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Abstract
In this paper, the phenomenon of reverse saturable absorption of offset-spliced graded index multimode fibers (OS-GIMF) is revealed. And based on that, the stable square-shaped and chair-like mode-locked pulses are demonstrated with the maximum pulse energy of 0.14 µJ and 23.8 nJ respectively, while the OS-GIMF acts as a saturable absorber (SA) in fiber laser. By adjusting polarization controller (PC) and the pump power, square-shaped and chair-like pulse can be switched to each other. This multimode SA could sever as high power light source owing to its high damage threshold, compact structure and low cost.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
All-fiber-format mode-locked laser has been widely applied among biomedicine, scientific research, and industry due to its compact structure, excellent beam quality and efficient pumping [1–4]. In practical application, it is significant to improve pulse energy of laser. One of feasible options is the square pulse laser whose pulse energy could increase infinitely as pump power increases while the amplitude remains constant [5–9]. It is rarely reported that new materials are used as SA to generate square pulses due to the low damage threshold of these materials, so square-pulse mode-locked fiber laser are generally generated based on nonlinear amplifying loop mirror (NALM) [10–12] and nonlinear polarization rotation (NPR) [13] mechanisms.
Recently, graded index multimode fibers (GIMF) have been extensively studied in communication network, supercontinuum generation [14], soliton molecules [15–17], self-beam cleaning [18–20], Nonlinear conversion material [21–23] and spatiotemporal mode-locking [17,24] owing to its low dispersion and unique nonlinear dynamics. In 2013, Nazemosadat and Mafi [25] suggested that, based on nonlinear multimode interference (NMI), the switching property in single mode fiber (SMF)-GIMF-SMF structures can be used as SA in mode-locked laser. Subsequently, researchers solve the problem of the length limit of the GIMF as SA based on NMI by several different methods such as adding a segment of step-index multimode fiber ahead of GIMF, introducing inner micro-cavity in GIMF and stretching the GIMF and so on [26–31], which is critical for practical application. In these methods, the number of modes in GIMF will increase, and the SA could be bended appropriately so that the mode field distribution in GIMF can be arbitrarily tuned within a certain range, both of which will lead to the change of the transmittance curve of SA and therefore remove the length limitation of GIMF. However, the reverse saturable absorption effect (the transmittance decreases with the increase of input power in a certain range) in GIMF has not been reported in experiments so far, and this effect play a crucial role in the formation of square pulses [32–35]. Because of its high damage threshold (the damage threshold of quartz), simple structure, easy fabrication and low cost, the SA is very suitable for applications in high-power square-pulse mode-locked fiber laser.
Here, we firstly demonstrate the reverse saturable absorption effect in spliced GIMF, after that, stable square-shaped and chair-like pulse laser with the repetition rate of 1.83 MHz is realized, in which the spliced GIMF acts as a SA based on nonlinear multimode interference. Besides, the chirp characteristics of square-shaped and chair-like pulse are characterized by the measurement system proposed by our group [36].
2. Experiment setups
The experimental configuration of the mode-locked laser is shown in Fig. 1. A double cladding Yb-doped fiber (LIEKKI, Yb1200, 10/125) of 3 m is pumped by a 976 nm multimode semiconductor laser with maximum pump power of 30 W through a 2×1 multimode fiber pump combiner. A polarization independent isolator ensures unidirectional propagation, and a polarization controller (PC) is used to adjust optimal mode-locked state. The SA device [double cladding fiber (DCF)-GIMF-GIMF-DCF] is placed after the PC. A bandpass filter with a 3 dB bandwidth of 3 nm is utilized to control the central wavelength of the laser. The energy of laser is extracted by a 60:40 optical coupler and a 99:1 coupler is connected to measure the power, spectral and time-domain characteristics. In our experiment, the type tail fibers of optical devices are DCF (LIEKKI, 10/125 passive). The total length of ring cavity is about ∼109 m. The instruments used in this experiment are Optical Spectrum Analyzer (OSA, ANDO AQ6317B), oscilloscope (Lecroy 640ZI), Power meter (Thorlab PM100D), RF spectrum analyzer (AV4021).
Fig. 1. Diagram of the fiber laser. MFPC, multimode fiber pump combiner; YDF, double cladding ytterbium-doped fiber; PI-ISO, polarization independent isolator; DCF, double cladding fiber; PC, polarization controller; SA, saturable absorber; Filter, bandpass filter.
