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We report on the dissipative soliton operation of a diode pumped Yb:NaY(WO4)2 (Yb:NYW) solid-state laser. The dissipative solitons and their features as the net cavity group velocity dispersion is changed from the normal to the anomalous dispersion regime are experimentally investigated. Taking advantage of the dissipative soliton shaping of the mode-locked pulses we have generated stable near transform-limited pulses as short as 54 fs. To our knowledge, this is so far the shortest pulse directly obtained from the mode-locked Yb:NYW oscillator.
© 2015 Optical Society of America
1. Introduction
Stable sub-100 fs optical pulses have widespread applications in modern science and technology, such as in the ultrafast laser spectroscopy, bio-imaging, and optical frequency comb. Since the laser was invented in the 1960s, the generation of ultrashort optical pulses has been one of the hottest research topics in the laser physics and engineering. Traditionally, ultrashort optical pulses are generated by the mode locking technique [1, 2]. It is shown that a stable train of optical pulses can be generated from a laser by synchronizing the phase of oscillating longitudinal modes. Theoretically, the shortest pulse generated in the mode-locked laser is limited by the gain bandwidth of laser material. However, it is difficult to synchronize all phase of oscillating longitudinal modes in practice, thus the actual obtained mode-locked pulses are usually much broader than that limited by the gain bandwidth. Martinez et al. first theoretically proposed a technique of incorporating the self-phase modulation and group velocity dispersion in a laser to shorten the mode-locked pulses in 1984 [3]. It has been shown the mode-locked pulses with duration below the limit set by the gain bandwidth could be generated through appropriately selecting the group velocity dispersion. We point out the mode-locked pulses predicted by Martinez et al. are actually chirp solitary waves that are known today as the dissipative solitons [4]. Recently, the dissipative soliton operation of mode-locked fiber lasers has attracted considerable attention [5–9]. A major difference of soliton operation between the mode-locked fiber lasers and solid-state lasers is that the soliton shaping is distributive in fiber lasers, while it is discrete in solid-state lasers. However, theoretically it could be proven that the pulse circulation in both lasers has essentially the same averaged dynamics, provided that the cavity length of the solid-state lasers is shorter than the soliton period. In the sense Martinez et al. could have firstly predicted the dissipative soliton operation of the mode-locked lasers.
On the other hand, the pulse broadening caused by the negative cavity dispersion could be naturally balanced by the nonlinear self-phase modulation in the mode-locked laser operating in the net negative dispersion regime. Under this condition the effective laser gain bandwidth is sufficiently broad so its bandwidth limiting effect could be ignored, and the nonlinear Schrödinger equation (NLSE) solitons could also be automatically formed. The NLSE solitons are chirp-free pulses. And a chirp-free pulse is much more desired for many ultrashort pulse applications. Therefore, great attention has been paid on the NLSE soliton formation and operation of the mode-locked lasers. Conventionally, if a mode-locked laser with the pulse shaping mechanism dominated by the balance between the negative group velocity dispersion and the nonlinear self-phase modulation, it would be regarded as a soliton laser. Obviously, it is a challenge to generate the NLSE solitons in mode-locked solid-state lasers except a few lasers that have super-broad gain bandwidth, e.g. the Ti:Sapphire lasers. Brabec et al. have analysed the influence of various effects on the pulse width of soliton mode-locked lasers [10]. In general, a pulse formed in a soliton laser is always significantly narrower than in a normal mode-locked laser due to the soliton shaping. However, there is a drawback for the soliton mode locking that it is difficult to obtain large energy mode-locked pulses due to the multiple soliton formation. Recently, in order to obtain large energy pulses from mode-locked solid-state lasers, the chirped-pulse oscillator (CPO) technique was proposed [11–13]. The chirped pulse oscillator is a mode-locked laser operating in the positive cavity dispersion regime. Extensive theoretical studies have shown that strongly chirped solitary pulses could be formed in the laser under existence of nonlinear self-phase modulation [14–16]. In particular, in comparison with the solitons formed in the negative cavity dispersion lasers, the chirped solitons can have much larger pulse energy. Experimentally, it has been shown that in combination with external cavity pulse compression micro-joule level femtosecond pulses could be obtained from a chirped-pulse oscillator mode-locked laser [17,18].
