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We report on the generation of high-energy pulses in an all normal dispersion photonic-crystal fiber laser. Two mode-locking techniques with and without passive spectral filtering are studied both numerically and experimentally to address a roadmap for energy scaling. It is found that high-contrast passive modulation is a very promising mode-locking technique for energy scaling in dissipative-soliton laser. Moreover, this technique does not need any additional spectral filtering than the limited gain bandwidth to stabilize high-energy ultrashort pulses. The presented laser generates 110 nJ chirped pulses at 57 MHz repetition rate for an average power of 6.2 W. The output pulses could be dechirped close to the transform-limited duration of 100 fs.
©2011 Optical Society of America
1. Introduction
High-energy and high peak power femtosecond oscillators have been an intense research area in recent years to replace the more complex and expensive master oscillator power amplifier systems. Such sources are interesting for many applications including surgery, biological imaging and micromachining of dielectrics on a sub-micrometer scale. The development of these applications outside the laboratory environment relies on the availability of compact, stable, maintenance- and alignment-free femtosecond pulse sources. Rare-earth-doped fiber lasers are good candidates to meet these requirements in a shift that could lead to significant advances in most of ultrafast laser applications.
In a relatively short period of time, the performance of fiber laser technology has reached the levels that traditional solid-state lasers offer [1–6]. The revolution arises from the discovery of new pulse shaping mechanisms [7–11] in combination with the emergence of large-mode-area (LMA) photonic crystal fiber (PCF) technology. Indeed, the exploration of all-normal dispersion LMA-PCF laser configurations has enabled significant energy scaling with performances approaching the microjoule barrier [1–6]. To stabilize ultrashort pulse operation, such dissipative-soliton lasers need a strong mode-locking mechanism, which could be provided by a high modulation depth semiconductor saturable absorber (SA) and/or nonlinear polarization evolution (NPE) [1–5]. In addition, it has been demonstrated that a stronger pulse shaping effect could be achieved by combination of self-amplitude modulation with passive spectral filtering [10,11].
In this paper, we compare the two mode-locking approaches both numerically and experimentally to address a roadmap for energy scaling. An all-normal dispersion laser based on an Yb-doped LMA photonic-crystal fiber with a core diameter of 40 µm is used as a basic platform.
2. Numerical model
To analyze the performances of the passively mode-locked laser, we performed numerical simulations using the standard split-step method with the arrangement of the laser cavity elements shown in Fig. 1(a) . The laser system under consideration includes a 1.4 m long Yb-doped fiber, an output coupler and the saturable absorber. A spectral filter could be added inside the cavity, as indicated in Fig. 1. Pulse propagation along the gain fiber is described by the extended nonlinear Schrödinger equation which includes the effects of dispersion, Kerr nonlinearity and saturated gain with a finite bandwidth [12]:
where A(z,t) is the complex pulse envelope and t is the time in the co-moving frame. We denote by β2 the group velocity dispersion, γ is the self phase modulation coefficient and g(z) is the saturated gain coefficient given by , where g0 is the small signal gain coefficient, E(z) is the pulse energy and Esat is the gain saturation energy which depends on the pump power. The Yb-doped fiber considered in this work is characterized by the finite gain bandwidth with a corresponding frequency width ΔΩg = 2πcΔλg/λ2. The related gain filtering effect is introduced in the frequency domain using a Gaussian shape with a bandwidth of nm and a central wavelength of 1030 nm. The gain fiber parameters used in the simulation are summarized in Table 1 . To describe the NPE effective saturable absorber we use the well known transmission equation in the instantaneous response approximation [12]:where ΔR corresponds to the saturable loss coefficient (modulation depth) and Psat the saturation power. An ideal saturable absorber with variable modulation depth is considered in this study. In the following section, we investigate the influence of the modulation depth on the starting conditions in the single pulse regime and the energy scaling potential.
Fig. 1 Schematic representation of the mode-locked all-normal dispersion fiber laser (a) and basin of attractors presented in the space of temporal and spectral width (RMS values) for the parameters of Esat = 20 nJ, ΔR = 35% and Psat = 100 W. The lines connect the measured values after each roundtrip (after the gain fiber). The arrows indicate the evolution from the initial condition to the attractor marked with a yellow circle.
