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Abstract
We report the dynamics of dissipative solitons in a ring cavity passively mode-locked fiber laser with a strict control of the polarization state. We study the relation between the polarization state of the pulses propagating in the cavity and the regimes of generation. We have found that at pulse ellipticities between 5° and 15°, the laser generates one bunch of pulses in the cavity, while at higher ellipticities the laser generates multiple bunches. At constant ellipticity we rotated the polarization azimuth and observed a regime transition from the generation of noise-like pulses (NLP) to that of soliton crystal. The NLP regime was found when the azimuth was rotated towards smaller low-power transmission through the polarizer. The number of solitons in the soliton crystal also depended on the azimuth in a straightforward way: the higher the initial transmission, the bigger the number of solitons.
© 2017 Optical Society of America
Introduction
Passively mode-locked fiber lasers were shown to operate in a wide variety of regimes [1,2] which include the generation of a single soliton in the cavity [3–5], multiple solitons [6,7] and complex patterns of solitons. Among them the generation of two bound solitons [8,9], multiple bound solitons [10], and very long packets of solitons with uniform spacing, named crystals of solitons [11], were evidenced. Besides, quasi stable patterns of solitons involved in dynamics such as the soliton rain [12], and noise-like pulses (NLP) [13,14] were also demonstrated in experiments. The regime of generation depends on many factors, such as cavity dispersion, amplification of the active fiber, attenuation caused by all elements inserted in the cavity, and nonlinearities. Lot efforts were done in the laser modeling to find the dependence of generation regimes on laser parameters, see for example Ref [15]. and references therein. Some regimes such as the dissipative soliton resonance (DSR) [16] and spiny solitons [17] were predicted first by the modeling.
Experimental investigations of the dependence of the regimes on the laser parameters is complicated by the uncertainty of the laser parameters. A very important aspect is the polarization dynamics of the pulses and the birefringence of the elements included in the cavity. In many cases desired regime of the laser can be found by proper adjustment of the polarization controllers inserted in the cavity. Several papers were published where switching between different regimes through PC adjustments was demonstrated. X. Zou et al. demonstrated the switching between Nth-order harmonic mode locking (N equally spaced pulses in the cavity) and the generation of “giant pulses” made of N bound solitons by adjusting the in-line polarization controller in the cavity [18]. M. Han et al. showed a switching between different regimes in a laser with graphene as mode locker [19]. V. Tsatourian et al. analyzed the different polarization dynamics in a ring laser cavity with carbon nanotubes as mode locker [20]. The transition from DSR to single soliton was observed in [21]. However, in most published papers the appropriate position of the PC was found randomly.
In this work we report an investigation on the dependence of the regime of generation on the polarization state in a ring cavity laser using nonlinear polarization rotation (NPR) for mode-locking. We used twisted fiber in the cavity to maintain constant the ellipticity of polarization, which allowed a strict control of the polarization state. We have found that at small ellipticity the laser generates one bunch of solitons (a soliton crystal or NLP) in the cavity, while at higher ellipticity the laser generates multiple bunches in the cavity. We focused on the regime of one bunch in the cavity and investigated how the pulse shape depends on the initial azimuth of polarization (the azimuth which prevails before mode-locking starts). This azimuth determines the initial transmission through the polarizer. We have found a regular transition from NLPs for low initial transmission to a soliton crystal for higher initial transmission. The number of solitons in the soliton crystal grew with increasing of the initial transmission through the polarizer.
