1. Introduction

When two or more intense optical fields with different wavelengths propagate simultaneously in an optical fiber, they will couple with each other through the fiber nonlinearity. The cross-phase modulation (XPM) is the most common way of coupling. While the XPM process always occurs and doesn’t cause energy transfer between the lights, therefore, referred to as an incoherent coupling, the four-wave-mixing (FWM) type of coupling occurs when the phase matching condition is fulfilled [1]. FWM involves in the energy transfer between the lights. Coupling of lights in a single mode fiber can result in a variety of interesting nonlinear optical phenomena, e.g. it is theoretically predicted by B. Malomed et al. that the incoherent coupling between two travelling plane waves could lead to the formation of optical domains [2, 3 ].

It is well known that due to the fiber bending and/or technical imperfection of fiber drawing, a single mode fiber always exhibits birefringence and hence supports two orthogonal polarization modes. The light propagation in a practical SMF also involves in the coupling between the two orthogonal polarization modes. It has been shown both theoretically and experimentally that the cross polarization coupling of light in a SMF could result in various effects, such as the polarization switching [4], polarization modulation instability [5], group velocity locked or phase locked vector solitons [6]. A fiber cavity is an interesting nonlinear system that possesses both the features of light propagation in SMFs and in a nonlinear cavity. The conventional soliton formation in the mode locked anomalous dispersion cavity fiber lasers is an effect that could be traced back to the nonlinear light propagation in the SMFs, which has been extensively investigated previously. The soliton period doubling route to chaos [7], soliton quasi-periodicity [8] were also observed in fiber lasers, which could be well understood based on the nonlinear cavity theory. Recently, Zhang et al. reported the induced soliton formation in a birefringence cavity fiber laser [9]. Tang et al. demonstrated the polarization domain formation in a quasi-isotropic cavity fiber laser [10]. Formation of these effects could be well explained based on the coherent or incoherent polarization coupling between the lights in the fiber cavity.

In this paper, we report on the experimental observation of soliton-dark pulse pair formation in a fiber ring laser. It was experimentally observed in a quasi-vector cavity fiber laser that due to the incoherent cross polarization coupling, a bright cavity soliton polarized along one principal cavity polarization axis could always automatically induce a dark pulse on the CW background of the laser polarized along the orthogonal polarization axis. The formation mechanism and features of the induced dark pulses are experimentally investigated. We show that the appearance of the dark pulse is a result of the incoherent cross polarization coupling between the soliton and the CW beam, its mechanism is similar to that of the polarization domain formation in the fiber laser.

2. Experimental setup and results

The fiber ring laser we used has a cavity configuration as shown in Fig. 1 . The fiber ring has a total length of 13.5 m, consisting of a piece of 3 m Erbium doped fiber (EDF) with a group velocity dispersion (GVD) parameter of −48 ps/nm/km, 9.7 m single mode fiber (SMF-28) with a GVD parameter of 18 ps/nm/km and 0.8 m of dispersion compensation fiber (DCF) with a GVD parameter of −4 ps/nm/km. The fiber laser is pumped by a 1480 nm single mode Raman fiber laser whose maximum output power is 5 W. A polarization independent isolator is inserted in the cavity to force the unidirectional circulation of light in the cavity. In addition, an intra-cavity polarization controller (PC) is used to fine-tune the linear cavity birefringence. A wavelength division multiplexer (WDM) is used to couple the pumping light into the cavity, and a 10% fiber output coupler is used to output the light. The components used in our experiment have very low polarization dependent loss (PDL) (WDM: 0.01 dB, Isolator: 0.04 dB, Coupler: 0.01 dB). Therefore, the PDL induced mode locking is unlikely to occur in our experiment [11]. The fiber ring cavity is estimated to have an average net anomalous GVD parameter of 2.03 ps/nm/km. An external cavity polarization beam splitter (PBS) is used to experimentally resolve the two orthogonal polarization components of the laser emission. To the end a polarization controller is inserted before the external polarization beam splitter to balance the linear polarization change caused by the lead-fibers. To appropriately set the PC orientation experimentally we first operate the laser in a stable polarization domain emission state. Based on the polarization switching between the domains we then carefully adjust the external PC position so that the two orthogonally polarized laser emissions can be well separated. The polarization resolved laser emissions are simultaneously monitored with a high-speed electronic detection system made of two 40 GHz photo-detectors and a 33 GHz bandwidth real-time oscilloscope.

 

Fig. 1 A schematic of the Erbium-doped fiber laser. EDF: Erbium-doped fiber. SMF: Single mode fiber. DCF: Dispersion compensation fiber. WDM: Wavelength division multiplexer. PC: Polarization controller.

