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We report on the experimental observation of bidirectional 100-fs bound solitons from a nanotube-mode-locked dispersion-managed Er-fiber laser with an ultra-simple linear cavity. Two mode-locked pulse trains in opposite directions are delivered simultaneously from the linear cavity. Under the pump power of <74 mW, both the bidirectional outputs of the laser work at the single-soliton state with pulse duration of 173 fs and 182 fs, respectively. Once the pump power is more than 74 mW, both the bidirectional outputs evolve into the two-soliton bound states with soliton separation of 1.53 ps. Interestingly, the bidirectional operations can show the different bound states, i.e. the forward bound solitons with phase difference of + π/2, and the backward ones with phase difference of -π/2. This is, to the best of our knowledge, the first demonstration of such compact bidirectional soliton fiber laser with the sub-200 fs pulses.
© 2016 Optical Society of America
1. Introduction
Femtosecond laser sources have been used as versatile tools for practical applications in material processing, laser surgery, biomedical optical imaging, ultrafast spectroscopy and ultraprecise metrology. Passively mode-locked fiber laser (PML-FL) [1–4] is one of the most popular techniques to obtain ultrashort femtosecond pulses, due to the advantages of compactness, high stability and free-maintenance. Because of the peak-power clamping effect and the nonlinearity accumulation in fiber cavity, such PML-FL could usually operate in multiple-pulse modes (e.g. harmonic mode-locking [5–8], soliton rains [9, 10], bound solitons [11, 12]), instead of the conventional single-pulse mode. Among all the multiple-pulse modes, bound solitons (BSs) in mode-locked fiber lasers have recently attracted considerable interest for special applications in multi-pulse machining and larger telecommunication capacity [13].
As the higher-order soliton solutions of the nonlinear Schrödinger equation, weakly-stable BSs were firstly predicted theoretically by Malomed [14], and stable BSs with 0, π, or π/2 phase difference were further predicted by Akhmediev et al. [12]. In 2001, Tang et al. experimentally observed for the first time the stable bound states of solitons in the passively mode-locked Er-fiber laser [15]. Subsequently, BSs in PML-FLs have been intensively investigated using various mode-locking techniques such as nonlinear polarization rotation (NPR) [16–19], nonlinear amplifying loop mirror [20], carbon nanotubes (CNTs) [21, 22], graphene [23], topological insulators [24]. Moreover, different-type BSs in fiber lasers operating in the normal-, zero- and anomalous-dispersion regimes have been widely reported. Grelu et al. have obtained the 600 fs BSs with ± π/2 phase difference in a stretched-pulse fiber laser [17]. Ortaç et al. reported the generation of 5.4 ps parabolic bound pulses in a Yb-doped double-clad fiber laser operating in the large normal-dispersion regime [16]. Zhao et al. presented the various bound states of ~700 fs dispersion-managed solitons in an Er-fiber laser at near-zero net cavity dispersion [25]. Gui et al. observed the ~900 fs BSs with the various phase difference of π, 0 and ± π/2 in a net-anomalous-dispersion Er-fiber laser [22]. Most recently, Wang et al. have even achieved the 9th-order harmonic mode-locking of ~580 fs BSs in an Er-fiber laser [18]. However, one should notice that the BSs previously reported in those PML-FLs could suffer from the following limitations: 1) the pulse duration of the BSs from a few hundreds of femtoseconds to several picoseconds is relatively longer; and 2) their fiber laser cavities with an unidirectional operation, usually requiring an optical isolator, an optical coupler and even wave plates (e.g. for NPR technique), still seem to be not compact enough and 3) bidirectional operations of BSs in PML-FL have not yet been reported and investigated. Therefore, there are research motivations to develop ultrashort (~100 fs), compact and low-cost PML-FLs with stable BSs output.
In this paper, we proposed and demonstrated an ultracompact, bidirectional passively mode-locked soliton Er-fiber laser with ~170 fs BSs output. The fiber laser with a simple linear cavity had a near-zero net cavity dispersion, and was mode-locked by a CNTs-based saturable absorber (SA). Both the forward and backward outputs of the PML-FL simultaneously emitted stable BSs with a discrete, fixed soliton separation. Especially, under the proper polarization states, it could be observed that the forward BSs had a phase difference of + π/2, but the backward BSs had a phase difference of -π/2.
