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An ytterbium-doped mode-locked fiber laser was demonstrated with a chirped fiber Bragg grating for dispersion management. The cavity net dispersion could be changed from large normal dispersion (2.4 ps2) to large anomalous dispersion (−2.0 ps2), depending on the direction of the chirped Bragg grating in laser cavity. The proposed fiber lasers with large normal dispersion generated stable pulses with a pulse width of <1.1 ns and a pulse energy of 1.5 nJ. The laser with large anomalous dispersion generated wavelength-tunable soliton with a pulse width of 2.7 ps and pulse energy of 0.13 nJ. A theoretical model was established and used to verify the experimental observations.
©2013 Optical Society of America
1. Introduction
In recent years, mode-locked operation of fiber lasers have attracted wide interests due to their numerous applications, such as range finding, telecommunications, industrial processing, and basic research. Among them, passively mode-locked Yb-doped fiber lasers operating near 1-μm wavelength have been investigated extensively, because of their short pulse width and high pulse energy which can be further amplified. The development of new pulse-shaping techniques in fiber lasers scaled up the pulse energy significantly. From soliton [1], stretched pulse [2], wave-breaking-free [3], self-similar operation [4] to dissipative soliton mode-locking [5], the output energy has been scaled up to as high as 10s of nJ. In most of mode-locked fiber laser configurations, some degree of dispersion management is required. However, dispersion management in 1-μm wavelength region is not as easy as that in 1.5 μm range. Different types of components have been used to provide anomalous dispersion at 1 µm such as grating pairs [6], photonic crystal fibers [7], fiber taper [8], and higher-order mode fibers [9]. However, the use of discrete optical components to manage dispersion increases the complexity of fiber lasers. Some of the dispersion management components, such as photonics crystal fibers, have high splice loss and often have mismatching fiber parameters.
Chirped fiber Bragg grating (cFBG) has been widely used for dispersion compensation in telecom [10]. For the dispersion management in mode-locked fiber laser, it processes many advantages: reliable fabrication technology, all-fiber configuration and dual functions as bandpass filter and output coupler simultaneously. Fermann et al. first reported Kerr mode-locked Er-doped fiber laser using cFBG for dispersion management [11]. The cFBG was also used as the anomalous dispersion components along with SESAM to obtain soliton [12], stretched pulse and wave-breaking-free pulse [13] in Yb-doped fiber laser. In those studies, the cFBG simultaneously served as the output coupler with proper reflection bandwidth and reflectivity. Using cFBG with anomalous dispersion in a bismuth-doped mode- locked fiber laser, E. J. R. Kelleher et al. achieved stable 4.7 ps soliton mode-locked output with a wavelength of 1177 nm [14]. In a 2 μm mode-locked fiber laser, where the cFBG was used as the normal dispersion component, Gumenyuk et al. observed dissipative dispersion managed (DDM) soliton with SESAM [15]. With single wall nanotubes as saturable absorber, Kelleher et al. achieved stable mode-locking with a cavity length up to 1200 m [16]. However authors concluded that no stable mode-locking could be obtained when a cFBG with a lumped large normal dispersion was present alone in the ring laser cavity.
In the aforementioned references, researchers used saturable absorbers and cFBG together to achieve stable mode-locking. As an amplitude modulator, a saturable absorber has fixed parameters, such as modulation depth and non-saturable loss etc. That made it difficult to evaluate the role of net dispersion in the ring cavity in mode-locking mechanism. On the other hand, the nonlinear polarization rotation (NPR) technique offers flexible amplitude modulation parameters [17] when used as an equivalent saturable absorber [18] to study different soliton generation mechanisms, such as dissipated soliton and noise-like soliton.
In this study, we try to determine the circumstances, at which, stable mode-locking can be achieved in a ring cavity with a lumped large dispersion. We report here the performance of an all-fiber Yb-doped mode-locked laser based on NPR technique. Depending on the inserting direction of the cFBG, the cavity dispersion could be changed from large normal to large anomalous dispersion. When the cavity had a large normal dispersion from a cFBG, the laser generated stable mode-locked pulses with pulse energy of 1.5 nJ which was different from the conclusion of [16]. With a large anomalous dispersion in the cavity, the laser generated tunable soliton with a pulse width of 2.7 ps and pulse energy of 0.13 nJ. For the first time, the stable mode-locked operation has been realized in a single configuration with such a wide dispersion range, to the best of our knowledge.
