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We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.
© 2016 Optical Society of America
1. Introduction
Passively mode-locked fiber laser as a flexible source of ultrafast optical pulses has been widely investigated over past decades, due to its advantages of compact size, high stability, and simple configuration [1–4]. In addition, such lasers act as a convenient experimental platform for the investigation of nonlinear waves subject to periodic boundary conditions and easy operation. In order to achieve self-started mode-locking, various techniques have been proposed, including the nonlinear polarization rotation (NPR) [5], nonlinear loop mirror (NOLM) [6], semiconductor saturable absorber mirror (SESAM) [7], and various two-dimensional optical materials [8–10]. Among those mode-locked techniques, the NPR technique has been commonly adopted, due to its comprehensive phenomena and easy implementation [11]. Because of the requirement of the polarization sensitive component in a NPR cavity, theoretically a scalar model is enough to describe the fiber laser even it is well known that a single mode fiber (SMF) always supports two orthogonal polarization modes. The theoretical results from the scalar model agree with the experimental observations very well. Therefore, the solitons generated from a NPR cavity are always considered as scalar solitons [12]. Light polarization is a traditional but newly discovered very useful feature for telecommunications [13, 14]. Polarization properties of ultrashort pulses are newly explored, which shows a distinctive regime for pulse generation. Therefore, a strong motivation to search for this new regime arises. On most occasions, due to the asymmetrical structure and bending, the birefringence of SMF gives rise to the differences of two orthogonal polarization modes in term of both phase and group velocities [15–17]. On the other hand, when the soliton propagates periodically within a laser cavity, phase locking between two orthogonal polarization modes can be achieved, leading to the generation of vector soliton [18–20]. Consequently, for a fiber laser without polarization sensitive components, it favors the generation of vector solitons. The dependence of the cavity birefringence versus the vector soliton generation and features are comprehensively investigated at different wavelengths [21, 22]. In order to generate vector solitons, polarization dependence of the laser cavity should be avoided as much as possible. Until now, SESAM and carbon nanotube (CNT) are the commonly-used mode-lockers to obtain vector soliton arising in the passively mode-locked fiber lasers [23–28]. Topological insulators can also be used as the saturable absorber for vector soliton generation [29]. Due to the absence of the polarization constraints, two orthogonal polarization modes in the fiber laser can develop freely. Therefore, much enriched characteristics emerge from vector soliton fiber laser compared with the scalar one [30, 31]. Local strong birefringence does not affect the polarization dependence. Therefore, it is possible to introduce fast polarization evolution during pulse propagation in a fiber laser with low average birefringence. Visible time delay may accumulate if a local strong birefringence is applied. Different from the mode-locking using physical saturable absorbers, for the case of NPR-based mode-locking, the use of inline polarizer restrains the pulse polarizations. Therefore, it is always considered that such type of mode-locked lasers could only generate scalar solitons. In fact, the pulse can exhibit vector characteristics at specific positions within the laser cavity. Here, we present our theoretical prediction and experimental demonstration, which shows an entirely new operation regime where the pulse develops into vector along the local strong birefringence fiber segment, and following polarization filtering, evolves into a scalar soliton and maintains its polarization in the rest of the cavity, when the fiber has weak birefringence. The scalar and vector characteristics are verified from the variation of corresponding optical spectra and autocorrelation traces by the use of an all-fiber polarization resolved measurement. All passively mode-locked lasers are generally outputted with either vector or scalar solitons after pulse propagation within the cavity. However, for our laser, distinctly vector solitons and scalar solitons co-exist, indicating that transitions between them are possible. The experimental results agree well with our numerical simulation. Compared with previous researches [32, 33], which also perform simulation and experiment about the generation of vector solitons, we first simultaneously realize the generation of vector and scalar solitons and investigate their evolution within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is novel and likely to be applied in various other nonlinear systems. Moreover, this experimental configuration is robust against perturbations.
