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Abstract
Herein, we present a fundamental and harmonic mode-locked figure-of-9 thulium-doped fiber laser using a nonlinear amplifying loop mirror. The generated fundamental mode-locked h-shaped pulse is centered at 1889 nm with an average output power reaching 282 mW and a pulse energy up to 1.23 µJ, which is the highest power and pulse energy of an h-shaped pulse. In the harmonic mode-locked regime, up to the 8th harmonic h-shaped pulse is obtained. The detailed characteristics of the h-shaped pulse are discussed. The proposed study shows that the figure-of-9 fiber laser can generate h-shaped pulses and also allows the generation of nanosecond pulses with a µJ-level pulse energy.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pulsed lasers, especially mode-locked lasers, are widely used in surgery [1,2], material processing [3–5], sensing [6,7], and supercontinuum generation [8,9]. Pulsed lasers also play a vital role in the medical, industrial production, and scientific research fields. A passively mode-locked fiber laser containing a saturable absorber (SA) is one of the main methods for generating laser pulses. The currently used SAs include SESAM, 2D-SA, and artificial SAs, such as a nonlinear polarization rotation (NPR), nonlinear polarization evolution, nonlinear amplifying loop mirror (NALM), and nonlinear optical loop mirror (NOLM) [10–15]. Among the abovementioned SAs, SESAM and 2D-SA are suitable for the generation of ultrashort pulses. However, owing to the low material damage threshold and soliton area theorem, SESAM and 2D-SA cannot generate pulses with large energies. On the contrary, artificial SAs show their application value in generating large-energy pulses.
High-energy pulses, such as dispersion soliton resonance (DSR) pulse, step-like pulse, and chair-like pulse, have been widely reported and use artificial SAs [14,16–19]. The maximum pulse energy originating directly from a NALM-based cavity can be up to 10 µJ [17]. Recently, h-shaped pulses have been demonstrated, showing potential for generating large energy. In 2018, Zhao et al. first reported h-shaped pulses from a NOLM-based mode-locked figure-of-8 thulium/holmium-codoped fiber laser (THDFL) [20]. The THDFL exhibited a maximum output power of ∼50 mW, and the corresponding pulse energy was 15.6 nJ. Then, Zhao et al. further studied the mechanism of mode-locked h-shaped pulses in an NOLM-based thulium-doped fiber laser (TDFL) [21]. The TDFL has a cavity length up to ∼3 km. Harmonic mode-locked h-shaped pulses can be switched up to the 48th order. Owing to the ultralong cavity length, the maximum pulse energy in the fundamental mode-locked regime was up to ∼0.74 µJ. However, the slope efficiency was only ∼2%. Luo et al. demonstrated an NPR-based ring-cavity mode-locked TDFL that produced h-shaped pulse at 1.985 µm [22]. The maximum output power and pulse energy were 235 mW and 163.7 nJ, respectively, with a slope efficiency of 4.7%. X. Wang et al. obtained noise-like h-shaped pulses from a figure-of-9 THDFL [23]. Noise-like h-shaped pulses of 97.4 nJ energy was obtained without any dispersion management. The obtained maximum power was 36.3 mW, and the corresponding slope efficiently was only 3.63%. In 2019, Bravo-Huerta et al. for the first time produced h-shaped pulses in a double cladding figure-of-8 erbium/ytterbium-codoped fiber laser; however, the relevant power parameters were not provided [24]. Dong et al. achieved rectangular and h-shaped pulses using an offset-spliced graded-index multimode fiber-based SA in a ring-cavity mode-locked ytterbium-doped fiber laser [25]. For the h-shaped case, pulse duration was tunable from 2.5 to 25 ns. The obtained maximum pulse energy was 23.8 nJ. Recently, h-shaped pulses were observed in the net normal dispersion regime, and detailed output characteristics have been discussed [26]. However, to the best of our knowledge, there are no studies on the generation of h-shaped pulses that are based on a figure-of-9 TDFL, and the energy of h-shaped pulses generated directly from the cavity is still at a relatively low level.
Herein, for the first time, we experimentally demonstrate the fundamental and harmonic mode-locked h-shaped pulses generated from a figure-of-9 TDFL. The detailed characteristics of h-shaped pulses are discussed. The maximum average output power is 282 mW, which is obtained in the fundamental mode-locked regime, and the corresponding pulse energy is up to 1.23 µJ, which is currently the highest power and pulse energy of h-shaped pulses.
