1. Introduction

The formation and evolution of ultrashort pulses are rich and fascinating subjects in nonlinear fiber optics [1, 2]. Due to the intrinsic stability, optical solitons can propagate undistorted over long distance and have been widely used in fiber-optic communications and signal processing [3]. In the anomalous dispersion regime, due to the interplay between cavity dispersion and fiber nonlinearity, conventional solitons (CSs) were achieved and had been found important applications [4, 5]. However, the pulse energy of CSs is limited by soliton energy quantization effect and multiple solitons are always generated in cavity at high pump regimes [1, 6]. Recently, dissipative solitons (DSs) have attracted a great deal of research interests due to its capacity of delivering pulses with ultra-high energy [3] [7–11]. It is shown that the formation of DSs is mutual interactions among normal cavity dispersion, fiber nonlinear effect, laser gain, losses, and spectral filtering [12, 13].

Usually, single-wavelength DSs have been observed experimentally and investigated extensively [14–18]. In our previous reports, we had investigated the formation and evolution of single-DS, dual-DSs, and multiple-DSs in erbium-doped fiber (EDF) lasers [15–17]. With nonlinear polarization evolution technique and a birefringent filter, Chichkov et al. have obtained the high-power DSs from an all-normal dispersion EDF oscillator [14]. In addition, the single-wavelength dark DSs in a photonic crystal fiber have been reported by Tlidi et al [18]. Recently, several dual- or multi-wavelength mode-locked fiber lasers have been proposed [19–22]. These studies mainly focused on fiber lasers with spectral filters, and thus the lasing wavelengths cannot be easily controlled [19]. Zhang et al. have reported multi-wavelength DSs in an all-normal-dispersion fiber laser passively mode-locked with a semiconductor saturable absorber mirror [20]. Two DSs with different wavelengths exhibit orthogonal polarization states, which can be regarded as a novel kind of vector soliton. However, no multi-wavelength DSs have been observed in passively mode-locked figure-eight fiber lasers.

In this paper, we report on the experimental observation of dual-wavelength DSs delivered from a figure-eight EDF laser for the first time. The dual-wavelength DSs exhibit double-rectangular spectral profile and have two different round-trip times. The 3-dB bandwidths of two spectra are ~11 and ~10 nm, respectively, and the separation between two central wavelengths is ~15 nm. Our experimental results show that the dual-wavelength DSs almost share the same polarization state, essentially distinct from the multi-wavelength vector DSs that two spectra exhibit orthogonal polarization states [20]. Furthermore, in contrast with other setups, our proposed scheme is easy to be constructed with low cost.

2. Experimental setup

The experimental setup is shown in Fig. 1 . It is a figure-eight laser based on a passive unidirectional ring (UR) cavity that is coupled to a nonlinear optical loop mirror (NOLM) through a 30/70 fiber coupler. The NOLM consists of a 21-m SMF and a polarization controller (PC). The UR contains a 40-m EDF with an absorption of 6 dB/m, a polarization-insensitive isolator (PI-ISO), a PC, and a 90/10 fused optical coupler (OC). Two 980-nm laser diodes with the maximum pump power of 1.1 W are used to provide pump source through two 980/1550 nm wavelength division multiplexers (WDMs). The other fiber in the UR is SMF with total length of 2 m. The dispersion parameters D of the EDF and SMF at 1550 nm are −16 and 17 ps/nm/km, respectively. The net cavity dispersion is estimated to be 0.32 ps². The total length of the laser is ~63 m, corresponding to the fundamental repetition rate of ~3.278 MHz. For an input pulse with proper intensity, the 30/70 coupler induces a relative nonlinear phase shift between the pulses within the loop mirror. When the pulses interfere at the central coupler, the high-intensity portions of the pulse undergoes smaller loss than that of low-intensity portions as the combination of the NOLM and isolator acts as an saturable absorber. The laser is monitored by an optical spectrum analyzer, a commercial autocorrelator, a digital storage oscilloscope, and a radio-frequency (RF) analyzer simultaneously. The output pulse can be polarization-resolved along two birefringence axes with a PC and an polarization beam splitter (PBS) external to the cavity.

