1. Introduction

Pulse shaping is widely used in high-speed optical communication, laser fusion and ultrafast nonlinear optics [1–8]. Over the past two decades, several pulse shaping techniques have been well developed and particularly, ultrashort laser pulses have been successfully tailored with ultrahigh precision control in both the time and frequency domain for quantum coherent control. Different pulse shaping methods are used to meet requirements of specific applications. Femtosecond pulses were shaped by using spectral pulse shapers with specially designed masks or spatial light modulators in the spectral Fourier plane. Picosecond pulse shaping was realized by direct space-to-time pulse encoding based on spatial filtering spectral components diffracted in different directions [9,10]. Ultrashort pulses of ultrabroad spectra may be possibly stretched and thus shaped to the nanosecond-duration region. Nevertheless, spectral chirps in the stretched pulses seriously limit their applications. It still lacks in efficient techniques to precisely shape sub-nanosecond or nanosecond narrowband laser pulses. The most conventional method for nanosecond pulse shaping relies on coherent pulse stacking, in which ultrashort pulses are split and then recombined after appropriate delays and intensity controls. In principle, a long pulse can be stacked with a large number of ultrashort pulses of appropriate delays [11,12], but the pulse-stacking processes are limited in practice by the small quality of split pulses as increasing the split pulse number typically requires very special and quite difficult optical designs. The failure in coherent phase control of the split pulses causes unwanted intensity modulations and the shaped pulses typically exhibit a quite low reproducibility. In addition, a common problem with currently available pulse shaping methods is unavoidable energy loss introduced by the fiber waveguide or spatial mask [13,14]. Recent progress in robust synchronization of ultashort laser pulses stimulates ever-growing experimental exploration on synchronized pulse shaping with ultrahigh-precision temporal and spectral control, which is promising to improve the reproducibility of pulse shaping [15–17].

In this paper, we report our experimental demonstration of gain-assisted pulse stacking, which facilitates coherent stacking of an increased number of ultrashort pulses to produce relatively long pulses of tunable duration from ps to sub-ns range. The advantages of the novel gain-assisted pulse stacker over the conventional one are the precise control, reproducibility and without energy loss of the shaped pulses. Such a gain-assisted pulse stacking was realized with a diode-pumped Yb-doped fiber amplifier (YDFA) in an external cavity of a round-trip transit delay appropriately mismatched to the high repetition rate of the seed pulses, where each ultrashort seed pulse encountered a regularly shifted delay after the round-trip circulation, resulting in coherent pulse stacking of multiple round-trip circulations. Without the limitation of the split sub-pulse number and intensity modulation, the output features of the novel gain-assisted pulse stacker is reproducible. As optical losses were compensated by the gain of the YDFA, each seed pulse was circulated more than ten times in the cavity without any energy losses or even got amplified. The pulse-shaping properties could be readily controlled by adjusting the intracavity dispersion and cavity length mismatch.

2. Experimental setup and results

The experimental setup for gain-assisted pulse shaping is schematically shown in Fig. 1 . An Yb-fiber gain-assisted pulse stacker was used in the experiments, which adopted a ring cavity configuration, consisting of a 60-cm-long Yb-doped fiber as the gain medium, several-meter silica fiber, and a 60-cm-long free space for bulk optical components. A pair of gratings was inserted in the pulse stacker cavity in order to compensate for the positive intracavity dispersion, and a space optical isolator was used to ensure a unidirectional laser operation. Two quarter-wave plates and a half-wave plate were employed to start possible mode-locking operation through nonlinear polarization evolution. A broadband Ti:sapphire laser which delivered 7-fs pulse trains at a repetition rate of 79.5 MHz and an average power of 200 mW at the center wavelength of 800 nm was used as the seed pulse train. The spectral portion from 990 to 1065 nm of the Ti:sapphire laser [shown in Fig. 2(a) ] was filtered out and injected into a guiding fiber, serving as the signal seed which was coupled into the Yb-fiber pulse stacker through the 40% branch of a coupler at 1040 nm. The average power of the coupled signal was about 0.1 mW. The Yb-fiber pulse stacker was pumped by a 980-nm laser diode via a 980/1040-nm wavelength-division multiplexer. The Ti:sapphire laser around the 800 nm was used as the reference pulses to characterize the synchronized pulse stacking.