2. Experiment configuration
The laser setup is illustrated in Fig. 1. Its gain medium is a piece of 30 cm long highly Yb-doped single mode fiber with nominal core absorption of about 750 dB/m at 976 nm. The pump light from a 400 mW single mode pigtailed laser diode, emitting at 976 nm, is launched into ring cavity through a 976/1030 fiber pigtailed multiplexer. The cFBG was fabricated into the core of a single mode fiber (Nufern HI1060) with a chirped phase mask of a 14 nm/cm chirp rate. Since the cFBG is 6.4 mm in length, its dispersion is ± 2.2 ps2, depending on the direction of the cFBG in the cavity. The net cavity dispersion of the cavity without cFBG is 0.26 ps2. The cFBG has a peak reflectivity of about 98% centered at 1054 nm with a spectral bandwidth of 14 nm (shown on the right in Fig. 1). A polarization maintaining (PM) circulator with its fast axis blocked is used as an isolator to ensure unidirectional light propagation. The same circulator serves also as a polarizer, together with two polarization controllers (PCs), to realize NPR operation. Approximately 30% of the beam is extracted from the cavity through a PM fiber coupler placed after the PM circulator, which insures highly polarized laser output. The free fiber termination in the setup is angle-cleaved to minimize unwanted reflections. An optical spectrum analyzer (Ando AQ6370) and a 500 MHz oscilloscope (Tektronix, TDS5054B) together with a 1-GHz bandwidth photodetector (New Focus, Model 1611) are used to measure simultaneously the spectrum and pulse train of the mode locked laser. The radio-frequency (RF) spectrum of the fiber laser is measured by a 3-GHz RF spectrum analyzer (Agilent, N9320B) and the same 1-GHz photodetector.
Fig. 1 Experimental configuration of the mode-locked fiber laser and the reflection spectrum of the cFBG
3. Experimental results and analysis
3.1 Mode locked fiber laser with large normal dispersion
Firstly, the cFBG was inserted into the laser cavity which introduced a large normal dispersion of 2.2 ps2. By carefully adjusting the PCs, self-starting and stable nanosecond mode-locked pulses were obtained as shown in Fig. 2(a). The laser produces a stable pulse train at a repetition rate of 18.8 MHz which matches well with the cavity length, indicating the mode-locking as the pulse generation mechanism. The RF spectra around the fundamental and harmonic repetition rates are shown in Fig. 2(b) and in its inset, measured at a resolution of 10 Hz and 1 kHz, respectively. Although two pedestrian sidebands could be seen, the laser achieved an excellent signal-noise-ratio of 67 dB, which is much higher than the 45 dB typically observed from noise-like mode-locked operation [19]. The relative pulse to pulse energy fluctuation is calculated to be about 7% [20]. In contrary to ref [16], this result clearly showed that stable mode-locking could be obtained with a large lumped normal dispersion.
Fig. 2 (a) The mode-locked pulse train; (b) the radio-frequency spectrum at the fundamental frequency; inset, rf spectrum at harmonic frequency; (c) single pulse shape of the laser at the maximum output power; and (d) output spectrum of the laser emission.
The full width at half maximum (FWHM) of the single pulse, shown in Fig. 2(c), is 1.1 ns, which is limited by the bandwidth of the oscilloscope. Since the pulse width also exceeds the measurement range (90 ps) of our autocorrelator, the actual pulse width could be between 1.1 ns and 90 ps. The laser emission spectrum shows a modulated structure with five equally distributed peaks as shown in Fig. 2(d). The center peak is at 1056.9 nm with a −3 dB bandwidth of 0.2 nm. The spectrum is apparently different from those reported dissipative soliton or noise-like soliton. The cause of this spectral modulation is not yet clear with one possible explanation of the soliton pair, or bound soliton. The subject is still under the study. At pump power of 370 mW, the maximum output power achieved was 28 mW, corresponding to single pulse energy of 1.5 nJ which was limited by the available pump power.
