1. Introduction

High-energy short optical pulses are important for many applications, especially in data inquiring process (e.g. the bio-imaging, ultra-fast sampling) where higher energy results in stronger interaction between the optical field and material sample, and then a higher signal-to-noise ratio. Fiber femtosecond lasers are appealing alternatives to bulk solid-state lasers owing to their compact size, excellent stability, and no-alignment requirement. However, their applications have been limited by the low pulse energy, due to the soliton breaking under overlarge fiber nonlinearity. Recently the dissipative soliton was proposed to increase the pulse energy, which exists in the all-normal-dispersion (ANDi) cavities [1,2]. With the normal chirp induced by self-phase modulation, the high-energy pulse would be broadened monotonically in fiber by the normal dispersion, which decreases the peak power and prevents the wave breaking. Pulses with tens of nJ have been reported [3–5].

Until now the dissipative solitons are only realized in passively mode-locked lasers. Extra operation is required if the pulse repetition rate should be synchronized to an external clock, which is typically a frequency comparison feedback followed by dynamically cavity length control. Such synchronization is often a must in data inquiring. Though active mode locking provides a much simpler operation, by modulating the cavity directly with the external clock, there are still two drawbacks in the reported schemes. Firstly, actively mode-locked lasers often have repetition rate of 10 GHz or larger, which is too high for many data inquiring processes (e.g. bio-imaging and optical sampling oscilloscope). Secondly, current actively mode-locked pulses have very limited energy (only a few pJ) [6–8], partly due to the high rate and limited average power. So an actively mode-locked fiber laser with high pulse energy and appropriate rate is expected for many applications. Besides, wavelength tunability is also useful in, e.g., medical, biological and optical precision metrological fields, which is ordinarily achieved through mechanically tuning filters [9].

In this paper, we experimentally demonstrate for the first time the active mode locking accompanied by the high-energy dissipative soliton shaping. In an ANDi cavity oscillating at 1060 nm band, dissipative soliton is reported with repetition rate around 44.1 MHz. Synchronization with external clock is achieved without additional feedback due to the active mode locking. High pulse energy of 1.58 nJ is obtained through dissipative soliton shaping. The pulse has a 10-ps duration and edge-to-edge bandwidth of 9 nm, and is extra-cavity compressed down to 560 fs. Dissipative soliton shaping inside such actively mode-locked fiber laser is confirmed by simulation. A wide wavelength tunability is also studied, and pulses from 1031 nm to 1080 nm are obtained by simply adjusting the driving frequency. Such tunability is confirmed by theory.

2. Design and simulations

The structure illustrated in Fig. 1 is employed to investigate the dissipative soliton generation in actively mode-locked fiber laser. The key elements of such a laser are a segment of Yb-doped fiber (YDF), a segment of single-mode fiber (SMF), and component that produces pulse-amplitude modulation. It is interesting to compare our laser design with former lasers: intensity modulator (IM) plays the similar role as saturable absorber in passively mode-locked laser; comparing with conventional actively mode-locked laser, a novel modulation format applied on the IM, which is driven by a modulation pattern containing one “1” among many “0”s instead. So the pattern period of IM is the same as the fundamental frequency of the cavity.

 

Fig. 1 Illustration of the fiber laser cavity elements used for the proposed model. IM: intensity modulator.

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In our numerical model, pulse propagation within each component in Fig. 1 follows that described in [10]. Simulation parameters: for YDF, the length is 1.5 m, group velocity dispersion (GVD) is −38.5 ps/nm/km, nonlinear coefficient (γ) is 4.928 W⁻¹/km, small-signal gain (g₀) is 2 m⁻¹, 3 dB-bandwidth of its parabolic-frequency-dependent gain profile (Ω_g) is 40 nm, and the gain saturation energy (E_sat) is 1 nJ. For SMF, the length is 3 m and GVD is −48 ps/nm/km. The IM in our scheme has a fixed Gaussian modulation profile with a full width at half maximum (FWHM) of about 33 ps. As an initial condition, white noise is used. With a standard split-step beam propagation method, the model is solved by iterating the initial field until the field becomes constant to ensure that a stable mode-locked pulse operation has been reached after a finite number of traversals of the cavity [10].

A stable solution is presented in Fig. 2(a) for the situation that small-signal gain (g₀) is 2 m⁻¹. The output pulse duration is 13.2 ps with large-normal-chirp and can be dechirped to 349 fs outside the laser. The corresponding 9.7-nm spectrum [Fig. 2(a) inset] has steep spectral edges and its profile approaches a rectangular shape, which, as well as the normal chirp, is typical characteristic of the dissipative soliton from the passive mode locking.

