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We report on the generation of modulated spikes distributed across a mode-locked pulse profile, which is termed as “additive mode-locked resembling (AMLR)”, in a Tm-doped fiber laser with a hybrid cavity configuration based on nonlinear polarization rotation (NPR) technique. The hybrid cavity configuration is composed of a ring cavity containing a micro Fabry-Perot (F-P) cavity. The F-P cavity is used to take the cavity-trip frequency (CTF) modulation on the mode-locked pulses for forming AMLR pulses. We observe AMLR pulses with uniform and chirped modulation depths, as well as uniform and nonuniform spike separations, respectively. Numerical simulations confirm the experimental observations and show that the filtering effect of the F-P cavity is the main mechanism for taking CTF modulation on mode-locked pulses to generate AMLR pulses.
© 2015 Optical Society of America
1. Introduction
Pulsed fiber lasers are attractive for their wide applications in fields of spectroscopy, industrial processing and optics communications, which require laser pulses with short pulse durations, high powers and broad spectral bandwidths [1–6 ]. Particularly, Tm-doped fiber lasers are considered as promising scientific sources for producing mid-infrared laser emission, which make them significant useful in laser medical, laser radar as well as nonlinear frequency conversion [7–9 ]. Different types of pulsed fiber lasers have been extensively investigated in the past few years, such as Q-switched [10,11 ], gain-switched [12,13 ], mode-locked [14,15 ] and mode-locked resembling (MLR) fiber lasers [16,17 ]. Up to date, MLR fiber lasers have attracted much attention because of their striking pulse characteristics. MLR pulses exhibit periodically modulated spikes in a Q-switched pulse profile, which means that they are simultaneously in both Q-switching and weak mode-locking states. The MLR pulses have been observed in Q-switched and gain-switched fiber lasers. The physical mechanisms for generating MLR pulses have been not thoroughly explained and should be analyzed more deeply. One probable reason is that the beating between the laser longitudinal modes is responsible for generating MLR pulses in Q-switched fiber lasers [18]. To our knowledge, however, few people pay attention to whether the similar phenomenon can exist in mode-locked fiber lasers, i.e., whether the periodical modulated spikes can distribute across a mode-locked pulse profile. It is hard to observe periodical modulated spike phenomenon in a typical mode-locked fiber laser because the mode-locked laser generally output either a single-pulse train or a multi-pulse structured bunching [19–22 ]. In addition, it is hardly reported on how to affect spike separations, modulation depths as well as asymmetric spike distribution in the mode-locked pulses.
In this work, we experimentally demonstrate the generation of modulated spikes distributed across a mode-locked pulse profile in a Tm-doped mode-locked fiber laser based on NPR technique. We use an additive intracavity to realize the modulated spikes in a mode-locked pulse profile generated from a primary laser cavity. The phenomenon of these modulated spikes in a mode-locked pulse is termed as “additive mode-locked resembling (AMLR)” in analogy to the MLR phenomenon of modulated spikes in a Q-switched pulse. The properties of AMLR pulses are experimentally analyzed. Under different weak mode-locking conditions, we achieve the AMLR pulses with uniform or nonuniform spike separations, respectively. The AMLR pulses with different modulation depths and asymmetric modulation distribution are also observed through adjusting pump powers, respectively. The generation of the AMLR pulses is further reconstructed theoretically for the understanding of the experimental observations.
