We propose and demonstrate a novel actively mode-locked fiber laser based on a stretch-type time-lens. The pulse generated by this scheme has high repetition rate and large bandwidth while no nonlinearity is participated. A 10-GHz chirped pulse train with 18-ps duration and 11.6-nm bandwidth is obtained, which is then extra-cavity compressed down to 825 fs. The pulse characteristics dependent on the cavity dispersion and time-lens strength are discussed. Pulse propagation in the laser is similar with dissipative soliton in all-normal-dispersion laser. The results demonstrate that the stretch-lens inside the actively mode-locked laser can effectively broaden the spectral bandwidth, instead of the fiber nonlinearity, which can then support a high-repetition-rate “linear dissipative soliton” pulse shaping in a very compact design.
© 2013 Optical Society of America
Femtosecond fiber lasers are attractive light sources as they offer many advantages such as compact size, maintenance- and alignment-free, and superior thermal handling. Generally, fs-pulse generation in fiber laser relies on the contribution of fiber nonlinearity, which could however induce instability or even collapse of the pulse . Moreover, the strong nonlinearity in the cavity requires high pulse energy, so the generation of fs-pulse usually exists in repetition-rate-limited passive mode-locked lasers [2, 3], where the repetition rate is fixed by cavity length. To generate high-repetition-rate pulses, actively mode-locked fiber laser is widely employed [4–10]. However, the pulse train in those lasers is based on soliton pulse shaping, and long cavity is needed to accumulate sufficient nonlinearity, which increases the cavity instability. Besides, the ultra-short pulse is usually sensitive to the in-cavity dispersion and nonlinearity map, which should also be carefully designed.
Without nonlinearity, the time-lens is a practicable technique to generate ultra-short pulses. A time-lens refers to a device that imposes a quadratic phase in the time domain onto a pulse, in analogy to a spatial lens imposing a quadratic phase in space onto a spatial profile [11, 12]. In practice, the quadratic phase modulation can be achieved approximately by applying a sinusoidal RF drive signal to an electro-optic phase modulator (PM). Just as a spatial lens can expand or focus a beam in space, so can a time-lens broaden or compress a pulse in the time domain with proper dispersion compensation. Femtosecond pulses with ~GHz repetition rate can be obtained, after de-chirping, based on an “open loop”  (i.e. the loop is actually not a lasing cavity). However, the bandwidth broadening of a pulse is positively related to the number of loops the pulse passing the time-lens, so the repetition rate could not be increased any more [14, 15]. Otherwise, optical nonlinearity is still necessary. For example, a long distance specifically designed dispersion decreasing fiber  for adiabatic soliton compression was used after a single-pass time-lens, in order to obtain 10-GHz fs-pulses.
In this paper, we demonstrate a novel actively mode-locked fiber laser combined with a “closed-loop” time-lens. The time lens imposes a quadratic phase onto the pulse, and the pulse in the cavity is linearly chirped. However, unlike all previous fiber lasers containing phase modulator, the pulse with linear chirp in our system is stretched. Therefore, the generated pulse has large bandwidth and high repetition rate without the participation of fiber nonlinearity. Besides, by changing the sign of the chirp imposed by time lens, the laser can work at either anomalous or normal cavity dispersion. Experimentally, a 10-GHz linearly-chirped pulse train is obtained with bandwidth of 11.6 nm, which is then de-chirped and compressed down to 825 fs. The pulse property dependent on the cavity dispersion and time-lens modulation depth is discussed. Furthermore, our simulation shows that the proposed laser operates in a “linear dissipative soliton” shaping regime.
2. Design rationale and numerical simulations
The structure illustrated in Fig. 1 is employed to investigate the principle of our actively mode-locked fiber laser. The key elements of such a laser are a segment of Er-doped fiber (EDF), a segment of single-mode fiber (SMF), and components that produce amplitude and phase modulation. When a mode-locked laser cavity consists of several optical elements, one can immediately obtain a steady-state solution (pulse width and chirp) of a mode-locked pulse by using the time-domain ABCD matrix, which is presented by Nakazawa et al. .
Using the Gaussian approximation, the time domain amplitude expression of a linearly chirped pulse is:Fig. 1 described by ABCD matrix is shown in Table 1.
The pulse forming process is determined by four primary factors: the amplitude modulation, the phase modulation, the fiber dispersion, and the gain fiber filtering. In our laser, the fiber nonlinearity is negligible, because of the low peak power and long pulse duration. Neglect the multiplication of the B and C matrix elements , the total ABCD matrix for the active mode locking pulse isEq. (3) into Eq. (2), we can obtain the analytical expression of the pulse Gaussian factorEq. (4), we draw the pulse properties depending on the cavity dispersion and phase modulation in Fig. 2.
