1. Introduction

Mode-locked fiber oscillators, known for their compact structure and high beam quality, are a key driving source behind various applications in the field of science and industry, such as bio-imaging, precision micromachining, and optical frequency combs [1]. The rapid development of these applications has driven research on mode-locked fiber oscillators over the past decades, aiming to achieve enhanced output performance and high environmental stability. A reliable mode-locking operation can be enabled by using material-based saturable absorbers (MSAs), including semiconductor saturable absorber mirrors, carbon nanotubes, graphene, and other nanomaterials. However, MSAs often suffer from drawbacks such as low damage thresholds, slow relaxation times, and a tendency to degrade over time [2], hindering the oscillator from achieving ultrashort and high-energy pulses. In contrast, mode-locking based on the optical Kerr effect, such as nonlinear polarization evolution (NPE) [3] and nonlinear amplifying loop mirror (NALM) [4], can avoid these issues and offer superior noise performance for oscillators [5,6]. Among them, NPE is one of the most promising mode-locking techniques because many breakthrough pulse characteristics of the oscillators are based on it. For example, so far, the highest pulse energy / average output power (∼1 µJ / 9 W [7]) and the shortest pulse duration (∼21.5 fs [8]) reported in self-starting mode-locked fiber oscillators were achieved using NPE technology. Despite these advancements, NPE's implementations have primarily been in non-polarization-maintaining (PM) fibers, which suffer from reduced environmental stability. This limitation is in contrast to NALM, which is highly compatible with PM fibers, thereby offering oscillators enhanced long-term stability and resistance to environmental disturbances when used in an all-PM configuration [9–12]. The implementation of NPE into PM fibers, therefore, represents a crucial research frontier. Advancing NPE technology to function effectively within PM fibers could preserve the pulse performance benefits unique to NPE while significantly enhancing the environmental robustness of the oscillators.

NPE mode-locking inherently depends on self-amplitude modulation arising from the interplay of pulse polarization evolution and a polarizer. However, the significant birefringence in PM fibers causes a walk-off between the two orthogonal polarization modes (OPMs), preventing effective polarization evolution. A technique involving 90° cross-splicing in either two or multiple segments of PM fibers has been proposed to eliminate the walk-off effect, thereby enabling successful PM-NPE [13–17]. Nevertheless, achieving mode-locking in these PM oscillators requires meticulous design of the splicing angle and precise management of the fiber length, adding complexity to the laser design [16]. A more convenient and effective method is to use a Faraday rotating mirror (FRM) as the end mirror in a linear cavity. When the two OPMs are reflected back into the PM fiber by the FRM, they get swapped, automatically compensating for the group velocity mismatch (GVM) and thereby effectively eliminating the walk-off effect. Such linear configuration also offers straightforward installation and alignment procedures. This method was first proposed in 1994 by Fermann et al. [18] and was used to create a mode-locked PM fiber oscillator that produced 360 fs, 60 pJ pulses at 1560 nm. In 2007, the approach was successfully implemented into an all-PM fiber oscillator operating at 1 µm capable of generating pulses with a pulse duration of 5.6 ps and an average power of 8 mW [19]. Since then, NPE-based mode-locked PM fiber oscillators in a linear cavity structure have been continuously reported [20–26].

In addition, mode-locked fiber oscillators face a limitation in output power and pulse energy owing to the relatively strong nonlinearities of the single-mode fiber (SMF). One method to alleviate these limitations is the use of large-mode-area (LMA) fiber. As we previously reported, by substituting SMF with LMA fiber, the output power and pulse energy of a thulium-doped mode-locked fiber oscillator can be increased by five times, coinciding with theoretical predictions [27]. It is foreseeable that by further integrating dispersion management techniques, an increase of at least an order of magnitude in these values can be expected [12]. However, LMA fiber usually contains a small number of high-order modes (HOMs), whose modal interferences can lead to reduced self-starting ability and stability in mode-locking, as well as degraded beam quality. Despite this, various methods to effectively suppress HOMs have been employed, including coiling the fiber, using mode filters based on SMF designs, and designing single-mode LMA fibers such as photonic crystal fiber (PCF) [28] and chiral coupled-core fiber [29]. So far, NPE mode-locked LMA fiber oscillators have been successfully reported in different wavelength regimes [7,27,29,30]. Most of these oscillators, however, use non-PM LMA fibers, which cannot provide long-term stability. Recently, Edelmann et al. reported the successful implementation of an NPE mode-locked PM-LMA Yb-doped fiber oscillator with a linear cavity structure, where the HOMs were suppressed by two mode-field adapters [31]. Compared with a reference oscillator constructed using standard fiber components with a 5.5 µm core size, this implementation resulted in a 36-fold increase in pulse energy. However, to date, there have been no reports of exploiting NPE mode-locked PM-LMA fiber oscillators in wavelengths other than 1 µm.

