A soliton mode-locked lead selenide (PbSe) quantum-dot-doped fiber laser (QDFL) is proposed and investigated by numerical simulation for the first time. Buildup dynamics in time and spectral domains are studied. Output properties starting from Gaussian and noise-like signals are characterized. The optimum quantum-dot-doped fiber lengths are revealed under various PbSe quantum dot doping concentrations. The evolutions of the pulse and spectrum in the resonator at the steady state are discussed. The results obtained facilitate the understanding of the operating principle of QDFL for solving emission wavelength problem.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Owing to their high peak power and extremely short pulse duration, ultrashort pulses are crucial in many fields, such as multiphoton microscopy [1,2], laser microprocessing [3,4], efficient nonlinear frequency conversion [5,6], and laser filamentation [7,8]. Mode locking is the most efficient approach for creating stable ultrashort pulses. Fiber lasers are ideal sources for achieving excellent beam quality at low cost [9–13]. Mode-locked fiber lasers have become the commercial ultrashort pulse source with excellent beam quality, compact configuration, free alignment, and low cost.
However, it is difficult to emit several particular wavelengths from the present mode-locked fiber lasers owing to the limitation of emission wavelengths from rare-earth-doped gain media in fiber lasers . For instance, rare-earth ions can radiate wavelengths of 1 μm, 1.5 μm, 2 μm, etc. However, there is no emission cross-section or extremely low emission cross-section at a number of particular wavelengths, such as the important biomedical wavelength of 1.7 μm [15,16]. This fact leads to a difficulty of obtaining 1.7 μm from a mode-locked rare-earth-doped fiber laser directly.
Quantum dots (QDs), a quasi-zero-dimensional semiconductor nanocrystal [17–19], is a promising candidate as a gain medium in fiber lasers for obtaining particular wavelengths; they are not included in rare-earth ion-doped fiber lasers. Because the emission wavelengths of QDs can be shifted continuously by only changing the QDs size, a QD-doped fiber laser (QDFL) can easily achieve a particular wavelength. To date, IV-VI PbSe QDs, which have large emission cross sections, high quantum yields, broad adjustable spectra, and can be easily embedded in fiber, are an interesting material for obtaining efficient particular-wavelength output from fiber lasers [20,21]. Recently, studies regarding continuous PbSe QDFL and amplifiers have been performed [22,23]; however, the mode-locked PbSe QDFL has not been studied yet.
Herein, a soliton mode-locked PbSe QDFL is proposed and investigated by numerical simulation for the first time. Combining the rate equation with the generalized Ginzburg–Landau equation (GLE) while using the split-step Fourier method, PbSe QD-doped fiber (QDF)-related parameters were optimized to obtain a stable soliton pulse train. It was discovered that optimum lengths existed for different doping concentrations of PbSe QDF. The pulse and spectrum evolutions in the resonator at the steady state are discussed in the final section. The results obtained facilitate the understanding of the operating principle of QDFL to achieve the emission of a particular wavelength from a mode-locked fiber laser.
The proposed soliton mode-locked PbSe QDFL is schematically shown in Fig. 1(a). This ring laser comprised a laser diode pump source with a central wavelength of 980 nm, a 980 nm/1700nm wavelength division multiplexer (WDM), a piece of QDF with an emission peak wavelength of 1700nm, a fiber-pigtailed isolator (ISO), an output fiber coupler (OC), a saturable absorber (SA), and four pieces of single-mode passive fibers (SMFs). A total loss was set in our model, including splicing loss, insertion loss, etc.In addition, all fibers had the same numerical aperture and core diameter.
Table 1 shows the parameters used in the rate equation.
When laser pulses pass through the SMF, g is treated as 0. As pulses pass through the ISO and OC separately, the pulse energy will decrease by a fixed percentage of each element. When the pulses pass through the SA, the SA can be modeled by the following simplified transfer function:
Table 2 shows the parameters used in the GLE.
3. Simulation results and analysis
The soliton buildup dynamics starting from a Gaussian signal and a noise-like signal were investigated in depth and characterized, as shown in Fig. 2. Figs. 2(a) and 2(b) illustrate the soliton buildup dynamics in time and spectral domains starting from a Gaussian signal. For pulse transformation, the pulse duration decreased, and the peak power increased at a low speed from the start to the 350th roundtrip, followed by a rapid narrowing and power increase from the 400th to 450th roundtrip, whereas a relaxation oscillation-like behavior was observed before a stable pulse was obtained at approximately the 500th roundtrip. Meanwhile, the spectrum evolution was narrow, i.e., less than 1 nm, without the Kelly sideband from the starting roundtrip to the 350th roundtrip, followed by the full-width at half maximum (FWHM) increasing significantly from the 400th to 450th roundtrips with a Kelly sideband (see Visualization 1). Meanwhile, the oscillation occurred before a stable spectrum was obtained at approximately the 500th roundtrip. Generally speaking, from the soliton buildup dynamics of Gaussian signal, it could be seen that the spectrum widens rapidly owing to peak power induced self phase modulation, before negative dispersion slows down the peak power to make a stable soliton pulse output.
