1. Introduction

In the past decades, fiber lasers have evolved into a powerful light source. Comparing to other alternatives, such as semiconductor lasers and free-space solid-state lasers, fiber lasers share a unique feature of combing a high degree of compactness, low costs, ease of operation, and, most importantly, the capability of generating mode-locked pulses, thus attractive to many laboratory and field applications [1–8]. In order to produce bright, ultra-short pulses with great simplicity and high stability, several passive mode-locking methods, for example based on nonlinear polarization rotation (NPR) [9–12], intracavity saturable absorbers [13], or nonlinear loop mirrors [14], have been developed. Meanwhile, many nonlinear effects and phenomena, such as self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM), stimulated Raman scattering (SRS), and so on, have been found important to the formation of ultrashort pulses [1, 15–18]. Thus, it is of great value for theoretically and/or experimentally investigating these optical processes.

As an interesting phenomenon, elliptically polarized solitons with two orthogonal polarization modes copropagating with the same group velocity in weakly birefringent fiber cavities have been previously demonstrated in polarization-locked vector soliton (and dissipative soliton) fiber lasers [14–25]. Theoretically, such solitons are solutions of coupled nonlinear Schrödinger equations [16, 17]. By balancing the linear fiber birefringence with intracavity nonlinear effects, the elliptical polarization state of the solitons may evolve stably. Consequently, the soliton polarization evolution frequency (PEF) can be precisely and passively locked to 1/N (N is an integer) of the pulse repetition rate (f_r). Solitons with such polarization dynamics have been found useful in many applications, varied from telecommunications to spectroscopy [20, 25]. On the other hand, further investigations on this polarization evolution locking (PEL) effect may lead to new understandings of mode-locking mechanisms of fiber lasers.

As a real-time method, time-stretch spectroscopy has been harnessed to reveal the spectrum dynamics of the polarization-rotating pulses at a frame rate as high as the laser repetition frequency [26–28]. However, experimentally studying the pulse temporal evolution remains challenging. Besides, investigating the PEL effect from perspective of individual frequency lines of a fiber laser has not yet been reported. In this paper, we employ a simple method based on a fast pulse picker for characterizing the time-evolved temporal and spectral features of pulses from a stretched-pulse fiber laser. The results are consistent with previous simulation works and experimental observations [14–28]. Moreover, a strong wavelength dependence of PEL is experimentally observed by using a wavelength-tunable filter at 1-nm bandwidth. This behavior of PEL is further examined for individual fiber laser comb lines.

2. Experimental setup

A typical NPR mode-locked erbium-doped fiber laser oscillator is shown in Fig. 1. A 1.5-meter-long erbium-doped fiber (LIEKKI 110/4) with second order dispersion of ~17 ps²/km around 1580 nm, pumped by a diode laser at 976 nm through a 1550/980nm wavelength division multiplexer (WDM), is used as a gain medium. The rest of the laser cavity includes a 2-meters-long single mode fiber (dispersion of ~ −16 ps²/km at 1580 nm), two collimators and an open-air section comprising two quarter-wave plates, a half-wave plate, a polarization-beamsplitter (PBS) and an optical isolator. The intra-cavity net dispersion is estimated to be around −0.007 ps². With such small negative dispersion, the laser possibly operates in the stretched-pulse mode-locking region [29]. The pump power is set to 250 mW. The laser output (~30 mW) from the PBS is coupled into a fiber collimator followed by a 20/80 fiber splitter, 80% being sent to a pulse picker and then measured with an optical spectrum analyzer (Yokogawa AQ6370D) and an optical autocorrelator (pulseCheck, APE). The rest of the output beam passes through a fiber-coupled tunable filter and is then split into two parts. 10% of the filtered light is detected by a fast photodetector (2-GHz bandwidth) and monitored by a digital oscilloscope (Tektronix MDO4054C) and the rest is used for beat note measurements with narrow-linewidth cw lasers.

 

Fig. 1 Experimental setup. EDF, erbium-doped fiber; WDM, wavelength division multiplexer; Col, collimator; PBS, polarization beam splitter; 1/4, 1/2, quarter and half wave plates; ISO, isolator; BS, beam splitter; PD, photo-detector; OSA, optical spectrum analyzer.

