1. Introduction

In recent years, much attention has been paid to square-wave pulse passively mode-locked fiber lasers for their potential applications in such as all-optical square-wave clocks, optical sensing and laser micromachining [1–4], etc. In 2008, W. Chang et al. theoretically found the phenomenon of dissipative soliton resonance (DSR) and showed that, under certain condition, the energy of soliton pulse can increase indefinitely while keeping its amplitude [1]. Subsequently, a great deal of studies on DSR fiber laser appeared [5–13]. The X. Liu team and the L. Zhao team respectively studied the DSR pulses in fiber lasers and elaborated their pulse characteristics [5–9]. They showed that the DSR pulse has a low linear chirp across its central region and large nonlinear chirps at its two edges. In addition to DSR pulse, other types of square-wave pulses also arouse researchers' interest, such as randomly chirped square-wave pulse [2], noise-like square-wave pulse [14–18], square-wave pulse with large tuning range [19,20], and so on. K. Özgören et al. reported a 1 ns-long randomly chirped square-wave pulse and pointed out that the pulse was incompressible [2]. The A. Luo team carried out a series of studies on the noise-like square-wave pulse [15–18], they showed that the noise-like square-wave pulses can be generated in several long-cavity fiber lasers with certain cavity parameters. X. Zhang et al. reported the generation of square-wave pulse with ultra-wide tuning range in a mode-locked fiber laser, and showed that high nonlinearity can increase the tuning range of pulse width [3]. L. Mei et al. obtained the width and amplitude tunable square-wave pulse using a dual-pump figure-8 fiber laser [4]. In addition, the energy of square-wave pulse generated from fiber laser, or fiber amplifier, is constantly improved [21–28]. Generally, the square-wave pulse has a large chirp, and its time-bandwidth product can reach to ${10}^4$ [26,28]. In past reports on square-wave pulse chirp, the DSR chirp has been studied fully [5–9], while other chirp characteristics of square-wave pulses received little attention. However, the pulse chirp is closely related to its temporal profile and spectrum, and square-wave pulses of different chirps may have different applications [2,8]. Therefore, the chirp characteristics of square-wave pulses are worthy of further study.

In this paper, we report on a passively mode-locked fiber laser to generate chirp-adjustable square-wave pulses. A chirp measurement system is designed to study the output pulse chirp. We show that the chirp of the square-wave pulse can be adjusted just by the polarization controllers inside the cavity, and three typical output chirp states, including random chirp, V-shaped chirp and linear chirp, were obtained. To the best of our knowledge, it is the first time to report on the generation of chirp-adjustable square-wave pulse in fiber laser. This kind of fiber laser cannot only help to further study the characteristics of square-wave pulse but also serve as multifunction light source for potential applications.

2. Experimental setups

2.1 Structure of the fiber laser

The experimental setup of the passively mode-locked fiber laser is shown in Fig. 1. It consists of two loops. The right loop and the left are connected with a 3 dB coupler. The right loop, also called nonlinear amplifying loop mirror (NALM), acts the role of artificial saturable absorber. The NALM contains a 5-centimeter-length heavily doped YDF (LIEKKI Yb1200-4/125), two 915/980 wavelength division multiplexers (WDM), a 915 nm single mode laser diode with 300 mW maximum output, a polarization controller (PC), and a section of single mode fiber (Corning HI1060, 45 m length). The left loop is composed of a band-pass filter with transmission band ranging from 960 nm to 990 nm, a 10% output coupler, a section of single mode fiber (Corning HI1060, 120 m length), a polarization controller, and a polarization independent isolator (PI-ISO). The PI-ISO ensures unidirectional operation in the left loop. The filter is used to eliminate the ASE around 1030 nm to ensure the laser operating at 980 nm. The total cavity length is 175 m.

 

Fig. 1 Experimental setup schematic of the fiber laser. WDM, wavelength division multiplexer; YDF, ytterbium-doped fiber; PC, polarization controller; SMF, corning single mode fiber HI1060; PI-ISO, polarization independent isolator.

Download Full Size | PDF

For the monitoring and measuring, the following equipment was used: a 4 GHz oscilloscope (Teledyne LeCroy WAVERUNNER 640ZI), 6 GHz photodetectors, a RF spectrum analyzer, an optical spectrum analyzer (OSA, ANDO AQ6317B) and a power meter (Thorlab PM100D/S145C).