2. Experimental designs and principles
Figure 1 shows the experimental setup of our proposed, ultracompact passively mode-locked Er-fiber laser with bidirectional BSs output. The pump laser from a 976 nm laser diode was injected into a 31-cm high-concentration Er-doped fiber (OFS EDF-150) by a 976/1550 nm wavelength division multiplexer (WDM). The group velocity dispersion (GVD) of the EDF is about −46 ps/(nm•km) at 1550 nm. The all-fiber linear cavity is simply constructed by a pair of homemade fiber end-facet mirrors (M1 and M2). They were fabricated by coating SiO2/Ta2O5 dielectric films onto single-mode-fiber (SMF) ferrules using a plasma sputter deposition system [26]. As can be seen in Fig. 2(a), the dielectric films can be uniformly deposited on the fiber ferrule, and show a high reflectivity of 88% in the spectral range of 1530-1590 nm. A piece of CNTs polymer film as a SA was inserted into the cavity for passive mode-locking. Using the balanced twin-detector technique with a home-made femtosecond (~210 fs) laser source [27], we measured the saturable absorption characteristics of the CNTs polymer film. As shown in Fig. 2(b), the CNTs-based SA has a saturation optical intensity of ~50 MW/cm2, modulation depth of 21.5% and the unsaturated loss of 40%. In order to control the near-zero net cavity dispersion, we purposely incorporated a section of 74 cm SMF with the GVD of 17 ps/(nm•km)@1550 nm into the laser cavity. The total cavity length is 1.05 m with a net dispersion of 0.0017 ps2. In addition, a fiber squeezer polarization controller (PC) was used in the cavity for optimizing the mode-locking operation.
Fig. 2 (a) The reflectivity spectrum of the fiber end-facet mirrors (M1 and M2), inset: the photograph of the M1; (b) The saturable absorption characteristics of the CNTs-based SA.
3. Experimental results and discussions
When the pump power is more than 39 mW, self-started mode-locking operations in both the forward and backward directions can be easily achieved. Figure 3 summarizes the output characteristics of bidirectional single-soliton operations at the pump power of 56 mW. Figure 3(a) gives the output spectra of the forward and backward solitons. Both of them show the Gaussian-like profiles with no spectral sideband, which are the typical features of dispersion-managed (near-zero GVD) solitons [25]. The central wavelengths are 1558.37 nm for the forward solitons and 1558.89 nm for the backward solitons, respectively. The 3-dB bandwidths of the forward and backward spectra are 14.7 nm and 14.8 nm, respectively. The slight differences between the two spectra could originate from the asymmetries of the Er-fiber gain and the dispersion evolution along the two directions. Figure 3(b) shows the typical oscilloscope traces of the bidirectional operations, and both the pulse trains is almost same with a pulse separation of 10.1 ns. As shown in Fig. 3(c), we measured the autocorrelation traces of the forward and backward solitons. The pulse durations are 173 and 182 fs if using a Sech2 fitting, respectively, which is similar to the stretched-pulse duration reported in [28]. Therefore, the time-bandwidth products can be calculated to be 0.318 and 0.337, indicating the near transform-limited pulses. As shown in Fig. 3(d), the bidirectional operations have the same pulse repetition rate of 98.348 MHz which exactly matches with the cavity round-trip frequency, confirming the fundamental mode-locking. The RF signal-to-noise ratio (SNR) is as high as 64 dB with a RF spectral resolution of 30 Hz. Meanwhile, we also measured the broadband RF output spectrum (inset of Fig. 3(d)), revealing the stable continuous-wave mode-locking of the bidirectional operations.
Fig. 3 Bidirectional single-soliton operations at the pump power of 56 mW. (a) the optical spectra, (b) the typical pulse trains, (c) the autocorrelation traces, and (d) the output RF spectrum (inset: the broadband RF spectrum).