In this letter, we demonstrate for the first time a dual-output-port PM-LMA Er/Yb-doped fiber oscillator based on NPE mode-locking, operating at a central wavelength of 1.56 µm and a fundamental repetition frequency of 34.47 MHz. The reliable self-starting mode-locking behavior of the oscillator is achieved by employing two short pieces of endlessly single-mode PCFs, which effectively suppress the HOMs in the PM-LMA fiber. Consequently, this design ensures high beam quality, with the M² values of both output ports being as low as 1.1∼1.17. On the other hand, the two output ports of the oscillator show distinct pulse characteristics; one port generates high-quality soliton-like pulses with a retrieved pulse width of 325 fs and a pulse energy of 1.15 nJ, while the other produces low-quality pulses due to the interacting nonlinear effects such as cross-phase modulation (XPM) in the PM fiber. For the port generating soliton-like pulses, there is a significant improvement in pulse energy compared to similar soliton-like pulses previously reported in NPE mode-locked fiber oscillators based on SMF at the 1.5 µm region, which had energies around 0.2 nJ in a variety of experimental studies; e.g., Refs. [17,23–25].

2. Experiment

Figure 1 shows the schematic of the linear cavity mode-locked fiber oscillator. A 1.6-m-long, double-cladding active PM-LMA Er/Yb-doped fiber (Nufern, PLMA-EYDF-25P/300-HE, 2.9 dB/m cladding absorption at 915 nm) with a core diameter of 25 µm and a numerical aperture (NA) of 0.09 serves as the gain fiber. The entire gain fiber is placed in water accordingly to dissipate the heat. It is pumped by a 976 nm multimode laser diode through a signal-pump combiner based on passive PM-LMA fiber (iXblue, IXF-2CF-PAS-PM-25-300-0.08) with a core diameter of 25 µm and a NA of 0.08. The length of the passive PM-LMA fibers is around 60 cm. The aforementioned active and passive fibers have almost similar structures and therefore have similar group velocity dispersion (GVD) parameters, which are around -28.6 ps²/km [12]. Moreover, they can support about four guiding transverse modes at emission wavelength (∼1.56 µm) according to the fiber parameters. To effectively suppress the HOMs, two short segments of endlessly single-mode (ESM), LMA-PCF (NKT, LMA-25), each with a core diameter of 25 µm and an NA of 0.05, are separately spliced to the active and passive PM-LMA fibers, while their remaining free ends are polished with an 8° angle to eliminate the parasitic oscillation. The total length of the two PCF segments is ∼0.4 m, and they have a GVD of approximately -24 ps²/km, a detail that will be elaborated on in the subsequent analysis. Although the LMA-PCFs are non-PM fibers, they are relatively short (∼0.4 m) compared with the total length of the active and passive PM-LMA fibers (∼2.2 m). Hence, nonlinear pulse shaping is then dominated by the PM-LMA fibers which provide high environmental stability to the oscillator [18]. Note that it was difficult for the oscillator to achieve mode-locked operation once the PCFs were removed in the experiment. Further eliminating unabsorbed pump light and signal light leaked into the cladding using two homemade cladding light strippers based on high index matching gel can slightly increase the self-starting ability.

 

Fig. 1. Experimental setup of the NPE mode-locked PM-LMA linear-cavity fiber oscillator. M, gold mirror; FR, Faraday rotator; CLS, cladding light stripper; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; NRPS, non-reciprocal phase shifter; port T, transmission port; port R, reflection port.