 

Fig. 1 Experimental setup of the figure-eight fiber laser.

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3. Experimental results and theoretical analysis

With proper settings of PCs, dual-wavelength mode-locking operation is observed when the pump power is beyond the threshold. As shown in Fig. 2(a) , mode-locked pulses operating at 1572 and 1587 nm are achieved simultaneously at forward pump of P_f = 200 mW and backward pump of P_b = 200 mW. The output spectra exhibit a double-rectangular profile, and each spectrum shows typical characteristics of DSs in normal dispersion regimes [18]. The 3-dB bandwidths of two spectra are ~11 and ~10 nm, respectively. The inset in Fig. 2(a) is the transmission spectrum of NOLM. Due to the fiber birefringence, two lights at contrary propagation directions have different optical lengths after propagation through the NOLM. They interfere with each other at the 30/70 coupler and the output spectrum exhibits strong modulations. Apparently, the mode-locked DS spectrum and transmission spectrum approximately have the same central wavelength and the same valley wavelength. The autocorrelation trace of the DSs is shown in Fig. 2(b). The full width at half maximum (FWHM) of dual-wavelength DSs is calculated as 3.6 ps by using Gaussian fit. Figure 2(c) shows the oscilloscope trace for the dual-wavelength mode-locking state. Because of different operating wavelengths and non-zero cavity dispersion, their pulse trains have different group velocities and round-trip times. As a result, the multiple pulses are scattered randomly in the cavity positions. Although the DSs pass through each other, no modulation or unstable transitional state is observed on the spectrum. The experimental results show that the pulses almost have the same peak intensity in oscilloscope trace. The small fluctuation on the pulses is from the limited sampling of the oscilloscope. The oscilloscope trace here is similar to the multiple solitons in single-wavelength mode-locked fiber lasers [1], where all the solitons share the same height and energy that is described as soliton energy quantization. The corresponding RF spectrum of dual-wavelength mode-locking is demonstrated in Fig. 2(d). The signal/noise ratios of two operations are higher than 50 dB. Different from the single-wavelength mode-locked operation that has only a fundamental repetition rate, the dual-wavelength operation exhibits two fundamental repetition rates corresponding to two mode-locking states. In particular, the separation between the two RF spectrum is estimated as 40 Hz and keeps a constant during experiments. Based on the above results, we conclude that the fiber laser operates at stable dual-wavelength DSs mode-locking state. The relationship between the wavelength difference and RF separation can be theoretically analyzed as [23]:

 

Fig. 2 (a) Optical spectrum, (b) autocorrelation trace, (c) oscilloscope trace, and (d) radio-frequency spectrum of dual-wavelength DSs at P_f = 200 mW and P_b = 200 mW. The inset in (a) is the transmission spectrum of NOLM.

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Here ΔT is the time difference when two pulses with spectral separation of Δλ propagate through a segment of fiber with length of L and dispersion parameter of D. T₁ and T₂ are the round-trip times for two mode-locked solitons at wavelengths of λ and λ + Δλ. c and n are the speed of light in vacuum and refractive index of fiber, respectively. Δf is the difference of two fundamental cavity repetition rates that relates to separation of two peak in RF analyzer. Here, c = 3 × 10⁸ m/s, D_{SMF + EDF} = −3.95 ps/(nm.km), Δλ = 15 nm, n = 1.46, L = 63 m, and then Δf is calculated as 40 Hz based on the aforementioned parameters. The theoretical results well confirm the experimental observations.

To further investigate the polarization features of the pulses, an additional PC and a PBS external to the cavity are used for the experiments. The PC acts as a wave plate inducing controllable linear birefringence, and PBS can orthogonal-polarization resolve the output pulse [20]. With appropriate orientation of the PC, there is a position of maximum spectral intensity at horizontal-axis output of PBS. Meanwhile, the other output of PBS is that of vertical polarized pulse. The maximum intensity difference between two axes of the polarization-resolved spectra is about 20 dB, as described in Fig. 2(a). We note that the intensities of two mode-locked spectra decrease or increase simultaneously, indicating that the dual-wavelength DSs almost share the same polarization state. In a previous report [20], through rotating the external cavity polarizer it was identified that one spectrum could be completely suppressed while the other still remained. However, our experimental results show that the two group of DSs almost share the same polarization state, as is very distinct from that dual-wavelength vector DS that two spectra have orthogonal polarization state.