2. Experimental setup
The experimental setup for producing h-shaped pulses is shown in Fig. 1. The pump source for the figure-of-9 TDFL is a high-power 1550 nm erbium/ytterbium-codoped fiber amplifier that delivers output power up to 2.57 W. The single-mode 1550 nm pump light is coupled into the segment of a thulium-doped single-clad fiber (TSF; Nufern, SM-TSF-9/125) through a wavelength multiplexer (WDM). The TSF is 5.5 m with a core numerical aperture (NA) of 0.15, core absorption coefficient of 13 dB/m at 1559 nm, and group-velocity dispersion (GVD) of −0.071 ps2/m at 1900 nm [27]. A ∼860-m-long single-mode passive fiber (Corning, SMF-28) with an NA of 0.14 and GVD of −0.067 ps2/m at 1900 nm is used to enhance the nonlinearity and introduce asymmetric gain of the cavity. In comparison with a high-nonlinearity fiber, SMF-28 has a lower transmission loss, which is more conductive for the generation of high-energy pulses in the long cavity [21]. A SMF-28-based polarization controller (PC) with three fiber coils is utilized to adjust the polarization state of the cavity. The SMF-28 is coiled with a diameter of 56 mm, and the winding number is two, four, and two in a sequence. To form an NALM, a 2 × 2 optical coupler (OC) with a beam splitting ratio of 5:95 is spliced to the PC and WDM. The other two ports of the OC are connected to a high-reflection mirror (HR) and isolator (ISO), where the HR reflects the signal light into the cavity, and the port connected to the ISO is used as the output port of the cavity. The pigtails of the optical devices used are all SMF-28. Including all the active and passive fibers, the total cavity length is ∼875 m and the total cavity dispersion is −58.7 ps2; therefore, the TDFL operates in a large-anomalous dispersion regime.
3. Results and discussion
3.1. High-energy fundamental mode-locked h-shaped pulses
Stable fundamental mode-locked h-shaped pulses can be generated when the pump power reaches 0.53 W even without a wide range of polarization state adjustment. The output characteristics of the fundamental mode-locked TDFL are shown in Fig. 2. The pulse profile is measured with a digital oscilloscope (Tektronix, DPO 7104C) connected to a photodetector (EOT, ET-5000). Figure 2(a) shows the output pulse profile, which looks like the letter ‘h’ and was named as an h-shaped pulse in the previous reports [20–22]. The h-shaped pulse contains a high amplitude leading edge and low amplitude trailing portion. The amplitude of the trailing portion remains approximately constant as the pump power increases, whereas the duration becomes wider and much larger than the leading edge. It can be seen that, when the pump power is increased from 0.67 to 2.57 W, the duration of the trailing portion is increased from ∼180 to ∼875 ns. Figure 2(b) shows the output pulse train. It is observed that as the pump power increases, no pulse splitting and high-order harmonic occurs, and the h-shaped profile of the pulse remains unchanged. Benefit from the km-level cavity length, the round-trip time of the generated pulse train is up to ∼4.2 µs. The output optical spectra are shown in Fig. 2(c), which are measured using a high-resolution long-wavelength optical spectrum analyzer (Yokogawa, AQ6375B). The spectra are centered at 1889 nm with a rectangular shape and corresponding 3 dB bandwidth up to 17–20 nm. As can be seen, there is significant depression distributed over the spectra, which is mainly caused by absorption lines of water and other atmospheric molecules. This phenomenon is very noticeable in the 2 µm region [21,28]. The radio frequency (RF) spectrum is monitored by a frequency spectrum analyzer (Agilent, E4407B) connected to an EOT 2 µm photodetector. As shown in Fig. 2(d), the RF spectrum measured at the maximum pump power is located at 288.8 kHz, corresponding to the total cavity length. Therefore, we can determine that the TDFL operates in the fundamental mode-locked regime. The signal-to-noise ratio (SNR) is measured to be 65 dB at a resolution bandwidth of 1 Hz, confirming that the fundamental mode-locked h-shaped pulse is stable. Output power characteristics are measured with a high-sensitivity power meter (Ophir Optronics, NOVA II). Figure 2(e) shows the output power and pulse energy versus pump power. The slope efficiency of the power curve is ∼13.8%, which is much larger than the efficiency reported in [21] because the fiber used herein is much shorter than that used in [21], and the loss introduced by the fiber is much lower. At the maximum pump power, the maximum output power of the TDFL is 282 mW, and pulse energy is up to 1.23 µJ. The h-shaped pulse exhibits the following characteristics that are similar to the DSR pulse: high pump power-related pulse duration, pulse-free splitting, and high pulse energy. However, unlike the complete peak power clamp of DSR pulse, the h-shaped pulse is considered to be partially clamped, primarily because the h-shaped pulse has a high intensity leading edge [20,22]. Besides, the power stability of the TDFL is tested for 120 min at the maximum pump power by connecting the power meter to the StarLab software. As shown in Fig. 2(f), the standard deviation (Std. Dev.) of the output power is 2.52 mW, suggesting that the power fluctuation during the long-term operation is small. The h-shaped pulse is also measured by an autocorrelator (APE, pulseCheck USB). As the inset in Fig. 2(f) shows, no fine structures are found in the long pulse envelope; therefore, we can confirm that the h-shaped pulse is not a noise-like pulse [29].