Download Full Size | PDF

The free-space section on the right side of the oscillator is an FRM, which consists of a 45° Faraday rotator (FR1) and a gold mirror to compensate for the GVM caused by the PM fiber. The other free-space section on the left side includes two quarter-wave plates (QWP1, QWP2), a 45° FR (FR2), a half-wave plate (HWP), a polarization beam splitter (PBS), and a gold mirror. The QWP1, HWP, and 45° FR collectively form a non-reciprocal phase shifter to improve the oscillator's self-starting mode-locking capability. Additionally, the PBS provides two output ports (port T and port R) and introduces intensity-dependent losses that serve as an artificial SA to establish NPE mode-locking. The output coupling ratio for port R is determined by the settings of the HWP and QWP1, while for port T, it is governed by the setting of the QWP2. The total cavity length of the oscillator including the fiber part (a total length of ∼2.6 m) and free-space arms (a total length of 47 cm) is ∼3.07 m.

3. Experimental results and discussions

To initiate the mode-locking operation, it’s crucial to correctly set the phase bias. This mainly involves adjusting the rotation angle θ_H for the HWP and θ_Q1 for the QWP1. In the experiment, the θ_H and θ_Q1 were set as 5° and -73° for optimum starting conditions, respectively, and could be slightly changed by ±1° and ±4° without significantly compromising the self-starting capability. Due to the use of non-PM PCF, we are unable to calculate the energy splitting ratio between the fast and slow axes of the PM-LMA fiber. However, this ratio is estimated to be around 80:20 or 20:80, which is a typical value for reliable self-starting based on previous experimental experiences [26,31,32]. In addition, the rotation angle θ_Q2 for the QWP2 mainly determines the output power of port T, thus affecting total cavity loss. It was initially set as 10° for quick starting. With these settings, as the pump power was increased to 7.07 W, the oscillator began operating in a multi-pulse state accompanied by continuous wave (CW) spikes. Reducing the pump power to 2.38 W enabled stable single-pulse operation with a fundamental repetition frequency rate of 34.47 MHz. To maximize the output power of port T, the θ_Q2 was changed to 26°. In this situation, the average powers measured at port T and port R were ∼40 mW and 8.6 mW, respectively, corresponding to pulse energies of 1.15 nJ and 0.25 nJ. Mode-locking disappeared when the pump power was further decreased to ∼2.24 W.

Figure 2 illustrates the relationship between the average output power and the pump power for both ports. An interesting observation is that, in the single pulse regime, the output power from both ports does not vary linearly with changes in the pump power. This is primarily because, as the pump power varies, the nonlinear phase difference accumulated after one round-trip propagation between the fast and slow axis pulses within the fiber is not constant but undergoes slight changes. These slight changes alter the energy-splitting ratio of reflection and transmission light at the PBS, leading to slight nonlinear variations in the output power. Strong evidence supporting this is the large difference in the total slope efficiencies between the single-pulse state (3.2%) and the CW state (13%). This discrepancy arises because the nonlinear phase shifts in these two states are completely different, resulting in distinctly different transmission losses at the PBS, thus affecting the slope efficiencies. It is worth noting that the total slope efficiencies observed in both states are relatively poor, which can be attributed to several factors: relatively high pump insertion losses (∼15%) from the customized light combiner; incomplete absorption of the pump light; and the waveplate angle settings resulting in a relatively low output coupling ratio. Despite this, the optical-to-optical conversion efficiency reported in this study is comparable to that of previously reported mode-locked LMA Er/Yb fiber laser oscillators [12,30,33], which also require several watts of pump power to maintain single-pulse operation with average output powers ranging from tens to hundreds of milliwatts.

 

Fig. 2. Pump power versus output power for ports T and R, including individual and combined outputs.