Table 1. Fiber parameters used in the simulation
3. Mode-locking with a high modulation depth saturable absorber
To study the starting dynamics of the laser, several initial conditions have been used and the transition to their attractor is analyzed in a Poincare map. The results obtained with 35% modulation depth SA and gain saturation energy of 20 nJ are depicted in Fig. 1(b). This figure shows the evolution of the spectral RMS width with respect to the temporal width after each roundtrip (after the gain fiber) and gives access to the time-spectral relation of the pulse. The black graphs show the evolution starting from different levels of quantum noise. For the color lines, a Gaussian pulse with different initial chirp settings and spectral widths is used as the initial condition. All simulations have been checked to converge to the same attractor when repeated with higher temporal or spectral resolution.
These simulations show that for a fixed set of laser parameters, there is only one accessible attractor corresponding to a fixed solution. Its parameters at the end of the gain fibre are and . This corresponds to a full width at half maximum (FWHM) of 14 nm and 4.7 ps, respectively. It is important to note that this solution remains stable for several thousands of round trips indicating a stable attractor. The spectral and temporal shapes of the corresponding solution are shown in Fig. 2 . The output pulses exhibit a quasi-Gaussian temporal shape and a parabolic top spectrum with steep edges which are typical of all-normal dispersion mode-locked lasers. Using a second-order dispersion delay line, the calculated pulses could be dechirped to ~250 fs duration which is close to the transform limit (see Fig. 2(c)). The little discrepancy with the theoretical limit indicates that output pulses suffer from nonlinear chirp as confirmed by the evolution of the instantaneous frequency shown in Fig. 2(b). By increasing the saturation energy, the spectral width of the fixed solution increases and its temporal width decreases.
Fig. 2 Results of simulations for Esat = 20 nJ, ΔR = 35% and Psat = 100 W: optical spectrum (a), pulse profile before (b) and after external dechirping (c). The dotted curves correspond to the instantaneous frequency.
However, for pulse energies exceeding 100 nJ, the fixed solution is not accessible when calculation are started from noise. This suggests that saturable absorbers with modulation depths lower than 35% are not suitable for energy scaling. To study the impact of the SA’ modulation depth on the laser performances, we varied ΔR and searched for the energy limits of the self-starting regimes by increasing the pumping parameter Esat. We note that the saturation power of the instantaneous saturable absorber is adapted to maintain fixed the saturation criteria for all the calculations. Figure 3 shows the evolution of the pulse parameters (energy, spectral width and dechirped pulse duration) versus ΔR at the limit of the self-starting regime (starting from quantum noise). Pulse energy calculated at the end of the gain fiber increases monotonically with the modulation depth to reach up to ~310 nJ for ΔR = 65%. For higher modulation depths, the maximum achievable energy changes only slightly. The spectral width follows the same trend and increases with ΔR thus allowing the generation of ultrashort pulses after external compression. Pulse durations as short as 85 fs are expected from our laser configuration. These results confirm the need for a strong mode-locking mechanism to initiate and stabilize high-energy ultrashort pulses in all-normal dispersion fiber lasers. Let us now analyze the evolution of the laser output versus the saturation energy parameter.
The performance of a fiber laser depends strongly on the accumulated nonlinear phase. So, we investigate the effect of the pump power on the pulse characteristics by varying the saturation energy parameter considering a high-modulation depth SA of ΔR = 80%. The energy evolution versus pump power is shown in Fig. 4(b) . The calculated energy for the self-starting regimes increases to reach up to 324 nJ. Interestingly, numerical simulations show that pulsed solutions with spectral widths close to the gain bandwidth could be stabilized by the high contrast saturable absorber. By increasing pump power, the shape of the spectrum evolves gradually from a parabolic shape to the M shape which is typical of all-normal-dispersion fiber lasers operating at high nonlinearity (Figs. 4(a)-4(c)).
The evolution of the output pulse characteristics versus pump power is depicted in Fig. 5 . The dechirped pulse duration is inversely proportional to the spectral bandwidth. Thereby, increasing the pump power results in high energy ultrashort pulses with broad spectra.