We propose an offset-spliced DCF-GIMF-GIMF-DCF structure, which introduce the offset splicing spot between two GIMFs could eliminated the restriction on the GIMF length by fusion splicer [31]. In order to achieve stable mode-locked state, the SA device must be fixed in an appropriate bending shape, which can tune the optical properties (such as transmittance, central wavelength) in certain range [27–31]. As illustrated in Fig. 2(a), the SA consists of a segment of 3-cm GIMF and 8-cm GIMF with an offset of 10-µm, whose core diameters are 62.5 and 50 µm respectively. According to the model described by Mafi et al. [25], the transmission curve of SA can be described as:
Where T is the power transmittance, P0, P1 and Pm are the power of fundamental mode LG00 and higher order modes (ie., LG10, LG20, LG30, …LGm0) respectively, $\gamma$ is nonlinear coefficient of GIMF, and $\tilde{L}=L \times \Delta \beta$, where $\Delta \beta$ is the difference of propagation constant. In our measurement setup, a 1.06 µm pulses laser (pulse-width of ∼10 ps and repetition rate of 19.3 MHz) after amplified are injected into the SA, and the transmittance curve can be obtained by recording the power change before and after passing through the SA, as can be seen in Fig. 2(b). The absorption modulation depth of SA is about 10% and reverse saturable absorption power density is approximately 11 MW/cm2. It is worth noting that the saturable absorber can be changed into the reverse saturable absorption region by increasing the input light power. Besides, according to the theoretical simulation results [25], the reverse saturable absorber characteristic of the SA could be improved by changing the parameters of SA (ie., the length of GIMF, input optical power, the curvature of GIMF).Fig. 2. (a)Schematic diagram of the saturable absorber (SA); (b) Saturable absorption property of the saturable absorber (SA), dots correspond to experimental data, and the red line is their fitting curve.
To study the pulse chirp characteristic of our mode-locked system, we use the chirp measure device designed by our group [36], as shown in Fig. 3. In our chirp measure system, it contains two fiber Bragg gratings (FBG1 and FBG2), a polarization independent isolator, a section of 10/125 double cladding fiber of 5 m length, and three 3 dB couplers. Considering that the spectrum of pulse is ranged from 1061 nm to 1067 nm, the central wavelength of FBG1 and FBG2 is designed as 1064 nm and 1061 nm with a reflection bandwidth of 0.135 nm and a 99.9% reflectivity, respectively. The pulse of laser is divided into two beams through a 3dB coupler, pulse of spectrum and waveform from output port A is measured by the OSA and the oscilloscope. The reflected pulses from port B sampled by grating are measured by OSA and oscilloscope respectively. The central wavelength of the FBG1 and FBG2 are adjusted by tension to cover the whole spectrum of the pulse, and the temporal and spectral changes of port A are recorded at the same time, so that the pulse chirp characteristics can be measured.
Fig. 3. Experimental schematic for pulse chirp system. PI-ISO, polarization independent isolator; FBG, fiber Bragg grating; DCF, corning 10/125 double cladding fiber; OSA, optical spectrum analyzer.
3. Experimental results and analysis
In our experiment, square-shaped and chair-like pulse can be switched to each other by adjusting the PC and pump power. For the case with square-shaped pulse, the stable mode-locked pulse is generated by adjusting the PC when pump power reaches 569 mW. Figure 4 shows the characteristic of the square-shaped pulse. As shown in Fig. 4(a), the spectrum of square-shaped pulse is located at 1063.42 nm with 3dB bandwidth of 0.62 nm. The pulse duration will be tuned from 350 ps to 52.6 ns as the pump power increased, while the pulse amplitude almost remains constant as illustrated in Fig. 4(b), which is consistent with the power clamp theory [6]. The signal to noise ratio (SNR) is measured by a RF signal analyzer and shown in Fig. 4(c). The fundamental repetition rate is 1.83 MHz with SNR exceeding 65 dB, which indicates stable mode-locked operation state. The characteristic modulation of amplitude envelope is another intrinsic feature of mode-locked square-shaped pulse, which can be observed on the RF spectra gathered for a wider span. The period of modulation is directly associated with the mode-locked pulse width, and varied continuously with increasing pump power. Figure 4(d) shows the duration of square-shaped pulse and the variation of the output single pulse energy with the pump power. When the pumping power reaches 3.24 W, the maximum single-pulse energy of the laser is 139.1 nJ. When the pump power increases further, the square-shaped pulse will be splitted and operated at multi-pulse states.