 

Fig. 2 Numerical simulation results. (a) Temporal intensity profile with linear chirp, inset: optical spectrum of the pulse. (b) Evolution of pulse width (blue) and spectral bandwidth (black) through the laser cavity.

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So far, the dissipative soliton shaping has only been demonstrated in passive mode locking, where the mode locking elements (e.g. nonlinear polarization rotation, NPR) provide power-dependent windowing on the passing optical pulse [9–11]. Instead, in the proposed scheme, the IM is driven by a digital pattern containing “1” and “0”s. Our numerical study has proved that such fixed modulation acts the same role (as NPR) during the dissipative soliton shaping process, which is illustrated in Fig. 2(b): in this all-normal-dispersion cavity, the evolution of the dissipative soliton properties (e.g. the bandwidth) are monotonically changed along the fiber; the fixed windowing, narrowing the pulse duration as well as the bandwidth due to the large chirp, reverse the above changes and thus restore the pulse after traversal of the cavity [10]. Obviously the above pulse shaping mechanism is totally different from soliton shaping in ordinary actively mode-locked lasers [6–8].

3. Experimental results and discussion

Figure 3 shows our experimental setup. A 1.5-m Yb-doped fiber (YDF, Nufern, SM-YSF-HI) with group velocity dispersion (GVD) of −38.5 ps/nm/km and absorption of 250 dBm @ 975 nm is used, which is forward pumped by a 974.3 nm laser diode through a 980/1060 nm wavelength division multiplexer (WDM). A LiNbO₃ Mach-Zehnder intensity modulator (EOSpace, 10 GHz) is employed to realize the active mode locking. Due to the polarization dependence of the IM, a polarizer is used before the intensity modulator to make sure the IM works at the correct polarization state, and a polarization controller to optimize the polarization state. Finally, an isolator is employed to ensure unidirectional operation, and a 10:90 optical coupler to output the signal. Besides the YDF, other fibers (pigtails) are single mode fibers (SMFs) with GVD of −48 ps/nm/km and length of about 3 m. The total length of the cavity is about 4.5 m, corresponding to a fundamental frequency of about 44.1 MHz.

 

Fig. 3 Experimental setup of the proposed active mode locking.

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Our simulation shows that increasing the length of SMF narrows the output spectrum, while appropriately increasing the length of YDF broadens the spectrum. Such trends are similar to those observed in passive ANDi laser [12, 13]. In our setup, the length of SMF is minimized so that the residual SMF is necessary to connect the AM, YDF and other passive devices, in order to obtain the shortest pulse after dechirping. Note that the length of the YDF has also impact on the lasing wavelength. Long YDF can enhance the gain at long wavelength, but a further lengthened YDF will reabsorb the power at the short wavelength [14]. The 1.5 m YDF is then chosen for getting a significant and flattened gain curve from 1030 nm to 1080 nm, in order to obtain a widely wavelength tuning.

It is known that a dissipative soliton requires much higher pulse energy than the regular soliton due to the normal-dispersion-induced pulse broadening [15, 16]. For the conventional active mode locking, which is always driven by a sinusoidal RF tone, the pulse repetition rate is as high as ~GHz. So the single pulse energy is quite low. In our active laser, the pattern generator has a data rate of 10.77 GHz, while there is only one “1” every m = 244 symbols, followed by 243 (m-1) “0”s. So the pulse sequence to drive the intensity modulator has a repetition rate of 44.1 MHz, the same as the fundamental frequency of the cavity. Correspondingly, only one single pulse exists during the cavity loop, and large pulse energy can be obtained under an average pump.