 

Fig. 1 Experimental setup. Dichroic mirrors: DM (HT@600-1000 nm & HR@1000-1120 nm); Wavelength division multiplexing (980/1040 nm): wavelength-division multiplexer (WDM); Collimator: CM1 and CM2; High-reflection mirror (990-1080nm): M1, M2 and M3; Grating: G1 and G2; Optics isolator: OI.

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Fig. 2 (a) The near-infrared spectrum of the filtered Ti:sapphire; (b) the spectrum of single-pass amplified laser (blue) and stacked laser pulses (red); (c) the RF spectrum of the stacked laser pulses.

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The cavity length of the Yb-fiber pulse stacker could be adjusted by controlling the space distance between two fiber collimators with one of collimators fixed on a translation stage. In order to align the cavity length for the synchronized pulse stacking, the Yb-fiber ring laser was at first intentionally self-started mode-locking at the fundamental repetition rate of 13.3 MHz by properly adjusting the polarization controllers, and fixed the 6th harmonic order of its repetition rate around the fundamental repetition rate of Ti:sapphire laser. In order to avoid any possible competition of self-started harmonic mode-locking and injection-triggered mode-locking, the Yb-fiber pulse stacker was then operated at the continuous-wave mode when there were no signal injection. With 0.1 mW signal injection around the central wavelength at 1030 nm, the Yb-fiber pulse stacker provided a pulse train of 65-mW under the pump power of 200 mW, with exactly the same repetition rate of the signal pulse train. Interestingly, the signal pulse train triggered a synchronized harmonic mode-locking for the Yb-fiber pulse stacker, and fundamental mode-locking was completely suppressed. The synchronization behavior was evidenced by comparing single-pass and ring-cavity-circulated amplifications of the signal pulses, as shown in Fig. 2(b). A remarkable optical gain was observed by stacking the pulses with multi-pass amplification in the Yb-fiber pulse stacker. As indicated by the RF spectra recorded with a RF spectral analyzer, the stacked pulse trains were quite stable without any sideband power spectra, indicating that the intracavity energy was fully extracted by the signal laser pulses [as shown in Fig. 2(c)], and the fundamental mode-locking was suppressed with a suppression ratio at least −20 dB.

The stacked pulse profiles could be measured by sum-frequency generation of the stacked pulses and Ti:sapphire reference pulses. The stacked and reference pulses were focused on a 0.5-mm β-barium borate (BBO) crystal. The sum-frequency signal was detected with a photomultiplier tube. Figure 3 shows the dependence of the pulse duration and interval of the stacked pulses on the cavity mismatch length. Figure 3(a) shows a periodic pulse train obtained by the Yb-fiber pulse stacker with 2.75-mm cavity mismatch length. As the fundamental frequency of the Yb-fiber pulse stacker was set at 13.3 MHz which was one-sixth of the Ti:sapphire laser’s, the periodic pulse train was originated from the 1, 7, 13, …, 6n + 1 round-trips of the signal pulse laser (from right to left). The pulse duration of the first pulse which was originated from the single-pass amplification was measured to be 3.8 ps, while the forthcoming stacked pulses, which were compressed by gratings, were measured to be 2.2 ps. The ~9-ps interval between adjacent pulses was consistent with the expected time delay increment per amplification in the stacker with 2.75-mm cavity mismatch length. The spacing between adjacent pulses was shifted as the cavity mismatch length was changed. As shown in Fig. 3(b), adjacent stacked pulses were merged into a long picosecond pulse of 15 ps pulse duration at 0.35-mm cavity mismatch length. It is worth to mention that, by further reducing cavity mismatch length, the intracavity pulse gain competition was observed, as shown in Fig. 3(c) for the cavity-length mismatch of 0.25 mm.

