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Abstract
An Er-doped mode-locked fiber laser with a saturable absorber based on single mode - graded index multimode - single mode fiber (SMF-GIMF-SMF) with inner micro-cavity is demonstrated. The modulation depth of the saturable absorber was measured to be 1.9% when the SMF-GIMF-SMF structure is bent to a certain state. Such a simple saturable absorber enables the mode-locking operation in a ring Er-doped fiber laser and ultrafast pulses with pulse energy of 0.026 nJ and pulse width of 528 fs at the fundamental repetition rate of 14.34 MHz can be generated. In addition, the harmonic mode-locking operation can also be achieved.
© 2018 Optical Society of America
1. Introduction
Nowadays, passively mode-locked fiber lasers (MLFLs) have attracted a great deal of research attention because of their advantages such as excellent spatial beam profile, cost-effectiveness, compact structure and good compatibility. These lasers have been used in diverse fields including laser machining, material processing, ultrafast optics and biology medical treatment [1–4]. To generate ultrafast pulses, saturable absorbers (SAs) are basic and key components to initiate mode-locking operation in fiber lasers [5]. The equivalent SAs based on nonlinear polarization evolution (NPE) [6] and nonlinear amplifier loop mirror (NALM) [7] are widely used due to their fast amplitude modulation. However, their environmental sensitivity and periodic SA curve with respect to the pulse power restrict their further development in ultrahigh-peak power mode-locked lasers. The actual SAs, such as semiconductor saturable absorber mirror (SESAM) [8–10], carbon nanotubes (CNTs) [11–13], and two-dimensional (2D) nanomaterials [14–21] such as graphene [14–17] have also been widely employed in MLFLs. Although as the most extensively used SA in the commercial laser products, SESAM has some shortcomings such as narrow working bandwidth and especially high manufacture cost which is not suitable for experimental research. Although the damage threshold of CNTs or graphene SA is obviously improved by being deposited on side-polished fiber or tapered fiber, the mechanical strength is reduced. Furthermore, the limited service life all the actual SAs have also limited their applications in ultrafast optics [12–15]. The urgent demand for overcoming the existing deficiencies of the present SAs have been inspiring persistent researches on new methods or materials.
Nonlinear switching in multicore [22,23] and multimode fibers [24–26], especially nonlinear multimodal interference (MMI) in the graded-index multimode fibers (GIMFs), provides a reliable alternative to overcome the disadvantages mentioned above. In 2012, A. Mafi proposed a simplified nonlinear Schrödinger equation to explore the pulse propagation and interaction of multiple modes in GIMFs and created a new pathway for further studies on the specific nonlinear phenomena such as self-phase modulation (SPM) and cross-phase modulation (XPM) effects in GIMFs [24]. In 2013, W. H. Renninger and F. W. Wise reported the observation of the optical solitons and soliton self-frequency shifting in the GIMFs and revealed its possible application in space-division multiplexing and mode-area scaling for high-power lasers and transmission [25]. E. Nazemosadat and A. Mafi presented a detailed investigation of nonlinear MMI in GIMF and SMF-GIMF-SMF structure as a SA in mode-locked fiber lasers [26]. The main advantages of this structure are its simple construction, high damage threshold, nonperformance-degradation and the ability to operate at a much higher power level. Since then, researches on fundamental nonlinear phenomena in GIMFs including Kerr self-cleaning [27], spatiotemporal instabilities [28], and classical wave condensation [29] have been carried out. Although S. Fu et al. reported Q-switched all-fiber laser based on a single mode - step index multimode - single mode structured SA [30], no SA based on GIMF for mode-locking operation has been achieved yet.
In this paper, we demonstrate a SMF-GIMF-SMF structure with an inner micro-cavity as the SA. The SA with the modulation depth of 1.9% and saturation intensity of 6.81 μJ/cm2 is achieved with the structure bent to a certain state. Based on this SA, an Er-doped mode-locked fiber laser operating at 1558 nm is produced, which emits ultrafast pulses with the repetition rate of 14.34 MHz and the pulse width of ~528 fs, corresponding to the peak power in the order of 49.2 W. In addition, a harmonic mode-locking operation can also be achieved. The experimental results obtained show that SMF-GIMF-SMF structure with inner micro-cavity can be used as an efficient SA for mode-locking operation.
2. Device fabrication and operation principle
Figures 1(a) and 1(b) show the flow chart of the construction process for an SA based on SMF-GIMF-SMF structure with an inner-cavity. One end face of a section of cleaved GIMF (Corning 62.5/125) is etched with hydrofluoric acid (HF) with the concentration of 40% for 5 minutes. Due to the different corrosion characteristics of the fiber core and cladding, a micro-hole is formed on the end face of the fiber. Then the etched GIMF is directly spliced with two sections of SMFs using a fusion splicer (Fujikura 80s). The length of the GIMF used in the experiment is estimated to be 23.7 cm. The discharge time and current adopted for the splicing of etched GIMF-SMF are 800 ms and 48 bit respectively, and the overlap length is 10 μm. Figure 1(c) shows the microscope image of the inner-cavity and the length of the inner-cavity is measured to be 45μm. Figure 1(d) shows the schematic diagram of the SA constructed. By bending the GIMF, the mode field distribution of the GIMF is varied, which has effective influence on the coupling efficiency from the GIMF to the SMF. Due to the SPM and XPM effects, the self-focusing length at high peak power is different from that at the low peak power. However, the mode distribution of GIMFs can affect the strength of the nonlinear effect and consequently, the bending of the GIMF with a micro-cavity changes the mode distribution of the optical signal in the GIMF. When the device based on SMF-GIMF-SMF structure with an inner cavity acts as an SA in a suitable bending state, optical signal of the high peak power from the MMF to the SMF can be focused on the fiber core of the SMF. This property is equivalent to an SA [24, 31].