For example, with the pump power of 195 mW, the typical results for the output of the laser are shown in Fig. 4 . Figure 4(a) shows the autocorrelation trace of the pulse having a FWHM of 13.7 ps. The one-pulse-per-loop mode locking is confirmed by intensity auto-correlation and electronic spectrum analysis after high-speed photo detector. Figure 4(b) is the RF spectrum of the pulse, which shows a stable 44.1-MHz pulse train. The measured output power of the pulse is 7 mW, accordingly, single pulse energy after YDF is about 1.58 nJ, which is much higher than conventional actively mode-locked lasers (a few pJ [6–8]). Such high pulse energy (m times of the conventional actively mode-locked lasers) will then support the dissipative soliton shaping. Under the same circumstance as Fig. 4(a), the measured optical spectrum of the output pulse is shown in Fig. 4(c). The spectrum is qualitatively similar to the simulated spectrum [Fig. 2(a) inset]. A striking feature is that the spectrum has steep spectral edges and its profile approaches a rectangular shape. The edge-to-edge width (20-dB bandwidth) is 9.0 nm, indicating that the pulse is strongly chirped. Simulation in Fig. 2(b) shows that under the active-modulation-based fixed windowing, dissipative soliton shaping still exists. As a result, the output shares the same typical characteristics as the dissipative soliton from the passive mode locking [4].

 

Fig. 4 (a) Autocorrelation trace of output pulse (black) and Gaussian fit (red, dashed curve). (b) 100-MHz-span RF spectrum. (c) Optical spectrum of the output pulse. (d) Autocorrelation function of the dechirped output pulses (black line), and the Fourier-limited autocorrelation function calculated by a fast Fourier transform of the optical spectrum are shown (red, dashed curve).

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The output pulse is externally dechirped using a grating pair (Thorlabs, 1200 lines/mm). The autocorrelation of dechirped pulse has a FWHM of 764 fs, which is shown in Fig. 4(d). Using the deconvolution factor of 1.364, which was calculated from the Fourier-limited pulse and autocorrelation widths, the pulse duration of the chirped and compressed pulses are 10 ps and 560 fs, respectively [17]. Obviously, the compressed pulse width is narrower than that in former actively mode-locked lasers (a few ps [6–8]). The dechirped pulse has a little tail on the trailing side due to the limited precision of our autocorrelator. The dechirped pulse duration is close to the transform limit (491 fs), which implies an approximately linear chirp on the generated pulse.

The tunability of the proposed actively mode-locked dissipative soliton laser is discussed. Firstly, as a characteristic of the passive dissipative soliton lasers, it has been demonstrated that the pump power increase will induce the output spectrum broadening [18, 19]. The same phenomenon is observed in our experiment, as shown in Fig. 5(a) . When the pump power is tuned from 18.6 dBm to 22.4 dBm, the output power is changed from 0.2 dBm to 7.1 dBm, and the edge-to-edge bandwidth change of 3.3 nm is obtained. Note that the characteristic of steep spectral edges is kept during the pump increase, while a maximum spectral peak change of 5 dB is observed.

 

Fig. 5 (a) Variation of the active dissipative soliton spectrum with pump power. Inset: the output power and bandwidth variations. (b) Spectrum shifting by tuning the modulation frequency, Inset: wavelength variation along with repetition rate tuning (the mean rate is 44.14 MHz).

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Secondly, due to the relatively large normal dispersion (estimated as −0.21 ps/nm) of the cavity, it takes different periods of time to travel the cavity loop once for pulses with different wavelengths. The pulse with the specific round-trip time that equals to the pattern period will be selected, since it suffers the minimum loss when passing the modulation window. As a result, the lasing wavelength could be tuned by simply adjusting the data rate of the pattern generator, which is faster than the usual mechanically tuning of the filters in passively mode-locked lasers [9]. In our experiment, when the pump power is kept unchanged (about 21.5 dBm), the center wavelength of the stable mode-locked pulses is tuned from 1031 nm to 1080 nm as the repetition rate is tuned from 44.129 to 44.149 MHz, resulting in a wavelength tuning rate of 2.45 nm/kHz, as shown in Fig. 5(b). According to [20], wavelength tuning rate is given by:

The normal dispersion of the cavity contributes to the mode locking stabilization too: variation of the cavity length from environmental changes (temperature, vibration, etc.) is compensated by the slight and self-adapting change of the wavelength [20]. We experimentally observe continuous mode locking for hours without any stabilization mechanism. Besides, polarization fluctuation can be prevented by using polarization-maintaining components.

4. Conclusion

In conclusion, we experimentally demonstrated the generation of dissipative soliton in an actively mode-locked ANDi fiber laser, with the specific characteristic of steep spectral edges or rectangular-like spectrum. The strongly-chirped output pulse was 10 ps, which was dechirped to 560 fs by a grating pair outside the cavity. Dissipative soliton with edge-to-edge bandwidth of about 9 nm and wavelength tuning from 1031 to 1080 nm was realized by adjusting the modulation rate. Due to the simple synchronization to external clock and large pulse energy, many applications would benefit from the novel laser.