2. Numerical simulations
We first perform the numerical simulations, based on the standard configuration of NPR-based fiber laser with two output ports, as shown in Fig. 1. A 2.2-m erbium-doped fiber (EDF) with a group velocity dispersion (GVD) parameter of −18 (ps/nm)/km is utilized as the gain medium, which is pumped via 980/1550 wavelength division multiplexing (WDM) by a 976-nm laser diode (LD) with maximum output power of 750mW. The fiber pigtailsof optical components are 15-m standard SMF with a GVD parameter of 17 (ps/nm)/km. Therefore, the ring cavity is at anomalous dispersion region, and the total cavity length is around 17.2m. The beat length of the EDF is about 5cm and that of the standard SMF is about 10m. The absorption coefficient of the EDF is around 21.9dB/m at 980nm. Two polarization controllers (PCs) together with an inline polarizer are used to implement the NPR-based mode-locking. The polarization-independent isolator is used to guarantee unidirectional propagation and suppress detrimental reflections. For the ease of simultaneously monitoring both the scalar and vector soliton within the same laser cavity, two optical couplers (OCs) with a power ratio of 20:80 are separately set before and after the polarizer. Following the output, the PC3 along with an inline polarization beam splitter (PBS) is used to implement all-fiber polarization resolved measurement. The laser operation is simulated based on the coupled Ginzburg-Landau equations, which describe the pulse propagation. The pulse propagation in fibers is governed by:
where and are normalized envelopes of the pulse along two orthogonal polarizations. is the wave number difference between two modes.is the inverse group velocity difference. is the second-order dispersion coefficient, is the third-order dispersion coefficient, and is the fiber nonlinearity coefficient. andrepresent the saturable gain coefficient and gain bandwidth of the EDF, respectively. We consider the gain saturation as:where is the small signal gain coefficient and is the normalized saturation energy. The parameters are set as follows:, ,,, , and .
Fig. 1 Schematic illustration of the experimental setup including both the laser cavity and polarization resolved measurement.
The mode-locking can be achieved under the condition of G = 1300. It is found that at the OC1, steady pulses with linear polarization are obtained. In other words, no matter how much the phase delay is introduced by the PC3, the horizontal spectrum always resembles the vertical spectrum after the all-fiber polarization resolved measurement, as shown in Fig. 2.
Fig. 2 Numerical simulation of the output spectrum of the polarization-resolved projections from the OC1.
However, it is found that at the OC2, two polarization-resolved outputs after the PBS have different spectra and pulse durations, as shown in Fig. 3. A pulse with a two-humped peak along one polarization and a single-humped peak along the orthogonal polarization can be observed, as shown in Figs. 3(a), 3(c), and 3(e). The spectral dip is formed due to the interference between two humps. Figure 3(b) shows a strong spectral dip at central wavelength, indicating a 180-degree phase difference. In addition, due to the gradual variation of the phase delay introduced by the PC3, the dip could move away from the central wavelength, as shown in Figs. 3(d) and 3(f). The details from Fig. 3 suggest that the pulse obtained at the OC2 is a vector soliton where the two orthogonal components of the vector soliton have certain time delay [34]. Obviously, the inline polarizer acts as a polarization selection component in the cavity. Therefore, the pulse after the polarizer will always be shaped into a scalar soliton, and then recirculates within the cavity. A linearly polarized pulse or a scalar soliton will be transformed into an elliptically polarized pulse then back to its originally linear polarization at every beat length. The time delay between two orthogonal polarizations arising in the fiber birefringence is generally neglected due to the weak birefringence. However, it is not the case here. Due to the strong local birefringence of the EDF, the time delay accumulating for two polarizations during propagation could not be ignored any more. Although the central wavelength of two orthogonal polarizations still keeps the same, the evident time delay makes them form a vector soliton. Consequently, a cycle is fulfilled. Therefore, the output from OC2 shows features distinct from that of the OC1, under the all-fiber polarization resolved measurement. After passing through the PBS, under a specific condition, the projection of the vector soliton may have single peak with maximum intensity, while the orthogonal projection shows a structure of two humps with a 180-degree phase difference, leading to the evident spectral dip at the central wavelength, as shown in Fig. 3(b). Additionally, when we set the beat length of EDF the same as SMF, the output from the OC2 always presents similar characteristics with that of the OC1. This strongly confirms that the strong local birefringence of EDF is the key issue in this scalar-vector soliton generation regime.
Fig. 3 Numerical simulation of the output spectrum of the polarization-resolved projections from OC2. (a)(c)(e) Intensity profiles and (b)(d)(f) corresponding optical spectra. (a)(b) Two orthogonal components with a 180-degree phase difference. (c)(d)(e)(f) The movement of pulse profile and spectral dip by gradually changing the phase delay introduced by the PC3.