2. Experimental setup
Figure 1 is the experimental configuration of the Tm-doped ring fiber laser. The laser cavity contains a segment of 14 cm self-developed Tm-doped single mode fiber (TDF) with the refractive index of 1.7, a 1570/1950 wavelength division multiplexer (WDM), a 90:10 fiber coupler, two sets of polarization controllers (PC), a polarization-dependent isolator (PD-ISO), a segment of 9 m commercial single mode fiber (SMF-28e) with the dispersion coefficient 37.6 ps/nm/km at 1920 nm and a self-made 1570 nm high power pump laser system with the maximum power up to 3.3 W. The TDF is heavily doped with the thulium dopant concentration of 4.5 × 1020 cm−3, which was drawn under 1000 °C by rod-in tube technique. The absorption and gain coefficients of TDF are 0.63 dB/cm at 1561 nm and 2.3 dB/cm at 1950 nm, respectively. The TDF has 8.6/125 μm core/cladding diameters with the numerical aperture (NA) of 0.145, which matches the NA of commercial SMF. The pigtails of the commercial devices are SM 1950 fibers with the dispersion and attenuation coefficients of 36.29 ps/nm/km and 10 dB/km at 1950 nm, respectively. The whole cavity length is about 15.5 m. The cavity net group velocity dispersion (GVD) is estimated as −1.12 ps2. The TDF is directly collimated to SMF with plane end faces. The two plane faces of SMF construct a potential micro F-P cavity of about 14 cm. It indicates that the whole laser cavity has a hybrid configuration of a ring cavity containing a micro linear cavity. The F-P cavity is an additive intracavity for a ring cavity. 10% port of the coupler is used as the output of the fiber laser. The spectral and temporal characteristics of the laser output are measured by an optical spectrum analyzer (Yokogawa AQ6375), a 1 GHz oscilloscope (Agilent DSO-X 3120A) with 12.5 GHz photoelectric detector (Newport 818-BB-51F) and a 3 GHz radio spectrum analyzer (Agilent N9320A), respectively.
3. Experimental observation and discussions
3.1 Uniform spike separation of AMLR pulses with different modulation depths
The joint operation of PD-ISO and PCs acts as an artificial saturable absorber in the laser cavity based on NPR technique, transmitting the intense laser and blocking the weak one. When the pump power reaches 1 W, a self-starting mode-locked pulse train with the separation of 76 ns is achieved through adjusting the PCs. Figures 2(a) and 2(b) present the temporal pulse profiles and radio frequency (RF) spectrum of AMLR pulses for the pump power of 1.0 W, respectively. Each mode-locked pulse contains 23 spikes with the uniform separation of 1.6 ns. The modulation depth of the spikes is about 82%. It is noted that the temporal separation between two neighboring spikes is strictly equal to the F-P cavity round-trip time. In Fig. 2(b), there are two types of characteristic RF peaks with a 1 GHz measurement span, which correspond to the ring and F-P cavities’ fundamental repetition rates (i.e., cavity-trip frequency, CTF) of 13.1 MHz and 625 MHz, respectively. The measured fundamental RFs fully satisfy with the mathematical relationships between the cavity length and the pulse separation. However, their signal-to-noise ratios (SNR) are 30 dB and 20 dB, respectively, which are much smaller than those of typical mode-locked pulses. It means that the AMLR pulses operate at a weak mode-locking state. The generation of periodical modulated spikes owes to the F-P cavity providing the steady tuning of the fundamental CTF modulation on mode-locked pulses. Meanwhile, the mode-locking effect of the artificial saturable absorber is not strong enough for reshaping the spikes into discrete mode-locked pulses. In the following experiments, we gradually increase the pump powers from 1.0 W to 2.7 W. We can find that the characteristic RF peaks of the mode-locked pulses are robustness to the pump powers except for the increase of SNRs with the pump powers increasing. As can be seen in Fig. 3 , however, AMLR pulses’ spectra change with the pump powers. The central wavelengths of AMLR pulses gradually shift to longer wavelength bands with the pump powers increasing, varying from 1915.8 nm to 1919 nm. Meanwhile, 10-dB spectral bandwidths increase from 0.64 nm to 1.39 nm. These properties are similar to those of the typical mode-locking.
Fig. 2 (a) Measured temporal pulse train. Inset, the fine structure of an AMLR pulse. (b) RF spectrum. Inset, the zoom-in of RF spectrum of mode-locked pulses.
