We present a self-starting passively mode-locked fiber laser operating in the chirped-pulse regime for the first time. A chirped fiber Bragg grating in the cavity provides positive dispersion with negligible nonlinearity. The laser generates positively-chirped pulses with a pulse duration of 22 ps at a repetition rate of 44 MHz, which are compressible down to 1.5 ps. We believe that the presented approach reveals a pulse energy scaling potential of mode-locked fiber lasers as nonlinear effects are significantly diminished compared the other known operation regimes.
© 2007 Optical Society of America
Ultra-short pulse generation has been an interesting scientific area for many decades. A number of mode-locking mechanisms in a variety of gain media has been developed making ultra-short pulse lasers to a versatile tool for many applications. In that sense fiber based mode-locked lasers have attracted considerable attention due to their inherent properties such as compactness, lack of misalignment, high efficiency and immunity against thermo-optical problems. From the scientific point of view, fiber oscillators may be likewise regarded as a very prominent example of nonlinear optical dissipative system where the nonlinear dynamics of the optical field is primarily governed by its energy exchange with the environment .
Different pulse dynamics in mode-locked fiber lasers have been reported in various operations of regimes. The combined action of anomalous group velocity dispersion (GVD) and self-phase modulation (SPM) maintains the shape and the duration in a purely anomalous (GVD) mode-locked fiber laser. The pulse generated in this regime is a transform-limited fundamental soliton possessing a sech2 pulse shape . However, the energy achievable in such laser systems is limited by the soliton area theorem to some tens of picojoules [3, 4].
Based on that fact, the dispersion-managed soliton regime has been developed. Such lasers are operating in the anomalous net-cavity dispersion, but comprise segments of anomalous and normal GVD and generated pulses can be described as average solitons with little temporal breathing inside the resonator . Recently, the possibility of energy scaling of fiber lasers operating in this regime has been demonstrated by the employment of low-nonlinearity large-mode-area fibers .
Close the zero net-cavity dispersion (called stretched-pulse regime), the pulse dynamics and shape change dramatically. Gaussian shaped pulses experience large variations of temporal width per cavity round trip, even with a change in the sign of chirp. Due to reduced average peak power stretched-pulse fiber lasers have been reported with significantly higher pulse energy than extractable in the soliton regime using comparable fiber dimensions [7, 8].
An increase of positive net-cavity dispersion leads to a transition to the wave-breaking-free regime . The nonlinear pulse evolution in the normal GVD fiber segment is monotonic and the pulse accumulates a positive chirp, which is partially compensated at points in the cavity using segments of anomalous GVD with no or negligible nonlinearity. In a subcategory of this regime, the called similarition laser, the output pulses are linearly chirped with a parabolic temporal intensity profile. The generation of parabolic pulses from rare-earth-doped fiber oscillator has been firstly numerical predicted  and subsequently experimentally demonstrated . In the meantime, wave-breaking-free femtosecond pulse generation has been reported in a variety of cavity configurations and fiber concepts [12, 13].
More recently, the generation of picosecond  and femtosecond  pulses in the purely normal GVD regime has been realized. In the femtosecond case i.e. larger spectral bandwidth, self-consistent pulse evolution is attributed to enhanced self-amplitude modulation via spectral filtering . A higher tolerance of accumulated nonlinear phase shifts has been observed with increasing the magnitude of normal net-cavity GVD. However, due to the non-negligible nonlinearity of added positive GVD segment the stability and quality of emitted pulses become worse in high-energy operation .
Mode-locked fiber lasers without any intra-cavity dispersion management can be considered as a further regime, i.e. net-cavity dispersion is only given by the GVD of the short gain fiber. Recently, a significantly enhancement of pulse energy to more than 200 nJ of femtosecond pulses has been demonstrated from a low-nonlinearity Ytterbium-doped dispersion compensation free fiber laser without additional spectral filtering . Hence, SPM is significantly reduced and the balance between gain filtering and the nonlinear action of the saturable absorber is sufficient to obtain self-consistent intra-cavity pulse evolution with very low temporal and spectral breathing.