Figures 2(c) and 2(d) show that the soliton buildup dynamics in time and spectral domains started from a noise-like signal. Compared with the evolution from the Gaussian signal, in the time domain, fewer roundtrips were required to form a stable pulse and the competition between pulses in noise-like signals was evident during the initial roundtrips, which resulted in the random pulse time coordinate (see Visualization 2). In the spectral domain, the initial noise spectrum bandwidth narrowed first because of the limit of Ωg, and then broadened quickly along the Kelly sideband, and a stable spectrum was obtained.
Figures 3(a) and 3(b) demonstrate the stable output pulse and spectrum starting from a Gaussian signal. The pulse had a pulse duration of 328 fs and a peak power of 156.1 W, whereas the spectra had an FWHM of 13.4 nm along the Kelly sideband. Figures 3(c) and 3(d) show the stable output pulse and spectrum started from noise-like signal. Identical pulse and spectrum characteristics were exhibited even though the pulse started from different initial signals. In other words, the output properties of the pulse and spectrum were independent of the initial signal, and coordinate position of stable pulse is uncertain while pulse was initialed from noise-like signal. Therefore, a Gaussian pulse was set as the initial signal in the following numerical analysis.
Based on a pump power fixed to 100 mW, the effects of the QDF length and doping concentration on the output peak power and pulse duration were investigated in this study. Figure 4 illustrates the peak power and pulse duration with respect to the QDF length under different PbSe QD doping concentrations. It was evident that an optimum QDF length existed for obtaining the maximum peak power under all selected doping concentrations. Meanwhile, with an increase in concentration, the optimum QDF length decreased. The optimum QDF lengths were approximately 0.6, 0.4, 0.3, and 0.25 m under N1, N2, N3, and N4, respectively. Furthermore, the optimum QDF lengths matched the shortest pulse durations of 242, 242, 241, 239 fs, under N1, N2, N3, and N4, respectively. In addition, compared with Hyperbolic Secant and Polynomial fitting, Gaussian fitting met the data of peak power and pulse duration more precisely.
To investigate the relationship between the spectrum and QDF length, spectra at various QDF lengths were compared, as shown in Fig. 5, while the pump power and doping concentration were fixed at 100 mW and 9 × 1021 m-3, respectively. As the QDF length increased from 0.2 to 0.4 m, the FWHM increased nonlinearly from 12.3 to 16.7 nm. Subsequently, as the QDF length increased from 0.4 to 0.6 m, the FWHM decreased nonlinearly from 16.7 to 10.4 nm.
Finally, the pulse and spectrum evolutions in one round trip at steady state were investigated. A doping concentration of 9 × 1021 m-3 and a QDF length of 0.4 m were set for this simulation. The time domain results are shown in Figs. 6(a) and 6(b), and the spectral domain results are shown in Figs. 6(c) and 6(d). The peak power and pulse duration increased as the pulse passed through the QDF, followed by the peak power decreasing after the pulse passing the elements successively. Compared with the pulse evolution, the spectrum evolution exhibited only a slight change in the Kelly sideband with almost the same spectral FWHM.
In summary, a soliton mode-locked PbSe QDFL was proposed and investigated through numerical simulation for the first time. To achieve a simulation that was similar to the real experimental situation, the gain coefficient g(z), which is a function of position in PbSe QDF, was applied. The buildup dynamics in time and spectral domains were investigated in depth. It was discovered that different initial signals resulted in different buildup dynamics but the same output property at the steady state. The peak power and pulse duration with respect to the QDF length under different PbSe QD doping concentrations were investigated. An optimum QDF length under a fixed pump power and doping concentration was determined. The results presented herein will facilitate the understanding of the operating principle of this novel laser, which further facilitates the optimization of resonator design and the development of the mode-locked fiber laser at particular wavelength.
National Natural Science Foundation of China (61705056, 61605039, 81601530); Natural Science Foundation of Zhejiang Province (LGF20F050004, LQ16F050002, LY20F050005, 2017C33143); Scientific Research Fund of Zhejiang Provincial Education Department (Y201533689).
The authors declare no conflicts of interest.
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