Fig. 1 (a) and (b) Schmatic diagram of the device fabrication; (c) The microscope images of device sample; (d) The schematic diagram of SMF-GIMF-SMF structure.
When the laser light propagates in the GIMF, several multiple modes get excited and transmit along the GIMF in a periodic interference pattern. This is the so-called self-focus effect. However, in the nonlinear regime, the self-imaging length is no longer the same due to SPM and XPM effects. The intensities of the SPM and XPM can be affected the following parameters: the length of the GIMF fiber, L, the total optical power, P, the ratio of the mode-field diameter of the LG00 mode in GIMF to the mode-field diameters of the SMFs, η, and the total excited modes, p [24]. The Introduction of the micro-cavity can inspire more high order modes and, by bending the GIMF, the mode field of the cross-section at the entrance of the GIMF can be arbitrarily changed within a certain range, which finally influence the nonlinear effects in the GIMF. In other words, the bending of the GIMF with micro-cavity can finally change the intensity-dependent transmission curve in the GIMF. Thus the device can act as an SA in a suitable bending state where lower power signal is attenuated while higher power signal is maintained. In this case, there is no essential limit on the length of GIMF. This means that the SMF-GIMF-SMF structure with an inner micro-cavity can provide a flexible means of generating ultra-short mode-locked fiber laser pulses.
Compared with other SAs, the proposed device has the advantages of low cost, simple structure, excellent mechanical performance and easily-controllable optical characteristics. Especially the high damage threshold of the device makes it have potential in achieving high power ultra-fast pulses in double cladding fiber lasers.
In order to characterize the nonlinear optical properties of the SA, the device was detected with the ultrafast pulses centered at ~1560 nm with 3dB bandwidth of 4.14 nm and the repetition rate of 14.34 MHz which was provided by a home-made NPR mode-locking fiber laser. Figure 2 shows the effective transmission dependence on the pulse intensity. Considering the different coupling efficiency at different bending states of the structure, the transmission curves for the pulse power at five states were illustrated in Fig. 2. The alteration of the transmission could be clearly observed. To be noted, at a certain state, the transmission increased from 6.6% to 8.5% as the input power increased due to the convergent self-focusing, as shown in Fig. 2(e). Being different from the traditional 2D materials, there was a sudden drop at the highest transmission value. This phenomenon is attributed to the power coupling to the radiation and cladding modes, which is consistent with the theoretical model described in [26]. The transmission spectrum of this structure was measured by a broadband light source (BBS, Amonics) as a loss of ~-12 dB. Such a great loss is mainly attributed to the introduced inner micro-cavity. For simplification, the fitting transmission curve is described by [32] as
Fig. 2 (a), (b), (c) and (d) Measured transmission curves with different bending degrees of SA; (e) Measured transmission cure, spectrum and corresponding fitting curve.
The modulation depth, saturation intensity and nonsaturable loss of the SA were measured to be 1.9%, 6.81 μJ/cm2 and 91.5%, respectively. The modulation depth is comparable to the other two-dimensional materials ever reported [11–18]. With such a low saturable intensity, it can be predicted that the mode-locking threshold can be very low. This SA can be used in the fiber laser for producing stable and robust mode-locked pulse trains.
3. Experimental results and discussion
The schematic of the fiber ring laser based on our proposed structure is shown in Fig. 3. The fiber laser was pumped by a 400mW laser diode centered at 1480 nm via a 1480/1550 nm wavelength division multiplexer (WDM). A 1.2 m Er-doped fiber (Nufern SM-ESF-7/125) with peak absorption of 55 dB/m at 1530 nm was used as the gain medium. A polarization-independent isolator was employed to ensure the unidirectional operation of the cavity. A polarization controller (PC) was used to adjust the state of polarization in the cavity. The 20% energy of the mode locking pulses was coupled out by using a 20:80 output coupler (OC). The SMF with inner cavity consisting of a length of ~23cm GIMF was inserted between PC and OC to initiate the mode-locking operation. The total cavity length was ~14.2 m. There are two types of fibers used in the cavity: dispersion coefficient of EDF and SMF are −46.25 ps/nm/km and 18 ps/nm/km, respectively, thus, the total net dispersion is anomalous (−0.52 ps2). The laser performance is observed using an optical spectrum analyzer (Yokogawa, AQ6370D), 1 GHz digital oscilloscope (Tektronix, TDS 5104B), 9 kHz–26.5 GHz RF spectrum analyzer (Agilent, E4407B) coupled with a 5 GHz photodetector (Thorlabs, DET08CFC/M), and an optical autocorrelator (APE, PulseCheck 150).