3. Experimental results and discussions
Encouraged by the simulations, we build up the proposed fiber laser as shown in Fig. 1. An optical spectrum analyzer (OSA, Yokogawa AQ6370C-20) with a resolution of 0.02nm and a 1-GHz oscilloscope (OSC, Agilent DSO9104A) together with a 2-GHz photodetector (PD) are applied to monitor the optical spectrum and the temporal trace, respectively. Additionally, the pulse duration can be measured by a commercial autocorrelator (Femtochrome FR-103HS). We set the pump power at 160mW, and carefully adjust the PC1 and PC2. The stable mode-locking can be easily achieved. To exclude the complications caused by soliton interactions, we reduce the number of solitons in the cavity by carefully decreasing pump power to 100mW, so that only one soliton remains in cavity. The average output power from OC1 and OC2 are 1.8mW and 2.6mW, respectively. The reduced output power comes from the loss of the used polarizer. Experimentally we reproduce all the details from the simulations. The direct output from the OC1, two polarization-resolved outputs are shown in Fig. 4(a). The optical spectra of two resolved polarizations after the PBS always move simultaneously with one rising up and the other falling down. We can achieve the maximum power of one direction, while the other is reduced to the lowest, as shown by the red and blue solid lines in Fig. 4(a). It is obvious that the spectra only have intensity difference while the spectral profile is maintained. The central wavelengths of the direct output and of the polarization-resolved outputs are the same. The polarization extinction ratio (ER) of PBS is about 30dB. Therefore, we are confident to conclude that the direct output from the OC1 has fixed linear polarization, which can be defined as the scalar soliton. Meanwhile, Fig. 4(b) shows the corresponding autocorrelation traces and pulse-trains. The full-widths at half maximum (FWHM) of two orthogonal polarizations are both 0.9ps if a sech2 pulse profile is assumed. The pulse-trains, as shown in the inset, present consistent peak intensity with a repetition rate of 11.76MHz, which corresponds to the cavity length. The intensity of the pulse trains of the two resolved polarizations simultaneously rises and decreases when the PC3 is tuned. When one resolved polarization reaches the maximum, the orthogonal polarization is close to zero.
Fig. 4 (a) Experimental optical spectra of the two orthogonal axes from the OC1 before and after the PBS. Exampled normal state: the horizontal axis (red dot) and vertical axis (blue dot). Maximum-minimum state: the horizontal axis (red solid), vertical axis (blue solid) and total spectrum (black). (b) Experimental autocorrelation traces and pulse-trains from the OC1 before and after PBS. Horizontal axis (red), vertical axis (blue) and total pulse profile (black).
The output from the OC2 is also examined following the same procedure. By adjusting the PC3, we can no longer observe entire extinction in any polarization direction. Instead, when the spectrum of one direction decline to the lowest, it appears an evident spectral dip at the central wavelength, as shown by blue line in Fig. 5(a). The red line illustrates that no such dip appears at the spectrum of its orthogonal direction. Additionally, the dip could be moved to either edge when the PC3 is rotated, as shown by the green and purple dot line. To identify the source of the spectral dip, we further measure the corresponding autocorrelation traces, as shown in Fig. 5(b). Note that the vertical direction has a double-humped intensity profile, which is similar to a bound state soliton [35–37]. The FWHM of the humps is about 0.48ps, and the separation between the humps is about 0.64ps. The horizontal direction has a sech2 profile with a FWHM of 0.44ps. Based on the autocorrelation measurement, we can infer that the direct output from the OC2 is a vector soliton with two orthogonal components having 0.64ps time delay [34]. The spectral dip is formed due to the anti-phase projections of the vector soliton along the two polarization directions of the PBS. The deepest dip at the central wavelength indicates that the two anti-phase projections have the same amplitude.
Fig. 5 (a) Experimental optical spectra of the two orthogonal axes from the OC2 before and after the PBS. The horizontal axis (red), vertical axis when two polarized components have a 180-degree phase difference (blue), vertical axis with dip movement (purple and green) and total spectrum (black). (b) Experimental autocorrelation traces and pulse-trains from the OC2 before and after PBS. Horizontal axis (red), vertical axis (blue), and total pulse profile (black).
4. Conclusion
We propose a simple and convenient configuration to investigate a novel mode-locking regime of an erbium-doped fiber laser, with scalar soliton and vector soliton propagation occurring in each half of the cavity. The vector solitons are the first experimental observation inside a fiber laser using NPR technique. It is caused by the strong local birefringence. In fact, we check the scalar-vector soliton fiber laser operation with another scheme: first we use all fibers of weak birefringence and find the pulse characteristics from the OC1 and the OC2 are the same, and only the scalar solitons are obtained from either output. Then, we insert a short segment (~10 cm) polarization-maintaining fiber between the polarizer and the OC1, and the vector solitons are obtained both from the OC1 and the OC2. The combination of a fiber segment with strong birefringence to undo the polarization selection from the polarizer is the key step for the experimental demonstration of a vector soliton from a NPR fiber laser. The transitions between the scalar and vector solitons are inherently interesting, due to their vastly different characteristics. Thus, this new mode-locking regime sits at a nexus of all other known regimes of operation. The co-existence of scalar and vector soliton in a mode locked fiber laser cavity can enrich the understanding of soliton dynamics. Meanwhile, the variation between vector soliton and scalar soltion can also find potential applications in the fields of optical communication, three-dimensional display, and polarization division multiplexing fiber optical transmission.
Funding
National Key Scientific Instrument and Equipment Development Project (2013YQ16048702); National Natural Science Foundation of China (61275109, 61275069, 61331010); open project funding of the Jiangsu Key Laboratory of Advanced Laser Materials and Devices, Jiangsu Normal University (KLALMD-2015-02).
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