Another striking feature is that the AMLR pulses have different modulation depths depending on different pump powers. The AMLR pulses are characterized by 100%, 82% and 46% modulation depths for the pump powers of 0.8 W, 1.0 W and 1.7 W, respectively, which are described in Fig. 4 . The modulated spikes symmetrically distribute across the whole mode-locked pulse profile with the uniform separation of 1.6 ns. We can further find that the spike positions of AMLR pulses with three different modulation depths can fully overlap in the temporal domain. There are still two characteristic peaks of 13.1 MHz and 625 MHz in the RF spectrum. The fixed spike separation demonstrates that the F-P cavity provides steady tuning of the fundamental CTF modulation on the mode-locked pulses generated from the ring cavity in the above-mentioned cases. However, the AMLR pulses exhibit the modulation depths gradually decreasing with the increase of the pump powers in the temporal domain. It means that the modulation operation of the F-P cavity gradually becomes weaker with the pump powers increasing. Therefore, the modulation operations of the F-P cavity are dynamically changing with the strengths of the light field in the ring cavity. It is noted that the AMLR pulses still exist for the pump power of 0.8 W which is lower than the self-starting mode-locking threshold due to the pump hysteresis phenomena [23,24 ].
3.2 Chirped modulation depths of AMLR pulses
It is worth noting that the spike modulation becomes lacking symmetry when the pump power is high enough, which means that the modulation depths change across a mode-locked pulse profile. Figure 5 shows the chirped spike modulation of AMLR pulses for the pump power of 2.7 W. The modulation depth gradually decreases from 100% in the leading edge to 30% in the tailing one. The inset is the corresponding spectrum. In negative GVD regime, the leading components in the mode-locked temporal pulses correspond to the shorter wavelength bands of the spectrum, which indicates that the spikes in the leading edge have more energy. Therefore, the spikes in the leading edge have stronger bound abilities, which results in that the spikes have strong mutual coherence and weak random oscillations. Then the AMLR pulses exhibit that the modulation depths are relatively large in the leading edge and the spectral profile is relatively smooth in the short wavelength bands. On the other hand, the spectral profile shows many small ripples in the longer wavelength bands, revealing the strong random oscillations among spikes in the tailing edge. The mutual coherence among the spikes becomes weaker. Thus, the modulation depths become smaller in the tailing edge.
3.3 Nonuniform spike separations of AMLR pulses
The collimation conditions between TDF and SMF can introduce different extra cavity losses. We slightly increase the air gap between TDF and SMF. Then the whole laser cavity has a relatively large loss. The AMLR pulses will become instable, exhibiting nonuniform spike separations and stronger random oscillations. An example of an AMLR pulse profile with nonuniform spike separations is described in Fig. 6(a) . The pump power is up to 3.1 W at this time due to a large intra-cavity loss. The pulses have evident chirped spike modulation depths. Moreover, the spike separations are no longer fixed, randomly equal to or not equal to the F-P cavity round-trip time. The left inset depicts that the random change trend of the separations between two neighboring marked spikes across the AMLR pulse profile from the leading edge to the tailing one, varying in the range between 1.54 ns and 1.84 ns. It means that the fundamental CTF modulation provided by the F-P cavity is detuning. Thus, the RF spectrum of the spikes may have several peaks. The right inset shows the RF spectrum of the spikes. There are ten peaks distributed in the RF spectrum. Furthermore, only SNRs of central four RF peaks of 569 MHz, 582 MHz, 595 MHz and 608 MHz are beyond 20 dB, which indicates that the spike separations have four dominative values. Note that the difference between two neighboring RF peaks, e.g. 608 MHz and 595 MHz, is 13 MHz. It indicates that different RF values originate from the beating between the first order CTF of the F-P cavity and different order CTF of the ring cavity. That is to say, 595 MHz RF results from the beating between the first order CTF (608 MHz) of the F-P cavity and the first order CTF (13 MHz) of the ring cavity. 582 MHz occurs from the beating between the first order CTF of the F-P cavity and the second order CTF (i.e, second harmonic repetition frequency) of the ring cavity. Therefore, nonuniform spike separations owe to the beating between CTFs of the F-P and ring cavities. Figure 6(b) is the corresponding spectrum. The whole spectral profile shows many strong ripples. The spectral information shows that the random oscillations among spikes become stronger and the mutual coherences become weaker than those in Fig. 5. Thus, the AMLR pulses with asymmetric modulation depths and nonuniform spike separations show much instability.