Experimental setup
The experimental setup is shown in Fig. 1. The ring cavity includes a double pass amplifier, a 10-m long twisted (6 turn/m) SMF-28 fiber, a 50/50 coupler, a LiNbO3 phase modulator which is also used as a polarizer, a polarization controller (PC1, made by coiling the fiber on plates), and an in-line polarization controller (PC2) model PLC-900, Thorlabs. The RF signal was applied to the phase modulator only at the beginning to start mode-locking. After mode-locking was started the RF signal was turned off and the phase modulator was used as the polarizer. The linearly polarized light at the modulator output is transformed into circularly polarized light by PC1 and then into elliptically polarized light by PC2. Using PC2 we can adjust polarization ellipticity by pressure applied to the fiber and independently the azimuth by rotation. The double pass amplifier includes an optical circulator, a 45-cm long erbium doped fiber (EDF) with an absorption coefficient of 80 dB/m at 1530 nm, and a Faraday mirror (FM). The use of FM allows compensation of the birefringence so that the polarization at the circulator output is orthogonal to the polarization at the circulator input independently on the birefringence changes in the fibers. It is particularly important because the birefringence of EDF depends on pump power [22]. A 980-nm laser diode used as the pump was coupled to the EDF through a wavelength division multiplexer (WDM). The use of twisted fiber allows maintaining the polarization ellipticity along all fiber length. The ring cavity is composed by the 16.7-m standard single mode Corning SMF-28 fiber with the value of total dispersion of 0.3 ps/nm. This length includes the 10-m twisted fiber and ports of couplers and other elements of the cavity. The cavity includes also the 2-m OFS-980 fiber (the ports of WDM), which gives the dispersion of −0.013 ps/nm for the double pass in the amplifier, the 0.45-m EDF with dispersion of 0.006 ps/nm for the double pass, and the 0.4-m PM panda fiber at the input of the modulator with dispersion approximately 0.001 ps/nm. The total cavity length is ~22 m with net anomalous dispersion of approximately 0.29 ps/nm. At Output-P we measured the state of polarization in the laser cavity. The pulse duration was measured with an autocorrelator (FR-103XL) at Output-1 where a polarization controller, PC3, is used to adjust the polarization required for the autocorrelator. The optical spectrum was measured at Output-2. The output pulses were detected by a 1-GHz photodetector with a 1-GHz oscilloscope at Output-3, and by a 10-GHz photodetector with a 20-GHz sampling oscilloscope at Output-4. Output-5 was used for triggering the sampling oscilloscope.
Results and discussions
The basic mechanism of mode-locking in ring fiber lasers is the nonlinear rotation of polarization from an azimuth corresponding to low transmission through the polarizer to an azimuth corresponding to higher transmission. The rotation angle depends on power, fiber length and ellipticity. Mode locking also depends on the initial transmission through the polarizer for low-power radiation. To begin we rotated PC2 and determined the azimuth of the polarization at the Output-P for minimal and for maximal transmission of low power radiation through the polarizer. In the following results, the angle for minimal transmission is referred to as 0° and the angle for maximal transmission as minus 90°. NPR in our experiments rotates the azimuth towards negative angles. To start mode locking we adjusted ellipticity by PC2, set the azimuth to 0°, set the pump power to ~230 mW, and then rotated the azimuth towards maximal transmission (−90°) until the mode-locked operation started. This procedure was repeated for different ellipticities. The black circles in Fig. 2(a) show the azimuths at which mode locking started for each tested initial ellipticity; the red circles show the azimuths and ellipticities of pulses after mode locking started. The corresponding initial and final points are connected by lines. We expected that ellipticity would not be modified when mode locking is started, however we observed that it changed slightly. It means that some degree of linear birefringence is still present in our setup. The results obtained by using the same procedure, but starting now from the azimuth corresponding to maximal initial transmission, are shown in Fig. 2(b). In this case we rotated the azimuth from −90° towards 0°. We can see from the figures that mode locking can be obtained for a wide range of ellipticities, from ~5° (close to linear polarization) to ~40° (close to circular polarization). In the case when we are searching for mode locking by rotating the azimuth from minimum to maximum transmission, Fig. 2(a), the initial azimuth varies with ellipticity from ~-70° to −30°, while in the second case, Fig. 2(b), the initial azimuth is about −85° for ellipticities ranging from ~5° to ~30°, and then varies from ~-85° to ~-40° for ellipticities between ~30° and ~40°.
Fig. 2 Area where the mode-locking starts. To start mode-locking the azimuth is rotated: (a) from minimum to maximum of the polarizer transmission, and (b) from maximum to minimum of the polarizer transmission. Black circles show the initial state; red circles – final state.
The values of the azimuth and the ellipticity allow the calculation of the initial (before mode locking is started) and final (after mode locking is started) transmissions through the polarizer. The Fig. 3(a) displays the initial and final transmissions through the polarizer calculated from the data of Fig. 2(a). It is easy to show that the angle of the NPR can be defined by the equation:
where: P is power, γ is the nonlinearity coefficient of the fiber, z is the fiber length, and e is the ellipticity measured in degrees. Using this equation, we can estimate the peak power of pulses that required to switch the transmission from the state shown by black circles to the state shown by red circles on Fig. 2. The result of the estimation is shown on Fig. 3(b). We see that the power grows smoothly when the ellipticity increases from 5° to approximately 35° and then drops abruptly.Fig. 3 Transmission through the polarizer before (black circles) and after (red circles) mode locking is started (a) and power required to switch the transmission (b).