As a consequence of the above described approaches of dispersion management an increase of output pulse energy of fiber oscillators should be possible by incorporation of one or more segments possessing large positive GVD and no or negligible nonlinearity. Perspectives of energy scaling of femtosecond laser pulses to the microjoule level by employment of the so-called chirped-pulse oscillator (CPO) concept is discussed for bulk mode-locked laser systems . In Kerr-lens mode-locked Ti: sapphire laser an increase of pulse energy accompanied by temporal broadening of the pulse inside the cavity is reported as the intra-cavity dispersion varied continuously from negative to positive net-cavity GVD . In general, Kerr-lens mode-locking is not self-starting. This issue has been addressed by employing a saturable Bragg reflector, however, the due to the absorber characteristics the performance in term energy and pulse duration were diminished .
In this paper, we report on a new approach of ultra-short pulse generation from a passively mode-locked Yb-doped fiber laser operating in the positive dispersion regime. Positive GVD is added by a chirped fiber Bragg grating which dominates the net-cavity GVD and possesses negligible nonlinearity. The self-starting chirped-pulse fiber oscillator generates positively-chirped pulses with a pulse duration of 22 ps at a repetition rate of 44 MHz, which are compressible down to 1.5 ps, hence, a novel intra-cavity pulse evolution is revealed. In addition, the CPO fiber laser opens the possibility of energy scaling by restraining nonlinear effects due to the reduced peak power, potentially in an all-fiber alignment-free configuration.
2. Experimental setup
The experimental setup of the mode-locked chirped-pulse fiber laser in a linear cavity configuration is shown in Fig. 1. As gain medium a highly ytterbium-doped (~300 dB/m absorption @ 976 nm) polarization-maintaining (PM) single-clad fiber with a mode-field diameter of 4.8 µm and a length of 30 cm is used. A thin-film PM WDM is inserted outside the cavity to pump the doped fiber through the CFBG by a single-mode diode emitting at a wavelength of 976 nm. A fiber pig-tailed thin-film 30/70 PM coupler is inserted in this configuration to monitor the laser operation and to select the polarization axis of the PM fiber resonator. The CFBG inscribed in a PM fiber is employed to provide positive dispersion together with negligible nonlinearity. It possesses a measured peak reflectivity of about 27% centered at 1035 nm with Gaussian-like spectral bandwidth of 16 nm (FWHM). Therefore, the CFBG serves as the output 1 of the linear cavity. The dispersion of the CFBG has been measured to be +0.19 ps2 at 1035 nm. The passive fibers used in the setup are Panda 980 PM fibers with mode field diameter of 7 µm. All PM fibers are fusion spliced with a high polarization extinction ratio (>35 dB) and a low loss (<0.03 dB). The output fiber end facets are angle cleaved to avoid undesired parasitic reflections or sub-cavity effects. Because of the incorporated PM fiber, the laser can be considered as environmentally stable. Self-starting passive mode-locking has been achieved by means of a semiconductor saturable absorber mirror (SAM) placed at the one end of the linear cavity. The SAM is based on a non-resonant design, using a GaAs/AlAs Bragg mirror with 27 layer pairs and 26 low temperature molecular beam epitaxy grown InGaAs quantum wells in front of the mirror. The anti-reflection coated device has a low-intensity absorption of 45 %, a modulation depth of ~30 % and a saturation fluence of 100 µJ/cm2. The SAM shows a bi-temporal impulse response with a short relaxation time of <200 fs and a slower part of 500 fs. To achieve the saturation threshold in the presented setup a telescope is used to image the output of the fiber onto the SAM. As an alternative, the SAM could be directly glued to the fiber end-facet leading to an all-fiber configuration of the chirped-pulse fiber oscillator. The total fiber length inside the cavity is 2 m resulting in a net-GVD of +0.286 ps2. Hence, the laser operates in the highly positive dispersion regime, mainly caused by the CFBG. The fiber laser directly generates positively-chirped picosecond pulses, which have been externally compressed by a 1250 lines/mm transmission grating pair (not shown in the figure).