3.2 Mode locked fiber laser with large anomalous dispersion
Next, the cFBG was reversed which inserted an anomalous dispersion of −2.2 ps2 in the cavity. The net cavity dispersion was calculated to be about −1.96 ps2. The dispersion management soliton operation was expected. At a pump power of 200 mW, self-starting multiple soliton generation and bound states of soliton were observed by adjusting the two PCs. Then we gradually reduced the pump power from 200 mW to 94 mW and observed reduction of wave-breaking in soliton; from multiple pulses, to 4, 3, 2-pulses and finally a single-pulse soliton as the pump power decreased. The corresponding output power as a function of pump power is shown in Fig. 3(a). The maximum output power of 2.5 mW was obtained for the single pulse operation which corresponded to the pulse energy of 0.13 nJ at a pulse repetition rate of 18.5 MHz. The polarization extinction ratio (PER) of the output radiation was measured to be 29 dB, which is excellent for various applications such as frequency conversion. The spectra of the mode-locked laser emission, which exhibits a typical characteristic of the soliton with clear side-bands, are shown in Fig. 3(b). For the 14 nm bandwidth cFBG, the soliton spectrum could be tuned from 1049 nm to 1054 nm by adjusting the PCs. The −3 dB bandwidth of the spectra was measured to be 0.7 nm.
Fig. 3 (a) Output power of the mode-locked fiber laser with respect to the pump power. (b) Tunable output spectrum of the laser. (c) Autocorrelation trace of the mode locked laser, inset, emitted pulse train at the maximum output power. (d) The radio-frequency (RF) spectrum around the fundamental repetition. Inset: RF spectrum at harmonic repetition rates of the laser.
The autocorrelation trace of the mode-locked pulses was measured with an autocorrelator (Femtochrome FR-103XL) at a 10 fs resolution. The autocorrelation trace fits well with a sech2 function which gives a pulse width of 2.7 ps, as depicted in Fig. 3(c). The time-bandwidth product is about 0.45, indicating that the pulse is almost chirp-free. The inset of the Fig. 3(c) shows pulse trains measured with a photodiode (1 GHz bandwidth) and exhibits a pulse spacing of 54 ns. The RF spectra around the fundamental and harmonic repetition rates are shown in Fig. 3(d) and in its inset, respectively. The corresponding resolutions are 10 Hz and 1 kHz, respectively. No obvious residual sidebands caused by Q-switched mode-locking could be observed. A 70 dB peak-to-background ratio indicates an excellent mode-locking stability and low pulse timing jitter for this laser with a lumped large anomalous dispersion.
4. Simulation results
To confirm the experimental observations, we numerically simulated the pulse formation in the laser cavity under different cavity dispersion. The modeling was conducted by propagating the electric field envelope in consecutive round-trips [12]. In one round-trip, the propagation of the optical pulses is solved in every part in the ring by nonlinear Schördinger Equation (NLSE) [shown as Eq. (1) below] using a split-step Fourier method [12, 21]. After one round-trip in the laser cavity, the resulted pulse from simulation was used as the input for the next round-trip calculation. This process was repeated until the optical field becomes self-consistent, i e. stable mode-locked pulse was achieved after many round-trip calculations. The temporal and spectral attributes of the output mode-locked pulses were obtained directly from the field envelope at the output coupler at the the final round-trip. The parameters of the intra-cavity components used in the simulation are given on Table 1.
where, A is the electromagnetic field amplitude of the optical pulse. Z is the spatial coordinate along the fiber length. T is relative time in the moving pulse frame of reference. The pulse propagates in the cavity is subjected to Kerr nonlinearity (γ) and second-order dispersion (β2). It will experience additional saturable gain (g) with a finite bandwidth when passing through the Yb-doped fiber (YDF) section. T2 is the gain dispersion coefficient which accounts for the decrease of the gain coefficient at the wavelength located far from the gain peak and inversely proportional to the gain bandwidth, Δνg, as 1/(πΔνg). The gain saturation is given in Eq. (2), where g0 is the small signal gain coefficient (related to dopant concentration), E is the instantaneous pulse energy and Esat, the gain saturation energy which is pump-power dependent. For the non-gain single mode fiber, saturated gain factor g is set to zero to eliminate the influence of the gain effect. The net cavity dispersion except the cFBG is 0.26 ps2. The cFBG in the simulation is assumed to have a Gaussian transmission profile with a bandwidth of 14 nm, centered at 1054 nm. The dispersions of the cFBG used in simulation varied from −20.2 ps2 to 2.2 ps2. The total cavity loss is estimated to be around 80% including both the output coupler ratio (30%) and insertion losses of the components. The NPR effect is modeled as a fast saturable absorber [22] by a transfer function shown in Eq. (3), where αs is the unsaturated loss, P is the instantaneous pulse power and Ps is the saturation power.