Fig. 6 (a) Temporal AMLR pulses with nonuniform separations. Left inset, the separation between two neighboring marked spikes. Right inset, RF spectrum of spikes. (b) The corresponding spectrum.
4. Numerical simulation and discussions
To get an understanding of the experimental observations, we theoretically study the dynamics of AMLR pulses in the fiber laser. For emphasizing the modulation effect of the F-P cavity, we numerically calculate a simplified propagation model, an extended nonlinear Schrödinger equation, which was widely applied in passive mode-locked fiber lasers [25–27 ]. The equation including GVD, self-phase modulation and saturable gain with a limited bandwidth is described as following:
where u is the slowly varying envelop. β 2, γ, g and Ω present the coefficients of group velocity dispersion, nonlinearity, saturable gain and gain bandwidth, respectively. Except for being set as zero for SMF, the saturable gain strength is expressed in TDF as follows:where g 0 and E s are small signal gain coefficient and gain saturation energy, respectively. The mathematical expression of the artificial saturable absorber constructed by a PD-ISO and two sets of PCs is designated as:where m 0, P(t) and P sat are the unsaturated loss, instantaneous pulse power and saturation power, respectively. From the physics point of view, particularly, the operation of the F-P cavity is equivalent to a filter. The filtering function of the F-P cavity is selected as:where A and R demonstrate absorption loss and reflectance for each plane end face, respectively. n, l and λ depict the refractive index, F-P cavity length and wavelength, respectively. For a modulation period, the modulated spectral separation induced by the F-P cavity is expressed as following:The theoretical spectral modulation separation induced by the filtering effect of the F-P cavity is 0.0077 nm for the cavity length of 14 cm. The modulated spectral separation is much less than our measured minimum resolution of 0.1 nm. In addition, the effective filtering of the F-P cavity becomes weaker and weaker with the increase of the light field. Thus, we do not observe the periodical modulation spectral profiles in the experiments. Our case is much different from those of periodically modulated spectra induced by the strong filtering functions. The generation of periodically modulated spectra of ultrahigh-repetition rate mode-locked pulses were achieved through the strong filtering functions of a microcavity resonator by Peccianti et al [28], a F-P filter by Qi et al [29] and a Mach-Zehnder interferometer by Mao et al [30], respectively. These filters took strong filtering modulation on the spectra of the pulses, resulting in the comb profiles on the spectra. According to the time-spectrum uncertainty relation, their and our cases are in opposite physical states.
The initial signal is the white noise in the simulation. After a cavity-trip calculation, the calculated results are used as the input signal for the next trip in the simulation until the light field remains self-consistent. According to the experimental conditions, the parameters are selected as follows in the simulation: β 2 = −72.3 ps2/km, γ = 0.9 W−1km−1, g 0 = 2.3 dB/cm, Ω = 120 nm, m 0 = 0.05, l = 14 cm and P sat = 500 W. The resolutions of numerical calculations are the same as those of the oscilloscope and optical spectrum analyzer. Figure 7 is the transient spectral evolution. It is shown that the pulses evolve into a steady state after 250 round-trips. We use the calculated results of the 300 round-trips as the outputs of the fiber laser.