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3. Results

By carefully rotating the wave plates, we obtain a mode-locking state of pulse intensity being modulated at a half (f_r/2) of the repetition rate (f_r=54.54 MHz). The pulse train (s-polarized) is shown in Fig. 2(a). We attribute these modulations to the PEL effect [14–27], in which case the polarization state of the intracavity pulses repeats itself every second (or multiple) roundtrip time. Because the PBS is highly polarization-selective, the PEL effect shows up as the pulse-to-pulse intensity modulation at the output port. This PEL effect is mostly reported for vector soliton (or multi-soliton) fiber lasers with two orthogonally polarized components propagating in the cavity with the same group velocity and identical intensity. Here, this bounding state is found in a stretched-pulse fiber laser. The rf spectra of the output is analyzed with a rf spectrum analyzer (Agilent N9000A) at a resolution bandwidth (RBW) of 30 kHz, as shown in Fig. 2(b). The pulse-to-pulse intensity modulation produces frequency sidebands at half of f_r. Furthermore, both the repetition frequency signal and the sidebands (RBW is set to 1 Hz) are found with a similar 3-dB linewidth of ~1 Hz (limited by the instrument), indicating a rather good frequency stability of PEL.

 

Fig. 2 Characterizations of the fiber laser. (a) A train of output pulses displayed within 200 ns and 1000 ns and (b) the corresponding rf spectrum. (c) The autocorrelation traces and (d) the corresponding spectra of the pulses A, B and the trains without the pulse picker. The autocorrelation traces and spectra are normalized so that the differences in their shapes can be noticed. In (d), the gray line is vertically shifted for display.

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By using a fast pulse picker made by an electrooptic modulator (bandwidth of 12 GHz; MXER-LN-10, Photline), we are able to study the high (marked as A in Fig. 2(a)) and low (marked as B) intensity pulses separately. The pulse picker is driven by a rf signal generator (SMC100A, R&S) producing a square pulse train at a frequency of 27.27 MHz (about half of f_r) with a pulse window of 10 ns. The repetition frequency of the fiber laser is synchronized to the signal generator by using a home-made electronic control system [10]. The time delay of the square wave is tuned so that only the low (or high) intensity pulses are selected by the pulse picker for the temporal and spectral measurements. The autocorrelation traces and the high-resolution (0.1-nm) spectra of the pulse A (B) are simultaneously measured and displayed in Figs. 2(c) and 2(d), respectively. The full widths at half maximum (FWHM) of pulses A and B are measured to be about 360 fs and 490 fs, respectively. The time-bandwidth products (TBP) of pulses A and B are 2.1 and 2.9, respectively. For a Gauss-shape pulse, the transform limited TBP is 0.44. Note that the measured pulses are not dispersion compensated and the total fiber length of the pulse picker is about 1 m (dispersion of −0.016 ps²). Also, no pulse splitting is observed for both the pulses A and B, as shown in inset of Fig. 2(c). This result with alternate pulse widths for the PEL pulse train agrees the simulation results demonstrated in Fig. 3 of ref. 19. Meanwhile, clear differences are found for the spectra of the pulses A and B (especially at the spectral edges), as pictured in Fig. 2(d). The observed spectrum variation of A and B is consistent with the measurements conducted with time-stretch spectroscopy [26–28], except that here the results are achieved by a well-developed spectrometer instead of a high-speed oscilloscope (usually with bandwidth of tens of GHz) with limited acquisition dynamic range (8-bits) and spectral resolution. We believe that the spectral as well as the temporal differences of pulses A and B are related to their pulse intensity variations which may affect the pulses through intracavity nonlinearity and dispersion. Note that with our pulse selection method the pulse-to-pulse spectral and temporal variations are also found with other PEL states for our fiber laser, e.g., modulating at one fourth of the repetition frequency.

 

Fig. 3 (a) The wavelength dependence of the fundamental repetition frequency (fr) signal and the fr/2 sideband. (b) The difference between the fr signal and the sideband. The signal and the sideband are measured with the rf spectrum analyzer at a RBW of 10 kHz. The absolute frequency for fr is 54.542 MHz and for the sideband 27.271 MHz. The measured wavelength range is limited the fiber optical filer (1520-1590 nm).

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Considering two successive pulses (A and B) having differences in their emission spectra, the wavelength-dependence of PEL is investigated. We measure the rf spectrum of the spectrally filtered pulses (setup in Fig. 1) while tuning the center wavelength of the filter at a fixed FWHM of 1 nm. The tuning range of the filter is from 1520 to 1590 nm. For each wavelength, the recorded rf spectrum is similar with Fig. 2(b). The peaks of the fundamental f_r (=54.54 MHz) signal and the sideband frequency at f_r/2 (=27.27 MHz) are measured and shown in Fig. 3(a). The blue squares for the f_r signal simply represent the spectral profile of the laser output. The relative difference of the peak values of the f_r signal and the sideband, plotted in Fig. 3(b), indicates the PEL-induced intensity modulation depth varying with laser wavelengths. At the edge of the laser spectrum (around 1530 nm), the PEL effect is found strongest, almost wiping out the low-intensity pulses as being monitored by the oscilloscope; while at some wavelengths (e.g., around 1550 nm), the PEL modulation becomes much weaker. Such behaver matches our spectral results in Fig. 2(d), where the most spectral difference of the pulses A and B appears around 1530 nm.