 

Fig. 3 The pulse envelope of the stacked pulse with different cavity-length mismatches (a) 2.75 mm, (b) 0.35 mm, and (c) 0.25 mm.

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The Yb-fiber pulse stacker was further characterized by measuring the timing jitters between the stacked and reference pulses. Optical cross correlations were obtained by crossing the stacked pulses with the reference pulses in a BBO crystal to generate sum frequency around 450 nm. And the reference pulses passed through a time-delay line to appropriately adjust the delay. The generated sum-frequency signals at the half-maximum of the rising edge were detected by a photomultiplier tube and the sum-frequency intensity-noise power spectral density was recorded by a FFT spectrum analyzer (Stanford, SR760). Figure 4 shows the power spectral density and the integrated timing jitter between the stacked and reference pulses. The orange curve represents the jitter spectral density of the single-pass amplification pulses with the pulse duration of 3.8 ps, resulting in a timing jitter of 6 fs as integrated with the frequency range from 100 kHz to 1 Hz. According to the orange curve in Fig. 4, a majority of the intensity noise and timing jitter were originated from the frequency range from 100 kHz to 1 Hz. The black one represents the jitter spectral density of the stacked pulses with the pulse duration of 2.2 ps, resulting in a timing jitter of 18 fs as integrated with the frequency range from 100 kHz to 1 Hz. We note that the significant difference between the jitter spectrum densities of the single-pass amplification and stacked pulses was mainly observed within the frequency range between 100 and 1 Hz. This could be ascribed to the fluctuation of the laser cavity length and environmental noises. We believe that the timing jitter in less than 100 Hz frequency range could be suppressed by using an additional feed-back control on the cavity length of the Yb-fiber pulse stacker [18].

 

Fig. 4 Relative power spectral density for the single-pass amplified pulse (orange curve) with the corresponding integrated RMS timing jitter (blue curve) versus relative power spectral density for the forthcoming shaped pulse (black curve) with the corresponding integrated RMS timing jitter (green curve).

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In order to further extend tunable range of pulse duration, we removed the gratings and increased the length of single-mode fiber to operate the Yb-fiber pulse stacker at the repetition rate of 3.6 MHz. Under the trigger of the injected signal pulse train with the repetition rate fixed at the 22th harmonics of the Yb-fiber pulse stacker, synchronously stacked pulses were generated with the pulse duration tunable from ps to sub-ns range by means of the change of the cavity mismatch length. Figure 5 shows cross-correlation trace between reference and stacked pulses and the dependence of the output temporal profile on the cavity mismatch length for a stacker cavity length changed from −12 to 12 mm. The pulse duration at zero cavity-length mismatch was measured to be 40 ps, while it was stretched to be more than 200 ps at a cavity mismatch length of 12 mm. By further increasing the cavity length and intracavity positive dispersion, the pulse profile could be extended to the nanosecond region. The picosecond and sub-nanosecond temporal profiles and the corresponding pulse interval confirmed that the signal pulses were coherently stacked in the Yb-fiber pulse stacker.

 

Fig. 5 The temporal shape of stacked laser pulses with decreasing (a) and increasing (b) cavity mismatch length.

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3. Conclusions

We demonstrated a robust method to generate shaped picosecond pulses of tunable pulse durations by using an Yb-fiber gain-assisted pulse stacker which benefits from high optical gain, properly time delay and laser synchronization. The energy loss during the pulse shaping process was compensated by the gain of an YDFA pumped by a diode laser. By changing the cavity length and intracavity dispersion of the Yb-fiber pulse stacker, the tunable pulse duration range and the temporal interval of adjacent stacking pulses could be changed in a controllable manner. The shaped pulse of the Yb-fiber pulse stacker is reproducible without the limitation of the split sub-pulse number and intensity fluctuation. With the spectral port around 1040 nm from a broadband 7-fs Ti:sapphire laser as a seed, the stacked pulse could be tuned from 5 to 200 ps and maintained as low as few femtosecond timing jitter with respect to the reference pulses. Such a gain-assisted pulse stacking is expected to be upgraded to high powers by using high-power Yb-doped double-cladding fiber amplifiers.