Fig. 5 Laser performances versus pump power for ΔR = 80%: (a) pulse duration and spectral width, (b) dechirped pulse duration and transform-limited duration. Pulse evolution inside the cavity for Esat = 70 nJ (c), OC: output coupler, SA: saturable absorber
Although a high nonlinearity phase shift is accumulated, the pulse can be dechirped with a linear dispersive delay line very close to the Fourier transform limit. After dechirping, pulse durations as short as 85 fs can be obtained. Analysis of the intra-cavity pulse dynamics shows that pulse stabilization is mainly ensured by the amplitude modulation provided by the SA in combination with gain spectral filtering (see Fig. 5(c)). These results show that high contrast amplitude modulation is an efficient technique for energy scaling in passively mode-locked fiber lasers. As gain spectral filtering is essential for pulse stabilization at high energy levels, the question arises, what will be the impact of passive spectral filtering on the performances of such a laser including a high contrast amplitude modulator.
4. Mode-locking with a high contrast saturable absorber combined with a passive spectral filter
As shown above, the stabilization of high-energy ultrashort pulses in all-normal-dispersion fiber lasers could be achieved efficiently using high-contrast saturable absorbers in combination with gain filtering. The second mode-locking method intensively studied during the last few years is characterized by using a passive spectral filter in combination with a saturable absorber. In this section, we investigate the properties of a mode-locked oscillator including a linear passive spectral filter and compare its performances to those obtained with passive nonlinear amplitude modulation. A Gaussian spectral filter (SF) is introduced inside the cavity just after the SA, as shown in Fig. 1. Numerical simulations were performed by varying the width of the passive spectral filter between 10 and 40 nm while maintaining a high-modulation depth SA of ΔR>65%. Numerical results reveal that for a fixed pump power, the peak power increases with decreasing the SF bandwidth (Fig. 6(a) ). This behaviour is a signature of the spectral filter action as already demonstrated in reference [13]. Indeed, as spectral filtering acts on highly chirped pulses, the induced spectral modulation is converted to amplitude modulation thus providing a strong pulse shortening mechanism. So, passive spectral filtering allows the generation of high peak power short pulses directly from the oscillator. To determine the energy scaling potential of this technique, the evolution of the laser performances versus the pump parameters are analyzed. The evolution of the maximum pulse energy calculated after the gain fiber is shown in Fig. 6(b) and highlights that pulse energy increases with increasing the SF bandwidth to reach 190 nJ for 40 nm SF bandwidth. This level is lower than that obtained with only amplitude modulation (see section 3). In general, the addition of dissipative losses inside the cavity through introduction of a spectral filter results in an energy decrease. The strong impact of passive spectral filtering on the laser performances is attributed to the squared shape of the optical spectrum which results from the nonlinear pulse propagation in a normal dispersion medium with saturable gain.
Fig. 6 Laser performances versus SF bandwidth for: (a) energy and peak-power for a fixed pump power (Esat = 10 nJ), (b) maximum pulse energy.
These results correspond to the stable single pulse solutions calculated from quantum noise. For higher pumping levels, simulations starting from quantum noise converge to multiple pulse solutions. However, single pulse solutions with higher energies could be obtained when initial conditions are changed to a Gaussian pulse. This suggests the existence of a bistability region where single pulse and multiple pulse solutions coexist (see Fig. 6(b)). Nevertheless, in all cases, the pulse energy remains much lower than that obtained without spectral filtering. These results suggest that the optimal design to achieve high-energy femtosecond pulses in all-normal-dispersion fiber lasers consist of using a high-contrast saturable absorber assisted by gain filtering.
Furthermore, we analyzed pulse properties in the case of 10 and 15 nm SF widths. First, we investigated the effect of the pump power level on the pulse characteristics by varying the saturation energy parameter. For a 10 nm SF width, we found that stable pulse solutions do exist for intra-cavity energies varying from few nano-joules to ~40 nJ when a Gaussian pulse is used as an initial condition (Fig. 7 ).
