of ${\mathrm{Nd}}^{3+}$ in the silica glass by co-doping with ${\mathrm{Al}}^{3+}$.

The emission from the Nd-doped fiber at 1.06 µm corresponds to a four-level ${{}^4\mathrm{F}}_{3/2}-{{}^4\mathrm{I}}_{11/2}$ transition, while the 0.9 µm emission corresponds to a three-level ${{}^4\mathrm{F}}_{3/2}-{{}^4\mathrm{I}}_{9/2}$ transition. The emission cross section of the Nd-doped fiber at 1.06 µm is double that at 0.9 µm. Meanwhile, the emission of the Nd-doped fiber at 1.06 µm corresponds to a four-level transition, which has a lower threshold than the 0.9 µm emission of the three-level transition. As a result, lasing at 0.9 µm with a high power output is challenging because of the strong competition with the 1.06 µm emission. So far, several strategies have been proposed to enhance the gain performance at 0.9 µm in the Nd-doped silica fiber, such as cooling active fibers with liquid nitrogen and filtering effect using the special photonic crystal fiber design^[21–24].

The NDF was drawn by the rod-in-tube method. First, the ${\mathrm{Al}}^{3+}/{\mathrm{Nd}}^{3+}$ co-doped core glass rod with a size of $\varphi 5\mathrm{mm}\times 100\mathrm{mm}$ was drawn to a thin rod with a diameter of 2 mm. It was inserted into a pure silica tube to prepare a fiber preform. Then, the preform was drawn into the NDF at a temperature of 2200°C.

The refractive index difference ($\mathrm{\Delta }n$) between the core and the cladding silica glass is $\sim 0.007$, which was measured by the PK2600 refractive index profiler (Photon Kinetics), giving rise to a corresponding NA of 0.14. For a core diameter of 4 µm, it falls in the single-mode operation at both 0.91 and 1.06 µm.

Figure 2(a) shows a Mach–Zehnder interferometer for the dispersion measurement. Figure 2(b) shows the measured group delay dispersion of the NDF in the range of 1030–1100 nm, and the $D$ parameter at 1.06 µm is $-35.4\mathrm{ps}/(\mathrm{nm}·\mathrm{km})$. Figure 2(c) presents the measured loss of the NDF by the cut-back method. The measured losses are 10 and 1 dB/m at 0.91 and 1.06 µm, respectively. The reason for the high loss at 900 nm is that this wavelength coincides with the absorption spectrum of ${\mathrm{Nd}}^{3+}$.

The schematic of the fiber laser oscillator is shown in Fig. 3. The fiber in the cavity includes an $\sim 0.2\mathrm{m}$ homemade NDF and an $\sim 9\mathrm{m}$ single-mode fiber (Hi1060) with a ${\beta }_2$ of $25{\mathrm{ps}}^2/\mathrm{km}$. The net dispersion of the whole laser cavity is calculated at about $0.232{\mathrm{ps}}^2$, indicating that the laser works in the all-normal dispersion regime.

The pump source is a single-mode 808 nm LD (Lumics, LU0808M250) with a maximum output power of 250 mW. A 10:90 optical coupler (OC) is used to couple out the laser power inside the cavity. Two polarization controllers (PC1 & PC2) and a polarization-sensitive isolator (PS-ISO) form an artificial saturable absorber (SA) based on the nonlinear polarization rotation (NPR) effect. The pulse trains, optical spectrum, radio frequency (RF) spectrum, and single pulse width are monitored by a 1 GHz mixed signal oscilloscope (OSC, Tektronix MSO4104) with a 5 GHz photodetector (PD, DET08CFC/M), an optical spectrum analyzer (OSA, Yokogawa AQ6374), a 7.5 GHz electronic spectrum analyzer (ESA, Keysight N9000A), and a commercial autocorrelator (APE, pulseCheck SM Type 2), respectively. Moreover, the average output power is measured by an optical power meter (PM, Thorlabs PM 100D).

We first achieved a stable mode-locked state using the filter with a bandwidth of 5 nm. Figure 4(a) shows the measured optical spectrum of the mode-locked laser at the central wavelength of 1064 nm with a spectral full-width at half-maximum (FWHM) of 6.34 nm. Figure 4(b) shows the measured pulse train of a 15.82 MHz repletion rate. The RF spectrum of the mode-locked pulse trains is presented in Fig. 4(c). The fundamental frequency is located at 15.82 MHz. The signal to noise ratio (SNR) of the RF spectrum is up to 74.06 dB, demonstrating a stable mode-locked status. The autocorrelation trace of the laser is shown in Fig. 4(d). The measured FWHM of the autocorrelation trace is 8.86 ps, and the corresponding pulse duration is 5.75 ps fitted by a ${\mathrm{sech}}^2$ profile. The corresponding time-bandwidth product (TBP) is $\sim 9.66$, implying excessive accumulated chirp in the all-normal dispersion regime. Figure 4(e) plots the average output power as a function of the pump power. The self-started CW mode-locking of the laser is achieved when the pump power reaches beyond 160 mW. A record of the spectrum acquired over two hours demonstrates the long-term stability of the laser, as shown in Fig. 4(f).