Fig. 4. Square-pulse measurement. (a) Output optical spectrum versus pump power; (b) pulse duration under different pump powers; (c) RF spectrum of pulse train in the range of 0–300 MHz, inset: RF spectrum with the span of 1 MHz and a resolution bandwidth of 30 Hz; (d) Variation of pulse energy and Pulse width on pump power.
The chirp characteristic of the square-shaped pulse is described in Fig. 5(a). As can be seen from the spectrogram, there is no significant difference in the time-domain characteristics of the pulse among different spectral positions, other than intensity variation. Based on the spectrogram, the spectral components of a pulse are chaotic in the time domain, we consider it is a random chirp pulse.
For the chair-like pulse case, the stable mode-locked pulse train is generated by adjusting the polarization controller when pump power reaches 340 mW. Figure 6 displays the characteristics of the chair-like pulse. As shown in Fig. 6(a), the spectrum of h-shape pulse locates around 1064.91 nm with a 3dB spectral width of 1.6 nm. When the pump power increases from 340 mW to 1.12 W, the shape of the spectrum doesn’t change significantly, but the height of the peaks increases. The pulse duration will be tuned from 2.5 ns to 25 ns as the pump power increases, while the pulse amplitude almost remain constant as illustrated in Fig. 6(b). The SNR is shown in Fig. 6(c). The fundamental repetition rate is 1.83 MHz with signal noise ratio exceeding ∼ 68 dB, indicating excellent mode-locked operation state. Figure 6(d) shows the duration of chair-like pulse and the variation of the output single pulse energy with the pump power. When the pumping power reaches 1.12 W, the maximum single-pulse energy is 23.86 nJ. When the pump power exceeds 1.12 W, the laser will operate at unstable mode-locked state.
Fig. 6. Chair-like pulse measurements. (a) Output optical spectrum under different pump powers; (b) Pulse duration under different pump powers; (c) RF spectrum of pulse train in the range of 0–300 MHz, inset: RF spectrum with the span of 1 MHz and a resolution of 30 Hz; (d) pulse energy and pulse width versus pump power.
The chirp characteristic of the chair-like pulse is described in Fig. 7(a), the front edge of the pulse is linear arrangement, and the others is nonlinear arrangement, which is like a trumpet. Compared to the square-shaped pulse, the chair-like pulse is similar to square-shaped pulse in time domain but shows a sharp leading edge. At present, the exact formation mechanism of chair-like pulse has not been thoroughly studied. One possible mechanism of chair-like pulse is that the sharp and flat parts of the pulse are generated at different positions of the transmittance curve of the SA. Thus, with certain settings of the PC and pump power, the flat-top and sharp pulse can coexist in the pulse evolution process and can lead to the formation of chair-like pulses [34,37]. To validate that the mode-locked mechanism of the laser is supported by the SA, the SA is removed intentionally. At this time, no matter how we adjust the pump power and PC, no mode-locked pulse is observed.
According to the Mei [38], the square-shaped and chair-like pulse is generated in fiber could be considered as the peaking power clamping effect, the pulse peak power will be clamped when reaching the switching power. The power camping effect is related to the nonlinearity of fiber laser cavity, high nonlinearity is beneficial to decrease the switching power [39]. In our fiber system, 100 m DCF not only decrease the switching power but also increase the tunability of pulse width. As shown in Fig. 4(b) and Fig. 6(b), different pulses profiles are observed by adjusting PC. It could be understood that the pulse characteristics (including shape, chirp, power, etc) depend on the cavity parameters (such as loss, nonlinearity and gain, and so on) which are affected by the state of PC and pump power. In other word, adjusting PC and pump power will affect the pulse shape of laser stable operation, which is consistent with the stable multistate of mode-locked fiber laser reported in [36,40,41].
4. Conclusion
In summary, we have demonstrated square-shaped and chair-like mode-locked pulse fiber laser based on GIMF SA. We find the reverse saturated absorption plays the key role in the mode-locked square-shaped and chair-like pulse, and prove that reverse saturated absorption is caused by GIMF fibers rather than NPR effect or nonlinear optical loop mirror. By adjusting PC and pump power, random chirp pulse and trumpet-shaped chirp pulse can be observed, which are measured by chirp measurement system. The square-shaped and chair-like mode-locked pulse based on GIMF fiber is of excellent pulse stability, and can be used in high power laser to serve in industrial processing.
Funding
National Natural Science Foundation of China (61675188); Fundamental Research Funds for the Central Universities (WK6030000086).
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