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Under low pump power the laser always emits continuous wave (CW). However, depending on the net cavity birefringence, the laser emission could exhibit different polarization features. In the special case of very weak net cavity birefringence, the laser could emit an elliptically polarized beam. However, the most frequent situation is that the laser emits simultaneously CW along the two orthogonal polarization directions of the cavity. Carefully tuning the orientation of the intra-cavity polarization controller, which alters the net linear cavity birefringence, the oscillation wavelength difference between the CWs could be tuned. The experimental result suggests that the laser emission wavelength difference is related to the linear cavity birefringence. In our experiment we used the wavelength separation as an indication on the strength of the net cavity birefringence. Operating the laser under different pump strength and net cavity birefringence, we could experimentally observe various interesting features of the laser emission. At first, we operated the laser at very small net cavity birefringence and under a pump power of about 2 W, where the intra-cavity light intensity is about 630 mW. By carefully setting the orientation of the intra-cavity PC, it is experimentally observed that the CW emission along one polarization direction could suddenly break up into a periodic bright pulse train, and associated with each of the bright pulses there is a dark pulse formed on the CW background along the orthogonal polarization direction, as shown in Fig. 2(a) .

 

Fig. 2 Experimental results of soliton-dark pulse pair formation in a fiber laser. (a) The polarization resolved oscilloscope traces of the laser emission. (b) Polarization-resolved spectra. (c) Autocorrelation trace of the bright solitons. (d) The zoom-in oscilloscope traces of a soliton-dark pulse pair.

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The automatic formation of a periodic bright pulse train in the fiber laser could be understood as a result caused by the cavity induced mode beating. Due to the nonlinear light propagation in the fiber cavity, the oscillation frequency of the laser, the “hot” mode, varies with the light intensity, and it is in general different from the oscillation frequency of a weak beam, the “cold” mode. Both the cold and hot modes coexist in a fiber laser. Under suitable conditions they could beat. It has been shown numerically that such a beating in a fiber laser could lead to the periodic pulse train or even bright soliton pulse train formation [12]. In our experiment we have investigated the features of the formed bright and dark pulses. Figure 2(b) shows the polarization-resolved spectra of the laser emission. The spectrum of the light polarized along the horizontal polarization is significantly broadened. Its 3-dB bandwidth is estimated ~8 nm. Moreover, clear Kelly spectral sidebands are formed on the spectrum. Formation of the Kelly sidebands is a typical characteristic of the soliton operation of a laser [13]. The appearance of Kelly sidebands on the pulse spectrum unambiguously shows that the formed bright pulses are solitons. The central wavelength of the solitons is at 1578.76 nm, which is different from that of the CW laser emission of the same polarization direction. So far we have not understood why the central soliton wavelength is far away from that of the CW. We suspect it could be due to that the soliton and the CW beam have different loss dispersion in the cavity. Due to the weak net cavity birefringence, the CW wavelengths of the laser along the two orthogonal polarization directions are almost the same, which is at ~1575.7 nm. The spectra of the CW lights are also slightly broadened. From the traces shown in Fig. 2(a), one can observe that the CW background is very noisy. This is due to the modulation instability of the beam, which occurs when the CW intensity is high and has a high modulation frequency [1]. This also explains why the spectra of the CW components are broad. Experimentally we measured the average output power of the laser emission along the two orthogonal polarizations. It has a ratio of about 1:6 (bright soliton side: dark pulse side).

Figure 2 (c) shows the autocorrelation trace of the bright solitons. It has a FWHM width of about 0.558 ps, suggesting that the width of the solitons at the laser output is about 362 fs if a Sech-shape pulse profile is assumed. Thus the time-bandwidth product (TBP) of the pulses is 0.348, which means that the solitons are slightly chirped. Figure 2(d) shows the zoom-in of a dark pulse. Different from the bright solitons, the dark pulses are broad intensity ‘holes’ embedded in the CW background. In our experiment if the total laser emission is measured, the oscilloscope trace then shows a dark-bright pulse pair on the CW background. A similar dark-bright pulse pair emission was also observed on a figure-of-eight fiber laser, and it was found that the dark and bright pulse belongs to different wavelength bands of the laser emission, respectively [14]. Experimentally we found that the dark pulse width decreased with the increase of the CW power and the coupling strength between the two polarizations. Under our experimentally accessible pump strength, dark pulses as narrow as several tens of picosecond could be obtained. However, the dark pulses are significantly broader than the bright pulses. Slightly tuning the intra-cavity PC or carefully reducing the pump power, the number of solitons in the cavity could be changed and the periodic pulse train could also become inhomogeneous. Nevertheless, no matter how the bright solitons are distributed in the cavity, corresponding to each bright soliton there is always a dark pulse appeared on the CW background. Here we note that if one observes the oscilloscope trace under a large time scale or using a low-speed detection system, this kind of soliton-dark pulse pair would look like a ‘bright-dark soliton pair’ [15, 16 ].