2.2 Chirp measurement system

To study the output chirp characteristic of the fiber laser, we designed a simple system to measure pulse chirp (as shown in Fig. 2), which contains two fiber Bragg gratings (FBG1 and FBG2), a section of single mode fiber of 5 m length, three 3 dB couplers, and a polarization independent isolator. The output pulse of fiber laser was spectrally sampled by fiber gratings (FBG1 and FBG2), and the chirp characteristic is determined according to the temporal waveform variation of different spectral components of the pulse. Considering that the output spectrum is ranged from 974 nm to 981 nm, the specific parameters of the FBGs were designed. The central wavelength of the FBG1 can be tuned from 977.5 to 980.5 nm with a constant reflectivity of 99.9% and a reflection bandwidth of 0.2 nm. Similarly, the central wavelength of FBG2 can be tuned from 974.5 to 977.5 nm with a constant reflectivity of 99. 9% and a reflection bandwidth of 0.2 nm. The total spectral sampling range of FBGs is 974.5 ∼980.5nm, which nearly covers the output spectrum of the fiber laser.

 

Fig. 2 Experimental setup schematic for pulse chirp measurement. PI-ISO, polarization independent isolator; FBG, fiber Bragg grating; SMF, corning single mode fiber HI1060; OSA, optical spectrum analyzer.

Download Full Size | PDF

For the pulse chirp measurement, the incident pulse was divided into two beams by a 3dB coupler, one beam from the output port B was sent to the oscilloscope (displayed in channel 2) and OSA for the waveform and spectrum measurement. Another beam passed through the spectral sampling system consisting of FBG1, 5 m single mode fiber and FBG2. The reflected pulses of FBG1 and FBG2 were output from port A, and then sent to a fast photodiode and monitored by the oscilloscope (displayed in channel 1). The corresponding wavelength components of reflected pulses were measured by the OSA. The section of SMF between two FBGs was employed to completely separate the two reflected pulses from the FBG1 and FBG2 in time domain. When channel 1 was triggered by channel 2, the waveforms from spectral sampling system were displayed in channel 1. The waveform of the reflected pulse versus the reflection wavelength in the range of 974.5 ∼977.5 nm was obtained by tuning FBG2’s central wavelength when the central wavelength of FBG1 was fixed. Similarly, the chirp characteristics in the range of 977.5 ∼980.5 nm were obtained by tuning FBG1’s central wavelength and fixing FBG2. Finally, the total chirp characteristics of the output pulse ranging from 974.5 nm to 980.5 nm were obtained.

3. Experimental results and analysis

In our fiber laser, when the pump power exceeded the threshold pump power of about 90 mW, stable mode-locking square-wave pulses were emitted by simply adjusting the two PCs inside the cavity. After analyzing the output with the chirp measurement setup, we found that the output pulse has complex chirp characteristics. And three typical chirp states of output pulse were observed just by adjusting the PCs, including random chirp, V-shaped chirp, and linear chirp (as shown in Fig. 3, Fig. 5, and Fig. 7, respectively).

 

Fig. 3 Randomly chirped pulse output: (a) waveform of single pulse, inset: RF spectrum of pulse train; (b) output spectrum; (c) waveform of the pulse reflected by FBGs versus reflection wavelength; (d) measured spectrogram.

Download Full Size | PDF

For the state of random chirp, the output waveform of the fiber laser at pump power of 180 mW is shown in Fig. 3(a). It is clear that the pulse exhibits a rectangle profile with a duration of 15 ns. To confirm the stability of the pulse train, the RF spectrum was measured by a RF spectrum analyzer. As shown in the inset of Fig. 3(a), the pulse repetition frequency is 1.14 MHz, corresponding to the total cavity length of 175 m. The resolution bandwidth (RBW) of the RF spectrum analyzer is 100 Hz. The signal-to-noise ratio (SNR) exceeds 50 dB. The corresponding output spectrum is presented in Fig. 3(b). The resolution of the optical spectrum analyzer is 0.01 nm. The spectrum is smooth, with a central wavelength of 978 nm and 3 dB spectral width of 4.01 nm. The waveform of the pulse reflected by FBGs versus reflection wavelength is presented in Fig. 3(c). Apparently, the temporal waveforms of different spectral components vary irregularly with their wavelengths. The durations of the reflected pulses centered at 977.26, 977.97, and 978.88 nm are approximately 15 ns, equal to that of the output square-wave pulse. The reflected pulses centered at 974.54, 975.11, 975.69, and 976.48 nm have durations of approximately 6, 11, 12.5, and 13.5 ns, respectively, and their temporal positions are closer to the trailing edge of the square-wave pulse. The reflected pulses centered at 979.32 and 979.98 nm have durations of approximately 13.5 and 8 ns, respectively, and their temporal positions are closer to the front edge of square-wave pulse. To further confirm the chirp characteristics, the corresponding spectrogram was measured with a spectral sampling interval of 0.2 nm and is given in Fig. 3(d). As can be seen from the spectrogram, it is a complex nonlinear chirp profile. Since the spectral components of the pulse do not have well-defined temporal positions like a linearly chirped pulse, we consider it to be a randomly chirped pulse.