After obtaining the mode locking we rotated the azimuth at fixed ellipticity and observed the change of the generation mode. This procedure was followed for different ellipticities. The summary of generation modes is depicted in Fig. 4. Depending on the polarization state we observed mainly three modes of generation: a single soliton crystal (black circles), a single noise-like pulse (red circles), and multiple pulses in the cavity (blue circles). The results show that at small ellipticities, between 5° and 15°, the laser has a tendency to generate a single bunch of pulses in the cavity, while at higher ellipticities multiple bunches in the cavity tend to be generated. At ellipticities of 20° and 25° only NLP are generated as a single pulse in the cavity.
Fig. 4 Summary of the generation modes obtained in the laser. Red circles – the single noise like pulse in the cavity; black circles – the single soliton crystal in the cavity; blue circles – multiple pulses in the cavity.
For each initial azimuth we measured the angle of NPR. The Fig. 5 depicts the angles of NPR for different initial states of polarization. We can see that the angle of NPR depends on the initial azimuth, decreasing for initial azimuths closer to the maximum transmission through the polarizer. The dependence of the angle of NPR on the initial azimuth can be linearly fitted as displayed in Fig. 5, revealing that the slope (m) of the dependence increases with the ellipticity. The Fig. 5(a) shows the results for the case of a single bunch in the cavity; the results shown in Fig. 5(b) were obtained for multiple bunches in the cavity and represent some averaging of nonlinear rotation angles of several pulses in the cavity.
Fig. 5 The nonlinear polarization rotation angles: (a) small ellipticities and (b) higher ellipticities. “m” is the slope of the linear fit.
Using Eq. (1) we can estimate the peak power of pulses at different polarization states. The result of the calculation is shown in Fig. 6. For calculations we used a value of nonlinearity coefficient equal to . These results give us some expectation of the pulse power for several ellipticities when the initial azimuth is set at different values. The calculations show that the peak powers become smaller when the initial azimuth values approach the maximum of the polarizer transmission.
The average power of the laser was about 14 mW and did not depend substantially on the initial azimuth so the pulse energy can be considered as a constant. If the pulse energy is maintained constant when the pulse power decreases, we can expect that the number of pulses in the soliton crystal becomes bigger when the azimuth is closer to the maximum transmission and the peak power is smaller. This was confirmed by the measurements, see Fig. 7 were the oscilloscope traces are shown for an ellipticity of 15° and different initial azimuths. The number of pulses is 38 at the azimuth of 80° and 29 at the azimuth of 70°. All traces show an increment of distance between adjacent solitons from the initial part to the end of the soliton crystal. The distances at the beginning of the soliton crystal are 65ps, 77ps, and 71ps and at the end of the soliton crystal the distances are 141ps, 177ps, and 186ps for initial azimuths of −70°, −75°, and −80°, respectively. For other ellipticities and azimuth values the soliton crystal display a behavior similar to that depicted in Fig. 7, with small differences in the distance between solitons.
The Fig. 8 shows the spectra and the autocorrelation traces corresponding to the temporal profiles of Fig. 7 with ellipticity of 15°, yielding values of FWHM equal to 3.9 nm and 1.35 ps, respectively. The results for ellipticity of 5° and 10° are similar, with a spectral bandwidth of ~3.5nm and autocorrelation traces with FWHM duration of ~1.36 ps for both cases. The peaks on each side of the central peak in Fig. 8 (b) confirm the separation of ~75ps between solitons at the leading edge of the soliton crystal shown in Fig. 7.
Fig. 8 Measurements for the ellipticity of 15°: (a) normalized spectra, and (b) autocorrelation trace for the azimuth of 70° (the inset shows close up of the central peak).