In this paper, we report on the passive mode-locked operation of a diode pumped Yb:NYW solid-state laser. Soliton operation of the laser both in the net normal and anomalous cavity dispersion regimes are experimentally obtained and investigated. We found that no matter if the laser operates in the net normal or net anomalous cavity dispersion regime, the features of the observed solitons are well in agreement with those of the dissipative solitons, which was theoretically predicted by N. Akhmediev et al. [4, 19,20]. Our experimental results suggest that even the solitons obtained in the solid-state lasers with anomalous cavity dispersion are dissipative solitons. Based on the theory of dissipative soliton operation of lasers, we carefully adjusted the laser operation conditions and firstly achieved 54 fs mode-locked pulses in the experiment. To the best of our knowledge, this is also the shortest mode-locked pulse directly obtained in the Yb:NYW oscillator. And we believe it is still possible to obtained even shorter mode-locked pulses through appropriate adjusting the laser operation conditions.
2. Experimental setup and results
The laser setup used in our experiment is shown in Fig. 1. An a-cut, oriented for the π- polarization Yb:NYW crystal with a Yb3+ concentration of 5 at.% was employed as the gain medium. The crystal was grown with the conventional Czochralski method and previous work has demonstrated that it was a very good laser gain material for efficient high-power continuous-wave (CW) laser [21]. In our experiment the crystal has dimensions of 3 × 3 mm2 in cross-section and 3.2 mm in length. It was antireflection-coated for both pump and laser wavelengths to minimize the Fresnel reflection losses. The crystal was wrapped with indium foil, and tightly mounted in a water-cooled copper block holder maintained 20.0 °C. A 980 nm distributed Bragg reflector (DBR) tapered diode laser was used as the pump source. The pump light was focused into the crystal via a spherical convex lens (F5) of 80-mm focal length after collimating by a home-made laser beam shaping system. The focused pump beam has a spot size of about 30 μm in diameter, measured by a commercial laser beam profiler. To achieve suitable laser mode size in the laser crystal and on the SESAM, an X-folded five-mirror cavity was used in the experiment. The radius of laser beam waist at the position of crystal is calculated as about 14 μm, which matches very well with that of the pump beam. The SESAM (BATOP GmBH) used in the experiment is designed to operate at 1064 nm with a modulation depth of 1.2%, non-saturable absorption of 0.8%, a relaxation time of 1.0 ps, and a saturation fluence of 60 μJ/cm2. A wedged plano-plano output coupler (OC) with a transmission of 0.4% for the laser wavelength is used to reduce the output loss of the cavity. To adjust the intracavity group-delay dispersion (GDD), a pair of prisms (SF10) with a tip-to-tip separation of ~40 cm was used. Each of the prisms was mounted on a precision one-dimensional translation stage to accurately control the prism introduced GDD via adjusting their insertion length.
Fig. 1 The schematic of the mode-locked Yb:NaY(WO4)2 dissipative soliton laser. F1: Focus lens; M1, M2, and M3: Folding mirrors; OC: Output coupler.