Table 1. Parameters used in the simulation
The numerical simulation started with a 1 ps Gaussian pulse as an initial condition and continued for ~5000 round trips through the cavity for a converged stable mode-locking solution. Figures 4(a) and 4(b) show the calculated spectra and pulse shapes of the mode-locked laser when the cFBG dispersion was changed in a range from −20 ps2 to 2.2 ps2. When the dispersion of the cavity varies from −20 ps2 to −0.2 ps2, the spectra show the sidebands due to the interference between the soliton and dispersive waves, and the simulated spectral bandwidth increases from 0.33 nm to 8.2 nm. The corresponding pulse width is ~200 fs, (shown as an inset of the Fig. 5). When the net cavity dispersion approaches zero, the spectrum becomes as broader as 9 nm with a Gaussian profile, which are typical dispersion managed solitons when the net cavity dispersion is near zero. The corresponding pulse width is ~200 fs, and the detailed pulse shape is shown in the inset of the Fig. 5. When the net cavity dispersion increases from 0.2 ps2 to 2.4 ps2, the laser spectrum exhibits sharp edges, a typical characteristic of the dissipative soliton lasing by spectral filtering of the highly chirped pulse in the all normal dispersion regime. The spectral width decreases from 14 nm to 0.2 nm and the corresponding pulse width increases from 7 to 180 ps.
Fig. 4 (a) Simulated mode-locked pulses at different cavity dispersion; (b) simulated output spectra of the mode-locked fiber laser at different cavity dispersion.
Fig. 5 Simulated output spectrum width and pulse width as a function of cavity dispersion. Inset: detailed pulse shape when the net cavity dispersion approaches to zero.
When the cavity dispersion becomes larger, it becomes more difficult to reach a stable solution. For the simulation with large cavity dispersion values at −20 ps2, −10 ps2 and 2.2 ps2, the unsaturated loss of the saturable absorber needed to be increased to 90% in order to achieve a stable solution; while in other low dispersion values it was set at 70%. This shows that the parameters of the saturable absorber need to be adjusted to achieve stable mode-locking when the net cavity dispersion is large. We noticed that in [16], when a cFBG with large normal dispersion was inserted into the laser cavity, no mode-locking but Q-switched operation was obtained. As is well-known, NPE-based mode-locking laser with two PCs offers a more convenient method to make continuously parameters adjustment as an equivalent saturable absorber, and therefore, they can be more efficient than the carbon nanotube saturable absorber to achieve stable mode-locking. Figure 5 depicts the −3 dB spectral width and pulse width as a function of the cavity dispersion.
The simulated spectrum and pulse shape with the cavity dispersion of −2 ps2 are shown in Fig. 6(a), which match well with our soliton experiments. For example, the calculated spectral and pulse width are 0.9 nm and 2.7 ps respectively; while the measured ones are 0.8 nm and 2.4 ps. When the cavity dispersion is 2.4 ps2, the calculated results are shown in Fig. 6(b). The simulated mode-locked laser pulses have a spectral bandwidth of 0.2 nm and a pulse width of 180 ps. We have not yet simulated the spectrum with modulation as shown in Fig. 2(d) for the laser cavity with a large normal dispersion.
Fig. 6 Output spectrum and pulse shape of the mode-locked fiber laser at (a) −2 ps2, and (b) 2.4 ps2 cavity dispersion.
5. Conclusion
In conclusion, we have successfully demonstrated the stable mode-locked operation with large normal and anomalous dispersion in a ring cavity with a cFBG for dispersion management. For the laser with large normal cavity dispersion of 2.4 ps2, stable mode-locked pulses with pulse energy of 1.5 nJ were obtained. With a cavity dispersion of −2 ps2, the laser produced tunable solitons with a pulse width of 2.7 ps and pulse energy of 0.13 nJ. A theoretical model was built to simulate the mode-locking under different cavity dispersions. By treating the NPR effect as a fast equivalent saturable absorber, we have achieved stable mode-locking for both large normal and anomalous cavity dispersion by the adjustment of NPR parameters.
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