The AMLR pulse temporal profiles with different gain saturation energies are illuminated in Fig. 8 . Calculated AMLR pulses have an uniform spike separation of 1.6 ns for the 14 cm cavity length, which confirms the fundamental CTF modulation of the F-P cavity. Moreover, the modulation depths of the AMLR pulses vary with the gain saturation energies. The modulation depths of 77% and 63% correspond to gain saturation energies of 200 pJ and 500 pJ, respectively. The increase of gain saturation energy means the increase of the pump power in the simulation. Thus, the modulation depths of AMLR pulses are decreasing with the pump powers increasing. The calculated results are consistent with the experimental observations [Figs. 2(a) and 4 ]. Moreover, we can further find that the modulated spikes will disappear if the filtering function is removed in the simulation. Therefore, it is proved that the filtering effect of the F-P cavity leads to the generation of AMLR pulses. Meanwhile, the numerical results also indicate that the CTF modulation strength of the F-P cavity on AMLR pulses gradually becomes weaker in the process of the light field becoming stronger.
Fig. 8 Calculated AMLR pulse profiles with different modulation depths. Up, E s = 200 pJ; Down, E s = 500 pJ.
When the extra loss induced by the collimation conditions is considered, we should further increase the pump powers through increasing the gain saturation energies in the simulation. The gain saturation energy and net effective gain are selected as E s = 800 pJ and g 0 = 1.8 dB/cm, respectively. We find that the periodically modulated spikes become asymmetric distribution across the pulse profile, as shown in Fig. 9 . The spike separations randomly vary from the leading edge to the tailing one, which reveals that the filtering effect of the F-P cavity is detuning since it does not take effective fundamental CTF modulation on the mode-locked pulses. The modulation depths become much smaller than those of the above two cases. Meanwhile, the modulation depths lose symmetry across the pulse profile. The central parts of AMLR pulses have relatively larger modulation depths, which are slightly different from the experimental observations. We also observe that the corresponding spectral profile shows much strong ripples [the inset of Fig. 9]. The strength of ripples depends on the gain saturation energy. The larger the gain saturation energy is, the stronger the strength of ripples is. The calculated results of the AMLR pulses with nonuniform separations nearly coincide with the experimental observations [Fig. 6]. As a result, the filtering effect of the F-P cavity is confirmed as a key mechanism for taking CTF modulation on the mode-locked pulses through numerical simulations. In addition, the fundamental CTF modulation of the F-P cavity is gradually detuning with the increase of the light field. It is noted that the output spectral bandwidth decreases with the gain bandwidth decreasing. However, the temporal profiles of the pulses do not show evident differences.
5. Conclusion
In summary, we construct a Tm-doped mode-locked fiber laser with a hybrid cavity configuration of a 15.5 m ring cavity containing a 14 cm micro F-P cavity. The mode-locked pulses are obtained based on NPR technique. F-P cavity will take an additive weak CTF modulation on the mode-locked pulses generated from the ring cavity. Then the AMLR pulses with uniform spike separations are achieved. The modulation depths of the spikes depend on the pump powers. The more the pump powers are, the less the modulation depths are. If the pump powers are high enough, the modulation depths will change across the pulse profile, decreasing from the leading edge to the tailing one. If the cavity has a large linear loss, AMLR pulses become instable, exhibiting chirped modulation depths and nonuniform spike separations across the mode-locked pulse profile. The nonuniform spike separations originate from the beating between the first order CTF of the F-P cavity and different order CTF of the ring cavity. The numerical calculations reconstruct the generation of the AMLR pulse and confirm the experimental observations. It is proved that the filtering effect of F-P intra-cavity is the main mechanism for taking CTF modulation on mode-locked pulses to form AMLR pulses.
Acknowledgments
This work is supported by the State 863 Hi-tech Programs (Grant Nos. 2013AA031502 and 2014AA041902), National Natural Science Foundations (Grant Nos.11204037, 11174085, 51132004 and 51302086), Guangdong Provincial Natural Science Foundations (Grant No. S20120011380), National Funds for Distinguished Young Scientists (Grant No. 61325024) and the fundamental Research Funds for Central Universities, China.
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