The pulse waveform as a function of pump power in the random-chirp state is shown in Fig. 4(a). When the pump powers were tuned to 100, 140, 180, 220, 260, and 300 mW, respectively, the corresponding pulse durations of 6.5, 10.8, 14.9 23.6, and 25.8 ns, were observed. The pulse width increases linearly with the pump power. The output spectrum versus the pump power is presented in Fig. 4(b). The spectra are smooth, and the 3 dB spectral widths at the pump power of 100 and 300 mW are 3.80 and 4.12 nm, respectively. It was confirmed by chirp measurement that the pulse chirps at different pump powers are similar to the one in Fig. 3(d).

 

Fig. 4 Pulse waveform (a) and output spectrum (b) versus pump power, when the laser operating in the random-chirp state. Pump power = 100, 140, 180, 220, 260 and 300 mW, respectively.

Download Full Size | PDF

For the state of V-shaped chirp, the pulse waveform at pump power of 180 mW is shown in Fig. 5(a). The pulse presents a rectangle profile with a duration of 17.8 ns. As shown in the inset of Fig. 5(a), the pulse repetition rate is 1.14 MHz, and the SNR exceeds 50 dB. The corresponding output spectrum is shown in Fig. 5(b), with a 3 dB spectral width of 3.98 nm. The waveform of reflected pulse versus reflection wavelength is depicted in Fig. 5(c). It is clear that the waveform of reflected pulse vary irregularly with its wavelength. Compared with Fig. 3(c), the chirp characteristic here is more complicated. The spectrogram of this state is shown in Fig. 5(d). It indicates that the chirp is non-monotonous across the pulse, appearing “V” shape profile. It is a positive chirp profile during 0∼6 ns while a negative chirp profile during 6∼17.8 ns. From another point of view, the shorter wavelength components of the pulse are located at the central part of the pulse, while the longer wavelength components are more close to the two edges.

 

Fig. 5 Pulse output of V-shaped chirp: (a) waveform of single pulse, inset: RF spectrum of pulse train; (b) output spectrum; (c) waveform of the pulse reflected by FBGs versus reflection wavelength; (d) measured spectrogram.

Download Full Size | PDF

The output waveform versus pump power in the state of V-shaped chirp is shown in Fig. 6(a). When pump powers were tuned from 100 mW to 300 mW, the corresponding pulse durations increased linearly from 9.6 ns to 30.1 ns. Figure 6(b) shows the output spectrum of the fiber laser versus pump power. The spectra are smooth, and the 3 dB spectral widths at pump power of 100 and 300 mW are 3.77 nm and 4.10 nm, respectively. It’s noted that the square-wave pulses under different pump powers all have V-shaped chirps.

 

Fig. 6 Pulse waveform (a) and output spectrum (b) versus pump power, when the fiber laser in the state of V-shaped chirp. Pump power = 100, 140, 180, 220, 260 and 300 mW, respectively.

Download Full Size | PDF

For the linear-chirp state, the output waveform at pump power of 180 mW is shown in Fig. 7(a). The pulse has a duration of 18.2 ns. Different from the square-wave pulses shown in Fig. 3(a) and Fig. 5(a), the front edge of the pulse is much higher than the trailing edge, exhibiting a triangular waveform. The corresponding RF spectrum is given in the inset of Fig. 7(a), and the SNR exceeds 50 dB, indicating a stable mode-locked pulse train. The output spectrum has two peaks around 978.5 nm and 979.8 nm, as shown in Fig. 7(b). The chirp characteristics of the pulse is given in Fig. 7(c) - 7(d). The temporal positions of the reflected pulses are gradually approaching the front edge of pulse as reflection wavelengths become longer, as shown in Fig. 7(c), which means a monotonous chirp across the pulse. It’s further confirmed from Fig. 7(d) that the pulse chirp is nearly linear across its central region and nonlinear at both edges. Besides, the chirp have a non-centrosymmetric profile, with the intensity of the pulse front higher than that of the trailing edge.