Download Full Size | PDF

Figures 3(a) and 3(b) display the spectra measured for port T and port R using an optical spectral analyzer (Yokogawa, AQ6375B) at a resolution bandwidth of 0.05 nm. The central wavelength is around 1566 nm, and the corresponding bandwidths at 10 dB below the spectral peaks are 19.95 nm and 21.17 nm, respectively. The presence of Kelly sidebands in the spectra indicates that the oscillator is operating in a net negative dispersion regime. Note that both ports exhibit slight modulations with a period of ∼2 nm in their spectra, resulting from the intermodal interference between the fundamental mode (LP₀₁) and the HOMs (mainly LP₁₁) in the PM-LMA fiber. Based on the position of the Kelly sidebands, we can calculate that the net intra-cavity dispersion is -0.145 ps² using the method described in [34]. By neglecting the tiny dispersion of free-space optics and considering the round-trip propagation characteristics of the linear cavity, the GVD value (-28.6 ps²/km) of the PM-LMA fibers, and the lengths of the fibers within the cavity, we can further deduce that the GVD of the LMA-PCF is around -24 ps²/km. Furthermore, the output spectra between the two ports are clearly different, with port R exhibiting more complex spectral modulation, indicative of lower pulse quality at this port. To gain a deeper understanding of the pulse characteristics, we used a well-known algorithm, i.e., phase and intensity from correlation and spectrum only (PICASO) [35], to retrieve the pulse shapes. The retrieved pulse autocorrelation (AC) traces agree fairly well with the measured results as shown in Figs. 3(c) and 3(d). The corresponding pulse shapes are displayed in the insets of these figures. Clearly, the pulse quality at port T is much higher than that at port R. Our recent researches suggest that this phenomenon could be attributed to XPM occurring between two OPMs within the PM fiber [26], making a pulse at port R that significantly differs from the Fourier transform-limited (FTL) pulse and is accompanied by distinct satellite pulses. In contrast, the pulse at port T is cleaner, with a retrieved width of 325 fs, close to the FTL width of 233 fs. The peak power is calculated to be 3.0 kW. Moreover, if we consider the pulse at port T to be a pure sech² soliton pulse, the deconvolution factor of 1.54 applied to its AC trace yields a pulse width of 305 fs (i.e., 470 fs /1.54 = 305 fs), which is in close agreement with the retrieved width of 325 fs. This further indicates that the pulses at port T are soliton-like.

 

Fig. 3. Pulse characterizations for both ports. (a) and (b) Optical spectra of the mode-locked pulse with a resolution bandwidth of 0.05 nm. (c) and (d) Measured AC traces together with retrieved traces obtained by PICASO algorithm, inset for FTL and retrieved pulses.

Download Full Size | PDF

To investigate the beam quality, one of the key parameters of LMA fiber lasers, we used a beam analyzer (DataRay, Beam'R2) to measure the M² values of both ports. The measurement results are displayed in Fig. 4, which includes insets showing the profiles of the corresponding collimated beams. The average M² value for port T is 1.17 (Fig. 4(a)), while it is 1.10 for port R (Fig. 4(b)). The slight difference between the two ports could be due to optical aberrations of the free-space optics inside the cavity and the suboptimal optical coupling/alignment. Despite this, the obtained values are close to the measured M² value (∼1.105) of a prototype SMF-based, all-fiber carbon-nanotube mode-locked laser in our laboratory. This indicates that the ESM-PCF used in the oscillator effectively suppresses HOMs, significantly enhancing beam quality and enabling the oscillator to operate in a near-fundamental transverse mode state. Owing to the single-mode transmission characteristics of the ESM-PCF, this oscillator also exhibits reliable pulse self-starting performance. Previously, in a NALM mode-locked fiber oscillator based on the same type of PM-LMA fiber [12], we attempted to suppress HOMs using techniques like coiling the LMA fiber and inserting pinholes as spatial filters, but the results were not satisfactory, with M² values often between 1.3 to 1.5 at both output ports, notably higher than the results of this work (1.1∼1.2). Benefiting from the use of ESM-PCF, the gain fiber does not need coiling here and can be freely placed in a water tank for thermal dissipation.

 

Fig. 4. Measured M² factors of (a) port T and (b) port R, insets for collimated beam profiles.