Through carefully aligning the laser cavity mirrors and the SESAM, stable (CW) mode-locking could be achieved under an incident pump power of about 2.40 W. Initially, we adjusted the insertion length of the two prisms to make the total GDD introduced by them was about 0 fs2 (corresponding to the estimated total intracavity GDD of about 900-950 fs2), resulting in that the laser operated in the net positive cavity dispersion region. Figure 2(a) shows the optical spectra of the mode-locked pulses in the linear (blue solid line) and logarithmic (red dotted line) coordinates, measured with an optical spectrum analyzer (ANDO, AQ6315B) with a resolution of 0.5 nm. It can be seen that the mode-locked spectra have a nearly rectangular-shape with the characteristic sharp steep edges, which is the distinctive feature of the dissipative solitons formed in the normal dispersion cavity mode-locked lasers. The FWHM bandwidth of the mode-locked spectrum was about 16.5 nm centered at ~1030 nm, which could support Fourier transform-limit sech2-shaped pulses with a pulse duration as short as 67.5 fs. Figure 2(b) shows the corresponding autocorrelation trace of the mode-locked pulses, measured with a commercial intensity autocorrelator (Pulsecheck 50, APE). Assuming that the pulses have a sech2 profile, the pulse duration is about 1.96 ps. The calculated time-bandwidth product is about 9.15, which is 29 times of the Fourier transform-limited value. This strongly chirped pulse is a distinctive characteristic of the dissipative solitons [4–6].
Fig. 2 Mode-locked spectrum (a) and autocorrelation trace (b) of the dissipative soliton when the GDD introduced by the prism pair is about 0 fs2.
To further demonstrate that the mode-locked pulses are dissipative solitons, we also investigated the evolution of the mode-locked pulse spectrum under different incident pump power, as shown in Fig. 3. It is obvious that the edge-to-edge spectral bandwidth of the pulses decreased as the pump power decreased, which is another typical feature of the dissipative solitons. The same phenomenon was also observed in other dissipative soliton lasers and it can be attributed to the decreasing nonlinearity within the cavity as the pump power decreased [5].
Fig. 3 Optical spectra of the mode-locked dissipative soliton pulses under three different incident pump powers.
By changing the insertion length of the prisms in the cavity, the intracavity GDD can be continuously tuned. After changing the prism-pair introduced GDD to about −500 fs2 (the corresponded estimated total intracavity GDD was about 400-450 fs2), the operation of the mode locking was stable as before and the mode-locked spectrum still had a nearly rectangular-shape. The spectrum had a wider bandwidth of ~20.7 nm, and centered at the wavelength about 1032 nm, as shown in Fig. 4(a). The mode-locked spectrum could support 54 fs Fourier transform-limit sech2-shaped pulses in theory. Figure 4(b) shows the corresponding autocorrelation trace of the mode-locked pulses, which had a pulse duration of about 1.1 ps. The time-bandwidth product is calculated as about 6.42, which is 20.4 times the value of the transform limited sech2-pulse. The experimental result suggests that the laser still operated in the net positive GDD region, and reducing GDD did reduce the soliton pulse width and frequency chirp, but did not affect the stability of the dissipative solitons. It can be noted that as the total GDD decreased, the dissipative soliton spectrum became wider but the chirp of the pulses was decreased.
Fig. 4 Mode-locked spectrum (a) and autocorrelation trace (b) of the dissipative soliton when the GDD introduced by prism pair of about −500 fs2.
To investigate the soliton operation of the laser in the anomalous cavity dispersion regime, we further increased the GDD introduced by the prism-pair to about −950 fs2 (the estimated total GDD was anomalous and closed to zero) by adjusting the insertion length of the prisms. It could be seen from Fig. 5(a) that the spectrum of the mode-locked pulses changed from the nearly rectangular-shape to a typical sech2-shape with obvious Kelly sidebands. The spectral bandwidth of the mode-locked pulses was about 22.3 nm centered at 1043.6 nm. The corresponding pulse width was about 54 fs, as shown in Fig. 5(b) . Therefore, it can be seen that the chirp of the mode-locked pulses was almost zero under this condition, and the time-bandwidth product of the pulses is about 0.33, which is very close to the value of Fourier transform-limit sech2-shaped pulses. We note that strong Kelly sidebands appeared on the mode-locked pulse spectrum. The appearance of Kelly spectral sidebands is a clear signature of the soliton operation of the laser.