The lasing performance with an 8 nm bandpass filter in use is found to be similar but with a higher mode-locked threshold. In Fig. 5(a), the measured laser emission spectrum has a FWHM of 9.02 nm. Figure 5(b) indicates the inter-pulse interval is 63.1 ns corresponding to a repetition rate of 15.84 MHz. The RF spectrum of the mode-locked pulse trains is presented in Fig. 5(c). The fundamental frequency is locked at 15.84 MHz. It is noted that the SNR of the RF spectrum is up to 74.38 dB. Figure 5(d) shows an autocorrelation trace of the pulse, which indicates that the pulse duration is 14.29 ps and the TBP of the laser is up to 34.2. Figure 5(e) plots the average output power as a function of the pump power. Figure 5(f) shows the long-term stability of the laser operation.

With the 8 nm bandwidth filter, the threshold for mode locking rises to 220 mW. Such an effect is attributed to the larger filter bandwidth, which plays a key role in pulse shaping^[25]. As the bandwidth of the filter increases, the pulse chirp increases, which results in an increase in the pulse duration and a decrease in the peak power. Due to the lack of sufficient nonlinear phase shift, the same transmission through the PS-ISO would require a higher pump power. In order to accumulate enough nonlinear phase shifts to achieve mode-locked operation, the threshold power for mode-locking increases.

We numerically simulate our fiber laser oscillator using the generalized nonlinear Schrodinger equation by the standard split-step Fourier method. The simulated temporal and spectral profiles of the pulses with five different filter bandwidths are presented in Figs. 6(a) and 6(b), respectively. The dependences of the pulse duration and spectral bandwidth on the filter bandwidth are summarized in Fig. 6(c). Figure 6(d) shows the simulated TBP for different filter bandwidths. As Fig. 6(d) shows, the TBP of the mode-locked pulse increases with the filter bandwidth, which indicates an increase in the pulse chirp.

As shown in Fig. 7, two 808 nm LDs as pump sources are used with the same maximum pump power of 460 mW. Two pieces of NDFs are cascaded in an active fiber-spectral filter-active fiber (ASFA) sequence with a 910/1060 WDM in between to filter out the amplified spontaneous emission (ASE) at 1060 nm. ASFA is regarded as favorable for self-starting and multi-pulsing suppression^[26,27].

A 10:90 optical coupler (OC) is used to couple the laser power out of the cavity. Two polarization controllers (PC1 & PC2) and a polarization-sensitive isolator (PS-ISO) form an artificial saturable absorber (SA) based on the nonlinear polarization rotation (NPR) effect.

In the experiment, a 180-m-long 780HP fiber is added into the ring cavity. Stable mode-locking is achieved without using any dispersion-compensation components or spectral filters in the all-normal dispersion regime. Figure 8(a) shows the measured optical spectrum of mode-locked lasing at 910 nm. Figure 8(b) shows the measurement of the pulse trains of 1.14 MHz repletion rate. The RF spectrum of the mode-locked pulse trains is presented in Figs. 8(c) and 8(d). The fundamental frequency is located at 1.14 MHz. The SNR of the RF spectrum is up to 68 dB. Figure 8(e) shows the temporal profile of the single pulse. It is noted as the asymmetric profile of the pulse in Fig. 8(e). We attribute it to the excessive dispersion and wall-off effect of the stimulated Raman scattering (SRS) accumulated in our long fiber cavity length. The mode-locked threshold was measured at a pump power of 380 mW. The slope efficiency was 1.44 % with a maximum output power of 3.1 mW, where the pulse energy is calculated at 2.7 nJ.

The artificial saturable absorber consisted of two polarization controllers and a PS-ISO, which introduced at least 3 dB loss into the cavity. Due to the self-absorption, a 15 cm length of NDF was preferred in the fiber laser setup, giving rise to a maximum 1.44 % slope efficiency in our experiment. The slope efficiency reached 1.44 %, which is the highest reported in the ${\mathrm{Nd}}^{3+}$-doped all-fiber nonlinear polarization rotation (NPR) ring cavity configuration.

Short lengths of 780HP fiber, e.g.,  10 and 30 m, had been tested in the ring cavity. while we hardly found the status of mode-locking in our setup using a shorter length of passive fiber. A much higher loss and the nature of three-energy-level transition result in a significantly higher lasing threshold and degraded slope efficiency at 910 nm. The insufficient peak power must require an excessively long fiber cavity to cumulative sufficient nonlinear phase shift for mode-locking. Consequently, it is inevitable to introduce the stimulated Raman scattering in the laser output. As shown in Fig. 8(a), the peak centered at 937 nm is due to the Raman shift of 11.32 THz in the silica glass.

In this Letter, we demonstrate two NDF-based mode-locked fiber lasers at 1.06 and 0.9 µm respectively. The concentration of the ${\mathrm{Nd}}^{3+}$ ion in the core glass is up to $1.71\times {10}^{20}\mathrm{ions}/{\mathrm{cm}}^3$ to achieve a high gain. When the 5-nm bandwidth filter is adopted, the slope efficiency at 1.06 µm reaches 7.2%. By adding 180 m passive fiber in the cavity, the stable mode-locking is realized at 910 nm with a slope efficiency of 1.44%. NDF-based all-fiber mode-locked lasers can find applications in vivo two-photon absorption fluorescence spectroscopy and imaging. All data of this Letter is found in Ref. [28].