Fig. 3 Experimental setup of fiber laser. LD: laser diode; WDM: wavelength division multiplexer; EDF: Er-doped fiber; PI-ISO: polarization-independent isolator; PC: polarization controller; SA: saturable absorber; OC: optical coupler.
The best output performance of mode-locking fiber laser was achieved at the pump power of 92.3 mW, Fig. 4 illustrated the corresponding output characteristics. As shown in Fig. 4(a), the spectrum of the mode-locking operation is centered at 1558 nm with spectral bandwidth of 4.14 nm, in which clear Kelly sidebands are observed, indicating that the pulses were conventional solitons, corresponding to the net anomalous dispersion of the fiber laser. Figure 4(b) is the measured autocorrelation trace of the mode locked pulses and its nonlinear fitting, which gives a FWHM width of approximately 816 fs. If a sech2-pulse profile is assumed, the pulse duration is equal to 528 fs. The value of the time-bandwidth product (TBP) of the pulses is ~0.374, which is slightly larger than that of a standard transform limited pulse, indicating a small chirp of the pulses. The measured pulse train in Fig. 4(c) shows an identical pulse interval of ∼70.9 ns, which is consistent with the cavity fundamental repetition frequency of 14.34 MHz (∼14.25 m total fiber length), verifying its single pulse state. The interpulse intensity fluctuation is less than 5%, indicating the good stability of the mode-locking state. With the 370.6μW of average power, the pulse energy is equal to 26 pJ with 49.2 W peak power. No signs of pulse pair generation or pulse breaking were observed. The soliton order N is equal [33] to
where the fiber nonlinear coefficient , the average dispersion of the laser resonator , the peak power P = 49.2 W, the pulse width τ = 528fs. It means that the obtained pulse energy and peak power are consistent with that expected from soliton area theorem, indicating the high stability of fundamental soliton.Fig. 4 Mode-locking pulse measurements: (a) Laser spectrum. (b) Autocorrelation trace of output pulses. (c) Oscilloscope trace and (d) RF spectrum measure around the fundamental repetition rate of 14.34 MHz. Inset: RF spectrum over a frequency range of 0-300 kHz.
In order to study the operation stability, the radio-frequency (RF) spectrum was measured with 10 Hz resolution bandwidth (RBW) and 200 kHz span, as shown in Fig. 4(d). The contrast signal-to-noise ratio (SNR) is at the level of 55 dB located at the cavity repetition rate of 14.34 MHz, which is comparable to the previous reports [9, 13, 14]. The insert of Fig. 4(d) described the RF spectrum with a wideband up to 300 MHz, showing that the laser generated a very broad spectrum of harmonics.
Figure 5(a) illustrates the evolution of the output power versus the launched power, the laser output power almost linearly increases with the pump power above the mode-locking threshold of 54 mW. However, it should be mentioned that the self-started mode-locking occurred under certain condition where pump power reached 155.6mW. Specially, the harmonic mode-locking (HML) with a stable and well organized pulse train could also be instantaneously achieved by increasing the pump power. As shown in Fig. 5(b), the fiber laser has realized HML from the 2nd order to the maximum order of 6th (corresponding to the repetition rate of 86.07 MHz, which is 6 times of the fundamental repetition rate). However, such a state is actually unstable, after a short time the pulses lose their synchronization and locate randomly again.
Fig. 5 (a) The output power of the fiber laser versus pump power. (b) Typical pulse train of the HML.
In our system, the mode-locking operation could also be initiated by adjusting the PC, and hence more studies have been done for clarifying that the structure is indispensable in this laser for achieving mode-locking operation. Firstly, the PC is removed from the cavity, the mode-locking pulses could still be obtained through bending the structure. On the contrary, if the structure is removed, the laser could no longer generate mode-locked pulses. Thus, it could be concluded that the mode locking is not due to the NPR effect in our proposed system and this contrast experiment verifies that the structure directly contributes to the mode-locking operation. In order to further verify the stability of the laser, a long-term stability test has been implemented. The spectrum is recorded every hour for 10 hours with minimized environmental perturbations, as shown in Fig. 6. It could be seen that there are no obvious changes in the output spectrum during the measurement process.
4. Conclusion
In conclusion, we have successfully achieved a mode-locked Er-doped all-fiber laser operating at 1558 nm based on a SMF-GIMF-SMF structure with an inner micro-cavity as SA. The ultrafast pulses with pulse width of 528 fs at a repetition of 14.34 MHz exhibit a good stability. The laser could also be applied for efficient harmonic mode-locked pulse generation. The fiber laser could generate the mode-locked pulses by bending the fiber without adjusting PC. The simple-construction, good stability and robust structure of the SA make it good candidate for potential applications in ultrafast photonics and optoelectronic devices.
Funding
National Key R. and D. Program of China (2016YFF0200204).
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