 

Fig. 7 Linearly chirped pulse output: (a) waveform of single pulse, inset: RF spectrum of pulse train; (b) output spectrum; (c) waveform of the pulse reflected by FBGs versus reflection wavelength, (d) measured spectrogram.

Download Full Size | PDF

The temporal waveform of the linearly chirped pulse versus pump power is presented in Fig. 8(a). Obviously, the pulse width is well tuned with pump power. The output spectrum versus the pump power is shown in Fig. 8(b), and each of the spectra has two peaks. Compare Fig. 8 with Fig. 7(d), and we can find that the pulse fronts in Fig. 8(a) are corresponding to the right peaks in Fig. 8(b). Furthermore, it was confirmed that the pulse chirps at different pump powers are similar to the one in Fig. 7(d).

 

Fig. 8 Pulse waveform (a) and output spectrum (b) versus pump power, when the laser in the linear-chirp state. Pump power = 100, 140, 180, 220, 260 and 300 mW, respectively.

Download Full Size | PDF

The square-wave pulse is generated in the fiber laser due to the peak power clamping effect. According to Mei [4], there is nonlinear switching in the fiber laser, and pulse peak power will be clamped when reaching the switching power. In our fiber laser setup, the 45 m SMF is used to increase nonlinearity in the NALM, and the high nonlinearity helps to decrease the switching power [3]. Thus the square-wave state of the fiber laser is easily achieved. The 120 m SMF in the unidirectional ring is employed to increase the pulse width tunability. It can be physically understood that the long SMF increases the cavity length, thus allowing more energy to be extracted during the time of one cavity round-trip. If the switching power remains unchanged, the pulse in long cavity will have large pulse width [29]. In the experiment, different pulse temporal heights and widths are observed by adjusting the PCs when fixing pump power, as shown in Fig. 3(a) and Fig. 5(a), which is consistent with the multistability of square-wave pulse reported in [23]. This phenomenon can be understood from the viewpoint that the transmittance of NALM is related to input polarization and birefringence within the NALM in addition to the relative nonlinear phase shift. So the nonlinear transmittance of NALM changes when adjusting PCs, leading to switching power varying.

During the chirp measuring process, the dispersion introduced by FBGs, 5 m SMF, and fiber pigtails of couplers will lead to duration variations of incident square-wave pulse and reflected pulses. However, the pulse duration variations are relatively smaller, compared with the durations of the square-wave pulse (>10 ns) and the reflected pulses (a few nanoseconds). Therefore, the influence of the dispersion introduced by chirp measurement system can be neglected when studying the chirp across the whole square-wave pulse. It is indicated from the experimental results that the output square-wave pulse indeed has complex chirp characteristics, and the chirp state can be adjusted by adjusting the PCs inside the cavity. To the best of our knowledge, it is the first time to report on the chirp-adjustable square-wave pulse in fiber laser.

The three typical chirped pulses obtained in the experiment are unique. Although the randomly chirped square-wave pulse reported in [2] is similar to the one in Fig. 3(d), their chirp characteristics are somewhat different. For the pulse in [2], the temporal widths of different spectral components are equal to that of the unfiltered pulse, while the temporal widths of the spectral components in Fig. 3(d) vary irregularly with their wavelengths. In addition, the DSR pulse reported in [8] is similar to the one in Fig. 7(d), and their chirps are linear in the central part of the pulse and nonlinear at the edges of pulse. However, the DSR pulse in [8] has a centrosymmetric chirp profile and a rectangular temporal waveform, while the linearly chirped pulse here possesses a non-centrosymmetric chirp profile and a triangular temporal waveform. Here, we think the giant-chirp pulse can be compressed because of the clear linear-chirp profile. According to Smirnov [30], the maximum compression ratio theoretically depends on the spectrum width $\Delta \text{ν}$ and frequency fluctuation ($\left|2\text{δν}\right|$). If the frequency fluctuation of the giant-chirp pulse is similar to that of the intermediate regime in [30], we think that the pulse compression can be achieved by conventional grating pairs, but the resulting pulse width is far from the transform limit.

4. Conclusion

In conclusion, we have demonstrated a passively mode-locked fiber laser to generate chirp-adjustable square-wave pulses. The fiber laser is based on the NALM technology and works at the 980 nm band. A simple chirp measurement system is employed to demonstrate that the output square-wave pulses have chirps adjustable by the PCs inside the cavity. By adjusting the PCs, three typical chirp states, including random chirp, V-shaped chirp and linear chirp, are achieved. This type of chirp-adjustable square-wave pulse fiber laser cannot only help to further understand the characteristics of square-wave pulse but also serve as multifunction light source for potential applications.