3. Experimental results
Self-starting mode-locked operation is initiated by optimizing the saturation threshold on the SAM. Due to employed PM fibers passive mode-locking can not be achieved by nonlinear polarization rotation. It has been observed that the mode-locking threshold of single-clad fiber laser in the chirped-pulse regime is considerable higher than the in so far reported mode-locked regimes using comparable cavity elements . At launched pump power of 130 mW, the mode-locking threshold is reached and the laser delivers a single-pulse train with a repetition rate of 44.2 MHz, as shown in Fig. 2.
We measured an average output power of 33 mW at 155 mW of pump power at output 1, which corresponds to an energy per pulse of 750 pJ. The operation of mode-locking is very stable and self-starting with the same characteristics of temporal and spectral operation for equal pump power. Furthermore, the operation of the laser is characterized by very low amplitude noise as can be seen in Fig. 2. Single-pulse operation is proven by using a background-free autocorrelator with a scanning range of 150 ps and a 200 ps rise time phot-odiode.
Figure 3 shows the optical spectrum obtained in the chirped-pulse regime for a pumping power of 155 mW at output port 1. The spectrum features steep edges, which are typically observed in mode-locked fiber lasers operating in the highly positive dispersion regime. By decreasing the pump power, the optical spectrum maintains the spectral profile but the spectral bandwidth decreases. The center emission wavelength at output 1 is 1033.5 nm and the spectral bandwidth at highest pump power is 2.4 nm (10 dB) and 1.79 nm (3 dB), respectively. Very similar spectral behavior has been measured at the output 2, indicating a low spectral breathing along the fiber inside the cavity.
The autocorrelation trace obtained directly at the laser output 1 is shown in Fig. 4. To investigate the emitted pulse shape, autocorrelation traces corresponding to Gaussian and sech2 pulses are fitted to the measured trace. As shown in Fig. 4 best agreement is found with a Gaussian intensity profile. The pulse does not present any pedestal or coherent spikes, indicating clean pulse generation. The positively-chirped output pulses present an autocorrelation width of 33.4 ps (FWHM) corresponding to a pulse duration of 21.8 ps, assuming a Gaussian pulse shape. The negative dispersion necessary for external compression of the chirped-pulse by the grating pair is approximately -7.78 ps2, which indicates highly positive chirped pulse coming out of the mode-locked fiber laser. It should be pointed out that there is no dispersion compensation element implemented intra-cavity and the pulses are always positively chirped inside the cavity. Hence, a novel pulse generation regime of mode-locked fiber lasers has been revealed. However, a full understanding of pulse dynamics in this laser configuration needs further experimental and theoretical work.
Figure 5 presents the measured autocorrelation trace of the extra-cavity compressed pulses at a pump power of 155 mW. An autocorrelation width as short as 2.1 ps (FWHM) has been obtained. This results in a pulse duration of 1.52 ps assuming a deconvolution factor of 1.38 (motivated by calculated transform-limited pulse from the measured spectrum), indicating a compression factor of more than 14. Additionally, the autocorrelation of the transform-limited pulse calculated from the power spectrum is shown in Fig. 5. The autocorrelation width of the transform-limited pulse is calculated to 1.7 ps duration, which reveals that the linear chirp is dominating. The pedestal structure of the autocorrelation trace can be attributed to the steep edge structure of the spectrum.
In conclusion, we have demonstrated, for the first time to our knowledge, a passively mode-locked chirped-pulse fiber oscillator. The environmentally-stable PM fiber-based linear cavity is constructed with a high modulation depth semiconductor saturable absorber mirror as self-starting mode-locking mechanism and a chirped fiber Bragg grating, providing most of the positive net-GVD with negligible nonlinearity, as pulse stretching element during the intra-cavity propagation. The fiber laser directly generates highly positive chirped picosecond pulses at a repetition rate of 44.2 MHz. These pulses can be compressed to 1.5 ps duration. The presented mode-locking regime reveals the possibility of better control of excessive nonlinearity which typically limit the performance of fiber oscillators. Further work will be devoted to the generation of femtosecond pulses from a fiber based chirp-pulse oscillator.
This work was partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N8721 as well as the support by the Deutsche Forschungsgemeinschaft (Research Group “Nonlinear spatial-temporal dynamics in dissipative and discrete optical systems,” FG 532).
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