Above this energy level, calculation converges to bound-states solutions of two or more pulses. As already mentioned, for calculations starting from quantum noise bound-states solutions are also predicted for energy levels lower than 40 nJ. The presence of a large bistability region indicates that high energy single pulse operation will be more difficult to achieve experimentally. The same trend is obtained when increasing the SF width to 15 nm. We note that the extension of the bistability region increases with the SF width. The evolution of the spectral profiles for 10 nm and 15 nm SF widths are shown in Figs. 7(a)-7(c) and Figs. 8(a) -8(c), respectively. By increasing pulse energy, the spectrum broadens while developing sharp peaks around its edges. This behaviour is typical of fiber lasers including a passive spectral filter [13,14].
The evolution of the pulsed solution characteristics versus saturation energy for a SF bandwidth of 10 nm is summarized in Fig. 9(a) . Spectral width increases with increasing pump power to reach 25 nm for 40 nJ pulse energy. The corresponding output pulses could be dechirped with a linear dispersive delay line very close to their theoretical limit. Pulse duration as short as 100 fs is expected from this laser configuration. The intra-cavity pulse dynamics obtained for 34 nJ pulse energy is shown in Fig. 9(b). Self-consistency is mainly ensured by the frequency modulation provided by the SF which is converted to amplitude modulation in the time domain. This strong pulse shaping mechanism leads to shorter pulses with higher lengthening ratio along the cavity. This is the main difference with pure amplitude modulation. The strong pulse shaping mechanism induced by the passive spectral filtering results in short pulses with high peak powers which in turn limit the achievable pulse energy.
Fig. 9 Laser performances versus pump power for a 10 nm SF (a) and pulse dynamics for 34 nJ pulse energy (b). OC, Output coupler; SA: saturable absorber; SF, Spectral filter.
5. Experimental setup and results
The experimental setup of the passively mode-locked fiber laser is shown in Fig. 10 . The fiber laser is based on a 1.4 m long microstructure double-clad fiber and is constructed in a sigma configuration around a polarization-sensitive optical isolator. The Yb-doped core has a mode-field diameter of 30 μm and an effective numerical aperture of 0.03. The inner cladding diameter is 200 μm. The large-mode-area photonic-crystal fiber is cladding-pumped with a fiber-coupled laser diode emitting at 976 nm. The fiber ends are polished at an angle of 8° to eliminate parasitic reflections. The rejected port of the isolator serves as a variable output leading to linearly polarized output power. A half-wave plate controls the output coupling ratio. Passive mode locking is achieved using nonlinear polarization evolution (NPE). A polarization beam-splitter inserted behind the isolator serves as the NPE port. Polarization controllers are inserted before the polarization beam-splitter and after the isolator to control the polarization state inside cavity.
Fig. 10 Schematic representation of the passively mode-locked fiber laser. SF: spectral filter; DM: dichroic mirror; HR: high reflection mirror
The operation of the laser is strongly dependent on the orientation of the intra-cavity polarization controllers. Here, we are interested in the generation of high energy single pulse regimes. The pulse train is monitored with a 7 GHz sampling oscilloscope via a high-speed photodetector (8-GHz bandwidth). Furthermore, a long scan range autocorrelator of 150 ps is used to check the single-pulse operation.
First, we studied the laser operation without the spectral filter. Polarization controllers are adjusted to optimize the laser output performances. The best results are obtained for an estimated output coupling ratio of about 50%. In this configuration, the laser starts in a mode-locking regime for a pump power of 25 W. Mode locking remains stable up to an average output power of 6.2 W. The laser repetition rate is 57 MHz resulting in output energy per pulse of ~110 nJ. Further pump power increase results in either Q-switch mode-locking instabilities or sometimes in bound-state regime. The optical spectrum is centred at 1033 nm wavelength with a spectral width (FWHM) of ~30 nm (Fig. 11(a) ). The full width at half-maximum of the autocorrelation trace is 2.3 ps (Fig. 11(b)). This corresponds to 1.6 ps pulse duration assuming a Gaussian pulse shape. We note that the output pulses present a structured shape which could be attributed to the strong action of the NPE mechanism. Indeed, the output pulses extracted through the NPE port present a duration of about 2.8 ps indicating a strong pulse shortening effect. The output pulses are extra-cavity dechirped to the transform-limited duration of 103 fs using transmission gratings (Fig. 11(b)). The compressor introduces ~20% losses; average power after extra-cavity compression is then ~5 W, which corresponds to a peak power of more than 851 kW.