Download Full Size | PDF

In addition to pulse energy and average power, pulse stability and noise performance are also important for certain applications. We used a fast 12.5 GHz photodetector (Newport, 818-BB-51F) and a radio-frequency (RF) spectrum analyzer (Agilent N9010B) to measure the RF spectrum of the mode-locked pulses. Figures 5(a) and 5(b) show the RF spectra centered around the fundamental repetition frequency (∼34.47 MHz) for both ports, with the insets displaying the corresponding 3.6 GHz wideband RF spectra. A high signal-to-noise ratio of ∼80 dB for both ports indicate a high energy stability of the pulse. Almost flat amplitudes of the higher harmonics imply single-pulse operation. The small dip observed near 3 GHz in the wideband RF spectrum is due to inherent equipment noise rather than intrinsic optical properties of the oscillator. We also carried out the relative intensity noise (RIN) measurements to further explore the noise characteristics of the pulses. Firstly, the average power of the signal light under test was attenuated to 0.21 mW (corresponding to a shot noise level of -147.1 dBc/Hz) and then sent to an amplified photodetector (APD, Thorlabs PDA10D2, 25 MHz bandwidth). Secondly, the APD converted the light signal into a voltage signal, which was subsequently connected to a homemade DC block circuit with a cut-off frequency of 1 Hz to prevent equipment damage. Finally, the processed signal was subjected to analysis using a noise spectrum analyzer (Rohde & Schwarz FSWP8) via the baseband port. The recorded power spectral density (PSD) of the RIN for two ports is depicted in Fig. 5(c). Additionally, the figure also includes the RIN-PSD of the pump source, the noise floor of the measurement system, as well as the shot noise of the detector for reference. Upon careful observation of these traces, it's evident that at low frequencies below 1 kHz, the oscillator noise is mainly inherited from the pump source. Above 1 kHz, the RIN noise from the oscillator starts to decrease and deviate from the pump noise, which is likely due to the gain dynamics of the Er/Yb-doped fiber acting as a low-pass filter. Note that the noise measurement for port T is limited by the noise floor of the system at frequencies above 5 kHz. Across the entire frequency range [1 Hz, 10 MHz], the integrated root mean square (RMS) RIN for port T is 0.046%, and for port R is 0.053%. Similar to other dual-port NPE/NALM mode-locked fiber oscillators, as indicated in Refs. [12,24,26], the RIN at port R is higher than at port T. These values are comparable to those of oscillators based on SMF [11], confirming the robustness of our fiber oscillator.

 

Fig. 5. Radio frequency (RF) spectra of (a) the port T and (b) the port R. (c) RIN-PSD and integrated RMS RIN for two ports. Pump RIN-PSD, noise floor of the system, and shot-noise of the detector are also included for reference.

Download Full Size | PDF

To further investigate the long-term stability of the oscillator, we used a power meter (Thorlabs, PM100D) to continuously monitor the average output power for more than 2 hours. The recorded results are shown in Fig. 6. We observed that the RMS power fluctuation for port R is 0.75%, markedly higher than the 0.2% noted for port T. This further confirms that most of the messy pulses generated by XPM, which are sensitive to environmental changes, are predominantly redirected to port R. Therefore, suppressing XPM in an NPE mode-locked fiber oscillator not only contributes to the enhancement of pulse quality but also significantly betters their stability and noise performance.

 

Fig. 6. Average output power monitoring over 2 hours for both ports.

Download Full Size | PDF

4. Conclusion

In summary, we have successfully developed a dual-port, NPE-based mode-locked PM-LMA Er/Yb-doped fiber oscillator. To overcome the challenge of initiating mode-locking in LMA fiber oscillators, which is often hindered by HOM disturbances, we have utilized an ESM-PCF as a mode filter. This approach not only significantly enhances the oscillator’s self-starting mode-locking capability but also ensures its high beam quality. The measured average M² value, as low as 1.1∼1.17, is comparable to that found in SMF-based oscillators. Due to the use of PM-LMA fiber, the oscillator efficiently produces high-quality soliton-like pulses with a duration of 325 fs and energy of 1.15 nJ, corresponding to a peak power of ∼3 kW. The successful demonstration of our PM-LMA fiber oscillator based on NPE mode-locking in a streamlined cavity structure opens up new possibilities for high-performance ultrafast oscillators at 1.5 µm.