When the pump power was more than 74 mW, we found that the laser operation transferred from the single-soliton state to a bound state of two solitons. The bidirectional BSs show the almost same characteristics [Fig. 4]. Figure 4(a) gives the typical spectra of the BSs in both directions. Both of them were strongly modulated, which are the interference fringes of two solitons closely spaced in the time domain. The spectral modulation has an asymmetric structure with the second maximum peak on the left side of the first maximum peak. Moreover, the intensity of spectral peaks satisfies the relationship as follows [22]:
where Ik represents the intensity of the kth maximum peak. These confirm the phase difference between the bound solitons is roughly –π/2. The spectral modulation period is 5.27 nm, corresponding to a soliton separation ts of 1.53 ps (calculated from the Fourier transformation). As shown in Figs. 4(b) and 4(c), we also measured the autocorrelation traces of both the forward and backward BSs. The soliton separation ts was measured to be 1.53 ps which agrees with the spectral modulation. Considering ~180 fs pulse width, the soliton separation is ~8.5 times of the pulse width, implying that the solitons in the bound state strongly interact with each other. Three peaks in the autocorrelation trace has a height ratio of 1:2:1, indicating the two solitons in the bound state has identical pulse intensity. Therefore, Both of the autocorrelation traces can be well fitted by calculating the convolution of the following intensity function I(t):where we adopt ts = 1.53 ps and the pulse width τp = 180 fs.Fig. 4 Bidirectional operation of the two-solitons bound states with phase difference of –π/2. (a) Bidirectional output optical spectra, (b) Autocorrelation trace of the forward output and (c) Autocorrelation trace of the backward output.
When we adjusted properly the polarization states, it was interestingly found that the bidirectional BSs could operate in the different bound states. As shown in Fig. 5(a), the optical spectrum in the forward direction shows an asymmetric structure with a dip in the center and the second maximum peak on the right side of the first maximum peak. Moreover, the intensity of spectral peaks satisfies the relationship of the Eq. (1). These indicate that the forward BSs have the phase difference of + π/2. In contrast, as given in Fig. 5(b), the optical spectrum in the backward direction still shows the two-solitons bound state with -π/2 phase difference, as same as the Fig. 4(a). Such different bound states from the bidirectional outputs of the passively mode-locked soliton fiber laser could attribute to the period doubling effect [19].The further study for this should be done in future.
Fig. 5 (a) The forward optical spectrum of the BSs with phase difference of + π/2, and (b) the backward optical spectrum of the BSs with phase difference of -π/2.
We found in our experiment that all these bound states of two solitons are stable if no perturbation is introduced. In order to evaluate the stability of the two-solitons bound state, we repeatedly scanned the optical spectrum of the backward BSs at a 1.5-minute interval in 3 hours. The corresponding results were plotted in Fig. 6. No evident wavelength drift and no power fluctuation per spectral modulation peak were found during the 3-hour test. This confirms that the bound states have the extremely excellent stability. Experimentally there exist bound states with other soliton separations if the pump power and the polarization state are arbitrarily selected.
Fig. 6 Stability measurement of the BSs operation during a 3-hour test. Red dotted line for the output spectral profile.
4. Conclusions
In summary, we have reported an ultracompact, linear-cavity PML-FL to stably generate the bidirectional BSs with sub-200 fs duration. The bidirectional mode-locking initially operated in the single-soliton mode, but could further evolve into the two-solitons bound states if the pump power was more than 74 mW. In general, both the bidirectional BSs has almost the same performances, e.g. the same phase difference –π/2 and the same soliton separation. However, under the proper polarization states, the bidirectional outputs could show the different bound states, i.e. different phase differences (forward + π/2 and backward –π/2).
Funding
National Natural Science Foundation of China (61475129, 61275109), the Open Project Program of Jiangsu Key Laboratory of Advanced Laser Materials and Devices (KLALMD-2015-02), the Open Project Program of the Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province (GD201604), and Program for New Century Excellent Talents in Fujian Province, China.
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