Fig. 11 Typical output characteristics of the NPE-based mode-locked laser: optical spectrum on a linear scale (a) and autocorrelation traces of the dechirped pulse (b) and the pulse (Inset).
For the estimated intra-cavity energy of 200 nJ, the numerical simulations presented in section 3 predict 2.8 ps Gaussian pulses with 30 nm spectral width. The output pulses measured experimentally exhibit a more structured shape which is typical for NPE mode-locked lasers. So, the very little quantitative discrepancy between simulations and experiments is attributed to the NPE mode locking mechanism which is not fully described by our scalar model.
To study the influence of passive spectral filtering on the laser performances in terms of energy, we insert a spectral filter of 10 nm bandwidth inside the cavity. Two types of filters are used in these experiments: a birefringent Lyot type and an interference bandpass filter. The results obtained with both filters are very similar. The results obtained with the birefringent filter are shown in Fig. 12 . The mode-locked operation is self-starting for 1.7 W average power and remains stable up to 2 W which corresponds to more than 35 nJ pulse energy. A further power increase results in a double-pulse operation. This result confirms the numerical predictions concerning the limited achievable pulse energy in presence of spectral filtering. Let us note that the Fig. 12(a) shows the typical optical spectrum obtained for an average output power of 1.9 W. It is centred at 1035 nm wavelength with a spectral width (FWHM) of 20 nm. The typical output pulse autocorrelation is shown in the inset of Fig. 12(b). The pulse autocorrelation width is 2 ps. These pulses could be dechirped to nearly transform limited duration of 126 fs (Fig. 12(b)). The average output power after compression is 1.2 W, which corresponds to a peak power of more than 100 kW. However, more than 40% of energy is contained in the pulse wings indicating that the output pulses suffer from a large amount of nonlinear chirp.
Fig. 12 Typical output characteristics of the laser including a 10 nm bandwidth SF: optical spectrum on a linear and logarithmic scales (a) and autocorrelation trace of the dechirped pulses (b). Inset: Autocorrelation trace of the output pulses.
The numerical simulations of section 4 show that the intra-cavity energy level corresponding to 20 nm output spectral width is ~30 nJ which is lower than experiments. Once again, the little discrepancy between theory and experiment is attributed to the NPE mechanism. Consideration of a full vectorial model could be interesting to get better quantitative agreement. Nevertheless, the most important predictions of our scalar model concerning the impact of spectral filtering on laser performances are qualitatively confirmed experimentally.
The stability of the mode-locking regime was evaluated by radio-frequency and beam quality measurements. The temporal pulse train of the mode-locked laser and the corresponding beam profile are shown in Figs. 13(a) -13(b), indicating a good beam quality. The radio-frequency (rf) power spectrum is recorded with a microwave spectrum analyzer via a high-speed photodetector (8-GHz bandwidth). It shows good amplitude stability with a contrast of more than 70 dB between the fundamental harmonic and the background (Fig. 12(c)). The amplitude noise level is estimated to be lower than 0.43% what confirms the good stability of the mode-locked regime.
Fig. 13 (a) Pulse train on a 7 GHz sampling oscilloscope, (b) high energy beam profile, (c) rf spectrum on a span of 50 kHz, resolution bandwidth 50 Hz.
6. Conclusion
In conclusion, we demonstrated a self-starting mode-locked laser featuring a large-mode-area Yb-doped fiber. We have discussed the impact of two mode-locking mechanisms on the laser performances. We show that the use of a spectral filter allows generation of high peak power short pulses but limits the achievable pulse energy. Our results demonstrate that high-contrast passive modulation without passive spectral filtering is very promising for energy scaling in mode-locked fiber oscillators. Pulse energy as high as 110 nJ at a repetition rate of 57 MHz was obtained without any passive spectral filtering.
Acknowledgments
We acknowledge support from the Inter Carnot & Fraunhofer Program under project APUS and the Conseil Régional de Haute Normandie under project MIST.
References and links
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