We then operated the laser under relatively large net cavity birefringence. In this case the wavelength separation between the two orthogonally polarized CW emissions has a large value. Figure 3 shows the case experimentally observed. Figure 3(a) shows the oscilloscope traces of the laser emission along the two orthogonal polarizations. Figure 3(b) is the polarization resolved optical spectra. As a result of the incoherent cross coupling between the two orthogonally polarized CW components, polarization domains are formed, characterized as the intensity alternation of the CW laser emissions between the two orthogonal polarization directions. We have shown previously that the appearance of the polarization domains is an intrinsic feature of the fiber laser emission under the incoherent coupling of the two orthogonal polarization modes [10]. However, in the current state as a result of the strong pumping, simultaneously a periodic bright soliton train is also formed on one polarization direction. The bright soliton train fills up the whole cavity. Again the formed bright solitons have different central wavelength than the CW component. When the oscilloscope is triggered by the edge of the polarization domain shown in the upper trace, the bright solitons move with respect to the polarization domain. It is to point out that in the polarization domain where there is coupling between the bright solitons and a CW beam polarized along the orthogonal polarization direction, the bright solitons induce dark pulse formation on the CW background, as shown in Fig. 3(a). Zooming in the region of the coupled soliton-dark pulse pairs, again corresponding to each bright soliton there is a dark pulse. Moreover, the dark pulses have a much broader pulse width than the bright solitons.

 

Fig. 3 The soliton-dark pulse pairs formed in a polarization domain where there is incoherent coupling between solitons and a CW beam. (a) Laser emissions along the two orthogonal polarization directions. (b) The corresponding polarization resolved spectra.

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The “soliton rain” is an interesting feature of the soliton fiber laser operation whose formation mechanism is not yet clearly explained [17]. Under the same pumping power, by appropriately setting the orientation of the intra-cavity PC, the soliton rain feature is also observed on the formed bright solitons in our fiber laser, as shown in Fig. 4 . Because of the incoherent coupling of the orthogonally polarized CW components, polarization domains are formed. On one polarization bright solitons are formed. In particular, the formed bright solitons exhibit the soliton rain feature where the solitons move with accelerated speed away from the soliton condensate. Again, each bright soliton induces a dark pulse on the orthogonally polarized CW. Consequently the dark pulses also exhibit the similar pulse evolution.

 

Fig. 4 The soliton rain effect of the soliton-dark pulse pairs. The two oscilloscope traces are the polarization resolved emissions of the fiber laser.

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3. Discussion

Our experimental results clearly demonstrate that as a result of the cross polarization coupling, a bright soliton could induce the formation of a dark pulse. To understand the dark pulse formation in our laser we note that the polarization domain formation is an intrinsic feature of the quasi-vector cavity fiber lasers under the cross polarization coupling. Required by the system minimum energy condition, within one polarization domain the laser would only emit in one polarization state. A soliton-dark pulse pair could be considered as a special case of the polarization domains, where the appearance of a soliton in one polarization will demand a temporal no lasing, or an intensity hole, on the orthogonal polarization direction. Hence, a dark pulse will always be formed associated with a bright soliton. We note that D. N. Christodoulides had once theoretically predicted the formation of a kind of black-white soliton pair in weakly birefringent SMF under coherent polarization coupling [15]. Although the bright soliton and the dark pulse observed in our experiment are coupled, their coupling is incoherent. Moreover, the formed dark pulses have an asymmetric pulse form and a much broader pulse width than the bright solitons. It is unlikely that the observed dark pulses are dark solitons.

In our fiber laser as there is no any mode-locking element in the cavity, so no mode locking could occur. We suspect that the bright soliton formation is initialed by the nonlinear beating between the “hot” and “cold” cavity modes under the gain bandwidth limitation. This also explains why initially a stable soliton pulse train is always formed in our laser. It is also a unique feature of the fiber laser that differs from the soliton operation of the mode locked fiber laser. Finally, we point out that the observed bright soliton-dark pulse pair formation is independent on the concert laser cavity parameters. Actually under different cavity conditions (different cavity length, net anomalous dispersion) we have observed the phenomenon, which shows that it is a general effect of the fiber lasers.

4. Conclusion

In conclusion, we have experimentally observed the formation of soliton-dark pulse pair in a birefringent cavity fiber laser. It is found that due to the incoherent coupling between the two orthogonal polarization modes of the fiber cavity, a bright soliton pulse always induces a dark pulse on the CW background polarized along the orthogonal polarization. In particular, the formed soliton-dark pulse pairs are stable in the cavity. The features of the formed bright solitons and dark pulses were experimentally investigated. Under our experimental accessible conditions it is found that the formed dark pulses always have a broader pulse width than the bright solitons. We pointed out that the mechanism of the dark pulse formation could be understood based on the polarization domain formation.