By fixing the PC states and appropriate decreasing the pump power, the single-wavelength DS is achieved from the dual-wavelength DS operation. The pink lines in Fig. 3 show a typical state at pump of P_f = 100 mW and P_b = 100 mW. Figure 3(a) shows the output spectrum. Compared with the dual-wavelength spectrum in Fig. 2(a), only one mode-locked spectrum is observed. The central wavelength of the DS is 1572 nm and the 3 dB bandwidth is ~10 nm, respectively. Figure 3(b) is the autocorrelation trace of the single-wavelength DS. The FWHM of the DS is 3.63 ps by using Gaussian fit. Thus, the time-bandwidth-product of the pulse is estimated as 4.4, which indicates that the output DS is highly chirped. Figure 3(c) shows the pulse trains of single-wavelength operation. The spacing between the adjacent pulses is ~300 ns, corresponding to the fundamental repetition rate of 3.278 MHz. The RF spectrum in Fig. 3(d) shows that the signal/noise ratio of the pulse is higher than 53 dB. From the oscilloscope train and autocorrelation trace, we confirms that the fiber laser operates at stable single pulse operation.

 

Fig. 3 (a) Optical spectrum, (b) autocorrelation trace, (c) oscilloscope trace, and (d) radio-frequency spectrum of single-wavelength dissipative soliton at 1572 nm (L) and at 1587 nm (R), respectively.

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With careful adjustment of PC states, we observe that the dual-wavelength DSs in Fig. 2 is changed to a single-wavelength DS, as described by the green curve in Fig. 3. Here, the pump powers are fixed at P_f = 200 mW and P_b = 200 mW. The central wavelength of DS spectrum is 1587 nm and the 3-dB bandwidth is estimated as ~10 nm. The FWHM of DS is about 3.84 ps if the Gaussian fit is used. In this case, the signal/noise ratio in RF spectrum is as large as 57 dB.

4. Formation mechanisms of dual-wavelength DSs

We have experimentally investigated the formation mechanism of the dual-wavelength DSs in our figure-eight fiber laser. In our experiments, we find that the dual-wavelength mode-locking is very sensitive to PC states, indicating that fiber birefringence plays a key role in the dual-wavelength operation [24]. The inset in Fig. 2(a) shows the transmission spectrum of NOLM. It is found from inset that the transmission spectrum have two peaks at ~1572 and ~1587 nm and a valley at ~1580 nm and the peak-to-valley ratio is about 4.5 dB. The modulation on the spectrum can be attributed to the birefringence-induced filtering effect. Due to the large fiber birefringence, two lights at contrary directions have slight different optical lengths. In the 30/70 coupler, two lights interfere with each other and the output spectrum is strongly modulated. Then, the dual-wavelength mode locking tends to be established at peaks of the transmission spectrum. Obviously, the mode-locked DS spectrum and transmission spectrum approximately have the same central wavelength and the same valley wavelength, which confirms the assumption that birefringence-induced filtering effect in NOLM results in the dual-wavelength mode locking.

5. Conclusions

In this paper, we have experimentally observed the dual-wavelength DSs in a passively mode-locked figure-eight fiber laser operating in net-normal dispersion regime. The proposed laser operates mode-locked state at central wavelengths of 1572 and 1587 nm simultaneously. The spectra of dual-wavelength DSs exhibit as double-rectangular profile with 3-dB bandwidths of ~11 and ~10 nm, respectively. The experiment observations show that the dual-wavelength DSs almost share the same polarization state, which is distinct from dual-wavelength vector pulses. It is demonstrated that dual-wavelength DSs mode locking mainly results from birefringence-induced filtering effect.