Fig. 5 The optical spectrum (a) and autocorrelation trace (b) of the dissipative solitons measured when the GDD introduced by the prism-pair is about −950 fs2.
The dissipative soliton operation of the laser in the net normal cavity dispersion regime is obvious [22,23]. To confirm that the solitons formed in the net anomalous dispersion regime is also dissipative solitons, we have experimentally carefully investigated their features, either by fixing the net cavity GDD but varying the pump intensity or by fixing the pump intensity but varying the cavity GDD. Figure 6 shows the evolution of the mode-locked pulse spectra under different incident pump powers. It was observed that with a fixed cavity dispersion, as the pump power was increased, the spectral bandwidth of the pulses broadened, in the meantime the mode-locked pulse width decreased. Again a similar spectral bandwidth evolution as shown in Fig. 3 was observed. Our experimental result clearly shows that the pulse width is a function of the pump intensity. And at a fixed pump intensity we observed experimentally that the mode-locked pulse width broadened (spectral bandwidth narrowed down) as the net cavity dispersion was increased, and the pulse width narrowed down (spectral bandwidth broadened) as the net cavity dispersion was decreased, as shown in Fig. 7. Figure 7(b) showed the pulse width of 78 fs when the GDD introduced by the prism-pair was ~-1000 fs2. In our experiment the narrowest pulse width was obtained by simultaneously decreasing the net cavity dispersion and increasing the pump strength. We note that the Kelly sidebands shown in Fig. 4 are asymmetric, which is a clear indication that the net cavity dispersion is anomalous but close to zero, where the net cavity dispersion is dominant by the third-order group velocity dispersion. The experimentally observed soliton features are well in agreement with those predicted by Martinez et al. [3].
Fig. 6 Optical spectra of the mode-locked pulses under three different incident pump powers in the anomalous dispersion regime.
Fig. 7 (a) Optical spectra of the mode-locked pulses under different prism-pair introduced GDDs in the net anomalous cavity dispersion regime; (b) autocorrelation trace of the dissipative solitons measured when the GDD introduced by the prism-pair was about −1000 fs2.
In the experiment, we also monitored the mode-locked pulse train with a high-speed detector (New Focus, 1611) and a 1 GHz bandwidth digital oscilloscope (Tektronix, DPO7104). Figure 8 shows the typical CW mode-locked pulse trains of the mode-locked laser in the nanosecond and millisecond time scales. The pulse repetition rate is about 113 MHz, corresponding to the laser cavity length of ~1.32 m. We note that in both cavity dispersion regimes the dissipative soliton operation of the laser was stable. No measureable difference could be identified from the oscilloscope trace measurement.
3. Conclusion
In conclusion, we have experimentally investigated the passive mode locking of a diode pumped Yb:NaY(WO4)2 laser. By changing the GDD introduced by the intracavity prism-pair we have operated the mode-locked laser either in the net normal or net anomalous cavity dispersion regime and experimentally achieved the soliton operation of the laser in both cavity dispersion regimes. And it can be found that the evolution of pulse parameters with the variations of cavity dispersion (from the net normal to net anomalous cavity dispersion region) in our experiment fitted very well with the theoretical results of Haus’s master equation in Ref [24]. Through investigating the features of the solitons and comparing them with those of the dissipative solitons of the mode-locked lasers, we conclude that the solitons even formed in the net anomalous cavity dispersion regime are dissipative solitons. Exploiting the dissipative soliton properties of the laser we have experimentally achieved stable 54 fs mode-locked pulses from the laser. To the best of our knowledge, this is so far the shortest mode-locked pulse directly obtained from the Yb:NYW oscillator. We believe by exploiting the dissipative soliton operation of the mode-locked solid-state lasers, sub-100 fs mode-locked pulses could be obtained in most Yb-doped lasers.
Acknowledgments
The research is partially supported by the funds of Minister of Education (MOE) Singapore, under Grant No. 35/12, and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
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