For the initial conditions marked by red circles in Fig. 4 we observed the transition between the generation of soliton crystal and the generation of NLPs. The oscilloscope traces are shown in Fig. 9. Black lines show the traces obtained in single shot regime; red lines show the average traces. Because of the use of the sampling oscilloscope, the single shot traces do not show exactly one single pulse. However the comparison of single shot traces and averaged traces makes it possible to conclude that the pulses consist of large numbers of separated pulses which are moving randomly within their envelope. The duration of the envelope decreases with ellipticity increasing. The Fig. 10(a) shows the typical NLP double-scaled autocorrelation traces. However the pedestal of the autocorrelation function is less than a half of maximum. The FWHM of the narrow peak is about 1.5 ps for all cases. The value of the pedestal grows for higher ellipticity. The Fig. 10(b) shows the spectra of the pulses with FWHM of 3.2nm, 3.8nm and 4.5nm for ellipticities of 5°, 10° and 15°, respectively. The spectra of the pulses reveal Kelly side bands which are a characteristic feature for soliton generation. However the amplitude of the Kelly side bands decreases with increasing ellipticity. The spectra and autocorrelation traces show that the characteristics of the pulses approach those of NLP at higher ellipticities.
Fig. 9 Waveforms of NLPs for different polarization states. The black lines show single-shot oscilloscope traces; the red lines show average oscilloscope traces. The ellipticities and initial azimuth are shown in the figures.
Fig. 10 Autocorrelation traces (a) and spectra (b) of NLPs at different ellipticities. Inset shows close-up on central peak of autocorrelation traces. Initial ellipticities and azimuths are shown in the figures.
It is important to understand under which conditions the transition between different regimes of generation is observed. This issue is not clear yet, in spite of the large amount of experimental and theoretical investigation that was published. The reason is the complexity of the laser operation which depends on many parameters some of which are not well known. Our configuration allows maintaining the polarization state stable and well known, which makes it possible to investigate the transition conditions. In the experiment we observed the transition from a single NLP to a single soliton crystal in cavity, and the transition from a single pulse to multiple pulses in cavity. The former was observed at pulse ellipticities of 5, 10, and 15 degrees. It occurs when the azimuth is rotated in the direction of the transmission maxima of the polarizer, thus increasing the transmission through the polarizer.
Figure 11(a) shows the dependence of the transmission on the power for pulse ellipticity of pulses of 15° and two value of the azimuth: 65° – red line, and 70° – black line. The red and black lines correspond to the generation of NLP and the soliton crystal respectively. The dependence at which the generation of the soliton crystal is observed has a value of saturation power lower than the dependence corresponding to NLP. As the azimuth was rotated, when mode locking first appeared we observed a NLP with peak power defined by transmission characteristics, in particular the saturation power. When we further modify the azimuth and reduce the saturation power, the pulses start to be clamped by the saturation power. This cause the transition from NLP to soliton crystals. It is interesting to note that NLP in our experiments were observed at quite different transmission characteristics. Figure 11 (b) shows the transmission characteristics corresponding to the red circles in Fig. 4. We see that the saturation power decreases from 400 W to 150 W when ellipticity increases from 5° to 25°, however the estimated pulse power increases from approximately 70 – 80 to approximately 120 W over that range. The increase of the estimated power with ellipticity is consistent with the measurements of the spectra, Fig. 10 (b), where we can see that the spectral bandwidth grows with ellipticity. This result to some extent contrasts with previously reported investigation of the dependence of the NLP characteristics on the saturation power in F8L configuration [23] and with the model of the NLP formation based on the soliton collapse [24,25].
Fig. 11 (a) Transmission through the polarizer at the point of transition from NLP (red line) to soliton crystal (black line). (b) Transmission corresponding to the generation of NLP at different ellipticities of the pulse. The ellipticity values are shown in the figure.
Conclusions
We investigated the mode locking regimes of a fiber ring laser with strict control of the polarization state in the cavity. The strict control makes it possible to investigate how the generation mode depends on the polarization state. We have found that at relatively small polarization ellipticity, between 5° and 15°, the laser operates with a single bunch of pulses in the cavity, whereas for larger values of ellipticity multiple bunches appear in the cavity. We also found that the value of initial (low-power) transmission through the polarizer (which is defined by the polarization azimuth) strongly affects the operation mode. For lower initial transmission the laser tends to generate NLPs. An increase of the initial transmission results in the generation of the soliton crystal. The number of solitons in the crystal was found to depend on the initial transmission through the polarizer and increases with its increasing. Pump power was maintained constant in the experiments; the average power in the laser was nearly constant in all experimental conditions.
Funding
Consejo Nacional de Ciencia y Tecnología project 237855.
Acknowledgments
H. Santiago-Hernandez thanks Consejo Nacional de Ciencia y Tecnología postdoctoral fellow 298828.
References and links
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