Figure 2 shows that under large phase modulation depth and small cavity dispersion, pulse with large bandwidth can be obtained in our proposed laser without the participation of fiber nonlinearity. The generated pulse with large chirp has large time-bandwidth product, which is very different from soliton. Although PM is used in our fiber laser, the above pulse properties indicate that the laser is not working at soliton shaping regime [6, 8]. Furthermore, the PM can impose either positive or negative linear chirp onto the pulse , so that stable spectral broadening can be achieved by either anomalous or normal cavity dispersion (by changing the sign of the fiber dispersion) under proper timing of the PM, which is very different from the nonlinearity-based spectral broadening: the soliton exists in anomalous-dispersion cavity, while the dissipative soliton exists in a normal-dispersion one.
To illustrate the pulse generation mechanism and reveal the details of pulse shaping in the cavity at different position, we calculate the master equation of mode locking . Assume that the in-cavity fibers are nonlinearity-free. We take no account of the fiber nonlinearity term. As an initial condition, white noise is used. The model is then solved by iterating the initial field until the field becomes constant to ensure that a stable mode-locked pulse operation has been reached after a finite number of traversals of the cavity . Under the condition of 14-m SMF and 1.7-m EDF, 5π radians phase modulation, and 10-GHz RF signal, a stable solution is obtained as shown in Fig. 3.
The numerical study has revealed the pulse shaping of the proposed actively mode-locked laser, which is explicated in Fig. 3(b) through the evolution of one pulse properties (e.g. the pulse width and bandwidth) along the fiber. In a regular phase-modulation-based active mode locking, the cavity dispersion will de-chirp and compress the pulse after phase modulation, which results in a short and slightly-chirped pulse whose bandwidth is however greatly limited by the dispersion [6, 8] and has to be further broadened by fiber nonlinearity. On the contrary, in our design the cavity dispersion will broaden the temporal pulse. Assume the fiber dispersion is anomalous. By adjusting the phase of the driven-signal, the PM generates a linear and anomalous chirp to the pulse, which is then broadened by the following fiber. In contrast to the conventional fiber laser, where the broad spectrum is provided by the nonlinear effect of high energy ultrashort pulse, the time-lens plays an important role of linear widening in our scheme. However, the intensity windowing by the AM reverses the above changes, both temporally and spectrally due to the linear chirp, and thus restores the pulse after traversal of the cavity. In addition, the EDF has the similar effect as AM because of the gain filtering.
Therefore, the pulse in the linear, time-lens-based laser is similar to the typical dissipative soliton in a nonlinear laser . The pulse has large linear chirp, and the spectrum profile [Fig. 3(a) inset] has similar property (also refer to the experiment results), due to the similar pulse shaping process. The reason is that the nonlinear phase modulation on a pulse by fiber self-phase-modulation (SPM) is analogous to the quadratic phase modulation by time-lens. Here the presence of the large chirp is critical, which is the same as dissipative soliton in normal-dispersion cavity. The pulse duration under large chirp as well as the matched dispersion is always long, which ensures an effective time-lens modulation to increase the spectrum bandwidth but does not destabilize the pulse.
Obviously a stronger phase modulation results in a larger pulse bandwidth, since the spectral broadening is induced by the time-lens. The calculation in Fig. 2 also reveals that small cavity dispersion is necessary to obtain a large bandwidth. This can be explained as follows: larger cavity dispersion results in longer pulse duration and thus more parts of pulse spectrum are cut off by the subsequence AM windowing due to the large chirp. Note that due to the large chirp, the pulse duration is always long even under very small dispersion, which is consistent well with the previous analysis in Fig. 2 and the nonlinearity-free assumption in the simulation.
Since the spectral broadening is induced totally by the pulse-energy-independent time-lens, a high repetition rate is then feasible without nonlinearity. As a result, the fiber length can be shortened greatly, and a very compact design is expected, which could be more stable.
3. Experimental results and discussion
The experimental setup of the proposed actively mode-locked fiber laser is illustrated in Fig. 4. A 1.7-m Er-doped fiber (EDF) with absorption of 55 dB/m @ 1530 nm is used, which is forward pumped by a 980-nm laser diode through a 980/1550-nm wavelength division multiplexer (WDM). A dual-drive LiNbO3 Mach-Zehnder amplitude modulator (AM; from EOSpace, 10 GHz), one port of which is driven by a RF sinusoidal source (Agilent E8267D, 250 kHz-20 GHz), is employed to realize the active mode locking. Due to the low polarization-dependent loss of the AM, a polarizer is used before to ensure the AM works at the correct polarization state. An isolator is employed for unidirectional operation, and a 30% optical coupler (OC1 in Fig. 4) outputs the laser pulses. A LiNbO3 PM with 10-GHz bandwidth, which is actually the in-cavity time-lens, is driven by the same RF sinusoidal wave which is amplified and carefully synchronized by a phase shifter. Adjusting the phase shifter to make sure the minimum point of the quadratic phase is aligned to the center of the pulse. The EDF and other single mode fibers (SMFs) in the cavity are polarization-maintained to prevent any polarization fluctuation. The total length of the cavity is approximately 17.5 m, corresponding to a fundamental frequency of about 11.4 MHz. Note that a pulse-intensity-feed-forward path, which consists of an optical tunable delay line (ODL), a fast photo detector (PD), and a microwave amplifier (from 75 kHz to 10 GHz) with tunable gain, is employed, which will be explained later.