Fig. 2. Output characteristics of the fundamental mode-locked TDFL. (a) Output pulse. (b) Pulse train. (c) Optical spectra. (d) RF spectrum. (e) Output power and pulse energy. (f) Long-term output power stability. Inset: autocorrelation trace.
According to equation $T = 1 - 2\alpha (1 - \alpha )\{ 1 + \cos (\Delta {\phi _{NL}})\}$[30], the transmittance T of the NALM depends on the OC’s beam splitting ratio $\alpha$ and nonlinear phase shift $\Delta {\phi _{NL}}$, where $\Delta {\phi _{NL}}$ is proportional to fiber nonlinear coefficient $\gamma $, optical peak power P, and fiber loop length L. One can see from the equation above that the transmittance T exhibits a periodic modulation and this periodic modulation corresponds to saturable absorption effect and facilitates the generation of mode-locked pulses. For the proposed ultralong cavity, periodic gain depletion and recovery will occur in a round-trip time of up to ∼4.2 µs. Therefore, the gain dynamics may be responsible for the h-shaped pulse with decaying intensity [23].
3.2. Harmonic mode-locked h-shaped pulses
Harmonic mode-locked h-shaped pulses can be achieved when the pump power is above 2.13 W and polarization state is properly adjusted. Herein, TDFL can be switched from the fundamental mode-locked regime to 2nd, 4th, and 8th harmonic mode-locked regimes by adjusting the polarization state of the cavity. Figure 3 shows the RF spectra in different mode-locked states with a fixed pump power of 2.57 W. The RF spectra are located at 228.8, 457.8, 915.7, and 1831 kHz, respectively. The higher the harmonic mode-locking frequency, the lower is the SNR of the RF spectrum, suggesting that the stability of TDFL gradually degrades in the high-order harmonic mode-locked regime. In the 8th harmonic mode-locked regime corresponding to a repetition frequency of 1831 kHz, the SNR is reduced to 50 dB.
Figure 4(a) shows the evolution of pulse trains in different mode-locked states under the maximum pump power of 2.57 W. As the repetition frequency increases, the number of pulses in the same time-domain increases, while the pulse interval decreases from ∼4.2 to 0.55 µs. Meanwhile, the leading edge intensity of the h-shaped pulse is reduced and duration of the trailing portion is considerably narrowed. The intensity of the tailing portion remains almost unchanged. Figure 4(b) shows the evolution of RF spectra in different mode-locked states with a span of 10 MHz and resolution bandwidth of 1 kHz. Similar to the DSR mode-locked pulse, the RF spectrum of the h-shaped pulse also shows a periodic frequency modulation [16,21,25], and the modulation frequency ${f_m}$ is determined by the corresponding duration of the trailing portion $\tau $ via equation ${f_m} = \frac{1}{\tau }$. When the repetition frequency is 228.8 kHz, the duration of the trailing portion is ∼875 ns, and corresponding modulation frequency is 1.14 MHz.
Fig. 4. Evolution of (a) pulse trains and (b) RF spectra with a 10 MHz span in different mode-locked states under the maximum pump power of 2.57 W.
In the case where the polarization state is fixed, the harmonic mode-locked h-shaped pulses can also be achieved by adjusting the pump power of the TDFL. To further understand the characteristics of the harmonic mode-locked h-shaped pulses, we compared individual pulses in different mode-locked states. As shown in Fig. 5, when the pump power is higher than 2.13 W, high-order harmonic mode-locked h-shaped pulses can be achieved. When the pump power is further increased, higher order harmonic mode-locking can be obtained, and the intensity of the leading edge and the trailing portion of the h-shaped pulse gradually decrease. Harmonic mode-locked h-shaped pulses may be caused by certain factors that limit the peak power clamping effect and lead to pulse breaking or splitting, such as nonlinearity, gain dynamics, and birefringence [21].
4. Conclusion
In conclusion, the fundamental and harmonic mode-locked h-shaped pulses are generated from a figure-of-9 TDFL based on NALM. In the fundamental mode-locked regime, the maximum average output power and pulse energy are 282 mW and 1.23 µJ, respectively. To the best of our knowledge, these are the first h-shaped pulses generated from a figure-of-9 TDFL with the highest power/pulse energy of h-shaped pulses. In the harmonic mode-locked regime, h-shaped pulses up to the 8th harmonic are obtained. Results obtained herein enrich the study on h-shaped pulses and figure-of-9 fiber lasers and provide a way to achieve large-energy nanosecond pulses.
Funding
National Natural Science Foundation of China (61905151, 61775146, 61575129, 61605122, 61905146, 11704260); Natural Science Foundation of Guangdong Province (2016A030310049); National Key R&D Program of China (2016YFA0401100); Major Science and Technology Project of Guangdong Province (2014B010131006); Shenzhen Science and Technology Project (JCYJ20160328144942069, JCYJ20160427105041864, JCYJ20160520161351540, JCYJ20170302151146995, KQJSCX20160226194031).
Disclosures
The authors declare no conflicts of interest.
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