Since a mode-locked fiber laser naturally has the comb structure in the frequency domain, it is interesting to investigate the PEL effect on the basis of comb lines of the fiber laser. For this purpose, the PEL fiber laser is heterodyned with a single-mode cw laser on a fast photodetector. As we know, in the frequency domain the intensity-modulated pulse train in the f_1/2 state can be seen as a line-spacing halved frequency comb. Assuming the nth fundamental comb line at f₀+nf_r (offset frequency: f₀), the PEL-induced sidebands can be written as f₀+nf_r±f_r/2. The beat note between a narrow-linewidth (~1 kHz) cw laser (center frequency: f_cw) and a fundamental comb line close to f_cw can be described as b₁ (=|f₀+nf_r-f_cw|), and between a frequency-close-by sideband of the comb line as b₂ (e.g., =|f₀+nf_r-f_r/2-f_cw|). In our experiment, the beat notes are experimentally measured by first combining the spectrally filtered comb with a cw laser via a 2x2, 50/50 fiber coupler and then by the balanced differential detection with a balanced photodetector (PDB470C, Thorlabs). The cw laser is linearly polarized and aligned with the pulse train polarization for optimizing the beating signals. The output of the detector is recorded with the rf spectrum analyzer at a RBW of 30 kHz, as displayed in Fig. 4(a). The center wavelength of the cw laser is 1550 nm (193.41 THz). Judging by the relative heights of the beat notes, the line at 11.7 MHz is assigned to b_2-1550 and the line at 15.4 MHz to b_1-1550.

 

Fig. 4 Beat note measurements. (a) The resulted rf spectrum for the beating between the fiber laser and a cw laser at 1550 nm; the zoom-in of (b) the b_1-1550 line at 15.54 MHz and (c) the b_2-1550 line at 11.73 MHz; the beat notes, (d) b_1-1540 and (e) b_2-1550, of the fiber laser with another cw laser around 1540 nm.

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These beat notes are further investigated in a rf span of 1 MHz at RBW of 5 kHz (sweep time of 46 ms). The results are shown in Figs. 4(b) and 4(c), respectively for the b_1-1550 and b_2-1550. Though the relative intensity of b_1-1550 and b_2-1550 is about 20 dBm, they share a very similar −3-dB linewidth of ~10 kHz. Note that our measurements are limited by the free-running linewidth of the fiber laser (f₀ is unlocked). Also, we notice that the beat notes are drifting, about 5 MHz per minute (3.8 kHz within 46 ms). Since no obvious linewidth broadening is observed between b_1-1550 and b_2-1550 with our current setup, the phase noise and fluctuations of PEL must be smaller than that of the passive mode-locking mechanism itself. The results of the fiber laser beating with another single-frequency cw laser at 1540 nm (194.67 THz) are shown in Figs. 4(d) and 4(e). The measured beat notes also show an identical linewidth of ~10 kHz, indicating a good frequency (or phase) stability of the PEL effect across a broad spectral range of the laser emission. Besides, the two beating signals (b_1-1540 and b_2-1540) have a difference ~5 dB, much smaller than the 1550-nm case. This wavelength dependence of the beat notes is consistent with the measurements in Fig. 3, except that Fig. 3 reflects a collective effect of 2200 comb lines (1-nm spectral width of the optical filter at 1550 nm) and here represents individual behavior of a comb line.

4. Conclusion

In conclusion, first, we develop a simple method for studying the PEL effect in a broadband stretched-pulse fiber laser, which indirectly reflects the temporal and spectral dynamics of the pulses without using high-speed devices such as an oscilloscope of tens of GHz bandwidth. Secondly, the PEL-induced rf sidebands are found highly sensitive to the laser emission wavelength. The strongest PEL-induced modulation is observed at the spectral edges of the fiber laser. Thirdly, the optical comb nature of the fiber laser is used as an ultrahigh resolution spectrometer, revealing the wavelength dependence of PEL at the comb-line level through beat note detection. We believe our results bring in new insights for the PEL phenomenon and our methods presented here may benefit further experimental and theoretical studies on fiber lasers.