In our experiment, the frequency of the RF sinusoidal wave is 10.0587 GHz, which is the 882th harmonics, and the pump power is 23.82 dBm. The RF power applied on the PM is 29 dBm, corresponding to a modulation depth of about 4 Vπ. Highly-stable active mode locking is observed, as is shown in Fig. 5. The pulse is firstly received by a 70-GHz PD and then measured by a high-speed sampling oscilloscope (HP 83485B) whose bandwidth is 40 GHz. The measured full-width at half-maximum (FWHM) of the output pulse is about 18 ps, as shown in Fig. 5(a). Experimentally the supermode noise of the generated 10 GHz optical pulse train is investigated using a RF spectrum analyzer (Agilent N9030A, with analysis bandwidth of 26.5 GHz). The electrical spectrum is plotted in Fig. 5(b). Within the span of 300 MHz, which covers more than 26 times the cavity frequency, the supermode noise suppression ratio is closed to 80 dB, which indicates a stable 10-GHz pulse train.
Under the same circumstance, the measured optical spectrum is shown in Fig. 5(c). A striking feature is that the spectrum has steep spectral edges and its profile approaches a rectangular shape, which is similar with the dissipative soliton in normal-dispersion cavity . The square top feature of the spectrum is indicative of aberration in the phase drive from the ideal quadratic profile, which agrees with the previous time-lens experiment [13–15], as well as the prediction in our simulation. The edge-to-edge, 20-dB bandwidth is 11.6 nm, indicating that the pulse is strongly chirped. In our setup, the length of SMF is minimized to connect the AM, PM, EDF, and other passive devices, in order to obtain the largest spectral bandwidth. The bandwidth is limited by the unflatten gain profile of EDF, which could be larger in an Yb-doped fiber laser with a much flatter one. Due to the fiber dispersion, the slight RF frequency tuning will result in wavelength shifting, so the RF modulation frequency is not so critical for stable mode locking . The measured output power is 3.4 mW. Accordingly, the single pulse energy inside the cavity is estimated to be 2.3 pJ, so the fiber nonlinearity is negligible in our fiber laser. The output pulse is de-chirped by a programmable liquid crystal spatial light modulator (Finisar WaveShaper 4000S). The programmable waveshaper is set to have an all-pass amplitude response with however a parabolic phase response (i.e. a linear frequency chirp), which is shown in Fig. 5(c) . As shown in Fig. 5(d), the FWHM after de-chirping is 825 fs, which is measured by an extremely high speed oscilloscope (EXFO PSO-102, with >500-GHz bandwidth). The compressed pulse duration is close to the transform limit (640 fs), which implies an approximately linear chirp of the pulse, as expected theoretically. The little pedestal shown in Fig. 5(d) is mainly caused by the nonlinear chirp introduced by the sinusoidal phase modulation.
Different from the conventional actively mode-locked fiber lasers, the proposed scheme includes a pulse-intensity-feed-forward path, as shown in Fig. 4, which is employed to suppress the supermode noise . The output optical pulse is firstly converted into electronic signal, and then fed forward to the “negative” port of the dual-drive AM, where the optical pulse is modulated by the reversed intensity profile of itself. Therefore, under the feed-forward control, pulse-to-pulse intensity fluctuation is suppressed with proper feed-forward strength. When the feed-forward loop is switched off, sidebands appear at the cavity-mode spacing with large intensity, and serious pulse-intensity fluctuation occurs in the time domain. Note that the feed-forward path has no relationship with “linear dissipative soliton” pulse shaping. Other than the normally used power-limiting method including nonlinear polarization rotation (NPR), the pulse-intensity-feed-forward scheme is also free from fiber nonlinearity.
In conclusion, we have proposed and demonstrated a novel actively mode-locked femtosecond fiber laser scheme, where an optical-power-independent time-lens is employed to spectrally broaden the optical pulse, instead of the conventional fiber nonlinearity. As a result, large bandwidth can be achieved under a high repetition rate and average optical pump power. Experimentally, a de-chirped pulse train with 825-fs duration at 10-GHz repetition rate was generated. Due to the nonlinearity-free requirement, the proposed scheme can be more compact by using integrated modulators and waveguide amplifier, where the bandwidth can be further broadened due to the cut of dispersive fibers. In addition, benefited from the development of digital optical communications, high-speed opto-electronic devices (e.g. modulators, photo detectors and RF drivers) will enable the proposed active mode locking with repetition rate up to 40 GHz or more.
This work was supported in part by 973 Program (2012CB315705), National 863 Program (2011AA010306), NSFC Program (61271042, 61107058, and 61120106001), the Fundamental Research Funds for the Central Universities, BUPT Excellent Ph.D. Students Foundation (CX201321), and the Fund of State Key Laboratory of Information Photonics and Optical Communications.
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